High Speed Videograpic Quick Stop Device for Orthogonal Machining 
 
by 
 
Chase Allan Wortman 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 14, 2013 
 
 
 
 
Keywords: orthogonal machining, metal cutting mechanics, quick stop device, 
high speed videography 
 
 
Copyright 2013 by Chase Allan Wortman 
 
 
Approved by 
 
Lewis N. Payton, Chair, Associate Research Professor, Mechanical Engineering 
Robert L. Jackson, Associate Professor, Mechanical Engineering 
Dan Marghitu, Professor, Mechanical Engineering 
 
ii 
 
 
 
 
 
Abstract 
 
 
Advances in digital high speed video acquisition make it possible to create 
a fully integrated virtual quick stop device to observe the orthogonal metal cutting 
process in real time.  This research aims to provide additional information and 
updated imagery to aid in the development of a predictive theory of the metal 
cutting process.  Existing shear zone models are applied to force data paired with 
high speed video footage to see if these models accurately predict the way in 
which metal is deformed during orthogonal machining.   
A high speed videographic quick stop device was developed to observe 
the metal cutting process.  This system allows force data from a dynamometer to 
be paired frame by frame with the imagery from a high speed camera.  Frame 
rates as high as 1,000 frames per second were used to obtain a high resolution 
data set for analysis.  The images of highly polished and etched metal surfaces 
allow the researcher to see how the grain structure of the metal deforms in front of 
the tool edge as it moves through the material.  The angle at which the grain 
structure deforms can then be measured. 
Analysis of the data indicates that the plane in which a metal undergoes 
plastic deformation is affected by the material properties of the metal samples and 
the cutting factors (tool angle, feed, etc.) used.  The hardness value of a metal 
undergoing the metal cutting process has been shown to have a significant effect 
iii 
on the resulting angle at which it will plastically deform.  Copper 101, Aluminum 
1100, and 1018 Steel were the materials used for this study.  The hardness of 
these metals was increased by cold rolling.  Tensile samples were cut from each 
unique metal sample and tested for precise material property values.  Customized 
high speed steel (HSS) tools at three different rake angles were used for the 
orthogonal machining of the metal samples.   
The utilization of a fully integrated, computer controlled cutting 
environment in conjunction with the high speed virtual quick stop device permits 
the collection of a highly synchronized data set for all parameters being studied.  
A statistical analysis of this data provides the additional information on the shear 
process under orthogonal metal cutting conditions.  The better understanding of 
the metal cutting process can aid in improvements to the control of metal 
machining processes.  
iv 
 
 
 
 
 
Acknowledgments 
 
 
 I would like to dedicate this thesis to my family and friends who have 
supported me throughout this entire process.  Foremost, I would like to thank my 
beautiful wife-to-be Jessica Geddes for all of her love and support throughout my 
entire graduate school career.  I cannot imagine a better experience at Auburn 
than I have had with you.   
 I have to thank my parents, Darryl and Cindy, for always keeping me on 
the right track and fully supporting me in all the decisions I have made in my life.  
To my brother and best friend, Grant, I have enjoyed being able to live with you 
during our time at Auburn and experience the best years of our lives together.  To 
my little sister Sarah I would like to say that I am amazed by the woman that you 
have become and thank you for being the greatest sister in the world. 
 Next, I have to acknowledge my life-long friends, Hans Driessnack, Zack 
Moore, and David Brown, who have been a source of encouragement as they also 
work their way through their respective post-college studies. 
 Finally, I would like to thank Dr. Payton for giving me the opportunity to 
work in the DML and providing guidance and support throughout my graduate 
school career.  I would also like to thank my colleagues Justin Evans, Vishnu 
Chandrasekaran, Drew Sherer, Wesley Hunko, and Michael Carter for all of your 
help in completing this thesis.  War Eagle. 
v 
 
 
 
 
 
Table of Contents 
 
 
Abstract ................................................................................................................. ii 
Acknowledgments................................................................................................ iv  
List of Tables ....................................................................................................... vi  
List of Figures ..................................................................................................... vii  
List of Symbols .................................................................................................... ix 
Introduction   ......................................................................................................... 1 
Scope and Objectives   .......................................................................................... 5 
Literature Review  ................................................................................................ 7 
Materials, Instruments and Machines   ............................................................... 36 
Construction and Methodology of the Experiment ............................................. 55 
Instrument Validation and Statistical Design of Experiments ............................ 69 
Data Results ........................................................................................................ 74 
Statistical Analysis .............................................................................................. 80 
Conclusions and Future Work ............................................................................ 87 
References   ......................................................................................................... 91 
Appendix 1   ........................................................................................................ 99 
Appendix 2   ...................................................................................................... 100 
Appendix 3   ...................................................................................................... 102 
Appendix 4   ...................................................................................................... 118 
Appendix 5   ...................................................................................................... 134 
vi 
 
 
 
 
 
List of Tables 
 
 
Table 1:  Specimen Percent Reduction Values ................................................... 57 
Table 2:  Hardness Values .................................................................................. 58 
Table 3:  Copper Etchant .................................................................................... 60 
Table 5:  Observed Data Results ......................................................................... 74 
Table 6:  Calculated Data Results ....................................................................... 75 
Table 7:  Run Parameters and Measured Force Data .......................................... 76 
Table 8:  Measured Optical Data and Calculated Forces .................................... 76 
Table 9:  Calculated Areas and Stresses ............................................................. 76 
Table 10:  Calculated Forces and Resultant Stresses .......................................... 77 
 
 
vii 
 
 
 
 
 
List of Figures 
 
 
Figure 1:  Shear Plane Angle and Tool Rake Angle ............................................. 9 
Figure 2:  Orthogonal Machining Cut ................................................................. 12 
Figure 3:  Type 1, 2, and 3 Chips Respectively .................................................. 13 
Figure 4:  Orthogonal Cutting Process................................................................ 14 
Figure 5:  Merchant Force Diagram .................................................................... 15 
Figure 6:  Merchant's Observation of Chip Formation ....................................... 18 
Figure 7:  Merchant's Stack of Cards Model ...................................................... 19 
Figure 8:  Okushima and Hitomi's Model ........................................................... 21 
Figure 9:  Zorev's Model of a Thick Zone .......................................................... 22 
Figure 10:  Oxley's Parallel-Sided Shear Zone Model ....................................... 23 
Figure 11:  Van Luttervelt's Stationary Shear Zone Model ................................ 24 
Figure 12:  Huang's Observation of Flow in Shear Zone ................................... 25 
Figure 13:  Huang's "New" Stack of Cards Model ............................................. 27 
Figure 14:  Elevated View of Equipment Setup ................................................. 39 
Figure 15:  Quick Stop Workpiece Holder ......................................................... 40 
Figure 16:  Yumo Rotary Encoder ...................................................................... 41 
Figure 17:  Kistler Dual Mode Amplifiers .......................................................... 42 
Figure 18:  National Instruments USB-6008 ...................................................... 43 
Figure 19:  Modified Load Lift Camera Stand ................................................... 44 
Figure 20:  DRS Technologies Lightning RDT Camera .................................... 45 
viii 
Figure 21:  Cincinnati Arrow VMC 750 CNC Mill ............................................ 45 
Figure 22:  Bridgeport Vertical Milling Machine ............................................... 46 
Figure 23:  Do All Vertical Band Saw ................................................................ 47 
Figure 24: Wilton Belt Sander ............................................................................ 48 
Figure 25:  STANAT Rolling Mill ..................................................................... 49 
Figure 26:  Rockwell Hardness Tester ................................................................ 50 
Figure 27: Brinell Hardness Tester ..................................................................... 51 
Figure 28:  Brinell Hardness Testing Scope ....................................................... 52 
Figure 29:  MTS Q Test 100 Tensile Tester ....................................................... 53 
Figure 30:  Tensile Testing Jaws with Specimen Inserted .................................. 54 
Figure 31:  ASTM E8 Sub-size Specimen Dimensions ...................................... 59 
Figure 32:  Workpiece in Position ...................................................................... 61 
Figure 33:  Average Force Selection Plot ........................................................... 65 
Figure 34:  Average Force Input ......................................................................... 66 
Figure 35:  GIMP Path Selection ........................................................................ 67 
Figure 36:  GIMP Path Output File..................................................................... 67 
Figure 37:  Measured Force Plot ......................................................................... 78 
Figure 38:  Observed Geometry of Shear Zone .................................................. 79 
Figure 39:  Cutting Force ANOVA .................................................................... 81 
Figure 40:  Hardness vs. Measured Stress .......................................................... 82 
Figure 41:  Hardness vs. Calculated Stress ......................................................... 83 
Figure 42:  Paired T-Test of All Copper Samples .............................................. 84 
Figure 43:  Paired T-Test of Low Tool Angle Copper Samples ......................... 85 
 
ix 
 
 
 
 
 
 
List of Symbols 
 
 
? Tool Rake Angle 
? Onset of Shear Plane Angle 
? Shear Front Angle 
? Mean Friction Angle Tool Face 
? Friction Coefficient 
tord Ordered Depth of Cut 
to Uncut Chip Thickness 
tc Cut Chip Thickness 
w Width of the Cut Chip 
rc Ratio of Chip to Un-cut Chip thickness 
Fc Horizontal Cutting Force 
Ft Vertical Cutting Force 
F Frictional Force upon Chip 
N Normal Force upon Chip 
R Resultant Force upon Chip 
Fs Shear Force on the Plane 
Fn Normal Force on the Plane 
As Area of the Shear Plane 
?s Shear Stress on the Shear Plane 
x 
? Shear Strain (also ? in some works) 
V Cutting Velocity 
Vc Chip Velocity 
Vs Shear Velocity 
HP Horsepower 
HPs Specific Horsepower 
P Power Required to Cut 
MRR Metal Removal Rate 
U Specific Total Cutting Energy 
Uf Specific Friction Energy 
Us Specific Shear Energy 
?s Normal Stress 
L chip contact length on tool face 
 
1 
 
 
 
 
 
Introduction 
 
 
 The machining of metals is the most widely used process in the production 
of mechanical products by the manufacturing industry in the United States as well 
as many other countries world-wide.  It was estimated that metal cutting was used 
to create approximately fifteen percent of all products produced by the 
manufacturing industry in the U.S. in 1989.  This percentage has remained 
virtually unchanged over the years making the economic impact today close to 
$300 billion.  This huge economic impact compels the continuing research into 
developing improvements in machining processes and practices. 
Machining can be defined as ?a machine-performed process suitable for 
utilization to produce products on an industrialized basis?.  Humans have been 
machining products since the invention of a boring machine capable of boring a 
cy1inder true ?within the thickness of a worn shilling? in 1775 (Merchant).  Yet, 
machining is still an art.  Ask any machinist and they will tell you the same.  
Three different machine shops can be given the same stock and asked to make the 
same part; three different sets of machining parameters will be used to create the 
part.  This is because there is currently no accepted formula that can take the 
material properties of a piece of stock and output the ideal machining parameters 
for that material.   
2 
Fred W. Taylor made it his life?s work to answer three questions necessary 
for any machining operation:  
1. What tool shall I use?   
2. What cutting speed shall I use?   
3. What feed shall I use?  (Taylor)   
He understood that to answer these three questions many variables must be 
investigated.  Over 26 years he studied twelve variables that he determined were 
the most influential to the machining process.  Of those twelve variables, he 
believed the most important was ?the quality of the metal which is to be cut? 
(Taylor).  This variable can be understood as the material properties of the metal.  
At the time of Taylors investigations there were very few methods to analytically 
define these material properties.  Therefore, he focused on the other variables that 
he could control and developed advances in metal cutting that would propel the 
manufacturing industry into what it is today.  
In the 107 years since Taylor published his findings in ?On the Art of 
Cutting Metals? many engineering advances have been made in the area of 
material testing.  Today, there are standardized tests to define almost every 
property of a piece of metal stock.  Using this information the ?quality of the 
metal which is to be cut? can be defined more precisely than ever before.  
Experiments relating these material properties to their effects on the cutting force 
required to machine them provides information necessary to better answer 
Taylor?s three great questions. 
3 
If a universal metal cutting formula is to be developed, a mathematical 
model must be developed that can accurately represent was happens as a tool 
removes metal from the stock.  Many theories have been developed over the years 
to try and do this.  In an effort to simplify this complex problem a form of 
machining called orthogonal metal cutting has been the subject of much study.  
Orthogonal metal cutting is a two-dimensional planar cutting process.  The 
orthogonal machining approach allows the application of geometrical 
relationships between the tool and material to calculate the force and direction of 
the shear strain during metal cutting in conjunction with other metal cutting 
properties.   
This research will address the geometrical relationships and attempt to 
relate the material properties obtained through standardized material testing to 
predict the cutting forces observed during orthogonal machining.  The metal 
specimens will be optically observed at high magnification using a high speed 
camera while undergoing the orthogonal machining process.  Cutting forces will 
be recorded simultaneously and synchronized with the high speed imagery.  This 
synchronized data will be used to study the relationship of cutting tool geometry, 
depth of cut, feed, and material properties with the recorded cutting forces.   
The work pieces in this experiment were cold rolled, causing a change in 
the grain structure of the metals.  Cold rolling causes an increase in the hardness 
or strength of the metal, decreases ductility, and increases the dislocation density (  
).  These known metallurgical effects, of which Taylor was unaware of at the time 
of his publication, now allow a detailed study of the ?metal quality? or hardness 
4 
and it?s previously unstudied effect on the shear plane models proposed by 
orthogonal machining experiments to date. 
5 
 
 
 
 
 
Scope and Objectives 
 
 
The goal of this thesis is to conduct orthogonal machining experiments to 
study the effects of machining parameters on the resulting cutting forces and shear 
angles in Copper 101, Aluminum 1100, and 1018 Steel.  A detailed observation of 
the orthogonal metal cutting process was made possible using an all-digital high 
speed videographic quick stop device.  The high speed videographic quick stop 
device consists of a high speed digital camera synchronized to force 
measurements from a dynamometer.  Precise feed control is also made possible 
by utilizing a variable frequency drive (VFD) electric motor to move the 
workpiece underneath the cutting tool.  National Instrument?s LabVIEW software 
was used to create a virtual instrument for automatic data collection and 
organization.  These updates to previous virtual quick stop devices permit more 
precise control over the orthogonal machining process than ever before.   
The objectives of the experiment included: 
1) Develop a better understanding of the metal cutting process 
2) Develop a technique that allowed the observation of the chip formation process 
using a digital high speed camera at high magnification 
3) Measure the Shear Plane Angle (?), Shear Front Angle (?), and other geometries 
of interest directly from the images obtained 
6 
4) Capture high resolution still images of the metal cutting process during cutting 
that clearly show the geometries of interest for future publication 
5) Investigate the propped Shear Front Angle (?) of Black and Huang in a new 
material not previously investigated; 1018 steel. 
6) Investigate how the crystal structure of the metal to be machined affects the 
resulting geometries of interest and cutting forces 
7) Perform tensile tests of the specimens to be machined for precise non-theoretical 
data of each specimen undergoing study 
8) Publish the data set in a format (as appendices) which other researchers may use 
as a quality resource in their studies 
7 
 
 
 
 
 
Literature Review 
 
 
Historical Survey 
 
 There have been various attempts to study, measure and quantify the 
variables in metal cutting since the beginning of the industrial revolution.  A 
number of machine tools (e.g. lathes) were developed in their present form in the 
1840?s and 1850?s during the emergence of the steam engine and its attendant 
uses.  It was at about this same time that the first scientific papers on metal cutting 
appeared. 
 Economics, which F.W. Taylor cited as the prime mover behind his own 
studies, and metal cutting, have been closely linked since the earliest attempts to 
study the metal removal process.  For example, in the earliest reference which 
could be found relating to scientific studies of the cutting process, Cocquilhat (23) 
in 1851, centered his studies upon the cutting with a drill of a rotating work piece.  
From these fundamental studies, he was able to extend his basic observations of 
the metal cutting process to more worldly interests.  With the knowledge of work 
required per unit volume of material removed and assumptions of wages and 
working days, he then made some calculations on the costs of digging tunnels, 
cutting marble and trench digging. 
8 
 The first experiments in which the influence of tool geometry was studied 
were reported by Joessel (47) in 1864.  Forces were obtained in lathe cutting and 
drilling by measuring the torque required to turn the machine while cutting, care 
being taken to subtract the torque required to overcome the friction of the 
machine.  The effects of depth of cut, speed, and rake angle were studied.  
References to ?cutting fluids? are also found in his work (linseed oil, quicklime 
and nitric acid to name a few), although no explanation of their benefit was 
attempted. 
 The first attempts to study chip formation are those of Time (75) in 1870 
and Tresca (76) in 1873.  Time was the first to correctly model the process ahead 
of the tool as one of shear, although he may be criticized for his viewpoint that the 
chip formation took place by fracturing of the metal on successive shear planes 
rather than by plastic deformation.  This is understandable though since the plastic 
deformation of metals in operations other than cutting was only beginning to be 
investigated at the time. 
 Mallock (55) produced a set of drawings of polished and etched chips in 
1881 which rival modern photomicrographs in quality.  He deduced that the 
cutting process was one of shear along a sharply defined shear plane with friction 
occurring along the tool face.  With Time, he thought of fracture as occurring on 
the successive shear planes and described the chip as a ?metallic slate.?  Mallock 
observed that the friction between the chip and the tool decreased when a ?cutting 
fluid? was applied.  His drawings clearly show that when cutting copper, the use 
of soap and water as a cutting fluid increased the shear plane angle, which is most 
9 
easily described as a line from the tip of the tool to the back of the undeformed 
chip, Figure 1.  He was also the first to attempt to categorize the bluntness of the 
leading edge of the tool (the cutting edge) as a factor. 
 In 1892, Haussner (35) was successful in building the first instrument 
which could directly measure the forces involved in metal cutting.  In this 
planning dynamometer, the work was restrained by a stiff spring.  Deflections of 
the spring were magnified and a record was drawn by the dynamometer of the 
force against the distance of the cut.  Although he was successful only in 
measuring the force horizontally along the cut, this was a major advance.  He also 
noted the earliest comments on what appears to be the built up edge in stating that 
?with ductile materials, after cutting starts, chips welded to the tool and were very 
hard to separate?.  He may also have been the first to deduce the presence of a 
normal stress along the shear plane, concluding that the elements were not ?freely 
sheared but is under a normal pressure?. 
 
Figure 1:  Shear Plane Angle and Tool Rake Angle 
 
10 
 Zvorykin (95) published an extensive review of planing in 1893 using his 
new hydraulic dynamometer.  He concurred with Haussner that the resultant force 
was not necessarily in the cutting direction.  Assuming that the force in the 
direction of the cutting velocity would be a minimum led him to conclude the first 
attempt to predict the shear plane angle of Figure 1 in terms of the tool rake angle 
? and friction angle ?. 
'? 45 2 2 2? ? ?? ? ? ? (1) 
 
? corresponds to the shear plane angle, ? is the friction angle on the chip and ?? is 
a friction angle for the shear plane itself.  This is the first of many formulations of 
the functional relationship amongst the various angles detailed shortly in an 
attempt to formulate a predictive relationship based upon the observed geometries 
at the tool interface.  This equation will appear again in the literature review of 
modern theory, with ?? equal to zero: 
2245 ??? ???  (2) 
 
Equation (2) was derived independently in 1896, in the German engineering 
handbook ?Ingenieur und Maschininenmechanick? (91).  The basis of derivation 
in that case was that the shear plane would be the plane of maximum shear stress.  
The German handbook marks the beginning of the ongoing search for a predictive 
approach to the shear plane angle which eludes engineers to the current day.  It 
carefully compared equations (1) and (2) at great length, offering reasons for the 
disagreement.  Those equations continued in the literature after the turn of the 
11 
20th century.  Linder (53) in 1907 and Ernst and Merchant (31) in 1941 obtained 
equation (1).  Piispanen (64) in 1937 and Merchant (56) in 1945 obtained 
equation (2).  The development of the many versions of this predictive equation 
will be detailed at great length in the Shear Zone Section of the literature review 
since one of the goals of the experiment is to compare the various models through 
a statistical analysis of the results. 
 Force analysis would continue to improve to the current day 
dynamometers and began to be joined with photographic studies in the ?Roaring 
Twenties? when Coker and Chakko (19) carried out experiments in 1922, and 
Coker (20) in 1925 carried out a series of photo elastic experiments on the action 
of cutting tools.  They were able to show in their photographs that there were 
zones of approximately radial compression and tension ahead of and behind a line 
going forward from the tool point, which corresponds to the plane defined by the 
angle ? in Figure 1.  His photographs were not taken during cutting however, but 
during a stoppage of the tool.  Ishii (44) in 1929 and Schwerd (71) were the first 
to study the cutting process while cutting was actually in progress.  Photographs 
were also taken through a microscope by Boston (14) which presented detailed 
appearance of the metal cutting process.  Their photographs were instrumental in 
the thought processes of the metal cutting investigators of the 1940?s and continue 
to be highly regarded today by photographic experts in the metal cutting field. 
 It was also at this time that one of the first experiments examining 
hardness was conducted by in 1926 by Herbert (36).  He showed that the chip 
material was harder than the work material and demonstrated that metal cutting 
12 
involved intense strain hardening which could only come about through the 
mechanisms of plastic flow. 
 
Cutting Geometry with a Single Edge 
 
 
Figure 2:  Orthogonal Machining Cut (12) 
 
 Orthogonal cutting such as depicted in Figure 2 is seldom used in practice, 
although it remains the simplest model for scientific analysis.  Nearly all practical 
cutting processes are oblique, where the leading tool edge is inclined to the 
relative velocity vector between the tool and work.  Even in today?s computer 
age, modeling such a difficult geometry remains a daunting task.  Thus, it is 
necessary to consider how the mechanics of the orthogonal cutting can be 
extended and altered to describe oblique cutting.  Beginning in the 1940s, the 
Orthogonal Machining Process (OMP) of Figure 2 became the basis upon which 
subsequent models and discussions were based.  The commonly used phraseology 
is provided in the List of Symbols.  Most of the derived equations are summarized 
13 
in Appendix 1.   A complete discussion of the model and the formulas derived 
from it are beyond the scope of this experiment, but excellent reviews may be 
found in Degarmo, Black and Kohser?s text (27) or the work of Shaw (68),   Trent 
(77) or Wright (78).  A short discussion is however necessary to set up the shear 
zone review and discussion. 
 There are three basic chip types formed during the orthogonal machining 
process as first denoted by Ernst (30).  Type 1 is a discontinuous or segmented 
chip type; Type 2 is continuous and smooth; Type 3 is continuous with a buildup 
of chip material between the tool and chip which is commonly referred to in the 
literature as ?built-up edge? or BUE.  All of the models discussed hereafter 
assume a Type 2 chip. 
 
Figure 3:  Type 1, 2, and 3 Chips Respectively (68) 
 
The modern era of metal cutting research began with the nearly simultaneous 
work of M.E. Merchant and V. Piispanen during the years leading up to and 
during World War II.  These two men independently proposed the classic force 
relationships that are used to describe the OMP model. 
14 
 
Figure 4:  Orthogonal Cutting Process (27) 
 
 Figure 4 depicts the commonly accepted symbology of the Merchant and 
Piispanen model, detailed in the List of Symbols.  Basically, the shearing process 
occurs on a single plane extending from the edge of the cutting tool to the free 
surface of the workpiece.  This plane is commonly referred to as the ?shear 
plane?.  The shear angle ? is measured from the horizontal to the plane as 
depicted in Figure 4 and varies depending upon the particular cutting conditions.  
The shape of the zone on or around this plane has been the topic of intense 
academic interest since publication of the models in the 1940s occurred.  Before 
beginning the review of the many ?shear zone? models, a basic review of the 
process which led to the development of the geometric force relationships of 
Appendix 1 will be made using the nomenclature of the List of Symbols. 
15 
 Both Merchant and Piispanen independently developed similar concepts 
for a force diagram which illustrates the geometrical relationship between the 
cutting force components during orthogonal machining.  This has become the 
fundamental basis allowing the formulation of the relationships detailed in 
Appendix 1.  Both researchers viewed the chip as an independent body held in 
mechanical equilibrium by the two equal and opposing resultant forces R and R?.  
The force R is due to the force exerted by the workpiece on the chip.  The force R 
is composed of two components; the shearing force along the shear plane (Fs) and 
a force normal to the shear plane (Fn).  The force R may also be resolved into two 
other components, the cutting force (Fc) and the thrust force (Ft).  Figure 5 shows 
these relationships in what is now commonly referred to as the Merchant force 
diagram. 
 
Figure 5:  Merchant Force Diagram (68) 
 
16 
 The Merchant force diagram applies the opposing force concept of the free 
body diagram of the chip to the orthogonal cutting process shown in Figures 2, 4 
and 6.  The force R? is the force that is exerted upon the chip by the cutting tool.  
It may be resolved into two components, F and N, where F is the friction force 
between the chip and the cutting tool and N is the force normal to the chip and the 
cutting tool.  The forces Fc and Ft are easily measured during the orthogonal 
cutting experiments by the use of a force dynamometer.  The force due to friction 
F can then be calculated from the measurement of the cutting and thrust forces as 
shown in the following equation: 
?? c o ss in ???? tc FFF  (3) 
 
The coefficient of friction ? that acts between the cutting edge of the tool and the 
chip is defined by the following equation: 
?? tan?? NF  (4) 
 
The angle ? is between friction force F and the normal force N as shown in Figure 
5.  Merchant?s orthogonal model permitted the calculation of values such as 
equations (3), (4), (5) and the others in Appendix 1 using forces readily 
measurable with modern dynamometers.  The angle ? is particularly important in 
the various predictive shear strain models as shall be demonstrated and 
investigated. 
The resultant R, which is equal, opposite and collinear with R? may be resolved 
into Fn and Fs using the measurement of the cutting and thrust forces as with the 
following equation: 
17 
?? s inc o s ???? tcs FFF  (5) 
 
Merchant?s and Piispanen?s work have permitted the quantification of forces at 
and along the tool-chip interface (Appendix 1).  This has formed the basis for 
modern attempts to develop a predictive mechanism for the shear front plane by 
establishing their own version of equations (1) and (2) using the geometry of 
Figure 5.  This marks the beginning of the modern ?shear zone? investigation. 
 
The Shear Strain Models 
 
 The Merchant model of orthogonal cutting permitted the development of 
expressions for flow stress, shear energy, temperature and chip morphology such 
as those listed in Appendix 1.  Shear strain, as well as shear stress, was described 
in his model but has not been as successful in predicting results.  Various models 
for the shear process have been proposed in the machining literature.  These 
models may be divided into two broad categories, the thin-zone and thick-zone 
models.  Neither model is completely successful but each has its proponents.  The 
thin-zone model appears to be most successful in describing cutting at a high 
speed, whereas the thick-zone model is most often used to describe the machining 
process at very low cutting speeds. 
Merchant?s model represented the shear zone as a single plane, or thin-zone 
model.  The angle of inclination of the shear plane to the cutting direction was 
defined by the angle ?.  Merchant observed that the crystal structure of the 
18 
material was elongated by the shear process and gave the direction of crystal 
elongation the direction ?. 
 
Figure 6:  Merchant's Observation of Chip Formation (56) 
 
Merchant did not develop the plastic deformation aspect of his observations.  
Both Merchant and Piispanen used a ?deck of cards? concept to visualize the 
shear zone process, where the shear mechanism during chip formation can be 
illustrated by the incremental displacement of cards in a stack (Figure 7).  Each 
card moves forward a small amount in respect to the next card in the stack as the 
cutting process occurs.  Merchant (57) proposed that the crystalline structure of 
the metal was elongated by the shear process, and that the direction of elongation 
was in a different direction than the shear plane. 
19 
 
Figure 7:  Merchant's Stack of Cards Model (56) 
 
 The thickness of each card element was ?X, and each element in the 
model was displaced through distance ?S with respect to its adjacent neighbor.  
Therefore, the shear strain, ?, could be expressed as ? = ?S / ?X.  From the 
geometry of his stack of cards, Merchant thus developed the following equation: 
)co s (s in co s ??? ?? ???
 (6) 
 
Ernst and Merchant would eventually observe (31) that the angle between the 
resultant force R and the shear plane was thus given by: 
2245 ??? ???  (7) 
 
Equation (7) was the first of many modern attempts to derive a functional angle 
relationship f (?, ?) of some type.  It has come to be referred to as the Ernst and 
20 
Merchant solution (29).  Although independently derived, this is again the result 
Zvorykin published in 1893 as equation 2 in this review. 
 Lee and Shaffer (52), in their 1951 paper, examined the geometry by 
considering that a part of the chip would behave as an ideal plastic solid.  Using 
Mohr diagrams they developed the following relationship amongst the angles of 
the Merchant model: 
??? ??? 45  (8) 
 
Thus both equation (7) and (8) suggest a strong interaction between the frictional 
angle and the tool rake angle in determining the shear plane angle.  This has not 
proven to be a very satisfactory observation.  Eggleston et al (29) noted in his 
detailed review of the observations of the angle relationships that neither the Ernst 
and Merchant formulation, based upon the minimum energy criterion, nor the 
ideal plastic-solid solution of Lee and Shaffer, nor the mathematical derivations of 
Hill are in agreement with all the experimental observations. 
 Merchant?s model has been extensively examined, published and cited as 
the first thin-zone model.  It has been seriously criticized by some academics 
because of its inability to describe the actual deformation process in machining.  
For example, a particle moving along the cutting direction into the shear plane 
must abruptly change direction at the plane and then flow in the direction of the 
chip.  This represents a discontinuity in the tangential component of velocity on 
the shear plane, requiring an infinite acceleration across the shear plane.  An 
examination of the actual shape of the deformation zone is one of the goals of this 
21 
experiment and a further review of the many shear zone models is continued 
below. 
 Okushima and Hitomi (60) developed a simplified thick-zone model in 
1961 which is depicted as Figure 8.  The suggested a very large transitional zone 
AOB. 
 
Figure 8:  Okushima and Hitomi's Model (60) 
 
The AOB zone existed for plastic deformation of metal between the rigid region 
of the workpiece and the plastic region of the steady chip as it moved away up the 
tool face.  Plastic deformation began to occur at the starting boundary line of the 
shear zone, OA, and the plastic strain gradually increased as the cut progressed.  
Shear strain inside the shear zone AOB was expressed as follows: 
)co t (co t ???? ???  (9) 
 
Here ? is the inclination angle of the arbitrary radial plane, and ? is the tangent to 
the free surface (curve between A and B in Figure 8) with the machined surface.  
22 
This model predicted that the shear strain was zero at the lower boundary of the 
shear zone and obtained the maximum at the upper boundary of the shear zone. 
 In 1966, Zorev (94) proposed the thick zone model detailed in Figure 9.  
Line OL defined the initial boundary of the zone and OM the final boundary of 
the shear zone.  Inside the shear zone LOM, there was a family of shear lines 
along which shear deformations were formed.  Work material passed through the 
shear zone and was subjected to increasing shear strain: 
 
Figure 9:  Zorev's Model of a Thick Zone 
 
The initial boundary of shear zone is similar to the onset shear plane proposed by 
Black in a later paper.  The direction of shear deformation was tangent to each 
23 
line.  The shear direction was approximately parallel to the initial boundary of the 
shear zone. 
 Zorev?s expression of the shear strain is the same as equation (9) above.  
The texture of the chip formation, due to shear deformation, changed from an 
equiaxial structure into a non-equiaxial structure, as shown in the lower (b) 
section of Figure 9.  The angle ? in his formulation, between the direction of the 
texture and the direction of the plastic shear, was a function of the degree of 
plastic deformation and was determined by the following relationship: 
2 2412co t ?? ????  (10) 
 
 Oxley (63) proposed a parallel-sided shear zone model in 1989 as depicted 
in Figure 10.  The total maximum shear strain in the shear zone was found by 
multiplying the average maximum shear strain-rate in the zone by the time a 
particle took to flow through the zone.   
 
Figure 10:  Oxley's Parallel-Sided Shear Zone Model (63) 
24 
 
Maximum shear strain was expressed as 
)c o s (s in c o s ??? ?? ???ef
 (11) 
 
It was assumed that one half of the total strain in the shear zone occurred at the 
centerline, AB.  The shear strain in the plane defined by AB was taken as 
)c o s (s in2 c o s ??? ?? ????ab
 (12) 
 
 A ?stationary? shear zone model was presented by Van Luttervelt (83) in 
1977 as depicted in Figure 11.  This model is similar to Oxley?s parallel sided 
shear zone model. 
 
Figure 11:  Van Luttervelt's Stationary Shear Zone Model (83) 
 
The material entered the shear zone with velocity Va, which might be resolved 
into two components, one parallel to the shear zone and the other perpendicular to 
the shear zone.  The material left the zone with a velocity Vb, which could also be 
25 
decomposed into its parallel and perpendicular components.  The shear strain 
within the zone was derived from these components as: 
)co s (s in )2co s ( ??? ??? ?? ???
 (13) 
 
The direction of maximum elongation described in Van Luttervelt?s model is the 
same as in Oxley?s model. 
 Another shear zone model was suggested in 1996 by Huang (39), working 
as a graduate student for J.T. Black.  During a review of Brigg?s (13) experiment 
using high speed magnification to observe the cutting of aluminum, Huang 
developed a new ?stack of cards? model and a new shear strain equation of 
orthogonal machining.  In reviewing the tapes made by Briggs, he observed that 
the material deformed in a totally different fashion than that which had been 
described in the machining literature.  The plastic deformation of material as 
observed by Huang and Black is depicted in Figure 12. 
 
Figure 12:  Huang's Observation of Flow in Shear Zone (39) 
26 
 
As the material in the workpiece moves from left to right, toward the cutting tool 
along the cutting direction, it approaches the shear zone, designated by the 
triangle AOB.  When the material encounters the onset shear plane AO, it changes 
direction and appears to move at an inclination angle, ?, to the plane.  This is the 
shearing of the metal caused by the massive movement of many dislocations.  
Upon reaching the plane BO, the shearing process stops, and the material changes 
direction a final time and moves in a direction parallel to the tool face.  The shape 
of AOB is triangular and the onset shear plane is flat.  The material encounters 
plane AO simultaneously and shear is in mass all along the boundary.  This onset 
of shear fronts creates the shear plane and defines the lower boundary of the shear 
zone.  Thus ? has been more properly termed by Black the Onset of Shear Plane 
angle (6).  The termination of the shear fronts forms the upper boundary of the 
shear zone as noted by Black and Briggs (9).  The shear fronts are inclined at an 
angle, ?, originating from the plane connecting the tool tip to the free surface.  
His reasoning behind this movement was the presence of dislocations in the 
material.  Figure 13 details the angular relationships as derived by Huang. 
27 
 
Figure 13:  Huang's "New" Stack of Cards Model 
 
Huang?s model is significantly different than Merchant?s model.  In the new card 
model, an element shears at the direction ? relative to the onset shear plane.  (In 
Merchant?s model, an element shears in the direction of the shear plane ?.  In 
Zorev?s model the work material shears tangentially to a shear line that is 
approximately parallel to the initial shear plane.)  Using minimum energy criteria 
Huang developed the following relationships for ? and ?: 
245 ??? ???  (14) 
 
28 
??? sin1 cos2???  (15) 
 
Reference (39) details all the mathematical derivations of Huang?s work as does a 
later appendix.  He explains the movement at the shear plane in terms of 
dislocation theory. 
 
Dislocations and Metal Cutting 
 
 Dislocations have been a major field of study in material engineering and 
applied physics for over seventy years now, but metal cutting researchers have not 
typically addressed hardness, dislocation density or dislocation movement in their 
work with a few noted exceptions.  Dieter (28) gives an excellent overview of 
dislocation theory in general as it applies to material.  His integrated overview of 
the effects of cold rolling in his discussion of metallurgical structure will prove 
useful later in discussing the conclusions of this experiment. 
 Research on the effects of material hardness in metal cutting since the 
efforts of Taylor at the turn of the century and Herbert in the 1920?s has been 
sparse.  P.K. Wright (92) made a great contribution to this area in 1982 when he 
suggested that the work hardening characteristics of the material are the most 
dominating influence on shear angle in machining.  The friction angle and the 
tool/chip contact interface are important, but not governing factors in his review 
of available data sets.  He was not able to develop a predictive theory from his 
analysis, but he believed that it would be possible to predict a ?? range? for a 
29 
material.  He ignored the effects of the frictional constraints at the chip-tool 
interface in his analysis. 
 Von Turkovich (84) discussed dislocation theory as it applied to shear 
stress in his 1967 paper.  Although he was primarily concerned with high speed 
machining in this paper, he believed that shear stress computation in a Type 2 
Chip was possible using the materials elastic constant G(T), the materials 
characteristic Burger?s vector (b) and the dislocation density. 
 Ramalingham and Black (66) showed that the important variables 
involving dislocations are the ?number and orientation of slip systems, certain 
characteristic dislocation parameters as the stacking fault energy, the interaction 
of dislocations with vacancies and solute atoms? in the scanning and transmitting 
electron microscopy studies of ? brass.  In their microscopic studies, they cut the 
material with diamond blades and studied the recrystallization at a molecular 
level. 
 Black (6) proposed a model in 1979 for the plastic deformation that occurs 
in metal cutting.  He demonstrated that the magnitude of the flow stress and the 
onset of shear angle ? correlated to the stacking fault energy of the material being 
cut.  His resultant flow stress model predicts a catastrophic shear front, or shear 
plane, ahead of the tool, created by the annihilation and subsequent heat 
generation as the metastable cells in his model rearrange themselves.  The model 
observes that dislocations sources originate near the tool tip, driving dislocations 
into the cell networks.  There is a rapid buildup of applied stress levels as the 
30 
number of dislocations increase, causing a forest hardening effect at the tip of the 
tool (24) 
 Black?s paper notes that more than one shear front would be crossing the 
material from the tool tip to the free surface at any one point in time, comparing 
this effect to waves at the seashore.  Waves from the ocean will intersect a jetty 
on the beach at many different points along the length of the jetty, but always at 
the same angle.  This is a good analogy to the deformation observed by Black 
Huang in aluminum as they developed the ?new stack of cards? model.  Note that 
there are many cards sitting on the ?onset of shear plane at angle ?.  The onset 
angle ? is dictated by other material properties.  Black?s theory predicted that as 
work-hardening increased; the resistance to the onset of shear will increase.  This 
delay in the initiation of shear would translate into an increase in the onset shear 
plane angle ?.  If measuring techniques existed for the angle ?, one could 
examine the relationships stated in equations (7), (8) and (14) as well as the shape 
of the shear zone. 
 Black and Krishnamurthy (11) conducted a small experiment where they 
examined the relationships between hardness and shear stress in 6061-T6 
aluminum.  They noted that shear stress varied with the material hardness over the 
four samples.  They were widely spaced, with varying hardness produced by 
annealing the as received aluminum.  There results suggested that dislocations 
could possibly explain the differences which they had observed.  In particular, 
when the aluminum was softened by heat treating, the dislocation density was 
reduced as predicted by Cottrell and others.  This reduces the amount of pinning 
31 
in the material, allowing more mobility which translates into a lower yield stress.  
This is also discussed in Dieter (28).  Cold rolling has a similar, although opposite 
effect which will be discussed later. 
 
High Magnification Photography 
 
 The observation of the shear zone and the geometries associated with it is 
a difficult task.  The deformation process is a complicated one occurring under 
very high rates of strain in a small area, making it extremely difficult to measure 
the shear strain expressions experimentally. 
 Photography and optics have advance dramatically since Coker?s photo 
elastic attempts in the 1930?s.  With the advent of scanning electron microscopy 
techniques, the fundamental structure of various chips that developed during 
micromachining has been observed at very high levels of magnification by Black 
(5), Ueda and Iwata (79), and others.  This coupled with advances in high speed 
film and digital imaging such as the Briggs experiment (13) permits a detailed 
study of the deformation zone ahead of the tool. 
 Cook and Shaw (21) used magnified cinematography as early as 1951 to 
analyze the shear process.  They observed a thick shear zone and at various times 
two shear zones.  One zone (the primary zone) extended from the tip of the tool 
along the shear plane while the secondary zone at times appeared adjacent to the 
tool face.  They noted that the frequency of the two zones was ?perhaps? more 
32 
pronounced when cutting materials that strain harden easily and produce thick 
chips. 
 Agrawal and Amstead (1) examined the cutting of mild steels with a 
FASTEX high speed motion camera in the 1960s.  They detected the presence of 
Built Up Edges (BUE), crack formations, and deformation ahead of and below the 
tool.  Their study would also indicate that the shear zone region was not a simple, 
narrow zone problem.  Agrawal and Amstead recognized that their system had 
technique problems common to all photographers: control of lighting, vibration, 
movement of the target, focal length, depth of field and magnification. 
 Oxley (61) conducted experiments with cinematography through a 
microscope up to 50X to directly observe the cutting zone.  These were 
instrumental in his formulations of the Oxley shear zone model. 
 Komanduri and Brown (51) recorded at rates up to 3000 frames per 
second to study chip formation at high (180 sfpm) rates of speed.  They 
encountered the standard problems that Agrawal, Amstead and others encountered 
when trying to trade off magnification for depth of field.  Lighting was a 
significant problem in their experiment. 
 Black and James (7) were more successful using high speed motion 
pictures to record at up to 4000 frames per second as they analyzed the results of 
their Quick Stop Device (QSD) experiments for orthogonal machining.  They 
were instrumental in studying the disengagement process of the chip from the 
tool. 
33 
 J.H.L. The (74) attempted to study the commencement of cutting (the 
incipient stage) using a high speed camera and a stroboscope.  The qualities of the 
films produced were not consistent and set-up was very difficult and time 
consuming. 
 Warnecke (89) used a microscope and a high speed 16 mm camera to 
study the chip formation process and the initialization of the BUE.  He produced a 
very good video of the overall process that has good classroom value, but the 
quartz plate technique used to provide optical contrast and limit lateral 
deformation of the chip limited the ability to observe the microscopic deformation 
of the chip.  Still, this was an excellent advancement in the use of lighting, with a 
wide range of cutting speeds being observed. 
 Briggs (13) used a high quality Kodak Ektapro Imaging System (using the 
EM Model 1012 Processor) and an Infinity K2 Lens with and intensified Imager 
to conduct an experiment examining some of the classical factors (?, depth of cut, 
V, tool contact length, and temperature) in an experiment whose primary video 
objective was to produce a classroom video for metal cutting.  The tapes produced 
of the shear zone were without doubt the best produced to date and formed the 
basis without further experimentation of Black and Huang?s ?new? deck of cards 
model.  The existence of a definitive, easily viewed zone of plastic deformation 
was strongly supported by his studies of aluminum.  The primary drawback with 
the system being used was the cost and availability.  The unit was borrowed and it 
usage was limited to a very small amount of time.  Since then, simpler video 
34 
cameras at a fraction of the cost have emerged on the top end of the consumer 
market that may be useful in a continued study of the shear zone.     
 Scanning Electron Microscope (SEM) technology has been invaluable in 
establishing the role of dislocations in the cutting process.  Black (4) studied 
single and polycrystals using the SME and published the work (5).  Von 
Turkovich and Black (86) used SME in studies of chip and workpiece 
deformation.  Ramalingham and Black (66) developed the first in-situ machining 
technique (machining microscopically within the SEM itself on a stage they 
developed) and observed the formation of shear fronts and heterogeneous plastic 
flow during chip formation.  It also established the validity of post cut (static) 
examination of chip morphology to explain the mechanics of chip formation.  
Black and Cohen (18) would later extend in-situ techniques to measure, for the 
first time, shear velocity directly, along with chip velocity, shear strain and the 
strain rate.  Their measured velocities were comparable to the calculated 
velocities of standard orthogonal mechanics from the equations listed in Appendix 
1.  Scanning electron microscopy is important also because it permits the before 
and after analysis of dislocation generation during work hardening by the tool 
face. 
 
Summary 
 
 In the time since F.W. Taylor?s generation, great advances have been 
made in modeling the metal cutting process.  Brinell invented a means to reliably 
35 
measure and compare the hardness of materials that escaped Taylor.  
Dynamometers have been developed with great accuracy to measure the forces 
involved in cutting as modeled by Merchant and others.  Photography now allows 
for a detailed study of the shear zone ahead of the tool, both macroscopically and 
microscopically.  Remarkably, no one has conducted a detailed study of the 
effects of hardness.  Predictive models for the metal cutting process are still 
inconsistent and incomplete. 
36 
 
 
 
 
 
Materials, Instruments, and Machines 
 
 
Many different materials, instruments, machines, electrical hardware, and 
software were used during this experiment.  The following lists and figures 
describe in great detail what was used to obtain the results presented in this thesis.  
All figures will include a detailed description of the particular piece of equipment 
and how it was used.  
The materials chosen for this experiment are listed below along with the 
source from which they were obtained.  The initial hardness temper or level of 
hardness is also listed for each material as they were specifically chosen prior to 
ordering. 
Copper 10100 OFE (oxygen free electronic) 
? Farmers Copper 
? Temper H01 
Aluminum 1100 
? McMaster-Carr 
? Temper H14 
1018 Steel 
? McMaster-Carr 
? Hardness: Medium (Rockwell B70) 
The equipment and instruments listed below were used together to create 
the virtual quick stop device in its entirety.  The equipment listed includes 
everything from the base machine, upgrades to the machines, fixturing of the 
37 
workpiece specimens, cutting tools, recording equipment for forces and feeds, 
lighting, video recording hardware, and software used data acquisition. 
CINCINNATI No. 2 HM Horizontal Milling Machine 
BALDOR 1/8 Horsepower Three Phase Induction Electric Motor 
WOOD?S E-Trac AC Inverter 
Quick-Stop Workpiece Holder  
HSS Stick Tools, (0.75 x 0.75 inches) at Various Rake Angles 
YUMO Rotary Encoder  
KISTLER Dual Mode Amplifier 
KISTLER Dynamometer 
NATIONAL INSTRUMENTS USB-6008 
DOLAN JENNER Fiber-Lite A-200 
STOCKER AND YALE Imagelite Lite Mite Model 20 
Fiber Optic Ring Light 
Modified Load Lift Camera Stand 
Cross Slide Vice 
DRS TECHNOLOGIES Lightning RDT Camera 
INFINITY InfiniVar Lens 
NATIONAL INSTRUMENTS LabVIEW 
XCITEX Midas 2.0 Video Capture Software  
38 
 
The following equipment was used to prepare the various copper, 
aluminum, and steel specimens to the appropriate dimensions and properties 
before undergoing the orthogonal machining process.  This list also includes any 
machinery used to create any custom fixtures or tooling required as well as the 
material testing equipment used to obtain the material properties of the final 
specimens.  Software used for design and post processing of data also listed.  
CINCINNATI Arrow VMC-750 CNC Mill 
BRIDGEPORT Vertical Milling Machine 
SOUTHBEND Lathe 
DO ALL Vertical Band Saw 
WILTON Belt Sander 
STANAT Rolling Mill 
ROCKWELL Hardness Tester 
BRINELL Hardness Tester 
MTS Q Test 100 Tensile Tester 
DASSAULT SYSTEMS Solidworks Modeling Software 
AUTODESK HSMWorks CAM Software 
MATHWORKS MATLAB 
MINITAB 15 Statistical Analysis Software 
MICROSOFT Excel 2010 
GIMP Image Manipulation Software 
39 
 
Figure 14:  Elevated View of Equipment Setup 
 
An elevated view of the testing area is shown in Figure 14 above.  The 
major components are notated.  A computer cart containing the data acquisition 
PC is seen in the left hand corner.  The cart also holds the NI USB modules as 
well as the amplifiers for the dynamometer.  The user must first start the data 
acquisition programs and start the camera recording before moving to the near 
side making sure not to hit the camera stand in the process to start the motor 
controller.  This location was necessary due to cable lengths and proximity to the 
power bus located on the wall. 
Figure 15 shows the workpiece holder with the camera moved out of the 
way.  The workpiece holder was made out of aluminum and covers the entire 
dynamometer face and attaches to it with socket head cap screws.  The socket 
head cap screws are recessed into the block so as to allow more room for the 
40 
camera lens to get close to the specimen.  The slot cut into the top of the 
workpiece holder is just over 4 inches long to hold a 4 inch long specimen. 
 
 
Figure 15:  Quick Stop Workpiece Holder 
 
The back side of the holder has ten threaded holes for set screws that apply a 
clamping force onto the specimen undergoing testing.  A finite element analysis 
was performed on the workpiece holder to ensure that the front wall of the slot 
would not yield when the set screws were all tightened.  The dynamometer itself 
is attached to a steel plate that is then attached to the horizontal milling table 
using T-nuts and bolts.   
 The tool holder can also be seen in Figure 15 in greater detail.  The tool in 
the figure is an older version of the tools used.  The tools used were ? by ? high 
speed steel tools ground to the correct angles.   
 
41 
 
Figure 16:  Rotary Encoder 
 
 In the figure above the rotary encoder can be seen attached to the lead 
screw of the horizontal milling machine.  A coupler was machined on the lathe 
that would couple the lead screw to the rotary encoder shaft.  The supporting bars 
going from the table to the encoder are there to make sure that the encoder does 
not rotate with the shaft.  The supports were attached to the horizontal milling 
table with T-nuts and bolts. 
42 
 
Figure 17:  Kistler Dual Mode Amplifiers 
 
The Kistler dual mode amplifiers can be seen in Figure 17 above.  Each 
axis of the dynamometer has its own amplifier.  All of the functions for the 
amplifiers are located on the front as shown for easy operation. 
 
 
43 
 
Figure 18:  National Instruments USB-6008 
 
The National Instruments USB-6008 can be seen on the above.  Two of 
these data acquisition device was used for many different purposes.  The rotary 
encoder connected to one and the other one took in the amplifier signals for data 
logging.  The device that took in the data from the amplifiers also output a signal 
to the high speed camera letting it know when to start recording.  This allowed 
software triggers to be defined for to aid in the capture of images for processing.   
44 
 
Figure 19:  Modified Load Lift Camera Stand 
 
The camera stand can be seen in full in Figure 14.  Figure 19 shows a 
close up view of the camera and how it is attached to the custom made camera 
stand.  Notice how the stand has a modular table that allows many different 
attachments.  The cross slide vise is mounted to the camera stand table with bolts 
and nuts that slide into the T-slot grooves in the table.  The camera is attached to a 
rectangular piece of aluminum which is clamped in the cross slide vice.  The 
piece of aluminum extends out to support the weight of the camera lens as well.  
The cross slide vice made adjusting the camera position on a very fine scale a 
much easier task.   
45 
 
Figure 20:  DRS Technologies Lightning RDT Camera 
 
 The DRS high speed camera can be seen above with some of the hardware 
specifications marked.  
 
 
Figure 21:  Cincinnati Arrow VMC 750 CNC Mill 
46 
 The Cincinnati CNC milling machine can be seen on the previous page.  
This machine was used to cut out the tensile samples from each specimen as well 
as size the samples to the correct thicknesses before cold rolling.  G-code was 
generated on a separate PC and then loaded via USB stick onto the CNC machine.  
 
 
Figure 22:  Bridgeport Vertical Milling Machine 
 
 The Bridgeport milling machine shown above was used to get the 
specimens to the correct size to fit into the workpiece holder after cold rolling.   
47 
 
Figure 23:  Do All Vertical Band Saw 
 
 The vertical band saw seen in Figure 23 was used to initially rough cut out 
the specimens from the raw metal stock.   
48 
 
Figure 24: Wilton Belt Sander 
 
 The belt sander was used to remove burrs from specimens while 
undergoing the machining down to thickness to make sure that they sat flat in the 
vice resulting in perfectly flat pieces.  The belt sander was also used for initial 
sanding of the samples after coming out of the rolling mill. 
49 
 
Figure 25:  STANAT Rolling Mill 
 
 The Stanat rolling mill was used to reduce the thickness of the specimen 
needing a percent reduction to increase the hardness.  Calibration of the rolling 
mill was performed before use to make sure that the thickness was being reduced 
evenly across the samples undergoing the cold working.  A powerful motor turns 
the rollers and the thickness gap is controlled by the large wheels seen in Figure 
25.  The wheels turn worm gears which turn spur gears connected to lead screws 
that adjust the roller gap.  Each side of the roller can be adjusted separately but 
the two wheels can be locked together also so that both sides of the roller move at 
the same time.  The thickness gap was reduced by just a couple mils at a time to 
slowly reduce the thickness of the specimen.  This was especially necessary for 
the steel samples which put a lot of load on the rolling mill motor.   
50 
 
Figure 26:  Rockwell Hardness Tester 
 
Figure 26 shows the Rockwell hardness tester used to test the aluminum 
and steel samples.  The appropriate tip was placed in the tester for a Rockwell B 
test.  The screw handle was turned to raise the sample to be tested into the testing 
tip.  The lever on the side is then pulled which releases the load required for the 
test.  Once the load has been fully applied another lever is pulled which removes 
the force and the deflection is shown on the dial on the front of the machine.  This 
dial has values that correspond directly to the Rockwell B scale.   
51 
 
Figure 27: Brinell Hardness Tester 
 
The Brinell tester used was located in the Materials Engineering building.  
The Brinell hardness tester is different than the Rockwell hardness tester in that 
the indentation is made and then measured optically.  An appropriate test load is 
selected and counter weights are hung from the back of the machine for that 
particular load.  The indentation ball is much larger than the Rockwell B test ball.  
The load is applied to the samples after being raised underneath the testing ball.  
52 
The testing ball makes an indentation in the workpiece that can be measured 
optically later.  
 
 
Figure 28:  Brinell Hardness Testing Scope 
 The testing scope shown above in Figure 28 was used to measure the 
indentation from the Brinell hardness tester.  The scope had an attached light to 
illuminate the indentation and inscribed lines on the lens that can be seen when 
focusing on the piece indentation.  The lines are aligned to the indentation and an 
optical measurement is taken.  This measurement is then looked up on an 
53 
empirical chart of Brinell hardness calculations for the testing load used.  This 
value in the chart is you Brinell hardness value.   
 
 
Figure 29:  MTS Q Test 100 Tensile Tester 
 
The tensile testing machine used can be seen in Figure 29.  It is an MTS Q 
Test 100.  The 100 stands for 100kN force that it is rated to apply.  A load cell is 
attached to the upper section of the tester which is attached to ball screws on both 
sides that move it up and down.  Various jaws or fixtures can be attached to the 
54 
upper section.  The tensile testing machine moves at a constant displacement rate 
and records the forces applied to the load cell.   
 
 
Figure 30:  Tensile Testing Jaws with Specimen Inserted 
 
 The jaws used for the tensile testing of the metal samples were of the 
screw clamping type.  A screw collar is tightened which clamps down on the 
piece.  The jaws are designed so that as the pulling force increases the clamping 
force does as well.  Figure 30 shows the jaws clamping a sub-size specimen. 
55 
 
 
 
 
 
Construction and Methodology of the Experiment 
 
 
Sample Preparation 
 
 Three different workpiece materials were studied in this experiment: 
Copper 10100, Aluminum 1100, and 1018 Steel.  Each material arrived in a 
different initial state.  The copper 10100 arrived as pre-cut ? inch by 3 inch by 4 
inch pieces.  The copper was manufactured to meet ASTM B152/2009 standards 
and included the appropriate documentation to verify its purity.  The aluminum 
1100 arrived as a 3/8 inch by 3 inch by 72 inch piece of rectangular stock.  The 
1018 steel arrived as a 3/16 inch by 3 inch by 72 inch piece of rectangular stock.  
The final size of all specimens to be tested needed to be 1/8 inch by 3 inch by 4 
inches.  The aluminum and steel stock was cut on a horizontal band saw to just 
over size in length.  All samples were then ready to be reduced in thickness to the 
appropriate thickness values before rolling.   
The thickness values were calculated so that the appropriate percent 
reduction would be administered to each sample during rolling to the final 
thickness of 1/8 inch.  The initial hardness of each metal had to be taken into 
account when calculating the percent reduction desired.  Aluminum and steel 
hardness tempers are defined by the ultimate tensile strength of the produced 
material and are controlled by various industry standards.  Empirical charts have 
56 
been derived that specify the increase in tensile strength that must be achieved 
from the annealed state to result in a full hard temper of H18 in the case of the 
aluminum samples.  The designation of H14 for the aluminum indicates that the 
tensile strength is approximately midway between that of the annealed temper and 
the H18 temper.  The medium hardness designation of the 1018 steel indicates the 
same approximate half hard temper as the aluminum.  Percent reductions were 
chosen for the aluminum and steel to achieve an additional 29% reduction for the 
hardest specimens.  Resulting hardnesses were compared against industry data to 
verify that a full hard temper was achieved.   
Copper temper designations are more simply defined as a percent 
reduction from the annealed state.  A graph from the ASM handbook defines the 
percent reduction required to achieve the desired hardness tempers.  Values were 
chosen from this graph for a wide temper gradient after the copper samples were 
rolled.  A table of the thicknesses and percent reduction required for each sample 
before rolling is shown on the next page 
57 
 
Material Thickness (in) Percent Reduction (%) 
Copper 10100 0.125 0 
Copper 10100 0.139 10 
Copper 10100 0.169 26 
Copper 10100 0.205 39 
Copper 10100 0.245 49 
Aluminum 1100 0.125 0 
Aluminum 1100 0.149 16 
Aluminum 1100 0.176 29 
1018 Steel 0.125 0 
1018 Steel 0.149 16 
1018 Steel 0.176 29 
Table 1:  Specimen Percent Reduction Values 
 
The samples were reduced to these calculated thicknesses using the 
Cincinnati CNC vertical mill.  A g-code program was written to remove material 
from the entire face of each sample at a prescribed depth per pass using a fly 
cutter.  Material was removed from both sides of each sample so that the two 
sides would be perfectly parallel to each other.  Allowing the CNC machine to 
reduce the thickness of each sample to its desired thickness allowed the researcher 
to prepare the next sample for insertion into the machine as soon as it had finished 
with the previous one.  Measurements for the thickness were taken off of the 
parallels that the samples were resting on resulting in very repeatable results. 
58 
 Once all of the samples were to the correct pre-rolled thickness, 
each one was cold rolled to 1/8 inch using the Stanat rolling mill.  Duplicates of 
each metal and thickness were produced as well for redundancy.  Hardness tests 
were performed on all specimens.  A Rockwell hardness tester was used to test 
the steel and copper samples.  A Rockwell B hardness test has the most 
appropriate range for these two metals.  The aluminum samples were too soft to 
be tested with a Rockwell hardness tester so a Brinell tester was used.  All 
hardness values were converted to the Brinell hardness scale as its range covers 
all hardnesses of all samples.  A table below lists the hardness values of all 
samples and their duplicates.  Names include the metal and initial thickness 
before reduction. 
 
Name Brinell Name Brinell Name Brinell 
Aluminum 
0.125 (1) 31.2 
Copper 
0.125 (2) 66 
Copper 
0.245 (1) 84 
Aluminum 
0.125 (2) 32.3 
Copper 
0.139 (1) 77 
Steel 
0.125 (1) 135 
Aluminum 
0.149 (1) 34.4 
Copper 
0.139 (2) 77 
Steel 
0.125 (2) 135 
Aluminum 
0.149 (2) 34.1 
Copper 
0.169 (1) 81 
Steel 
0.149 (1) 154 
Aluminum 
0.176 (1) 39.8 
Copper 
0.169 (2) 82 
Steel 
0.149 (2) 157 
Aluminum 
0.176 (2) 40.2 
Copper 
0.205 (1) 83 
Steel 
0.176 (1) 171 
Copper 
0.125 (1) 67 
Copper 
0.205 (2) 83 
Steel 
0.176 (2) 171 
Table 2:  Hardness Values 
59 
 At this stage the samples were all the same thickness of 1/8 inch, however 
they were now all different lengths due to the cold rolling deformation.  A 
Bridgeport vertical milling machine was used to resize all of the samples to 3 
inches by 4 inches in preparation for tensile test removal and polishing.  The 
Cincinnati CNC machine was utilized again to mill out the tensile test specimens 
for each specimen.  The tensile test design conformed to the ASTM E8 sub-size 
specimen standard.  Figure 31 illustrates the dimensions of the ASTM E8 sub-size 
specimen. 
 
 
Figure 31:  ASTM E8 Sub-size Specimen Dimensions 
 
60 
  The specimens were remachined to a rectangle shape after tensile test removal 
and were ready for sanding and polishing.   
 The sanding process began by putting the samples back in the CNC 
milling machine and making a light pass with the fly cutter.  This reduced the 
sanding required significantly.  After the fly cutting operation the samples were 
sanded using various grit sandpapers.  The samples were sanded first with 180 grit 
paper, followed by 240, 320, 400, 500, 600, 1000, and finally 2000 grit.  Samples 
were then polished using a polishing compound designed for each metal.  At this 
point the samples had reached an almost mirror finish and were ready for etching.   
 All copper and steel workpieces were etched to provide optimum 
reflective characteristics and definition to the material microstructure.  Chemical 
etchants were prepared for the copper and steel samples according to Table 3 and 
Table 4. 
 
Water Nitric Acid Silver Nitrate 
H2O HNO3 AgNO3 
250 ml 250 ml 2.5 grams 
Table 3:  Copper Etchant 
 
Nitric Acid Ethanol 
HNO3 CH3CH2OH (95%) 
10 ml 500 ml 
Table 4:  Nital Etchant for Steel 
 
61 
The aluminum samples were not etched due to the extremely dangerous nature of 
the chemicals required for aluminum etching.  The optical quality of the 
aluminum samples was sufficient without etching.   
 
Cutting Setup 
 
 The now prepared samples were ready to undergo the orthogonal 
machining process.  The workpiece to be cut was placed in the workpiece holder 
that was attached to the dynamometer and held in place with up to ten set screws.   
 
Figure 32:  Workpiece in Position 
 
Figure 32 shows a workpiece in the workpiece holder looking down the y axis.  
The position of the sample underneath the cutting tool is near the front edge of the 
tool and the camera is in position to record the run.  The camera is shown with the 
fiber optic lights off as they are so bright that it is hard to take a picture of it. 
62 
During the experiment, the table fed the workpiece directly into the tool.  
The dynamometer measured the cutting force (Fc) and the thrust force (Ft), 
passing its output signal to the charge amplifier.  Output from the charge amplifier 
was then directed to the NI USB-6008 data acquisition modules and recorded 
using a LabVIEW program.  During the experiment, the camera was at all times 
focused slightly to the left of the tool tip so as to magnify and record the shear 
plane region ahead of the tool.  Detailed information about the machine setup and 
instrument validation is included in the next section.   
 
Experiment Sequence 
 
 Before runs were made on a given day the machine was calibrated.  This 
calibration included checking the camera focus and scale against the micrometer 
slide as well as a couple test runs in a scrap sample to check for proper machine 
movement.  After calibration a workpiece was selected according to the run 
number and mounted in the workpiece holder.  The cutting tool corresponding to 
the run number was loaded into the tool holder and tightened down.  The cutting 
tool was then used to remove a small amount of material from the workpiece (less 
than .005 inches).  This topping cut also corrected for any non-parallelism 
between the cutting tool and the workpiece thus reducing the possibility of a non-
uniform feed.  The effectiveness of the topping cut was monitored using the 
Midas software.  Once uniform cuts were established, the forces would stabilize 
63 
across the entire topping cut.  This was clearly evident in the LabVIEW graph 
display. 
 After the first cut the z-axis was zeroed so that the following cut would be 
the correct depth from the now perfectly parallel face.  The tool was returned to 
the starting side of the workpiece and readied for a data run.  It was now time to 
turn on the signal amplifiers for the dynamometer.  They were switched on and 
then flipped into recording mode.  This starts the transmission of force data to 
LabVIEW.  The LabVIEW data acquisition program was started which takes in 
the force data and tells the camera when to start recording.  The camera was put 
into recording mode and awaiting the signal from LabVIEW.  The z axis of the 
horizontal milling machine was adjusted to the desired depth of cut for the run.  
The feed on the motor controller was then adjusted as well.  With everything now 
in the correct state for the start of a run, the forward feed button is pressed on the 
motor controller.  This started moving the tool into the workpiece generating a 
force signal which in turn started the data recording. 
 As soon as the run completed the camera video was saved and the tool 
moved back to the starting position.  The force data was saved automatically with 
an auto-incrementing file name format.  All force data and images are time 
stamped from the system clock to the nearest millisecond.  This time stamp from 
the same clock is critical to synchronizing the force data with the images of the 
material undergoing shear. 
64 
 The process continued through all of the required data runs.  If there was 
any error in the recording process the run would be repeated until the desired 
number of replicated was achieved for each set of parameters.   
 
Post Processing 
 
 The post processing of all the data was done using various programs 
selected for their performance in their respective areas of data processing.  
LabVIEW was utilized to convert the data generated by the data collection 
program into an Excel format that is readable by MATLAB for force data 
analysis.  MATLAB used the Excel files generated by the LabVIEW program to 
extract the force data and output the average force for each run during a period of 
steady state forces.  This data was exported to another Excel file for use to 
calculate the resultant forces, strains, and stress according to Merchant?s model.  
GIMP is an image analysis program that was used to measure the angles of 
interest as well as the tool angle and uncut chip thicknesses.  Pixel paths were 
drawn at the appropriate points and these pixel paths were exported to a text file 
that was then analyzed using another MATLAB program to calculate the angles 
from the pixel coordinates.  How each program accepted and generated data will 
be detailed here.  All programs mentioned have the full code published in 
Appendix 5.   
  LabVIEW produced data files of the force measurements from the 
dynamometer in a proprietary .TDM file format.  A LabVIEW program 
65 
incremented though all the .TDM force data files and generated a formatted Excel 
file.   
 MATLAB incremented through all Excel files generated by the previous 
LabVIEW file and displays a graph of the cutting force data.  The figure below 
shows a plot that is displayed to select the appropriate range of data for average 
force calculation.   
 
0 200 400 600 800 1000 1200 1400
- 2 0
0
20
40
60
80
100
120
D a t a  P o i n t
F
o
r
c
e
 
(
lb
f
)
 
Figure 33:  Average Force Selection Plot 
 
The figure on the next page is a snapshot of the command window which asks for 
the data range.  Once a range is specified it outputs the average forces. 
66 
 
Figure 34:  Average Force Input 
 
The MATLAB program also writes all of the force data to an Excel file for further 
study. 
 The figure on the next page shows the GIMP screen and the paths drawn 
for angle measurement.  Make note of each lines purpose.  There is a line defining 
the surface of the uncut specimen.  There is a line defining the tool face.  There is 
a line defining the angle of onset shear and another defining the angle of shear 
motion.  Drawing these lines often required watching the movie of the footage to 
get accurate lines for the shear lines.   
67 
 
Figure 35:  GIMP Path Selection 
 
The figure below shows the outputs of GIMP in the form of a text file.  Notice the 
data points in the file.   
 
 
Figure 36:  GIMP Path Output File 
 
68 
The points are listed in the order of the lines being drawn.  This made it necessary 
to draw the lines in the same order every time.  Once this was done the text file 
would be in a set format that could be post processed later.   
  Another MATLAB program took these pixel coordinates and used basic 
trigonometry equations to calculate the angles of interest and other optical values.  
The full code for these calculations can be viewed in Appendix 5. 
69 
 
 
 
 
 
Instrument Validation and Statistical Design of Experiments 
 
 
Machine Setup  
 
The goal of instrument validation is to verify that the High Speed 
Videographic Quick Stop Device for Orthogonal Machining is a valid instrument 
for making orthogonal cuts at predetermined parameters and its ability to record 
the resulting information.  This study is valid for the quick stop device as it exists 
in its current form in 2013.  Any modifications to the system will require a 
reevaluation of the machine and its capabilities.  The foundation of the virtual 
quick stop device is a Cincinnati Milacron horizontal milling machine.  The 
horizontal milling machine is used as a rigid base for making the orthogonal cuts.  
The machine itself is never powered up as none of the powered functions of the 
machine are utilized.   
A 1/8 horsepower Baldor three-phase induction electric motor is used to 
move the milling table in the x direction underneath the stationary tool holder.  
The Baldor electric motor is connected to a Wood?s E-Trac motor controller.  
This motor controller permits precise speed control of the motor using a variable 
frequency drive (VFD).  The frequency at which this motor controller sends 
power to the motor directly controls the motor RPM.  The formula for calculating 
the RPM of an electric motor using VFD is calculated as 
70 
Pfn ??120  (16) 
 
where n is the RPM, f is the frequency of the power, and P is the number of pole 
pairs in the electric motor.  A 20/1 gear reducer is installed on the motor to 
increase the torque provided by the motor.  The speed of the motor is monitored 
in real time using a rotary encoder.   
The tool holder is attached to the overarm dovetail of the horizontal 
milling machine.  If the horizontal milling machine was being used for traditional 
milling, an arbor support would attach to the overarm dovetail.  The overarm is 
designed to incur very high loads during normal horizontal milling operations and 
is extremely rigid and perfectly parallel to the milling table making it an ideal 
platform to attach the tool holder to.  The overarm is adjustable in the y direction 
to reduce the distance of the tool holder from the main base.  This distance was 
minimized to increase rigidity even further.  The tool holder is designed to hold a 
high speed steel (HSS) tool that has been ground to a specified angle to the 
milling table below.  The tool is also held perfectly perpendicular to the table 
motion so that it is a true orthogonal cut with all force being exerted into the piece 
in a single plane.  
A workpiece holder was designed to attach to the Kistler dynamometer 
and also provide maximum clamping force on the sample being cut.  The 
dynamometer is attached to the milling table via a steel adapter plate that fixes 
into the milling tables T-slots.  This fixture ensures that the workpiece will be 
perfectly parallel to the x direction of the table.  
71 
The camera for recording the deformation of the workpiece during cutting 
is attached to a custom made stand.  The stand is a load lift modified to allow the 
fixture of various attachments.  A cross slide vice has been attached to the load lift 
table which allows the camera to be precisely moved in the x and y directions for 
easy camera positioning.  A winch on the back of the lift moves the camera in the 
z direction.   
 
Run Setup 
 
The correct initial setup of the machine is necessary for repeatable 
measurements to be made on any given day.  The setup begins be positioning the 
camera and calibrating the focus and scale.  This is accomplished by moving the 
camera stand into position in front of the tool holder.  The cross slide vice and be 
used for fine adjustments in the x direction and the height should be adjusted 
using the winch.  Insert a tool into the tool holder and tighten the screws that hold 
the tool in place.  It is important to make sure that the tool is inserted all the way 
up into the tool holder for repeatable tool rigidity.  Insert a workpiece into the 
workpiece holder and tighten it down with the set screws.  It is important to make 
sure that the sample is firmly contacting the bottom of the workpiece slot during 
tightening of the set screws.   
Place the calibration slide against the workpiece with the etched side 
against the material.  This places the scale on the same plane as the workpiece.  
Move the workpiece holder underneath the tool and raise it until the top of the 
72 
calibration slide is just touching the tool.  This will keep the slide from falling.  
Be sure not to crush the slide while raising the workpiece holder.   
Start the Midas software on the computer connected to the camera and 
make sure you can see a live feed.  Turn on the fiber optic ring light to provide 
enough light for the camera at the high magnification.  The camera lens has two 
adjustment knobs.  One is for the zoom level and the other for focusing.  Adjust 
the camera lens zoom to the maximum level and the focus to the closest setting.  
When the object is in focus at these settings the camera is achieving the maximum 
zoom possible by the lens.  Move the camera in the y direction until the 
micrometer scale comes into focus.  The y-direction of the horizontal mill table 
can be adjusted as well to bring the scale into focus as long as the workpiece 
remains underneath the tool.  Once the scale is clearly visible do not move the 
camera or adjust the zoom or focus of the camera lens until all runs are completed 
for the session.  Record the scale for a couple seconds.  This video will be used 
for a pixel to inch ratio.  This ratio can be calculated in the Midas software or later 
in an external program.  Carefully remove the micrometer scale from against the 
workpiece.   
Raise the workpiece underneath the tool so that both can be observed by 
the camera.  Run the motor in reverse until the tool is just to the side of the 
workpiece.  Adjust the workpiece holder to remove 0.002? of material.  The 
adjustment of the workpiece can be measured using a dial indicator attached to 
the milling machine base and then contacting the milling table.  Check the depth 
of cut for the first cut with the video from the camera.  This provides a check for 
73 
the dial indicator.  Set the motor controller to the desired run speed and make a 
pass with the tool.  This will establish a perfectly parallel plane between the 
workpiece and tool for the rest of the runs.  Once the cut in completed lower the 
workpiece just enough so that when it is run in reverse to start the next run the 
tool does not slide back over the workpiece.  If necessary the workpiece can be 
refocused by moving the milling table to bring the piece into better focus.  As 
long as the camera has not been adjusted, when the sample is in focus it will be at 
the same scale as when it started. 
74 
 
 
 
 
 
Data Results 
 
 
The experimental data was collected, during which time the process was 
carefully monitored for any irregularities or obvious discrepancies.  The following 
types of data were collected through direct measurement (electronically for the 
forces and stresses, and optically for the angles). 
Data Symbol Units 
Tool Rake Angle ?? degrees 
Uncut Chip Thickness to inches 
Cut Chip Thickness tc inches 
Horizontal Cutting Force Fc pounds force (lbf) 
Vertical Cutting Force Ft pounds force (lbf) 
Shear Plane Angle ?? degrees 
Shear Front Angle ?? degrees 
Ultimate Stress Fu pounds force (ksi) 
Table 5:  Observed Data Results 
 
During initial selection of the parameters to be used it appeared that the three tool 
angles selected would produce nice type 2 chips for all materials at all hardnesses.  
It was discovered during testing that this was not the case.  The 25 degree tool 
would not reliably produce type 2 chips in the aluminum, steel, and softer copper 
specimens.  The 25 degree tool would produce nice type 2 chips every now and 
75 
then but often it would plow into the material making it unsuitable for subsequent 
runs.  This caused significant time delays and made it practically impossible to 
collect a reliable data set for analysis.  During the course of the experiment it was 
also noted that during some runs the tool underwent minor deflections in some 
materials.  The tool angle was verified using the optical data and is noted in the 
data set in Appendix 3. 
Using the collected data collected during the experiment it was possible to 
calculate the values of primary interest in metal cutting using the relationships 
derived by Merchant, Payton, and others.  The table below details the values that 
were calculated. 
Data Symbol Units 
Chip Thickness Ratio rc none 
Friction Force Upon Chip F newtons 
Normal Force Upon Chip N newtons 
Shear Force on Plane Fs newtons 
Normal Force on Plane Fn newtons 
Mean Friction Angle at Tool ? degrees 
Area of Shear Plane As in2 
Shear Stress on Shear Plane ?s MPa 
Friction Coefficient ? none 
Shear Strain ? none 
Resultant Force R newtons 
Resultant Shear Stress R? MPa 
Table 6:  Calculated Data Results 
76 
 
Below is a sample data set of all measured and calculated results.  Values 
with the light grey background are set values as specified by the design of 
experiments.  Values with the dark grey background are measured values and 
values with the white background are calculated values. 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
98 Cu 0.139 77 35 7.5 0.008 2 34.7 7.8 19.25 127.89 
99 Cu 0.139 77 35 7.5 0.008 3 34.4 8.2 19.20 132.08 
100 Cu 0.139 77 35 7.5 0.004 1 34.9 4.1 9.46 66.89 
101 Cu 0.139 77 35 7.5 0.004 2 35.5 3.5 10.09 75.91 
Table 7:  Run Parameters and Measured Force Data 
 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
98 0.027 0.30 16.3 20.8 19.4 46.2 396.44 416.91 522.01 241.84 186.75 544.15 
99 0.0265 0.30 16.7 22.0 22.5 45.8 406.96 432.28 538.42 250.19 195.52 560.59 
100 0.012 0.33 18.7 19.2 20.8 43.8 205.15 219.60 268.46 135.06 100.06 283.37 
101 0.0125 0.32 17.8 17.3 26.1 44.7 230.44 250.86 307.78 145.95 116.11 320.24 
Table 8:  Measured Optical Data and Calculated Forces  
 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
98 43.6 0.0034 0.0034 0.0037 236.54 84.62 79.25 0.76 
99 43.3 0.0034 0.0034 0.0036 249.09 90.46 84.53 0.76 
100 43.1 0.0015 0.0015 0.0016 277.29 103.35 95.53 0.75 
101 42.6 0.0016 0.0016 0.0017 303.82 114.61 106.42 0.74 
Table 9:  Calculated Areas and Stresses 
 
 
77 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
98 3.08 1.04 0.39 575.30 260.69 260.69 244.13 279.93 
99 3.01 1.04 0.40 593.70 274.67 274.67 256.69 279.93 
100 2.67 1.04 0.46 300.52 310.40 310.40 286.93 279.93 
101 2.81 1.04 0.43 340.63 336.25 336.25 312.22 279.93 
Table 10:  Calculated Forces and Resultant Stresses 
 
Results of the Videographic Study 
 
The virtual quick stop videographic analysis proved very capable of doing 
the analysis intended.  Video of each run was captured in real time resulting in a 
massive amount of data for each run.  The video of each run had its share of 
useful and unusable images.  As the tool progressed through the material the 
material would often move in and out of focus during the duration of the cut.  
This was due to the material specimens either not being perfectly flat or being 
bent slightly out of flat when it was being secured in the workpiece holder.  
After each run completed a portion of the video from the run was saved 
for further analysis.  The selection was determined by the focus of the image and 
a clear view of the shear plane.  As force data was recorded during the entire cut, 
there was sufficient force data for any range of image selection.  The figure on the 
next page illustrates a sample of the force data collected during a run sequence.   
78 
0 200 400 600 800 1000 1200 1400
- 2 0
0
20
40
60
80
100
120
D a t a  P o i n t
F
o
r
c
e
 
(
lb
f
)
 
Figure 37:  Measured Force Plot 
The range of images was exported as a video file which would be analyzed with 
software during post processing.   
During post processing individual images were selected from the video 
file which best represented the shear plane during the cut and when forces has 
stabilized.  This individual image was used to measure the angles of interest as 
well as the tool angle and depth of cut.  Measured shear angles were compared 
with the calculated values of Merchant?s model with extremely good effect.  This 
system of measurement greatly reduced the time required and decreased the 
margin of error typically associated with measuring the angles of interest using 
traditional methods.  The depth was cut was observed to vary up to +-0.0005 
inches and is attributed to slight slack in the lead screw controlling the z axis of 
the horizontal milling machine.   
79 
The figure below illustrates the observed geometry of the shear zone in all 
materials.   
 
Figure 38:  Observed Geometry of Shear Zone 
 
This geometry is consistent with the observations of Briggs (13), Huang and 
Black (40), and Payton (96).  The movement of the crystals into and through the 
shear zone definitely follows the Huang model of movement.  The large amount 
of data collected was prepared for statistical analysis to be detailed in the next 
section.   
80 
 
 
 
 
 
Statistical Analysis 
 
 
 Statistical analysis was performed on the data collected from the 
dynamometer and optical methods.  Statistics have proven useful in verifying 
models developed by others as well as suggesting new models.  It is an integral 
part of the modern engineering solution; however it requires sufficient amounts of 
data to make it truly useful.  This experiment produced a sufficient amount of data 
on the forces predicted by Merchant?s model and it modified models.  In addition, 
the angle measurements ?, ?, ?, and ? tied to these forces were available for 
analysis.  The statistical software package Minitab was used to examine the data 
collected and to compare the predictive models for the angles of interest.  More 
importantly, the effects of material hardness induced by cold working the 
materials upon the cutting process were examined. 
 The statistical technique of analysis of variance (ANOVA) is used to 
determine the effect of various factors on a particular response.  This technique 
measures the degree of variation among factors and determines which factors 
have a statistically significant effect on the response.  ANOVA was performed for 
a variety of responses and for individual materials as well as the entire data set as 
a whole. 
81 
 The first interactions examined were the effects of the run selection 
parameters on the cutting forces.  The figures below detail how each factor 
influenced the cutting forces seen by the cutting tool. 
 
 
 
Figure 39:  Cutting Force ANOVA 
 
 The results show that the work piece material had the largest influence on 
the cutting forces.  The second most influential factor was the depth of cut 
82 
followed by the tool rake angle.  These results also show that the feed rate at 
which the material was cut had no statistical influence on the resulting cutting 
forces.  The replicate also had no influence which is a good indicator of a well-
designed experiment.   
 Workpiece material hardness was one of the main areas of interest in this 
thesis.  Additionally, the comparison of calculated stress values to the real world 
tensile pull data was to be examined.  The following figures illustrates the data 
obtained when observing the material hardness vs. the calculated resolved stress 
in the material as well as the material hardness vs. the measured ultimate stress 
data obtained from the tensile testing. 
 
 
Figure 40:  Hardness vs. Measured Stress 
 
83 
 
Figure 41:  Hardness vs. Calculated Stress 
 
These figures show that the caluculated values for the resultant stress 
follow almost the exact same trend as those from the measured stress values.  This 
data gives hard evidence in favor of the Black and Huang shear zone model.  It 
must be pointed out however that even though the trend is almost identical, the 
calculated values were often higher than those measured.  The reason for this is 
beyond the scope of this thesis but is listed as a topic for future work. 
 Since the values for the calculated stress were very close to the measured 
values for copper, a paired t-test was performed.  The results of this test are 
shown in the figures below.   
84 
 
 
Figure 42:  Paired T-Test of All Copper Samples 
 
In the histogram of differences generated by the paired t-test it can be seen 
that a cluster of values are apart from the rest.  Investigating this reveals that the 
values are associated with the 45 degree tool.  Another paired t-test was 
performed without the 45 degree tool and the following results were obtained.   
85 
 
 
Figure 43:  Paired T-Test of Low Tool Angle Copper Samples 
 
The results of this t-test show that the difference between the calculated 
stress values and those of the measured samples are statistically the same.  This is 
further evidence in favor of the Black and Huang model.  Investigation into why 
the 45 degree tool was producing values that do not agree with the current model 
is listed as another area of future research.  Initial thoughts into this matter are 
centered on the idea that as the tool angle increases the friction force of the chip 
moving across the tool for an extended length start to play a much larger role in 
86 
their contribution to the cutting force.  This same topic has been discussed by P.K. 
Wright (92) as well as more recently by Payton (96). 
87 
 
 
 
 
 
Conclusions and Future Work 
 
 
The results generated by the high speed videographic quick stop device 
led to the following conclusions: 
(1)  The videographic technique for acquiring data on the angles of 
interest in synchronization with the direct measurement of the cutting 
forces reduces the time required for data collection by an order of 
magnitude from traditional methods 
(2) Software was developed that streamlines the optical measurement of 
the angles of interest as well as other data points to define the cutting 
parameters as well as the resulting cutting action during orthogonal 
machining 
(3) It has been shown that shear plane angles can be accurately measured 
using frames acquired using a high speed digital camera during the 
orthogonal machining process 
(4) Hardness values of various materials have been shown to have a 
significant effect on shear angles as well as the stress required to shear 
the metal under orthogonal machining 
(5) For specific materials at low tool angles, the ultimate stress of a 
material can be calculated from the cutting forces and shear angles 
88 
(6) High resolution still images of the metal cutting process showing the 
geometries of interest can be acquired using the high speed 
videographic quick stop device 
(7) Additional experimental data was acquired for a new material not 
previously investigated: 1018 Steel 
 
Recommendations for Future Work 
The high speed videographic quick stop device for orthogonal machining 
is a significant improvement over prior dynamometer techniques used to 
study the orthogonal machining process.  The costs of the high speed 
camera and electronic drive were small compared to the time savings 
permitted.  However, there were still some shortcomings with the system.  
Lighting of the workpiece was very difficult due to the very small area of 
interest.  Fiber optic lights had to be used to provide very localized light 
for any images to be obtained.  Providing additional light is difficult since 
the distance between the camera lens and the workpiece is very short.  
Additionally, the field of view of the camera lens was very small and this 
resulted in the workpiece moving in and out of focus during the length of 
the cut.  The following recommendations would greatly enhance th4e 
capabilities and usefulness of the high speed virtual quick stop device.   
(1) A new lens which provides a higher depth of field and possibly higher 
magnification would help with the focusing of the workpiece during 
the duration of the cut 
89 
(2) Acquire an additional fiber optic light source or a higher wattage light 
source to prove more light to the workpiece during cutting 
(3) Develop image analysis software that can automatically define the 
angles of interest to remove the manual definition currently required 
(4) Develop a method for printing or etching a pattern onto the workpiece 
to better observe the material as it moves through the shear zone 
(5) Acquire a faster computer with more memory that would permit a 
longer recording time as well as making high frame rates possible for 
the duration of the run 
(6) Develop a process for measuring the chip contact distance along the 
tool face to help investigate the effects of chip friction along the tool 
face for higher tool angles 
(7) Borrow or acquire a laser interferometry system that is capable of 
measuring the strain rates and strain directly from the optical qualities 
of the material 
(8) Coordinate studies with the use of a scanning electron microscope to 
measure dislocation density in the materials to be studied 
(9) Acquire additional materials for study to provide additional data for 
the orthogonal machining process 
 
The high speed videographic quick stop device can be easily modified 
or upgraded for a variety of additional research areas.  The high speed at 
which data can be acquired and analyzed using specially designed 
90 
software permit the development of more complete models for the 
complex system of metal cutting.  Ideally the future world of metal 
machining may no longer be an art form but a well understood area of 
engineering.  Fully understanding all of the interactions between the tool 
and workpiece will give way to the optimization of machining practices to 
level currently unobtainable.  This optimization will lower the cost of high 
precision goods and increase the overall quality of products worldwide. 
91 
 
 
 
 
 
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92 
 
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93 
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94 
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95 
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96 
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97 
 
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98 
 
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99 
 
 
 
 
 
Appendix 1 
 
 
Common Formula in Orthogonal Plate Machining Models 
 
VVttttr ccoc ??? 21
 
???????? ??? ??? s in1 c o sa rc t a n cc rr  
?? c o ss in tc FFF ???  
?? s inc o s ???? tc FFN  
NF??  
22 tc FFR ??  
??????? NFarctan?  
?? s inc o s ???? tcs FFF  
?? c o ss in ???? tcn FFF  
?? sinsin 10 wtwtAs ????
 
s
ss AF??  
000,33 12
VFHP c ??  
10 twVtwVM R R ??????  
MRRHPHPs ?  
)cos( sin?? ???? VVc
 
)cos( cos?? ???? VVs
 
Vw FUUU cfs ????  
Vw VFU cf ???  
Vtf VFU r sss ???? 0
 
Black and Huang Model Predicts: 
???? sin1 cos2????  
245 ?? ????  
Merchant Model Predicts: 
)c o s (s in c o s ??? ??? ????
 
2245 ??? ???  
 
100 
 
 
 
 
 
Appendix 2 
 
 
Relevant Calibration and Specification Certificates 
 
The calibration certificate for the Kistler 9257A dynamometer is given below. 
 
 
101 
The material composition certificate for the copper 10100 is given below.   
 
 
102 
 
 
 
 
 
Appendix 3 
 
 
Measured Values 
 
The first table below lists the specified runs parameters and the measured 
force, measured rake angle, and measured depth of cut collected by the high speed 
virtual quick stop device.  The second table lists the measured chip thickness, chip 
thickness ratio, calculated and measured angles, and calculated forces.  
 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
1 Al 0.125 32.3 35 7.5 0.008 1 35.8 7.5 19.98 75.80 
2 Al 0.125 32.3 35 7.5 0.008 2 35.6 7.1 15.57 67.66 
3 Al 0.125 32.3 35 7.5 0.008 3 36.6 8.8 21.75 84.12 
4 Al 0.125 32.3 35 7.5 0.004 1 34.7 4.2 13.70 46.81 
5 Al 0.125 32.3 35 7.5 0.004 2 35.3 4.1 10.22 35.00 
6 Al 0.125 32.3 35 7.5 0.004 3 34.5 3.9 15.38 52.62 
7 Al 0.125 32.3 35 3.75 0.008 1 36.4 10.4 18.49 87.42 
8 Al 0.125 32.3 35 3.75 0.008 2 34.8 9.2 21.73 92.67 
9 Al 0.125 32.3 35 3.75 0.008 3 35.9 8.1 19.98 86.94 
10 Al 0.125 32.3 35 3.75 0.004 1 37.7 4.6 14.51 55.26 
11 Al 0.125 32.3 35 3.75 0.004 2 35.6 4.0 8.25 38.78 
12 Al 0.125 32.3 35 3.75 0.004 3 34.4 4.1 10.67 46.17 
13 Al 0.125 32.3 45 7.5 0.008 1 45.0 7.8 15.67 64.12 
14 Al 0.125 32.3 45 7.5 0.008 2 47.7 7.2 16.15 58.94 
15 Al 0.125 32.3 45 7.5 0.008 3 45.9 6.4 15.74 58.23 
16 Al 0.125 32.3 45 7.5 0.004 1 46.6 4.7 15.28 38.08 
17 Al 0.125 32.3 45 7.5 0.004 2 44.7 3.5 14.85 37.84 
18 Al 0.125 32.3 45 7.5 0.004 3 44.7 3.7 15.84 38.67 
19 Al 0.125 32.3 45 3.75 0.008 1 47.2 8.5 15.91 57.62 
20 Al 0.125 32.3 45 3.75 0.008 2 44.6 8.1 16.00 57.78 
21 Al 0.125 32.3 45 3.75 0.008 3 44.4 8.2 15.68 56.64 
22 Al 0.125 32.3 45 3.75 0.004 1 43.2 4.1 15.69 38.90 
23 Al 0.125 32.3 45 3.75 0.004 2 46.6 4.1 16.67 39.35 
24 Al 0.125 32.3 45 3.75 0.004 3 44.2 4.1 15.53 37.38 
103 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
25 Al 0.149 34.4 35 7.5 0.008 1 37.8 7.7 22.54 94.95 
26 Al 0.149 34.4 35 7.5 0.008 2 38.1 6.9 22.30 89.44 
27 Al 0.149 34.4 35 7.5 0.008 3 38.3 8.2 21.68 95.45 
28 Al 0.149 34.4 35 7.5 0.004 1 35.8 5.3 14.71 57.28 
29 Al 0.149 34.4 35 7.5 0.004 2 36.8 5.2 15.54 57.88 
30 Al 0.149 34.4 35 7.5 0.004 3 36.0 5.0 13.31 55.78 
31 Al 0.149 34.4 35 3.75 0.008 1 32.4 9.0 21.24 91.51 
32 Al 0.149 34.4 35 3.75 0.008 2 33.1 10.6 22.75 93.14 
33 Al 0.149 34.4 35 3.75 0.008 3 34.9 8.3 21.87 91.99 
34 Al 0.149 34.4 35 3.75 0.004 1 34.2 4.4 12.43 51.32 
35 Al 0.149 34.4 35 3.75 0.004 2 34.4 4.9 13.24 52.83 
36 Al 0.149 34.4 35 3.75 0.004 3 34.5 5.0 12.16 50.90 
37 Al 0.149 34.4 45 7.5 0.008 1 45.4 8.1 15.51 59.60 
38 Al 0.149 34.4 45 7.5 0.008 2 44.4 8.2 16.08 56.41 
39 Al 0.149 34.4 45 7.5 0.008 3 44.2 7.7 16.13 55.92 
40 Al 0.149 34.4 45 7.5 0.004 1 42.6 4.6 15.05 39.95 
41 Al 0.149 34.4 45 7.5 0.004 2 43.8 4.7 15.19 36.62 
42 Al 0.149 34.4 45 7.5 0.004 3 45.1 4.1 15.07 37.56 
43 Al 0.149 34.4 45 3.75 0.008 1 44.2 7.6 15.49 53.69 
44 Al 0.149 34.4 45 3.75 0.008 2 44.8 8.2 15.34 55.34 
45 Al 0.149 34.4 45 3.75 0.008 3 45.7 7.8 15.46 55.01 
46 Al 0.149 34.4 45 3.75 0.004 1 44.6 4.3 15.33 35.84 
47 Al 0.149 34.4 45 3.75 0.004 2 45.1 4.6 15.35 37.37 
48 Al 0.149 34.4 45 3.75 0.004 3 43.7 4.4 15.34 36.97 
49 Al 0.176 39.8 35 7.5 0.008 1 36.5 9.7 21.71 83.46 
50 Al 0.176 39.8 35 7.5 0.008 2 34.9 9.7 22.00 83.19 
51 Al 0.176 39.8 35 7.5 0.008 3 34.6 8.6 21.00 82.77 
52 Al 0.176 39.8 35 7.5 0.004 1 33.8 4.1 10.93 42.25 
53 Al 0.176 39.8 35 7.5 0.004 2 35.2 4.3 11.94 42.14 
54 Al 0.176 39.8 35 7.5 0.004 3 34.4 4.3 13.03 42.42 
55 Al 0.176 39.8 35 3.75 0.008 1 35.9 8.1 18.18 70.38 
56 Al 0.176 39.8 35 3.75 0.008 2 35.3 7.8 18.35 76.59 
57 Al 0.176 39.8 35 3.75 0.008 3 35.7 8.2 17.34 69.34 
58 Al 0.176 39.8 35 3.75 0.004 1 35.1 5.9 12.04 45.74 
59 Al 0.176 39.8 35 3.75 0.004 2 35.8 5.6 12.12 44.87 
60 Al 0.176 39.8 35 3.75 0.004 3 36.8 5.7 11.73 43.65 
61 Al 0.176 39.8 45 7.5 0.008 1 46.2 7.8 16.44 52.71 
62 Al 0.176 39.8 45 7.5 0.008 2 44.4 7.3 16.77 53.38 
104 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
63 Al 0.176 39.8 45 7.5 0.008 3 46.5 7.7 17.10 53.63 
64 Al 0.176 39.8 45 7.5 0.004 1 47.2 4.9 16.06 33.84 
65 Al 0.176 39.8 45 7.5 0.004 2 48.6 4.5 15.91 35.06 
66 Al 0.176 39.8 45 7.5 0.004 3 47.0 4.1 16.04 35.16 
67 Al 0.176 39.8 45 3.75 0.008 1 44.2 7.6 16.09 49.73 
68 Al 0.176 39.8 45 3.75 0.008 2 43.6 7.9 16.04 46.53 
69 Al 0.176 39.8 45 3.75 0.008 3 44.5 7.8 15.98 50.84 
70 Al 0.176 39.8 45 3.75 0.004 1 47.8 3.9 16.58 34.95 
71 Al 0.176 39.8 45 3.75 0.004 2 48.1 4.2 16.75 35.94 
72 Al 0.176 39.8 45 3.75 0.004 3 48.7 4.5 16.66 36.58 
73 Cu 0.125 67 35 7.5 0.008 1 35.1 8.1 13.87 154.57 
74 Cu 0.125 67 35 7.5 0.008 2 34.3 7.7 12.13 142.27 
75 Cu 0.125 67 35 7.5 0.008 3 35.8 7.2 11.06 132.65 
76 Cu 0.125 67 35 7.5 0.004 1 35.1 3.7 8.13 63.07 
77 Cu 0.125 67 35 7.5 0.004 2 34.3 4.1 8.81 74.43 
78 Cu 0.125 67 35 7.5 0.004 3 34.9 3.5 8.60 70.97 
79 Cu 0.125 67 35 3.75 0.008 1 34.4 8.6 11.59 145.21 
80 Cu 0.125 67 35 3.75 0.008 2 35.1 8.8 11.23 137.02 
81 Cu 0.125 67 35 3.75 0.008 3 34.7 7.9 11.06 135.74 
82 Cu 0.125 67 35 3.75 0.004 1 35.5 3.3 8.01 67.85 
83 Cu 0.125 67 35 3.75 0.004 2 34.8 4.0 8.03 67.79 
84 Cu 0.125 67 35 3.75 0.004 3 36.0 4.2 8.05 67.72 
85 Cu 0.125 67 45 7.5 0.008 1 44.6 7.5 21.99 105.04 
86 Cu 0.125 67 45 7.5 0.008 2 44.6 7.7 21.52 99.38 
87 Cu 0.125 67 45 7.5 0.008 3 44.4 7.7 20.97 99.31 
88 Cu 0.125 67 45 7.5 0.004 1 45.0 4.0 28.14 70.77 
89 Cu 0.125 67 45 7.5 0.004 2 46.5 4.2 30.43 70.59 
90 Cu 0.125 67 45 7.5 0.004 3 43.6 3.9 29.62 73.75 
91 Cu 0.125 67 45 3.75 0.008 1 44.8 7.9 21.07 96.80 
92 Cu 0.125 67 45 3.75 0.008 2 44.2 7.4 21.72 94.68 
93 Cu 0.125 67 45 3.75 0.008 3 45.0 7.8 20.33 99.96 
94 Cu 0.125 67 45 3.75 0.004 1 46.7 3.5 31.14 69.08 
95 Cu 0.125 67 45 3.75 0.004 2 43.0 3.9 30.57 70.60 
96 Cu 0.125 67 45 3.75 0.004 3 44.0 3.8 30.78 69.65 
97 Cu 0.139 77 35 7.5 0.008 1 35.1 7.8 16.28 151.58 
98 Cu 0.139 77 35 7.5 0.008 2 34.7 7.8 19.25 127.89 
99 Cu 0.139 77 35 7.5 0.008 3 34.4 8.2 19.20 132.08 
100 Cu 0.139 77 35 7.5 0.004 1 34.9 4.1 9.46 66.89 
105 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
101 Cu 0.139 77 35 7.5 0.004 2 35.5 3.5 10.09 75.91 
102 Cu 0.139 77 35 7.5 0.004 3 34.4 3.9 9.23 67.12 
103 Cu 0.139 77 35 3.75 0.008 1 35.8 8.2 15.15 149.18 
104 Cu 0.139 77 35 3.75 0.008 2 34.5 8.5 14.05 146.72 
105 Cu 0.139 77 35 3.75 0.008 3 34.8 7.5 12.16 134.77 
106 Cu 0.139 77 35 3.75 0.004 1 34.4 4.1 7.73 68.77 
107 Cu 0.139 77 35 3.75 0.004 2 35.0 4.1 7.84 69.23 
108 Cu 0.139 77 35 3.75 0.004 3 34.9 3.8 7.80 63.04 
109 Cu 0.139 77 45 7.5 0.008 1 44.1 8.7 2.15 88.55 
110 Cu 0.139 77 45 7.5 0.008 2 44.3 7.3 4.74 77.64 
111 Cu 0.139 77 45 7.5 0.008 3 43.8 8.0 3.58 85.47 
112 Cu 0.139 77 45 7.5 0.004 1 44.6 3.9 8.53 49.86 
113 Cu 0.139 77 45 7.5 0.004 2 44.4 3.6 8.75 47.12 
114 Cu 0.139 77 45 7.5 0.004 3 43.6 3.7 11.61 54.91 
115 Cu 0.139 77 45 3.75 0.008 1 43.8 7.4 3.57 76.28 
116 Cu 0.139 77 45 3.75 0.008 2 44.0 7.6 3.43 76.68 
117 Cu 0.139 77 45 3.75 0.008 3 44.4 8.0 3.50 82.93 
118 Cu 0.139 77 45 3.75 0.004 1 45.5 4.0 29.55 70.48 
119 Cu 0.139 77 45 3.75 0.004 2 44.6 3.9 32.16 70.17 
120 Cu 0.139 77 45 3.75 0.004 3 43.9 3.7 31.67 69.91 
121 Cu 0.169 81 35 7.5 0.008 1 35.4 8.6 22.18 115.40 
122 Cu 0.169 81 35 7.5 0.008 2 35.1 8.0 21.71 106.61 
123 Cu 0.169 81 35 7.5 0.008 3 36.3 7.8 21.67 107.24 
124 Cu 0.169 81 35 7.5 0.004 1 35.2 4.2 23.29 64.45 
125 Cu 0.169 81 35 7.5 0.004 2 35.1 3.9 23.31 65.01 
126 Cu 0.169 81 35 7.5 0.004 3 35.1 4.2 23.44 66.27 
127 Cu 0.169 81 35 3.75 0.008 1 36.0 6.9 22.64 110.62 
128 Cu 0.169 81 35 3.75 0.008 2 34.9 8.4 21.97 105.82 
129 Cu 0.169 81 35 3.75 0.008 3 34.6 8.2 21.49 108.34 
130 Cu 0.169 81 35 3.75 0.004 1 34.9 3.8 23.97 63.63 
131 Cu 0.169 81 35 3.75 0.004 2 34.5 4.5 24.01 66.38 
132 Cu 0.169 81 35 3.75 0.004 3 35.0 4.2 24.12 66.18 
133 Cu 0.169 81 45 7.5 0.008 1 45.8 7.9 29.82 99.39 
134 Cu 0.169 81 45 7.5 0.008 2 44.7 8.1 29.27 98.75 
135 Cu 0.169 81 45 7.5 0.008 3 46.2 7.7 29.47 97.41 
136 Cu 0.169 81 45 7.5 0.004 1 46.4 3.7 37.37 71.56 
137 Cu 0.169 81 45 7.5 0.004 2 45.8 4.0 37.02 72.24 
138 Cu 0.169 81 45 7.5 0.004 3 47.7 3.4 37.39 69.06 
106 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
139 Cu 0.169 81 45 3.75 0.008 1 45.7 7.6 29.59 98.47 
140 Cu 0.169 81 45 3.75 0.008 2 46.4 7.5 30.23 98.09 
141 Cu 0.169 81 45 3.75 0.008 3 45.7 7.5 30.32 97.44 
142 Cu 0.169 81 45 3.75 0.004 1 47.7 3.6 38.17 69.76 
143 Cu 0.169 81 45 3.75 0.004 2 46.5 4.2 37.41 73.15 
144 Cu 0.169 81 45 3.75 0.004 3 47.9 3.7 38.11 70.33 
145 Cu 0.205 83 25 7.5 0.008 1 20.6 8.3 45.16 221.50 
146 Cu 0.205 83 25 7.5 0.008 2 22.8 7.8 46.62 247.24 
147 Cu 0.205 83 25 7.5 0.008 3 20.0 9.2 46.42 239.03 
148 Cu 0.205 83 25 7.5 0.004 1 23.2 5.0 31.15 133.18 
149 Cu 0.205 83 25 7.5 0.004 2 22.3 4.5 40.00 171.85 
150 Cu 0.205 83 25 7.5 0.004 3 24.7 4.8 33.95 140.64 
151 Cu 0.205 83 25 3.75 0.008 1 22.4 9.0 48.95 252.51 
152 Cu 0.205 83 25 3.75 0.008 2 19.5 7.8 43.52 219.33 
153 Cu 0.205 83 25 3.75 0.008 3 21.7 9.0 44.52 234.69 
154 Cu 0.205 83 25 3.75 0.004 1 22.3 4.9 31.98 138.06 
155 Cu 0.205 83 25 3.75 0.004 2 21.0 3.5 31.27 136.05 
156 Cu 0.205 83 25 3.75 0.004 3 24.4 4.0 34.88 159.45 
157 Cu 0.205 83 35 7.5 0.008 1 35.0 7.8 9.69 100.87 
158 Cu 0.205 83 35 7.5 0.008 2 34.9 8.1 8.84 96.24 
159 Cu 0.205 83 35 7.5 0.008 3 34.2 7.8 8.87 95.32 
160 Cu 0.205 83 35 7.5 0.004 1 33.9 4.6 5.51 51.53 
161 Cu 0.205 83 35 7.5 0.004 2 34.8 3.6 6.38 46.16 
162 Cu 0.205 83 35 7.5 0.004 3 34.4 4.0 6.24 51.61 
163 Cu 0.205 83 35 3.75 0.008 1 34.5 7.7 8.24 95.78 
164 Cu 0.205 83 35 3.75 0.008 2 34.7 8.2 7.96 96.01 
165 Cu 0.205 83 35 3.75 0.008 3 34.2 8.2 6.92 90.93 
166 Cu 0.205 83 35 3.75 0.004 1 33.7 3.9 6.61 47.09 
167 Cu 0.205 83 35 3.75 0.004 2 34.3 4.1 6.45 51.24 
168 Cu 0.205 83 35 3.75 0.004 3 34.4 3.6 5.88 44.38 
169 Cu 0.205 83 45 7.5 0.008 1 45.1 7.9 31.01 103.78 
170 Cu 0.205 83 45 7.5 0.008 2 45.7 7.3 33.29 101.76 
171 Cu 0.205 83 45 7.5 0.008 3 45.7 7.7 33.37 101.07 
172 Cu 0.205 83 45 7.5 0.004 1 46.8 4.4 40.76 74.63 
173 Cu 0.205 83 45 7.5 0.004 2 47.0 4.3 40.32 72.95 
174 Cu 0.205 83 45 7.5 0.004 3 47.6 3.7 40.20 72.52 
175 Cu 0.205 83 45 3.75 0.008 1 45.7 7.9 33.70 100.20 
176 Cu 0.205 83 45 3.75 0.008 2 45.4 8.1 33.00 100.64 
107 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
177 Cu 0.205 83 45 3.75 0.008 3 45.6 7.5 34.27 96.72 
178 Cu 0.205 83 45 3.75 0.004 1 47.0 3.2 40.57 70.85 
179 Cu 0.205 83 45 3.75 0.004 2 45.5 3.7 40.35 72.69 
180 Cu 0.205 83 45 3.75 0.004 3 48.4 3.8 40.70 70.84 
181 Cu 0.245 84 25 7.5 0.008 1 21.5 8.4 42.78 207.55 
182 Cu 0.245 84 25 7.5 0.008 2 21.4 8.4 45.39 220.28 
183 Cu 0.245 84 25 7.5 0.008 3 24.2 8.3 46.71 224.34 
184 Cu 0.245 84 25 7.5 0.004 1 20.5 4.8 30.50 136.75 
185 Cu 0.245 84 25 7.5 0.004 2 21.8 4.1 32.92 141.26 
186 Cu 0.245 84 25 7.5 0.004 3 21.3 6.4 41.76 191.31 
187 Cu 0.245 84 25 3.75 0.008 1 20.0 7.8 41.26 200.70 
188 Cu 0.245 84 25 3.75 0.008 2 20.6 8.2 41.96 208.83 
189 Cu 0.245 84 25 3.75 0.008 3 20.1 8.7 40.30 199.03 
190 Cu 0.245 84 25 3.75 0.004 1 20.1 6.0 27.42 111.20 
191 Cu 0.245 84 25 3.75 0.004 2 21.3 4.2 34.48 149.46 
192 Cu 0.245 84 25 3.75 0.004 3 20.7 3.7 28.40 114.42 
193 Cu 0.245 84 35 7.5 0.008 1 34.3 8.0 8.87 91.59 
194 Cu 0.245 84 35 7.5 0.008 2 34.9 8.1 7.72 89.99 
195 Cu 0.245 84 35 7.5 0.008 3 34.6 8.0 7.56 91.30 
196 Cu 0.245 84 35 7.5 0.004 1 36.3 4.5 7.47 50.01 
197 Cu 0.245 84 35 7.5 0.004 2 36.4 4.1 7.65 50.17 
198 Cu 0.245 84 35 7.5 0.004 3 36.0 3.9 7.75 48.69 
199 Cu 0.245 84 35 3.75 0.008 1 34.6 7.8 9.10 91.23 
200 Cu 0.245 84 35 3.75 0.008 2 34.1 7.8 7.42 85.99 
201 Cu 0.245 84 35 3.75 0.008 3 34.7 7.8 6.77 83.26 
202 Cu 0.245 84 35 3.75 0.004 1 38.2 4.2 7.80 47.71 
203 Cu 0.245 84 35 3.75 0.004 2 37.1 4.1 8.09 49.00 
204 Cu 0.245 84 35 3.75 0.004 3 36.9 4.1 7.62 48.55 
205 Cu 0.245 84 45 7.5 0.008 1 45.7 7.6 36.14 102.08 
206 Cu 0.245 84 45 7.5 0.008 2 46.0 7.8 35.59 103.21 
207 Cu 0.245 84 45 7.5 0.008 3 45.5 7.8 35.42 102.91 
208 Cu 0.245 84 45 7.5 0.004 1 46.7 3.9 42.90 75.46 
209 Cu 0.245 84 45 7.5 0.004 2 47.0 3.8 42.78 75.13 
210 Cu 0.245 84 45 7.5 0.004 3 48.6 3.5 42.99 73.36 
211 Cu 0.245 84 45 3.75 0.008 1 45.6 7.8 35.67 100.69 
212 Cu 0.245 84 45 3.75 0.008 2 46.1 7.5 36.83 97.63 
213 Cu 0.245 84 45 3.75 0.008 3 45.9 7.3 36.21 98.33 
214 Cu 0.245 84 45 3.75 0.004 1 48.7 3.7 42.94 71.16 
108 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
215 Cu 0.245 84 45 3.75 0.004 2 48.0 3.7 42.59 71.63 
216 Cu 0.245 84 45 3.75 0.004 3 48.6 3.8 42.65 71.74 
217 St 0.125 135 35 7.5 0.008 1 33.5 8.5 40.18 270.99 
218 St 0.125 135 35 7.5 0.008 2 34.8 8.2 53.33 290.60 
219 St 0.125 135 35 7.5 0.008 3 34.8 7.4 55.78 277.80 
220 St 0.125 135 35 7.5 0.004 1 32.4 3.3 30.43 133.06 
221 St 0.125 135 35 7.5 0.004 2 35.6 4.6 30.22 154.13 
222 St 0.125 135 35 7.5 0.004 3 36.1 4.6 28.37 143.93 
223 St 0.125 135 35 3.75 0.008 1 33.6 9.4 37.67 280.03 
224 St 0.125 135 35 3.75 0.008 2 35.0 8.8 40.05 303.74 
225 St 0.125 135 35 3.75 0.008 3 32.8 7.9 42.90 258.27 
226 St 0.125 135 35 3.75 0.004 1 34.8 4.7 21.31 116.68 
227 St 0.125 135 35 3.75 0.004 2 35.8 4.1 20.17 118.54 
228 St 0.125 135 35 3.75 0.004 3 35.3 4.0 21.08 121.33 
229 St 0.125 135 45 7.5 0.008 1 42.6 9.1 49.03 254.98 
230 St 0.125 135 45 7.5 0.008 2 45.5 7.3 56.18 229.78 
231 St 0.125 135 45 7.5 0.008 3 43.7 9.2 53.29 249.84 
232 St 0.125 135 45 7.5 0.004 1 47.7 4.2 63.67 164.49 
233 St 0.125 135 45 7.5 0.004 2 46.9 2.4 61.51 168.29 
234 St 0.125 135 45 7.5 0.004 3 43.7 5.0 63.89 162.76 
235 St 0.125 135 45 3.75 0.008 1 42.7 7.7 55.16 244.21 
236 St 0.125 135 45 3.75 0.008 2 43.0 7.3 54.82 243.75 
237 St 0.125 135 45 3.75 0.008 3 44.3 7.7 54.18 243.18 
238 St 0.125 135 45 3.75 0.004 1 42.7 4.8 11.14 112.65 
239 St 0.125 135 45 3.75 0.004 2 47.2 3.7 12.24 93.96 
240 St 0.125 135 45 3.75 0.004 3 46.8 4.9 11.49 115.25 
241 St 0.149 154 35 7.5 0.008 1 33.2 9.4 44.28 280.35 
242 St 0.149 154 35 7.5 0.008 2 34.4 8.8 53.71 282.69 
243 St 0.149 154 35 7.5 0.008 3 34.1 7.2 56.14 271.53 
244 St 0.149 154 35 7.5 0.004 1 34.7 2.3 25.21 118.13 
245 St 0.149 154 35 7.5 0.004 2 33.7 4.5 24.91 124.39 
246 St 0.149 154 35 7.5 0.004 3 33.7 4.3 24.47 116.26 
247 St 0.149 154 35 3.75 0.008 1 33.7 9.2 45.54 285.84 
248 St 0.149 154 35 3.75 0.008 2 35.9 7.2 49.18 261.71 
249 St 0.149 154 35 3.75 0.008 3 31.8 8.1 50.25 269.01 
250 St 0.149 154 35 3.75 0.004 1 33.8 2.5 35.19 134.95 
251 St 0.149 154 35 3.75 0.004 2 34.7 3.7 32.50 139.39 
252 St 0.149 154 35 3.75 0.004 3 34.4 3.8 32.50 139.39 
109 
Run 
Ma
teri
al 
Initial 
Thickn
ess (in) 
Materi
al 
Hardn
ess 
(BHN) 
Rake 
Angle 
(degrees) 
Feed 
Rate 
(in/min) 
Depth 
of Cut 
(in) 
Re
plic
ate 
Measu
red 
Rake 
Angle 
(degre
es) 
Measu
red 
Depth 
of Cut 
(mil) 
Fz 
Thrust 
Force 
(lbf) 
Fy 
Cutting 
Force 
(lbf) 
253 St 0.149 154 45 7.5 0.008 1 46.7 9.6 59.22 267.34 
254 St 0.149 154 45 7.5 0.008 2 43.7 7.8 62.19 239.90 
255 St 0.149 154 45 7.5 0.008 3 44.5 3.3 61.39 246.20 
256 St 0.149 154 45 7.5 0.004 1 45.9 6.0 68.00 177.50 
257 St 0.149 154 45 7.5 0.004 2 46.9 4.0 71.23 165.16 
258 St 0.149 154 45 7.5 0.004 3 46.7 3.0 70.08 166.45 
259 St 0.149 154 45 3.75 0.008 1 45.0 5.2 64.85 246.81 
260 St 0.149 154 45 3.75 0.008 2 47.3 6.9 65.49 235.02 
261 St 0.149 154 45 3.75 0.008 3 45.9 5.0 63.41 252.95 
262 St 0.149 154 45 3.75 0.004 1 45.2 4.1 72.10 177.66 
263 St 0.149 154 45 3.75 0.004 2 45.3 4.3 72.36 171.55 
264 St 0.149 154 45 3.75 0.004 3 42.9 4.2 71.27 171.45 
265 St 0.176 171 35 7.5 0.008 1 33.2 8.8 45.83 263.77 
266 St 0.176 171 35 7.5 0.008 2 33.6 8.7 52.52 252.48 
267 St 0.176 171 35 7.5 0.008 3 33.3 8.3 56.37 265.73 
268 St 0.176 171 35 7.5 0.004 1 35.0 4.4 28.00 125.81 
269 St 0.176 171 35 7.5 0.004 2 33.3 4.2 26.61 116.78 
270 St 0.176 171 35 7.5 0.004 3 34.1 3.9 25.90 118.88 
271 St 0.176 171 35 3.75 0.008 1 33.9 8.7 43.73 261.54 
272 St 0.176 171 35 3.75 0.008 2 33.6 7.8 48.86 254.71 
273 St 0.176 171 35 3.75 0.008 3 33.3 7.6 46.70 244.59 
274 St 0.176 171 35 3.75 0.004 1 34.1 3.3 33.10 121.65 
275 St 0.176 171 35 3.75 0.004 2 34.7 4.5 33.81 143.09 
276 St 0.176 171 35 3.75 0.004 3 34.7 3.8 32.84 130.27 
277 St 0.176 171 45 7.5 0.008 1 45.0 9.0 65.90 262.80 
278 St 0.176 171 45 7.5 0.008 2 46.9 7.1 69.14 235.31 
279 St 0.176 171 45 7.5 0.008 3 46.9 7.6 68.09 235.05 
280 St 0.176 171 45 7.5 0.004 1 43.5 4.6 68.39 159.66 
281 St 0.176 171 45 7.5 0.004 2 47.1 3.5 71.12 157.26 
282 St 0.176 171 45 7.5 0.004 3 47.3 3.8 70.29 159.61 
283 St 0.176 171 45 3.75 0.008 1 45.2 8.2 69.10 239.92 
284 St 0.176 171 45 3.75 0.008 2 44.8 7.7 67.37 237.51 
285 St 0.176 171 45 3.75 0.008 3 43.8 7.4 67.59 233.14 
286 St 0.176 171 45 3.75 0.004 1 47.1 4.0 72.59 164.93 
287 St 0.176 171 45 3.75 0.004 2 45.6 3.9 75.35 168.28 
288 St 0.176 171 45 3.75 0.004 3 48.2 3.4 75.96 163.92 
 
 
110 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
1 0.028 0.29 15.6 14.4 44.3 46.9 266.20 225.24 300.76 176.47 76.87 340.13 
2 0.027 0.30 16.3 14.4 43.1 46.2 229.37 206.80 269.43 150.95 77.53 298.94 
3 0.028 0.29 15.6 17.4 46.5 46.9 293.87 251.02 334.25 194.03 86.96 376.58 
4 0.015 0.27 14.5 11.8 49.5 48.0 169.37 135.62 186.42 111.02 42.09 212.85 
5 0.014 0.29 15.6 13.8 51.4 46.9 126.56 101.45 137.67 85.76 31.55 159.10 
6 0.015 0.27 14.5 11.5 46.8 48.0 190.29 152.51 209.58 124.68 47.41 239.21 
7 0.029 0.28 15.0 16.2 38.5 47.5 290.42 271.34 354.22 180.26 106.59 382.89 
8 0.028 0.29 15.6 16.7 41.0 46.9 315.60 282.21 370.89 204.19 104.60 410.26 
9 0.028 0.29 15.6 14.2 40.0 46.9 294.60 265.81 348.45 189.81 99.74 384.05 
10 0.017 0.24 12.6 12.9 48.5 49.9 193.86 164.35 225.90 116.45 56.26 247.84 
11 0.015 0.27 14.5 14.0 40.4 48.0 128.98 120.25 157.86 78.59 47.10 169.93 
12 0.017 0.24 12.6 13.4 35.6 49.9 156.66 141.02 190.14 90.97 52.75 204.08 
13 0.0185 0.43 23.8 17.8 34.3 43.7 250.98 152.38 232.91 178.77 44.73 290.19 
14 0.018 0.44 24.6 21.4 37.0 42.9 236.18 134.61 208.43 174.52 33.98 269.71 
15 0.018 0.44 24.6 16.5 39.0 42.9 232.66 133.64 206.30 171.56 34.43 266.10 
16 0.0085 0.47 26.5 17.6 36.7 41.0 167.84 71.72 121.25 136.42 2.03 182.51 
17 0.0085 0.47 26.5 14.4 38.4 41.0 165.75 72.32 121.16 134.25 3.38 180.81 
18 0.008 0.50 28.7 15.4 36.4 38.8 171.44 71.81 117.11 144.35 0.74 185.87 
19 0.018 0.44 24.6 23.3 38.2 42.9 231.29 131.20 203.53 171.13 32.70 263.90 
20 0.018 0.44 24.6 23.3 37.5 42.9 232.09 131.42 204.01 171.80 32.60 264.71 
21 0.018 0.44 24.6 23.2 35.8 42.9 227.46 128.84 199.99 168.36 31.99 259.45 
22 0.0085 0.47 26.5 19.1 35.3 41.0 171.72 73.01 123.71 139.69 1.74 186.59 
23 0.0085 0.47 26.5 20.0 28.6 41.0 176.19 71.33 123.54 144.47 -1.53 190.08 
24 0.008 0.50 28.7 17.6 29.4 38.8 166.41 68.73 112.74 140.38 -0.18 180.05 
25 0.027 0.30 16.3 12.3 40.9 46.2 324.38 288.46 377.23 214.77 106.08 420.92 
26 0.028 0.29 15.6 11.3 43.2 46.9 309.45 269.02 356.40 202.76 95.73 398.70 
27 0.027 0.30 16.3 13.4 41.7 46.2 322.53 292.49 380.46 211.73 110.51 421.15 
28 0.017 0.24 12.6 10.5 43.0 49.9 199.75 171.16 234.45 119.29 59.59 256.21 
29 0.0185 0.22 11.4 10.0 44.2 51.1 204.32 171.26 238.67 118.80 57.56 260.31 
30 0.017 0.24 12.6 10.2 43.9 49.9 190.81 169.30 229.31 111.74 62.06 247.43 
31 0.028 0.29 15.6 15.5 42.5 46.9 310.85 279.26 366.52 200.69 104.17 404.68 
32 0.029 0.28 15.0 14.9 37.3 47.5 320.54 281.31 373.88 205.17 101.52 414.22 
33 0.028 0.29 15.6 15.4 40.4 46.9 314.39 279.38 367.82 203.99 102.64 407.88 
34 0.018 0.22 11.8 10.9 48.7 50.7 176.24 155.26 212.16 100.76 56.34 228.02 
35 0.0175 0.23 12.2 11.7 42.8 50.3 183.04 158.73 217.33 107.08 56.27 235.65 
36 0.018 0.22 11.8 12.3 42.7 50.7 174.19 154.46 210.61 99.20 56.57 225.83 
37 0.017 0.47 26.5 24.4 29.9 41.0 236.28 138.68 206.47 180.08 37.71 271.36 
38 0.0165 0.48 27.6 24.4 33.6 39.9 228.02 126.86 189.40 179.49 29.95 259.21 
111 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
39 0.016 0.50 28.7 25.0 27.6 38.8 226.62 125.16 183.81 182.30 28.91 257.26 
40 0.009 0.44 24.6 18.9 28.4 42.9 173.00 78.31 133.65 134.90 6.15 189.80 
41 0.0085 0.47 26.5 23.7 29.9 41.0 162.98 67.40 115.62 133.18 -0.10 176.37 
42 0.0085 0.47 26.5 20.7 31.9 41.0 165.53 70.75 119.60 134.54 2.02 180.00 
43 0.016 0.50 28.7 23.9 32.7 38.8 217.60 120.16 176.48 175.05 27.74 247.02 
44 0.016 0.50 28.7 27.9 30.2 38.8 222.33 125.81 183.23 178.00 31.15 253.55 
45 0.016 0.50 28.7 25.1 34.8 38.8 221.68 124.41 181.70 177.77 30.11 252.41 
46 0.008 0.50 28.7 25.7 35.0 38.8 160.94 64.50 107.14 136.33 -2.00 173.38 
47 0.008 0.50 28.7 23.8 30.9 38.8 165.83 69.27 113.09 139.68 0.53 179.72 
48 0.0085 0.47 26.5 22.8 29.9 41.0 164.53 68.04 116.72 134.45 -0.11 178.05 
49 0.027 0.30 16.3 17.6 42.8 46.2 292.05 248.72 329.23 196.88 85.77 373.90 
50 0.028 0.29 15.6 16.0 47.5 46.9 292.43 247.00 329.98 194.00 84.06 373.44 
51 0.027 0.30 16.3 16.7 47.6 46.2 287.70 248.04 327.19 192.99 87.16 369.73 
52 0.015 0.27 14.5 11.8 51.0 48.0 147.63 126.04 169.83 94.02 43.63 189.15 
53 0.016 0.25 13.4 12.1 55.1 49.1 151.04 123.07 169.95 95.26 39.42 190.80 
54 0.0155 0.26 13.9 11.2 51.0 48.6 155.72 121.32 169.19 101.71 35.71 194.15 
55 0.026 0.31 17.0 15.3 47.2 45.5 245.80 210.09 275.71 168.94 72.85 315.04 
56 0.025 0.32 17.8 15.0 43.5 44.7 262.26 232.26 299.43 181.84 84.92 339.87 
57 0.0255 0.31 17.4 15.7 47.2 45.1 240.07 208.41 271.24 165.82 74.01 309.18 
58 0.016 0.25 13.4 17.2 50.6 49.1 160.59 135.94 185.43 99.41 46.43 205.21 
59 0.016 0.25 13.4 14.7 52.9 49.1 158.65 132.57 181.59 98.85 44.34 201.94 
60 0.0155 0.26 13.9 13.6 48.8 48.6 154.10 129.12 175.88 97.39 43.38 196.31 
61 0.015 0.53 31.2 23.6 32.7 36.3 217.51 114.10 162.71 183.99 22.17 244.61 
62 0.015 0.53 31.2 23.7 33.1 36.3 220.66 115.14 164.48 186.81 21.93 247.93 
63 0.015 0.53 31.2 23.1 31.0 36.3 222.47 114.89 164.66 188.62 21.01 249.50 
64 0.008 0.50 28.7 21.4 31.0 38.8 156.94 55.92 97.77 134.90 -8.40 166.39 
65 0.008 0.50 28.7 23.9 33.8 38.8 160.33 60.24 102.88 136.93 -5.70 171.18 
66 0.008 0.50 28.7 23.7 34.1 38.8 161.03 60.16 103.00 137.63 -6.05 171.80 
67 0.015 0.53 31.2 23.0 31.6 36.3 207.03 105.83 152.18 175.79 18.55 231.77 
68 0.015 0.53 31.2 24.2 34.3 36.3 196.81 95.90 140.10 168.24 13.29 218.53 
69 0.015 0.53 31.2 21.5 32.8 36.3 210.18 109.64 156.63 177.94 20.86 236.14 
70 0.006 0.67 41.7 18.9 32.9 25.8 162.09 57.80 66.96 158.53 -8.63 171.87 
71 0.007 0.57 34.1 19.8 30.2 33.4 165.73 60.38 90.53 151.38 -7.63 176.22 
72 0.007 0.57 34.1 21.4 32.8 33.4 167.48 62.65 93.08 152.67 -6.21 178.70 
73 0.028 0.29 15.6 18.7 28.5 46.9 444.92 527.84 645.50 244.76 262.76 638.38 
74 0.027 0.30 16.3 17.2 35.2 46.2 407.18 487.46 592.28 229.39 244.37 586.26 
75 0.027 0.30 16.3 18.2 30.8 46.2 378.75 455.12 552.53 212.83 228.81 546.10 
76 0.012 0.33 18.7 19.8 31.1 43.8 190.54 209.09 254.26 124.00 97.48 265.56 
112 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
77 0.0125 0.32 17.8 18.2 29.8 44.7 222.00 248.70 303.23 138.53 118.09 311.76 
78 0.012 0.33 18.7 17.1 36.4 43.8 212.40 236.65 286.86 137.22 111.83 297.68 
79 0.027 0.30 16.3 20.0 29.3 46.2 412.70 499.54 605.49 230.75 252.53 596.73 
80 0.0265 0.30 16.7 19.4 34.0 45.8 390.50 470.61 569.61 222.49 237.13 563.68 
81 0.026 0.31 17.0 19.9 30.0 45.5 386.63 466.36 562.95 223.77 235.14 558.29 
82 0.0125 0.32 17.8 18.6 32.0 44.7 202.31 226.79 276.47 126.20 107.75 284.17 
83 0.0125 0.32 17.8 19.3 32.2 44.7 202.21 226.51 276.17 126.18 107.54 283.95 
84 0.0125 0.32 17.8 22.3 45.2 44.7 202.11 226.22 275.87 126.17 107.34 283.73 
85 0.0135 0.59 35.8 29.7 30.5 31.7 399.57 261.23 321.74 352.67 88.43 469.12 
86 0.013 0.62 37.6 31.4 20.9 29.9 380.29 244.88 291.77 345.63 80.71 445.05 
87 0.013 0.62 37.6 27.0 24.0 29.9 378.31 246.43 293.04 343.47 82.89 443.82 
88 0.005 0.80 52.5 25.0 28.3 15.0 311.12 134.07 92.41 325.93 4.81 338.74 
89 0.005 0.80 52.5 25.8 21.7 15.0 317.75 126.31 83.84 331.50 -4.91 341.90 
90 0.005 0.80 52.5 27.8 23.5 15.0 325.13 138.83 95.30 340.44 3.84 353.51 
91 0.013 0.62 37.6 32.8 22.9 29.9 370.76 238.20 283.91 337.04 78.18 433.69 
92 0.0125 0.64 39.6 32.0 21.2 27.9 366.13 229.48 263.04 342.81 71.90 426.08 
93 0.013 0.62 37.6 28.4 24.7 29.9 378.34 250.47 297.06 342.98 86.62 445.40 
94 0.005 0.80 52.5 24.9 23.1 15.0 315.24 119.32 77.25 328.10 -10.39 336.91 
95 0.005 0.80 52.5 26.4 29.1 15.0 318.21 125.90 83.38 331.90 -5.45 342.17 
96 0.005 0.80 52.5 29.0 24.4 15.0 315.86 122.26 80.08 329.10 -7.92 338.61 
97 0.0275 0.29 16.0 18.0 23.0 46.5 446.06 510.82 628.38 255.03 247.13 631.52 
98 0.027 0.30 16.3 20.8 19.4 46.2 396.44 416.91 522.01 241.84 186.75 544.15 
99 0.0265 0.30 16.7 22.0 22.5 45.8 406.96 432.28 538.42 250.19 195.52 560.59 
100 0.012 0.33 18.7 19.2 20.8 43.8 205.15 219.60 268.46 135.06 100.06 283.37 
101 0.0125 0.32 17.8 17.3 26.1 44.7 230.44 250.86 307.78 145.95 116.11 320.24 
102 0.012 0.33 18.7 19.1 21.0 43.8 204.88 221.01 269.74 134.40 101.44 283.78 
103 0.0275 0.29 16.0 20.6 24.4 46.5 435.82 504.95 619.49 247.26 246.66 619.73 
104 0.027 0.30 16.3 21.3 23.5 46.2 425.55 498.76 608.87 243.17 245.90 607.77 
105 0.027 0.30 16.3 17.9 19.6 46.2 388.15 460.05 560.21 220.15 228.84 556.72 
106 0.0125 0.32 17.8 20.6 34.2 44.7 203.61 230.86 280.75 126.24 110.76 287.21 
107 0.012 0.33 18.7 18.9 27.2 43.8 205.19 232.26 280.62 131.53 111.27 289.25 
108 0.012 0.33 18.7 16.5 29.4 43.8 189.26 209.78 254.57 122.57 98.69 264.74 
109 0.0145 0.55 32.6 27.5 16.8 34.9 285.30 271.75 326.65 220.32 141.88 367.57 
110 0.0135 0.59 35.8 25.8 13.9 31.7 259.12 229.28 267.75 219.14 112.66 327.14 
111 0.014 0.57 34.1 26.1 18.5 33.4 280.10 257.55 305.71 226.55 130.75 357.34 
112 0.005 0.80 52.5 21.7 17.2 15.0 183.66 129.99 104.96 199.03 49.81 219.43 
113 0.005 0.80 52.5 22.6 21.1 15.0 175.72 120.69 96.77 189.94 44.26 208.53 
114 0.005 0.80 52.5 22.0 22.5 15.0 209.23 136.20 107.78 225.19 45.76 245.42 
113 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
115 0.013 0.62 37.6 26.4 16.3 29.9 251.16 228.67 259.08 219.66 115.15 319.55 
116 0.0125 0.64 39.6 28.1 20.0 27.9 251.99 230.38 253.16 229.10 116.41 320.97 
117 0.0135 0.59 35.8 25.6 18.8 31.7 271.85 249.85 290.10 228.41 126.80 346.77 
118 0.005 0.80 52.5 25.4 15.9 15.0 314.61 128.75 86.68 328.70 -1.45 339.94 
119 0.005 0.80 52.5 23.4 25.5 15.0 321.86 119.55 76.60 334.69 -12.72 343.11 
120 0.005 0.80 52.5 26.6 18.0 15.0 319.50 120.29 77.65 332.45 -11.13 341.22 
121 0.02 0.40 23.0 22.1 18.8 39.5 375.27 363.90 433.79 291.69 149.50 500.90 
122 0.019 0.42 24.5 24.0 19.5 38.0 351.11 333.08 391.73 284.21 133.32 465.24 
123 0.019 0.42 24.5 22.5 23.1 38.0 352.58 335.48 394.35 285.21 134.77 467.65 
124 0.0095 0.42 24.5 20.7 22.5 38.0 249.29 175.40 218.07 212.97 40.47 302.11 
125 0.01 0.40 23.0 22.0 21.1 39.5 250.80 177.41 225.54 208.58 41.55 304.38 
126 0.0095 0.42 24.5 21.6 22.2 38.0 254.48 181.66 225.18 216.93 43.63 309.61 
127 0.02 0.40 23.0 20.4 15.9 39.5 364.72 345.33 413.43 285.22 137.90 482.97 
128 0.019 0.42 24.5 27.7 17.7 38.0 350.04 329.53 388.03 283.80 130.66 462.64 
129 0.019 0.42 24.5 25.5 19.7 38.0 354.75 339.95 399.14 286.52 137.73 471.63 
130 0.009 0.44 26.0 22.3 23.8 36.5 249.67 170.69 207.48 220.04 36.12 300.27 
131 0.0095 0.42 24.5 23.9 25.6 38.0 256.85 180.59 224.55 219.45 41.58 311.21 
132 0.009 0.44 26.0 24.2 25.2 36.5 256.73 179.59 217.37 225.64 40.75 310.65 
133 0.012 0.67 41.7 24.9 19.2 25.8 406.42 218.81 241.66 393.26 46.62 459.22 
134 0.012 0.67 41.7 31.5 24.3 25.8 402.69 218.53 241.17 389.56 47.79 455.67 
135 0.012 0.67 41.7 27.8 22.0 25.8 399.08 213.72 236.16 386.23 44.73 450.49 
136 0.005 0.80 52.5 27.3 21.4 15.0 342.61 107.53 61.99 353.70 -31.77 357.68 
137 0.005 0.80 52.5 26.4 19.1 15.0 343.67 110.80 65.09 355.17 -29.15 359.91 
138 0.005 0.80 52.5 24.3 20.7 15.0 334.82 99.62 55.16 344.94 -36.09 347.46 
139 0.0115 0.70 44.1 30.6 23.5 23.4 402.79 216.63 223.13 399.23 46.00 455.03 
140 0.012 0.67 41.7 29.5 18.8 25.8 403.63 213.46 236.16 390.78 42.75 454.59 
141 0.012 0.67 41.7 28.7 23.0 25.8 401.85 211.09 233.69 389.14 41.24 452.05 
142 0.005 0.80 52.5 24.9 19.0 15.0 339.46 99.36 54.30 349.51 -38.11 351.65 
143 0.005 0.80 52.5 25.8 18.7 15.0 347.73 112.41 66.16 359.41 -29.21 364.28 
144 0.005 0.80 52.5 25.1 19.9 15.0 341.07 101.33 56.04 351.37 -36.91 353.89 
145 0.039 0.21 11.5 15.3 28.0 46.0 598.46 808.09 925.43 393.37 359.99 938.92 
146 0.041 0.20 10.9 13.9 27.3 46.6 652.73 909.09 
1040.6
5 411.76 416.01 
1038.9
6 
147 0.041 0.20 10.9 16.3 25.6 46.6 636.50 876.37 
1004.9
6 403.99 397.13 
1007.6
9 
148 0.021 0.19 10.6 13.8 27.6 46.9 375.94 478.37 556.69 245.48 201.46 574.09 
149 0.023 0.17 9.7 9.4 27.2 47.8 484.32 617.62 723.77 303.61 260.67 740.32 
150 0.023 0.17 9.7 12.6 29.1 47.8 401.26 503.16 591.41 253.80 208.76 608.77 
151 0.0445 0.18 10.0 17.0 24.9 47.5 672.01 925.96 
1068.3
4 409.46 419.88 
1064.2
9 
152 0.041 0.20 10.9 14.6 27.7 46.6 587.79 802.40 921.36 374.74 360.92 926.86 
114 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
153 0.0415 0.19 10.8 17.5 27.8 46.7 620.67 862.47 988.58 389.60 393.92 986.87 
154 0.023 0.17 9.7 12.7 25.6 47.8 388.46 496.48 581.58 243.22 210.01 594.38 
155 0.023 0.17 9.7 10.4 28.7 47.8 381.81 489.71 573.29 238.61 207.87 585.13 
156 0.024 0.17 9.2 9.2 25.9 48.3 440.36 577.26 675.22 266.90 250.25 681.56 
157 0.0185 0.43 25.2 23.1 28.2 37.3 292.67 342.80 387.52 230.21 168.93 417.89 
158 0.0175 0.46 26.9 24.7 26.9 35.6 277.74 328.11 363.93 228.81 162.79 397.87 
159 0.018 0.44 26.0 22.3 24.9 36.5 275.54 324.69 363.64 221.62 160.77 394.33 
160 0.008 0.50 29.9 21.9 23.9 32.6 151.55 173.69 186.55 135.41 84.09 214.63 
161 0.0075 0.53 32.2 19.0 28.0 30.3 141.04 151.93 158.67 133.41 69.64 195.26 
162 0.008 0.50 29.9 18.4 29.0 32.6 154.43 172.14 185.26 138.41 81.38 216.47 
163 0.018 0.44 26.0 24.3 23.1 36.5 274.39 327.99 366.72 219.97 164.23 394.84 
164 0.018 0.44 26.0 25.9 24.3 36.5 273.96 329.51 368.15 219.30 165.78 395.15 
165 0.018 0.44 26.0 24.6 27.3 36.5 257.20 313.69 349.91 205.21 159.49 372.98 
166 0.0075 0.53 32.2 21.8 27.9 30.3 144.22 154.72 161.61 136.46 70.64 199.37 
167 0.0075 0.53 32.2 17.9 23.0 30.3 154.25 170.26 177.62 145.71 79.80 215.44 
168 0.007 0.57 34.8 18.6 26.8 27.7 134.64 146.70 147.06 134.25 67.96 187.16 
169 0.011 0.73 46.6 29.2 22.7 20.9 423.96 228.89 216.71 430.31 49.23 479.28 
170 0.011 0.73 46.6 30.3 20.7 20.9 424.77 215.35 203.15 430.74 36.40 474.85 
171 0.011 0.73 46.6 28.0 18.8 20.9 422.88 212.93 200.79 428.78 34.89 472.17 
172 0.005 0.80 52.5 26.0 15.7 15.0 362.95 106.52 58.34 373.73 -40.48 376.08 
173 0.005 0.80 52.5 25.0 18.9 15.0 356.28 102.61 55.33 366.61 -41.55 368.42 
174 0.005 0.80 52.5 24.4 18.0 15.0 354.53 101.65 54.60 364.75 -41.77 366.44 
175 0.011 0.73 46.6 30.4 21.1 20.9 421.15 209.17 197.08 426.94 32.08 469.14 
176 0.011 0.73 46.6 28.5 22.5 20.9 420.36 212.74 200.67 426.26 35.68 469.78 
177 0.011 0.73 46.6 30.4 21.1 20.9 412.01 196.41 184.59 417.44 23.79 455.81 
178 0.005 0.80 52.5 21.4 20.5 15.0 350.45 95.23 48.78 359.87 -46.13 360.22 
179 0.005 0.80 52.5 25.8 17.7 15.0 355.54 101.72 54.54 365.76 -42.08 367.40 
180 0.005 0.80 52.5 25.8 18.0 15.0 350.85 94.82 48.31 360.21 -46.66 360.42 
181 0.035 0.23 12.9 16.8 27.7 44.6 562.65 756.32 857.36 391.84 335.56 880.91 
182 0.035 0.23 12.9 15.9 28.4 44.6 597.10 802.73 909.95 415.80 356.19 934.89 
183 0.035 0.23 12.9 15.8 27.6 44.6 610.04 816.59 926.22 425.55 360.94 953.26 
184 0.023 0.17 9.7 14.9 37.7 47.8 380.04 493.98 576.94 235.76 212.43 585.94 
185 0.0225 0.18 9.9 12.1 34.8 47.6 398.25 507.61 593.90 252.09 214.13 608.62 
186 0.0235 0.17 9.4 13.8 28.4 48.1 528.00 692.75 809.01 322.78 300.57 817.52 
187 0.035 0.23 12.9 15.9 30.8 44.6 543.62 731.55 829.15 378.42 324.89 851.55 
188 0.035 0.23 12.9 17.3 35.7 44.6 561.72 763.00 863.69 389.52 341.70 883.71 
189 0.035 0.23 12.9 18.6 31.7 44.6 536.61 726.64 822.88 372.59 324.52 842.99 
190 0.0195 0.21 11.5 18.4 34.7 46.0 319.61 396.75 460.38 218.20 162.89 482.73 
115 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
191 0.0225 0.18 9.9 13.3 31.1 47.6 419.96 537.73 628.65 265.19 227.87 643.12 
192 0.02 0.20 11.2 12.3 26.5 46.3 329.60 407.87 474.72 222.79 166.90 497.13 
193 0.015 0.53 32.2 29.4 29.2 30.3 265.98 311.09 323.77 250.40 153.12 379.58 
194 0.015 0.53 32.2 29.3 31.7 30.3 257.74 308.22 320.50 242.30 154.39 370.93 
195 0.015 0.53 32.2 27.2 30.2 30.3 260.51 313.40 325.80 244.82 157.70 375.79 
196 0.006 0.67 41.5 25.5 29.8 21.0 154.83 163.16 144.64 172.27 73.23 212.68 
197 0.006 0.67 41.5 28.9 23.7 21.0 155.88 163.28 144.63 173.32 72.85 213.66 
198 0.006 0.67 41.5 26.3 25.8 21.0 152.48 157.64 139.41 169.30 69.42 208.04 
199 0.016 0.50 29.9 27.8 30.8 32.6 265.93 309.22 331.77 237.20 151.48 378.67 
200 0.015 0.53 32.2 28.4 29.0 30.3 246.44 294.38 306.12 231.70 147.33 354.53 
201 0.0155 0.52 31.0 28.0 31.3 31.5 237.10 286.12 302.01 216.50 144.31 342.43 
202 0.006 0.67 41.5 27.6 26.9 21.0 150.15 153.94 136.00 166.57 67.21 204.26 
203 0.006 0.67 41.5 30.7 32.3 21.0 154.50 157.89 139.43 171.34 68.71 209.95 
204 0.0065 0.62 37.9 27.2 29.8 24.6 151.62 157.47 149.53 159.45 69.67 207.20 
205 0.01 0.80 52.5 30.8 14.8 15.0 434.74 207.39 149.00 458.05 25.23 481.02 
206 0.01 0.80 52.5 31.1 15.3 15.0 436.57 212.67 154.00 460.56 29.42 484.73 
207 0.01 0.80 52.5 31.5 18.8 15.0 435.09 212.29 153.81 459.03 29.63 483.21 
208 0.0045 0.89 59.4 26.2 11.9 8.1 372.29 102.39 6.47 386.06 -47.87 383.13 
209 0.0045 0.89 59.4 24.9 14.8 8.1 370.86 101.75 6.21 384.52 -47.92 381.57 
210 0.0045 0.89 59.4 24.4 15.5 8.1 365.94 95.53 1.41 378.20 -51.78 374.64 
211 0.01 0.80 52.5 31.3 16.9 15.0 428.92 204.51 146.90 451.91 24.80 474.54 
212 0.01 0.80 52.5 32.4 14.4 15.0 422.95 191.25 134.53 444.26 14.83 463.94 
213 0.01 0.80 52.5 31.8 13.6 15.0 423.19 195.39 138.60 445.04 18.57 465.75 
214 0.0045 0.89 59.4 27.6 14.2 8.1 358.89 88.78 -3.37 369.70 -55.32 365.55 
215 0.0045 0.89 59.4 28.8 15.7 8.1 359.28 91.33 -1.00 370.71 -53.12 366.88 
216 0.0045 0.89 59.4 25.0 12.9 8.1 359.78 91.50 -0.96 371.23 -53.14 367.41 
217 0.02 0.40 23.0 18.8 34.1 39.5 837.81 884.90 
1039.3
5 636.18 398.06 
1151.7
5 
218 0.02 0.40 23.0 18.1 30.5 39.5 935.74 922.82 
1096.7
5 724.12 386.47 
1256.1
2 
219 0.019 0.42 24.5 16.1 33.8 38.0 912.02 869.93 
1022.1
7 737.37 350.51 
1210.6
6 
220 0.006 0.67 41.5 23.7 25.7 21.0 450.37 407.20 353.74 493.47 153.23 587.51 
221 0.0065 0.62 37.9 27.4 26.7 24.6 503.35 484.53 458.25 527.40 197.36 670.21 
222 0.006 0.67 41.5 24.9 28.0 21.0 470.59 452.08 396.06 518.63 183.71 626.17 
223 0.02 0.40 23.0 20.5 35.6 39.5 851.72 924.25 
1080.7
3 641.63 426.54 
1182.2
6 
224 0.0215 0.37 21.2 18.7 32.6 41.3 920.91 1004.56 
1195.4
4 654.32 465.83 
1280.7
1 
225 0.0195 0.41 23.7 17.3 33.2 38.8 815.24 831.62 974.97 636.90 361.22 
1107.1
3 
226 0.006 0.67 41.5 28.3 29.6 21.0 375.32 370.78 326.03 414.79 155.58 504.12 
227 0.006 0.67 41.5 25.2 24.6 21.0 375.94 380.49 335.60 416.50 163.91 509.15 
116 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
228 0.006 0.67 41.5 25.3 21.7 21.0 386.37 388.34 342.23 427.75 166.06 522.03 
229 0.016 0.50 28.7 22.5 37.5 38.8 956.20 647.79 890.45 735.56 232.56 
1131.3
1 
230 0.015 0.53 31.2 21.2 41.2 36.3 899.47 546.05 744.93 743.16 160.27 
1039.9
6 
231 0.016 0.50 28.7 23.7 37.8 38.8 953.45 618.22 861.29 741.23 206.29 
1117.4
5 
232 0.007 0.57 34.1 21.8 31.3 33.4 717.66 317.12 446.67 645.05 18.34 784.39 
233 0.007 0.57 34.1 18.6 31.1 33.4 722.81 335.89 466.08 646.57 33.71 796.33 
234 0.007 0.57 34.1 23.3 32.5 33.4 712.88 310.98 439.74 641.51 14.50 777.62 
235 0.015 0.53 31.2 20.8 38.9 36.3 941.63 594.66 802.20 772.50 189.05 
1097.5
2 
236 0.0155 0.52 29.9 21.7 38.1 37.6 939.12 594.25 818.56 751.69 189.63 
1095.0
4 
237 0.015 0.53 31.2 20.2 36.7 36.3 935.28 594.47 800.50 766.39 191.30 
1091.5
8 
238 0.007 0.57 34.1 23.4 36.4 33.4 389.36 319.30 386.95 322.21 146.00 481.91 
239 0.007 0.57 34.1 19.2 30.4 33.4 334.04 257.05 315.39 279.62 109.65 406.98 
240 0.007 0.57 34.1 20.6 28.7 33.4 398.64 326.38 395.65 330.00 148.98 493.20 
241 0.02 0.40 23.0 21.7 37.9 39.5 876.62 908.56 
1070.5
5 669.24 401.13 
1197.1
0 
242 0.0195 0.41 23.7 20.0 43.1 38.8 916.96 893.01 
1055.0
7 724.65 368.70 
1225.7
0 
243 0.019 0.42 24.5 17.0 41.4 38.0 897.33 846.18 996.14 727.27 336.23 
1186.6
6 
244 0.006 0.67 41.5 23.5 29.6 21.0 393.26 366.11 319.36 432.08 143.16 517.87 
245 0.006 0.67 41.5 26.3 27.8 21.0 408.14 389.72 341.14 449.53 157.23 541.97 
246 0.006 0.67 41.5 26.4 26.1 21.0 385.80 361.18 315.31 424.11 142.23 508.98 
247 0.021 0.38 21.8 21.0 42.2 40.7 895.24 925.33 
1105.6
9 659.65 407.40 
1221.3
6 
248 0.019 0.42 24.5 16.6 44.9 38.0 846.93 828.12 969.16 681.03 343.49 
1133.6
2 
249 0.02 0.40 23.0 18.5 40.6 39.5 869.44 852.02 
1013.7
4 673.93 354.29 
1164.6
2 
250 0.006 0.67 41.5 22.3 24.9 21.0 472.52 401.94 346.02 514.89 138.34 604.73 
251 0.006 0.67 41.5 23.7 29.1 21.0 474.08 425.00 368.75 519.03 158.07 616.75 
252 0.006 0.67 41.5 26.2 23.8 21.0 474.08 425.00 368.75 519.03 158.07 616.75 
253 0.015 0.53 31.2 21.6 34.6 36.3 1027.16 654.62 880.84 841.25 211.72 
1199.4
8 
254 0.015 0.53 31.2 21.7 37.3 36.3 950.16 558.97 769.57 789.31 152.81 
1091.7
4 
255 0.015 0.53 31.2 12.7 33.6 36.3 967.49 581.27 795.36 800.81 166.78 
1116.2
8 
256 0.0065 0.62 37.6 23.4 35.2 29.9 772.18 344.40 440.87 721.46 22.68 845.19 
257 0.0065 0.62 37.6 21.3 37.9 29.9 743.52 295.44 388.63 699.34 -11.58 799.99 
258 0.0065 0.62 37.6 19.3 34.3 29.9 743.97 303.11 396.29 698.80 -4.67 803.33 
259 0.014 0.57 34.1 17.2 39.6 33.4 980.29 572.33 746.80 854.88 153.62 
1124.6
9 
260 0.014 0.57 34.1 21.0 39.2 33.4 945.19 533.23 701.79 827.77 130.94 
1077.3
0 
261 0.014 0.57 34.1 20.2 39.1 33.4 995.09 596.18 773.01 864.92 169.99 
1147.4
9 
117 
Run 
Cut 
Chip 
Thickn
ess (in) 
Chip 
thick
ness 
ratio 
Phi 
(degr
ees) 
Meas
ured 
Phi 
(degr
ees) 
Meas
ured 
Psi 
(degr
ees) 
Psi 
(degr
ees) 
Friction 
Force, 
F 
(newton
s) 
Normal 
Force, 
N 
(newton
s) 
Fs 
Merch
ant 
(newto
ns) 
Fn 
Merch
ant 
(newto
ns) 
Fs 
Payton 
(newto
ns) 
Fn 
Payton 
(newto
ns) 
262 0.0065 0.62 37.6 22.4 37.8 29.9 785.58 332.04 430.34 736.34 6.14 852.85 
263 0.006 0.67 41.7 20.6 39.9 25.8 767.18 311.98 355.27 748.12 -5.36 828.17 
264 0.006 0.67 41.7 18.9 31.7 25.8 763.44 315.09 358.17 744.20 -1.05 825.90 
265 0.019 0.42 24.5 21.4 41.8 38.0 839.96 844.19 983.68 671.24 360.96 
1134.8
6 
266 0.0185 0.43 25.2 21.5 43.3 37.3 835.53 785.98 916.44 689.93 311.37 
1104.0
5 
267 0.018 0.44 26.0 19.7 43.2 36.5 883.41 824.44 951.94 744.25 323.37 
1164.2
8 
268 0.0055 0.73 45.6 25.5 22.1 16.9 423.02 386.96 302.31 487.13 147.90 553.90 
269 0.005 0.80 50.5 27.7 20.6 12.0 394.89 357.62 239.48 475.89 134.87 515.40 
270 0.006 0.67 41.5 27.1 16.8 21.0 397.66 367.09 319.84 436.57 141.99 522.23 
271 0.018 0.44 26.0 21.5 40.3 36.5 826.64 841.40 959.85 685.53 364.63 
1121.7
5 
272 0.017 0.47 27.8 19.0 43.2 34.7 827.91 803.43 900.43 721.22 330.36 
1105.3
5 
273 0.017 0.47 27.8 18.0 41.5 34.7 794.21 772.07 865.12 691.70 318.11 
1060.9
8 
274 0.005 0.80 50.5 25.2 20.2 12.0 430.99 358.79 231.00 511.00 119.25 547.96 
275 0.006 0.67 41.5 25.9 21.2 21.0 488.28 435.12 377.20 534.28 160.49 634.02 
276 0.0055 0.73 45.6 24.8 22.0 16.9 452.04 390.89 300.82 516.37 137.99 581.45 
277 0.014 0.57 34.1 21.8 33.0 33.4 1033.90 619.32 803.05 898.67 176.52 
1192.2
0 
278 0.013 0.62 37.6 22.2 31.4 29.9 957.62 522.66 641.51 882.43 116.41 
1084.7
4 
279 0.013 0.62 37.6 24.0 31.6 29.9 953.50 525.16 643.45 878.03 120.30 
1081.8
9 
280 0.005 0.80 52.5 26.9 16.9 15.0 717.29 287.08 191.21 748.57 -9.27 772.55 
281 0.005 0.80 52.5 23.5 16.7 15.0 718.33 270.93 175.06 747.50 -24.58 767.33 
282 0.005 0.80 52.5 29.1 19.2 15.0 723.12 280.96 184.38 753.56 -17.15 775.60 
283 0.013 0.62 37.6 24.4 39.2 29.9 971.98 537.29 657.85 894.79 124.43 
1103.6
1 
284 0.013 0.62 37.6 22.9 37.1 29.9 958.97 535.15 654.07 882.16 127.44 
1090.7
7 
285 0.013 0.62 37.6 24.7 31.3 29.9 945.90 520.69 638.04 871.06 119.07 
1073.1
6 
286 0.005 0.80 52.5 25.2 19.4 15.0 747.09 290.42 190.63 778.55 -17.59 801.36 
287 0.005 0.80 52.5 27.1 21.6 15.0 766.31 292.28 189.98 797.86 -23.22 819.83 
288 0.005 0.80 52.5 26.6 18.0 15.0 754.51 276.69 176.06 784.12 -33.11 802.96 
 
118 
 
 
 
 
 
Appendix 4 
 
 
Calculated Values 
 
The first table below lists calculated shear areas according to three 
different theories and calculated friction coefficients.  The second table lists the 
calculated shear strains according to three theories and resultant calculated 
stresses as well the measured ultimate stresses from the tensile testing. 
 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
1 49.8 0.0036 0.0036 0.0038 130.89 33.45 31.45 0.87 
2 48.0 0.0034 0.0034 0.0037 122.09 35.13 32.90 0.84 
3 49.5 0.0036 0.0036 0.0038 145.47 37.85 35.58 0.86 
4 51.3 0.0019 0.0019 0.0020 150.32 33.94 32.15 0.90 
5 51.3 0.0018 0.0018 0.0019 119.84 27.46 25.82 0.90 
6 51.3 0.0019 0.0019 0.0020 169.00 38.23 36.21 0.90 
7 46.9 0.0037 0.0037 0.0039 148.28 44.62 42.11 0.82 
8 48.2 0.0036 0.0036 0.0038 161.42 45.52 42.80 0.84 
9 47.9 0.0036 0.0036 0.0038 151.65 43.41 40.81 0.84 
10 49.7 0.0022 0.0022 0.0023 158.64 39.51 37.92 0.87 
11 47.0 0.0019 0.0019 0.0020 127.29 37.98 35.98 0.82 
12 48.0 0.0022 0.0022 0.0023 133.53 37.05 35.55 0.84 
13 58.7 0.0024 0.0024 0.0024 151.59 29.11 28.85 1.03 
14 60.3 0.0023 0.0023 0.0023 140.20 22.86 22.53 1.05 
15 60.1 0.0023 0.0023 0.0023 138.77 23.16 22.83 1.05 
16 66.9 0.0011 0.0011 0.0011 174.74 2.92 2.85 1.17 
17 66.4 0.0011 0.0011 0.0011 174.61 4.87 4.75 1.16 
18 67.3 0.0010 0.0010 0.0010 181.46 1.14 1.10 1.17 
19 60.4 0.0023 0.0023 0.0023 136.91 22.00 21.68 1.05 
20 60.5 0.0023 0.0023 0.0023 137.23 21.93 21.61 1.06 
21 60.5 0.0023 0.0023 0.0023 134.53 21.52 21.21 1.06 
22 67.0 0.0011 0.0011 0.0011 178.29 2.51 2.44 1.17 
23 68.0 0.0011 0.0011 0.0011 178.03 -2.20 -2.14 1.19 
24 67.6 0.0010 0.0010 0.0010 174.69 -0.28 -0.27 1.18 
119 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
25 48.4 0.0034 0.0034 0.0037 170.94 48.07 45.01 0.84 
26 49.0 0.0036 0.0036 0.0038 155.11 41.67 39.17 0.86 
27 47.8 0.0034 0.0034 0.0037 172.40 50.08 46.89 0.83 
28 49.4 0.0022 0.0022 0.0023 164.65 41.85 40.16 0.86 
29 50.0 0.0024 0.0024 0.0025 152.74 36.84 35.65 0.87 
30 48.4 0.0022 0.0022 0.0023 161.04 43.59 41.83 0.85 
31 48.1 0.0036 0.0036 0.0038 159.52 45.34 42.62 0.84 
32 48.7 0.0037 0.0037 0.0039 156.51 42.50 40.11 0.85 
33 48.4 0.0036 0.0036 0.0038 160.08 44.67 42.00 0.84 
34 48.6 0.0024 0.0024 0.0024 139.92 37.16 35.86 0.85 
35 49.1 0.0023 0.0023 0.0024 147.83 38.28 36.84 0.86 
36 48.4 0.0024 0.0024 0.0024 138.90 37.31 36.01 0.85 
37 59.6 0.0022 0.0022 0.0022 148.77 27.17 26.47 1.04 
38 60.9 0.0021 0.0021 0.0021 141.44 22.36 21.66 1.06 
39 61.1 0.0020 0.0020 0.0021 142.41 22.40 21.56 1.07 
40 65.6 0.0012 0.0012 0.0012 179.81 8.27 8.15 1.15 
41 67.5 0.0011 0.0011 0.0011 166.62 -0.14 -0.14 1.18 
42 66.9 0.0011 0.0011 0.0011 172.36 2.91 2.83 1.17 
43 61.1 0.0020 0.0020 0.0021 136.73 21.49 20.69 1.07 
44 60.5 0.0020 0.0020 0.0021 141.96 24.13 23.23 1.06 
45 60.7 0.0020 0.0020 0.0021 140.77 23.33 22.45 1.06 
46 68.2 0.0010 0.0010 0.0010 166.01 -3.10 -2.99 1.19 
47 67.3 0.0010 0.0010 0.0010 175.23 0.83 0.80 1.18 
48 67.5 0.0011 0.0011 0.0011 168.20 -0.15 -0.15 1.18 
49 49.6 0.0034 0.0034 0.0037 149.19 38.86 36.39 0.87 
50 49.8 0.0036 0.0036 0.0038 143.61 36.59 34.40 0.87 
51 49.2 0.0034 0.0034 0.0037 148.26 39.50 36.99 0.86 
52 49.5 0.0019 0.0019 0.0020 136.94 35.19 33.33 0.86 
53 50.8 0.0021 0.0021 0.0022 127.61 29.60 28.23 0.89 
54 52.1 0.0020 0.0020 0.0021 131.57 27.77 26.39 0.91 
55 49.5 0.0033 0.0033 0.0035 130.28 34.42 32.10 0.86 
56 48.5 0.0031 0.0031 0.0034 147.78 41.91 38.92 0.85 
57 49.0 0.0032 0.0032 0.0034 130.96 35.73 33.25 0.86 
58 49.8 0.0021 0.0021 0.0022 139.23 34.86 33.25 0.87 
59 50.1 0.0021 0.0021 0.0022 136.34 33.29 31.75 0.87 
60 50.0 0.0020 0.0020 0.0021 136.77 33.73 32.06 0.87 
61 62.3 0.0019 0.0019 0.0019 136.06 18.54 17.64 1.09 
62 62.4 0.0019 0.0019 0.0019 137.54 18.34 17.45 1.09 
120 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
63 62.7 0.0019 0.0019 0.0019 137.70 17.57 16.71 1.09 
64 70.4 0.0010 0.0010 0.0010 151.50 -13.02 -12.53 1.23 
65 69.4 0.0010 0.0010 0.0010 159.41 -8.83 -8.50 1.21 
66 69.5 0.0010 0.0010 0.0010 159.59 -9.37 -9.02 1.21 
67 62.9 0.0019 0.0019 0.0019 127.26 15.51 14.75 1.10 
68 64.0 0.0019 0.0019 0.0019 117.16 11.11 10.57 1.12 
69 62.5 0.0019 0.0019 0.0019 130.98 17.44 16.59 1.09 
70 70.4 0.0007 0.0007 0.0008 143.92 -18.54 -17.16 1.23 
71 70.0 0.0009 0.0009 0.0009 164.06 -13.83 -13.01 1.22 
72 69.5 0.0009 0.0009 0.0009 168.68 -11.26 -10.59 1.21 
73 40.1 0.0036 0.0036 0.0038 280.93 114.36 107.52 0.70 
74 39.9 0.0034 0.0034 0.0037 268.38 110.73 103.70 0.70 
75 39.8 0.0034 0.0034 0.0037 250.37 103.68 97.09 0.69 
76 42.3 0.0015 0.0015 0.0016 262.63 100.69 93.07 0.74 
77 41.8 0.0016 0.0016 0.0017 299.32 116.57 108.24 0.73 
78 41.9 0.0015 0.0015 0.0016 296.29 115.51 106.78 0.73 
79 39.6 0.0034 0.0034 0.0037 274.37 114.43 107.16 0.69 
80 39.7 0.0034 0.0034 0.0036 263.53 109.70 102.52 0.69 
81 39.7 0.0033 0.0033 0.0035 266.01 111.11 103.62 0.69 
82 41.7 0.0016 0.0016 0.0017 272.91 106.36 98.76 0.73 
83 41.8 0.0016 0.0016 0.0017 272.61 106.16 98.57 0.73 
84 41.8 0.0016 0.0016 0.0017 272.32 105.96 98.39 0.73 
85 56.8 0.0016 0.0016 0.0018 303.88 83.53 78.17 0.99 
86 57.2 0.0016 0.0016 0.0017 287.49 79.53 74.09 1.00 
87 56.9 0.0016 0.0016 0.0017 288.75 81.68 76.09 0.99 
88 66.7 0.0006 0.0006 0.0006 236.69 12.32 11.48 1.16 
89 68.3 0.0006 0.0006 0.0006 214.75 -12.57 -11.71 1.19 
90 66.9 0.0006 0.0006 0.0006 244.09 9.83 9.16 1.17 
91 57.3 0.0016 0.0016 0.0017 279.75 77.04 71.77 1.00 
92 57.9 0.0015 0.0015 0.0016 270.60 73.96 68.64 1.01 
93 56.5 0.0016 0.0016 0.0017 292.71 85.35 79.52 0.99 
94 69.3 0.0006 0.0006 0.0006 197.86 -26.62 -24.81 1.21 
95 68.4 0.0006 0.0006 0.0006 213.58 -13.96 -13.01 1.19 
96 68.8 0.0006 0.0006 0.0006 205.11 -20.29 -18.90 1.20 
97 41.1 0.0035 0.0035 0.0037 279.00 109.73 102.96 0.72 
98 43.6 0.0034 0.0034 0.0037 236.54 84.62 79.25 0.76 
99 43.3 0.0034 0.0034 0.0036 249.09 90.46 84.53 0.76 
100 43.1 0.0015 0.0015 0.0016 277.29 103.35 95.53 0.75 
121 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
101 42.6 0.0016 0.0016 0.0017 303.82 114.61 106.42 0.74 
102 42.8 0.0015 0.0015 0.0016 278.61 104.77 96.85 0.75 
103 40.8 0.0035 0.0035 0.0037 275.06 109.52 102.77 0.71 
104 40.5 0.0034 0.0034 0.0037 275.90 111.43 104.35 0.71 
105 40.2 0.0034 0.0034 0.0037 253.86 103.70 97.11 0.70 
106 41.4 0.0016 0.0016 0.0017 277.13 109.34 101.52 0.72 
107 41.5 0.0015 0.0015 0.0016 289.85 114.93 106.24 0.72 
108 42.1 0.0015 0.0015 0.0016 262.94 101.94 94.23 0.73 
109 46.4 0.0018 0.0018 0.0019 284.20 123.45 116.77 0.81 
110 48.5 0.0016 0.0016 0.0018 252.89 106.41 99.59 0.85 
111 47.4 0.0017 0.0017 0.0018 277.01 118.47 111.45 0.83 
112 54.7 0.0006 0.0006 0.0006 268.84 127.58 118.88 0.95 
113 55.5 0.0006 0.0006 0.0006 247.86 113.35 105.63 0.97 
114 56.9 0.0006 0.0006 0.0006 276.07 117.21 109.21 0.99 
115 47.7 0.0016 0.0016 0.0017 255.28 113.46 105.71 0.83 
116 47.6 0.0015 0.0015 0.0016 260.43 119.76 111.14 0.83 
117 47.4 0.0016 0.0016 0.0018 273.99 119.76 112.09 0.83 
118 67.7 0.0006 0.0006 0.0006 222.01 -3.70 -3.45 1.18 
119 69.6 0.0006 0.0006 0.0006 196.21 -32.59 -30.37 1.22 
120 69.4 0.0006 0.0006 0.0006 198.89 -28.51 -26.57 1.21 
121 45.9 0.0025 0.0025 0.0027 274.07 94.46 85.64 0.80 
122 46.5 0.0023 0.0023 0.0026 261.81 89.11 80.40 0.81 
123 46.4 0.0023 0.0023 0.0026 263.56 90.07 81.27 0.81 
124 54.9 0.0012 0.0012 0.0013 291.49 54.10 48.81 0.96 
125 54.7 0.0012 0.0012 0.0014 285.00 52.51 47.61 0.96 
126 54.5 0.0012 0.0012 0.0013 300.99 58.32 52.62 0.95 
127 46.6 0.0025 0.0025 0.0027 261.21 87.13 79.00 0.81 
128 46.7 0.0023 0.0023 0.0026 259.34 87.33 78.79 0.82 
129 46.2 0.0023 0.0023 0.0026 266.76 92.05 83.05 0.81 
130 55.6 0.0011 0.0011 0.0012 294.15 51.21 45.98 0.97 
131 54.9 0.0012 0.0012 0.0013 300.16 55.59 50.15 0.96 
132 55.0 0.0011 0.0011 0.0012 308.17 57.77 51.87 0.96 
133 61.7 0.0014 0.0014 0.0016 259.70 50.10 46.37 1.08 
134 61.5 0.0014 0.0014 0.0016 259.17 51.36 47.53 1.07 
135 61.8 0.0014 0.0014 0.0016 253.79 48.07 44.49 1.08 
136 72.6 0.0006 0.0006 0.0006 158.77 -81.37 -75.82 1.27 
137 72.1 0.0006 0.0006 0.0006 166.71 -74.67 -69.58 1.26 
138 73.4 0.0006 0.0006 0.0006 141.30 -92.43 -86.13 1.28 
122 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
139 61.7 0.0014 0.0014 0.0015 250.58 51.66 47.73 1.08 
140 62.1 0.0014 0.0014 0.0016 253.78 45.94 42.51 1.08 
141 62.3 0.0014 0.0014 0.0016 251.13 44.32 41.01 1.09 
142 73.7 0.0006 0.0006 0.0006 139.09 -97.60 -90.95 1.29 
143 72.1 0.0006 0.0006 0.0006 169.46 -74.83 -69.73 1.26 
144 73.5 0.0006 0.0006 0.0006 143.54 -94.53 -88.08 1.28 
145 36.5 0.0048 0.0048 0.0055 298.04 115.93 100.55 0.64 
146 35.7 0.0051 0.0051 0.0058 317.98 127.12 110.54 0.62 
147 36.0 0.0051 0.0051 0.0058 307.08 121.35 105.52 0.63 
148 38.2 0.0026 0.0026 0.0030 331.70 120.04 104.51 0.67 
149 38.1 0.0029 0.0029 0.0033 391.97 141.17 123.47 0.67 
150 38.6 0.0029 0.0029 0.0033 320.29 113.06 98.88 0.67 
151 36.0 0.0055 0.0055 0.0063 299.53 117.72 102.79 0.63 
152 36.2 0.0051 0.0051 0.0058 281.53 110.28 95.90 0.63 
153 35.7 0.0051 0.0051 0.0059 298.25 118.84 103.40 0.62 
154 38.0 0.0029 0.0029 0.0033 314.97 113.74 99.47 0.66 
155 37.9 0.0029 0.0029 0.0033 310.48 112.58 98.46 0.66 
156 37.3 0.0030 0.0030 0.0034 349.72 129.62 113.59 0.65 
157 40.5 0.0023 0.0023 0.0025 266.64 116.23 104.62 0.71 
158 40.2 0.0021 0.0021 0.0024 265.95 118.96 106.58 0.70 
159 40.3 0.0022 0.0022 0.0024 257.76 113.96 102.33 0.70 
160 41.1 0.0010 0.0010 0.0011 300.00 135.22 120.42 0.72 
161 42.9 0.0009 0.0009 0.0010 272.94 119.80 106.39 0.75 
162 41.9 0.0010 0.0010 0.0011 297.93 130.87 116.55 0.73 
163 39.9 0.0022 0.0022 0.0024 259.95 116.42 104.54 0.70 
164 39.7 0.0022 0.0022 0.0024 260.96 117.51 105.52 0.69 
165 39.3 0.0022 0.0022 0.0024 248.03 113.05 101.51 0.69 
166 43.0 0.0009 0.0009 0.0010 277.99 121.51 107.91 0.75 
167 42.2 0.0009 0.0009 0.0010 305.54 137.26 121.90 0.74 
168 42.5 0.0008 0.0008 0.0009 271.35 125.40 111.23 0.74 
169 61.6 0.0013 0.0013 0.0014 254.37 57.78 53.40 1.08 
170 63.1 0.0013 0.0013 0.0014 238.45 42.73 39.49 1.10 
171 63.3 0.0013 0.0013 0.0014 235.68 40.96 37.86 1.10 
172 73.6 0.0006 0.0006 0.0006 149.42 -103.69 -96.62 1.29 
173 73.9 0.0006 0.0006 0.0006 141.71 -106.41 -99.16 1.29 
174 74.0 0.0006 0.0006 0.0006 139.85 -106.97 -99.68 1.29 
175 63.6 0.0013 0.0013 0.0014 231.32 37.65 34.80 1.11 
176 63.2 0.0013 0.0013 0.0014 235.54 41.88 38.71 1.10 
123 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
177 64.5 0.0013 0.0013 0.0014 216.66 27.92 25.81 1.13 
178 74.8 0.0006 0.0006 0.0006 124.93 -118.15 -110.09 1.31 
179 74.0 0.0006 0.0006 0.0006 139.71 -107.78 -100.43 1.29 
180 74.9 0.0006 0.0006 0.0006 123.74 -119.52 -111.37 1.31 
181 36.6 0.0043 0.0043 0.0050 309.39 121.09 104.44 0.64 
182 36.6 0.0043 0.0043 0.0050 328.37 128.54 110.87 0.64 
183 36.8 0.0043 0.0043 0.0050 334.24 130.25 112.34 0.64 
184 37.6 0.0029 0.0029 0.0033 312.46 115.05 100.61 0.66 
185 38.1 0.0028 0.0028 0.0032 329.15 118.67 103.68 0.67 
186 37.3 0.0029 0.0029 0.0033 428.37 159.15 139.33 0.65 
187 36.6 0.0043 0.0043 0.0050 299.21 117.24 101.12 0.64 
188 36.4 0.0043 0.0043 0.0050 311.68 123.31 106.35 0.63 
189 36.4 0.0043 0.0043 0.0050 296.95 117.11 101.01 0.64 
190 38.9 0.0024 0.0024 0.0028 296.53 104.92 91.00 0.68 
191 38.0 0.0028 0.0028 0.0032 348.40 126.29 110.33 0.66 
192 38.9 0.0025 0.0025 0.0028 297.74 104.68 90.91 0.68 
193 40.5 0.0018 0.0018 0.0020 278.46 131.70 116.96 0.71 
194 39.9 0.0018 0.0018 0.0020 275.65 132.78 117.92 0.70 
195 39.7 0.0018 0.0018 0.0020 280.22 135.63 120.45 0.69 
196 43.5 0.0007 0.0007 0.0008 309.38 156.65 139.84 0.76 
197 43.7 0.0007 0.0007 0.0008 309.36 155.82 139.10 0.76 
198 44.0 0.0007 0.0007 0.0008 298.20 148.49 132.56 0.77 
199 40.7 0.0019 0.0019 0.0022 266.76 121.80 108.47 0.71 
200 39.9 0.0018 0.0018 0.0020 263.29 126.71 112.53 0.70 
201 39.6 0.0019 0.0019 0.0021 251.06 119.97 106.67 0.69 
202 44.3 0.0007 0.0007 0.0008 290.90 143.77 128.35 0.77 
203 44.4 0.0007 0.0007 0.0008 298.24 146.96 131.20 0.77 
204 43.9 0.0008 0.0008 0.0009 296.77 138.26 122.80 0.77 
205 64.5 0.0012 0.0012 0.0013 190.82 32.32 30.11 1.13 
206 64.0 0.0012 0.0012 0.0013 197.22 37.67 35.10 1.12 
207 64.0 0.0012 0.0012 0.0013 196.98 37.94 35.35 1.12 
208 74.6 0.0006 0.0006 0.0006 18.00 -133.08 -126.95 1.30 
209 74.7 0.0006 0.0006 0.0006 17.25 -133.22 -127.08 1.30 
210 75.4 0.0006 0.0006 0.0006 3.91 -143.96 -137.33 1.32 
211 64.5 0.0012 0.0012 0.0013 188.13 31.76 29.60 1.13 
212 65.7 0.0012 0.0012 0.0013 172.28 19.00 17.70 1.15 
213 65.2 0.0012 0.0012 0.0013 177.51 23.78 22.16 1.14 
214 76.1 0.0006 0.0006 0.0006 -9.37 -153.78 -146.69 1.33 
124 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
215 75.7 0.0006 0.0006 0.0006 -2.79 -147.66 -140.85 1.32 
216 75.7 0.0006 0.0006 0.0006 -2.66 -147.74 -140.93 1.32 
217 43.4 0.0025 0.0025 0.0027 656.67 251.50 228.03 0.76 
218 45.4 0.0025 0.0025 0.0027 692.93 244.18 221.40 0.79 
219 46.4 0.0023 0.0023 0.0026 683.16 234.26 211.36 0.81 
220 47.9 0.0007 0.0007 0.0008 756.66 327.77 292.60 0.84 
221 46.1 0.0008 0.0008 0.0009 909.43 391.69 347.88 0.80 
222 46.1 0.0007 0.0007 0.0008 847.17 392.96 350.80 0.81 
223 42.7 0.0025 0.0025 0.0027 682.81 269.49 244.35 0.74 
224 42.5 0.0027 0.0027 0.0029 697.40 271.76 248.24 0.74 
225 44.4 0.0024 0.0024 0.0026 633.35 234.65 212.24 0.78 
226 45.3 0.0007 0.0007 0.0008 697.38 332.79 297.09 0.79 
227 44.7 0.0007 0.0007 0.0008 717.86 350.60 312.98 0.78 
228 44.9 0.0007 0.0007 0.0008 732.03 355.20 317.09 0.78 
229 55.9 0.0020 0.0020 0.0021 689.87 180.18 173.45 0.98 
230 58.7 0.0019 0.0019 0.0019 622.93 134.02 127.50 1.03 
231 57.0 0.0020 0.0020 0.0021 667.28 159.82 153.86 1.00 
232 66.2 0.0009 0.0009 0.0009 809.45 33.24 31.27 1.15 
233 65.1 0.0009 0.0009 0.0009 844.62 61.09 57.47 1.14 
234 66.4 0.0009 0.0009 0.0009 796.89 26.27 24.72 1.16 
235 57.7 0.0019 0.0019 0.0019 670.83 158.09 150.40 1.01 
236 57.7 0.0019 0.0019 0.0020 658.54 152.56 145.99 1.01 
237 57.6 0.0019 0.0019 0.0019 669.40 159.97 152.19 1.00 
238 50.6 0.0009 0.0009 0.0009 701.23 264.57 248.89 0.88 
239 52.4 0.0009 0.0009 0.0009 571.55 198.71 186.94 0.91 
240 50.7 0.0009 0.0009 0.0009 716.99 269.98 253.98 0.88 
241 44.0 0.0025 0.0025 0.0027 676.38 253.44 229.79 0.77 
242 45.8 0.0024 0.0024 0.0026 685.38 239.51 216.63 0.80 
243 46.7 0.0023 0.0023 0.0026 665.76 224.71 202.75 0.81 
244 47.0 0.0007 0.0007 0.0008 683.12 306.21 273.36 0.82 
245 46.3 0.0007 0.0007 0.0008 729.71 336.31 300.23 0.81 
246 46.9 0.0007 0.0007 0.0008 674.45 304.24 271.60 0.82 
247 44.1 0.0026 0.0026 0.0028 662.03 243.93 222.27 0.77 
248 45.6 0.0023 0.0023 0.0026 647.73 229.57 207.13 0.80 
249 45.6 0.0025 0.0025 0.0027 640.49 223.84 202.96 0.80 
250 49.6 0.0007 0.0007 0.0008 740.14 295.91 264.17 0.87 
251 48.1 0.0007 0.0007 0.0008 788.76 338.12 301.85 0.84 
252 48.1 0.0007 0.0007 0.0008 788.76 338.12 301.85 0.84 
125 
Run 
Beta 
(degrees) 
Shear 
Area, As 
Merchant 
(in^2) 
Shear 
Area, 
As 
Payton 
(in^2) 
Shear 
Area, As 
Adjusted 
(in^2) 
Shear 
Stress, Ts 
Merchant 
(MPa) 
Shear 
Stress, 
Ts 
Payton 
(MPa) 
Shear 
Stress, 
Ts 
Adjusted 
(MPa) 
Friction 
Co-
efficient 
253 57.5 0.0019 0.0019 0.0019 736.59 177.04 168.43 1.00 
254 59.5 0.0019 0.0019 0.0019 643.54 127.78 121.57 1.04 
255 59.0 0.0019 0.0019 0.0019 665.11 139.47 132.69 1.03 
256 66.0 0.0008 0.0008 0.0008 868.81 44.70 41.65 1.15 
257 68.3 0.0008 0.0008 0.0008 765.87 -22.82 -21.26 1.19 
258 67.8 0.0008 0.0008 0.0008 780.96 -9.21 -8.58 1.18 
259 59.7 0.0017 0.0017 0.0018 676.67 139.19 130.94 1.04 
260 60.6 0.0017 0.0017 0.0018 635.89 118.64 111.61 1.06 
261 59.1 0.0017 0.0017 0.0018 700.42 154.03 144.90 1.03 
262 67.1 0.0008 0.0008 0.0008 848.06 12.10 11.27 1.17 
263 67.9 0.0007 0.0007 0.0008 763.57 -11.52 -10.66 1.18 
264 67.6 0.0007 0.0007 0.0008 769.80 -2.26 -2.09 1.18 
265 44.9 0.0023 0.0023 0.0026 657.43 241.24 217.66 0.78 
266 46.8 0.0023 0.0023 0.0025 630.57 214.24 192.83 0.82 
267 47.0 0.0022 0.0022 0.0024 674.78 229.22 205.83 0.82 
268 47.5 0.0007 0.0007 0.0007 697.80 341.40 308.11 0.83 
269 47.8 0.0006 0.0006 0.0007 596.31 335.82 309.05 0.83 
270 47.3 0.0007 0.0007 0.0008 684.14 303.72 271.14 0.83 
271 44.5 0.0022 0.0022 0.0024 680.38 258.46 232.09 0.78 
272 45.9 0.0021 0.0021 0.0023 678.81 249.05 222.65 0.80 
273 45.8 0.0021 0.0021 0.0023 652.19 239.82 214.39 0.80 
274 50.2 0.0006 0.0006 0.0007 575.19 296.92 273.25 0.88 
275 48.3 0.0007 0.0007 0.0008 806.83 343.29 306.47 0.84 
276 49.1 0.0007 0.0007 0.0007 694.36 318.52 287.46 0.86 
277 59.1 0.0017 0.0017 0.0018 727.64 159.95 150.47 1.03 
278 61.4 0.0016 0.0016 0.0017 632.10 114.71 106.86 1.07 
279 61.2 0.0016 0.0016 0.0017 634.02 118.53 110.43 1.07 
280 68.2 0.0006 0.0006 0.0006 489.75 -23.73 -22.11 1.19 
281 69.3 0.0006 0.0006 0.0006 448.39 -62.97 -58.68 1.21 
282 68.8 0.0006 0.0006 0.0006 472.26 -43.93 -40.94 1.20 
283 61.1 0.0016 0.0016 0.0017 648.21 122.60 114.22 1.07 
284 60.8 0.0016 0.0016 0.0017 644.48 125.57 116.98 1.06 
285 61.2 0.0016 0.0016 0.0017 628.69 117.33 109.30 1.07 
286 68.8 0.0006 0.0006 0.0006 488.27 -45.06 -41.98 1.20 
287 69.1 0.0006 0.0006 0.0006 486.60 -59.48 -55.42 1.21 
288 69.9 0.0006 0.0006 0.0006 450.94 -84.81 -79.03 1.22 
 
126 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
1 3.22 1.04 0.37 348.71 151.76 151.76 142.69 118.59 
2 3.08 1.04 0.39 308.83 139.94 139.94 131.05 118.59 
3 3.22 1.04 0.37 386.49 168.21 168.21 158.14 118.59 
4 3.50 1.04 0.34 216.97 174.96 174.96 165.73 118.59 
5 3.22 1.04 0.37 162.20 141.19 141.19 132.74 118.59 
6 3.50 1.04 0.34 243.86 196.64 196.64 186.27 118.59 
7 3.36 1.04 0.35 397.45 166.38 166.38 157.02 118.59 
8 3.22 1.04 0.37 423.38 184.26 184.26 173.24 118.59 
9 3.22 1.04 0.37 396.79 172.69 172.69 162.36 118.59 
10 4.08 1.04 0.28 254.15 178.48 178.48 171.28 118.59 
11 3.50 1.04 0.34 176.34 142.20 142.20 134.69 118.59 
12 4.08 1.04 0.28 210.78 148.03 148.03 142.06 118.59 
13 1.88 0.83 0.58 293.61 191.09 191.09 189.40 118.59 
14 1.81 0.83 0.61 271.84 182.86 182.86 180.22 118.59 
15 1.81 0.83 0.61 268.31 180.49 180.49 177.88 118.59 
16 1.67 0.83 0.68 182.52 263.03 263.03 256.25 118.59 
17 1.67 0.83 0.68 180.84 260.61 260.61 253.89 118.59 
18 1.54 0.83 0.77 185.88 288.01 288.01 277.27 118.59 
19 1.81 0.83 0.61 265.91 178.88 178.88 176.29 118.59 
20 1.81 0.83 0.61 266.71 179.41 179.41 176.82 118.59 
21 1.81 0.83 0.61 261.42 175.85 175.85 173.31 118.59 
22 1.67 0.83 0.68 186.60 268.91 268.91 261.97 118.59 
23 1.67 0.83 0.68 190.08 273.94 273.94 266.87 118.59 
24 1.54 0.83 0.77 180.05 278.98 278.98 268.58 118.59 
25 3.08 1.04 0.39 434.08 196.70 196.70 184.20 122.73 
26 3.22 1.04 0.37 410.03 178.46 178.46 167.78 122.73 
27 3.08 1.04 0.39 435.41 197.30 197.30 184.76 122.73 
28 4.08 1.04 0.28 263.05 184.73 184.73 177.28 122.73 
29 4.51 1.04 0.25 266.60 170.61 170.61 165.11 122.73 
30 4.08 1.04 0.28 255.09 179.14 179.14 171.92 122.73 
31 3.22 1.04 0.37 417.87 181.86 181.86 170.99 122.73 
32 3.36 1.04 0.35 426.47 178.53 178.53 168.49 122.73 
33 3.22 1.04 0.37 420.59 183.05 183.05 172.10 122.73 
34 4.36 1.04 0.26 234.87 154.90 154.90 149.50 122.73 
35 4.22 1.04 0.27 242.27 164.80 164.80 158.62 122.73 
36 4.36 1.04 0.26 232.81 153.53 153.53 148.18 122.73 
37 1.67 0.83 0.68 273.97 197.41 197.41 192.32 122.73 
38 1.60 0.83 0.72 260.94 194.87 194.87 188.72 122.73 
127 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
39 1.54 0.83 0.77 258.88 200.57 200.57 193.09 122.73 
40 1.81 0.83 0.61 189.90 255.49 255.49 251.80 122.73 
41 1.67 0.83 0.68 176.37 254.17 254.17 247.61 122.73 
42 1.67 0.83 0.68 180.01 259.42 259.42 252.73 122.73 
43 1.54 0.83 0.77 248.57 192.58 192.58 185.40 122.73 
44 1.54 0.83 0.77 255.46 197.92 197.92 190.53 122.73 
45 1.54 0.83 0.77 254.20 196.94 196.94 189.59 122.73 
46 1.54 0.83 0.77 173.39 268.66 268.66 258.64 122.73 
47 1.54 0.83 0.77 179.72 278.48 278.48 268.09 122.73 
48 1.67 0.83 0.68 178.05 256.59 256.59 249.96 122.73 
49 3.08 1.04 0.39 383.61 173.83 173.83 162.78 135.14 
50 3.22 1.04 0.37 382.78 166.59 166.59 156.63 135.14 
51 3.08 1.04 0.39 379.86 172.13 172.13 161.19 135.14 
52 3.50 1.04 0.34 194.11 156.53 156.53 148.27 135.14 
53 3.79 1.04 0.31 194.83 146.28 146.28 139.51 135.14 
54 3.65 1.04 0.32 197.40 153.51 153.51 145.92 135.14 
55 2.94 1.04 0.41 323.35 152.79 152.79 142.49 135.14 
56 2.81 1.04 0.43 350.32 172.90 172.90 160.55 135.14 
57 2.87 1.04 0.42 317.91 153.50 153.50 142.84 135.14 
58 3.79 1.04 0.31 210.40 157.97 157.97 150.66 135.14 
59 3.79 1.04 0.31 206.75 155.24 155.24 148.05 135.14 
60 3.65 1.04 0.32 201.04 156.34 156.34 148.61 135.14 
61 1.41 0.83 0.87 245.62 205.39 205.39 195.40 135.14 
62 1.41 0.83 0.87 248.90 208.13 208.13 198.01 135.14 
63 1.41 0.83 0.87 250.39 209.38 209.38 199.20 135.14 
64 1.54 0.83 0.77 166.60 258.15 258.15 248.52 135.14 
65 1.54 0.83 0.77 171.27 265.39 265.39 255.49 135.14 
66 1.54 0.83 0.77 171.90 266.36 266.36 256.43 135.14 
67 1.41 0.83 0.87 232.51 194.43 194.43 184.98 135.14 
68 1.41 0.83 0.87 218.94 183.08 183.08 174.18 135.14 
69 1.41 0.83 0.87 237.06 198.23 198.23 188.59 135.14 
70 1.06 0.83 1.53 172.09 369.86 369.86 342.27 135.14 
71 1.28 0.83 1.02 176.39 319.65 319.65 300.71 135.14 
72 1.28 0.83 1.02 178.81 324.04 324.04 304.83 135.14 
73 3.22 1.04 0.37 690.34 300.45 300.45 282.48 248.21 
74 3.08 1.04 0.39 635.15 287.81 287.81 269.52 248.21 
75 3.08 1.04 0.39 592.10 268.31 268.31 251.25 248.21 
76 2.67 1.04 0.46 282.89 292.19 292.19 270.09 248.21 
128 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
77 2.81 1.04 0.43 333.37 329.08 329.08 305.56 248.21 
78 2.67 1.04 0.46 317.99 328.45 328.45 303.61 248.21 
79 3.08 1.04 0.39 647.97 293.62 293.62 274.96 248.21 
80 3.01 1.04 0.40 611.52 282.91 282.91 264.39 248.21 
81 2.94 1.04 0.41 605.79 286.25 286.25 266.95 248.21 
82 2.81 1.04 0.43 303.91 300.00 300.00 278.56 248.21 
83 2.81 1.04 0.43 303.63 299.72 299.72 278.30 248.21 
84 2.81 1.04 0.43 303.35 299.45 299.45 278.05 248.21 
85 1.22 0.83 1.11 477.38 450.88 450.88 421.99 248.21 
86 1.17 0.83 1.22 452.31 445.68 445.68 415.20 248.21 
87 1.17 0.83 1.22 451.49 444.87 444.87 414.45 248.21 
88 0.90 0.83 3.06 338.77 867.71 867.71 808.55 248.21 
89 0.90 0.83 3.06 341.94 875.81 875.81 816.10 248.21 
90 0.90 0.83 3.06 353.53 905.51 905.51 843.77 248.21 
91 1.17 0.83 1.22 440.68 434.22 434.22 404.53 248.21 
92 1.11 0.83 1.36 432.10 444.51 444.51 412.52 248.21 
93 1.17 0.83 1.22 453.74 447.09 447.09 416.52 248.21 
94 0.90 0.83 3.06 337.07 863.34 863.34 804.47 248.21 
95 0.90 0.83 3.06 342.21 876.51 876.51 816.75 248.21 
96 0.90 0.83 3.06 338.70 867.52 867.52 808.37 248.21 
97 3.15 1.04 0.38 678.16 301.11 301.11 282.54 279.93 
98 3.08 1.04 0.39 575.30 260.69 260.69 244.13 279.93 
99 3.01 1.04 0.40 593.70 274.67 274.67 256.69 279.93 
100 2.67 1.04 0.46 300.52 310.40 310.40 286.93 279.93 
101 2.81 1.04 0.43 340.63 336.25 336.25 312.22 279.93 
102 2.67 1.04 0.46 301.36 311.27 311.27 287.73 279.93 
103 3.15 1.04 0.38 667.02 296.16 296.16 277.90 279.93 
104 3.08 1.04 0.39 655.63 297.09 297.09 278.21 279.93 
105 3.08 1.04 0.39 601.92 272.75 272.75 255.42 279.93 
106 2.81 1.04 0.43 307.82 303.86 303.86 282.15 279.93 
107 2.67 1.04 0.46 309.92 320.11 320.11 295.90 279.93 
108 2.67 1.04 0.46 282.54 291.83 291.83 269.76 279.93 
109 1.34 0.83 0.94 394.01 342.80 342.80 324.27 279.93 
110 1.22 0.83 1.11 345.99 326.79 326.79 305.85 279.93 
111 1.28 0.83 1.02 380.51 344.77 344.77 324.34 279.93 
112 0.90 0.83 3.06 225.01 576.33 576.33 537.03 279.93 
113 0.90 0.83 3.06 213.17 546.00 546.00 508.78 279.93 
114 0.90 0.83 3.06 249.65 639.44 639.44 595.84 279.93 
129 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
115 1.17 0.83 1.22 339.67 334.69 334.69 311.80 279.93 
116 1.11 0.83 1.36 341.43 351.24 351.24 325.96 279.93 
117 1.22 0.83 1.11 369.23 348.73 348.73 326.38 279.93 
118 0.90 0.83 3.06 339.94 870.70 870.70 811.33 279.93 
119 0.90 0.83 3.06 343.34 879.42 879.42 819.46 279.93 
120 0.90 0.83 3.06 341.40 874.44 874.44 814.81 279.93 
121 2.14 1.04 0.62 522.73 330.27 330.27 299.45 321.30 
122 2.01 1.04 0.67 483.97 323.45 323.45 291.84 321.30 
123 2.01 1.04 0.67 486.68 325.27 325.27 293.47 321.30 
124 2.01 1.04 0.67 304.81 407.44 407.44 367.61 321.30 
125 2.14 1.04 0.62 307.20 388.19 388.19 351.97 321.30 
126 2.01 1.04 0.67 312.67 417.94 417.94 377.09 321.30 
127 2.14 1.04 0.62 502.27 317.34 317.34 287.73 321.30 
128 2.01 1.04 0.67 480.74 321.30 321.30 289.89 321.30 
129 2.01 1.04 0.67 491.33 328.38 328.38 296.28 321.30 
130 1.89 1.04 0.74 302.44 428.76 428.76 385.01 321.30 
131 2.01 1.04 0.67 313.98 419.69 419.69 378.67 321.30 
132 1.89 1.04 0.74 313.31 444.17 444.17 398.85 321.30 
133 1.06 0.83 1.53 461.58 496.03 496.03 459.02 321.30 
134 1.06 0.83 1.53 458.17 492.36 492.36 455.63 321.30 
135 1.06 0.83 1.53 452.71 486.50 486.50 450.20 321.30 
136 0.90 0.83 3.06 359.09 919.75 919.75 857.04 321.30 
137 0.90 0.83 3.06 361.09 924.86 924.86 861.80 321.30 
138 0.90 0.83 3.06 349.32 894.74 894.74 833.73 321.30 
139 1.02 0.83 1.75 457.35 513.62 513.62 474.59 321.30 
140 1.06 0.83 1.53 456.60 490.67 490.67 454.07 321.30 
141 1.06 0.83 1.53 453.92 487.80 487.80 451.41 321.30 
142 0.90 0.83 3.06 353.71 905.96 905.96 844.19 321.30 
143 0.90 0.83 3.06 365.45 936.03 936.03 872.21 321.30 
144 0.90 0.83 3.06 355.81 911.34 911.34 849.20 321.30 
145 4.67 1.27 0.28 1005.57 323.85 323.85 280.88 341.29 
146 4.94 1.27 0.26 1119.15 341.97 341.97 297.36 341.29 
147 4.94 1.27 0.26 1083.12 330.96 330.96 287.79 341.29 
148 5.07 1.27 0.25 608.41 362.52 362.52 315.62 341.29 
149 5.60 1.27 0.23 784.87 425.06 425.06 371.75 341.29 
150 5.60 1.27 0.23 643.57 348.54 348.54 304.82 341.29 
151 5.40 1.27 0.24 1144.12 320.78 320.78 280.09 341.29 
152 4.94 1.27 0.26 994.66 303.93 303.93 264.28 341.29 
130 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
153 5.00 1.27 0.26 1062.58 320.58 320.58 278.93 341.29 
154 5.60 1.27 0.23 630.39 341.40 341.40 298.58 341.29 
155 5.60 1.27 0.23 620.96 336.30 336.30 294.11 341.29 
156 5.87 1.27 0.21 726.05 376.05 376.05 329.56 341.29 
157 1.95 1.04 0.70 450.74 310.14 310.14 279.15 341.29 
158 1.83 1.04 0.78 429.88 314.14 314.14 281.45 341.29 
159 1.89 1.04 0.74 425.85 301.86 301.86 271.06 341.29 
160 1.65 1.04 0.92 230.51 370.69 370.69 330.13 341.29 
161 1.54 1.04 1.06 207.30 356.59 356.59 316.68 341.29 
162 1.65 1.04 0.92 231.26 371.89 371.89 331.20 341.29 
163 1.89 1.04 0.74 427.63 303.12 303.12 272.20 341.29 
164 1.89 1.04 0.74 428.52 303.75 303.75 272.76 341.29 
165 1.89 1.04 0.74 405.65 287.54 287.54 258.20 341.29 
166 1.54 1.04 1.06 211.51 363.83 363.83 323.11 341.29 
167 1.54 1.04 1.06 229.74 395.19 395.19 350.96 341.29 
168 1.43 1.04 1.23 199.12 367.42 367.42 325.91 341.29 
169 0.97 0.83 2.04 481.80 565.52 565.52 522.68 341.29 
170 0.97 0.83 2.04 476.24 558.99 558.99 516.65 341.29 
171 0.97 0.83 2.04 473.46 555.73 555.73 513.64 341.29 
172 0.90 0.83 3.06 378.26 968.84 968.84 902.78 341.29 
173 0.90 0.83 3.06 370.76 949.64 949.64 884.89 341.29 
174 0.90 0.83 3.06 368.82 944.66 944.66 880.25 341.29 
175 0.97 0.83 2.04 470.23 551.94 551.94 510.14 341.29 
176 0.97 0.83 2.04 471.13 553.00 553.00 511.11 341.29 
177 0.97 0.83 2.04 456.43 535.75 535.75 495.17 341.29 
178 0.90 0.83 3.06 363.16 930.17 930.17 866.75 341.29 
179 0.90 0.83 3.06 369.80 947.18 947.18 882.60 341.29 
180 0.90 0.83 3.06 363.43 930.87 930.87 867.40 341.29 
181 4.15 1.27 0.32 942.65 340.18 340.18 293.40 343.36 
182 4.15 1.27 0.32 1000.45 361.03 361.03 311.39 343.36 
183 4.15 1.27 0.32 1019.30 367.83 367.83 317.26 343.36 
184 5.60 1.27 0.23 623.25 337.54 337.54 295.20 343.36 
185 5.47 1.27 0.23 645.19 357.57 357.57 312.38 343.36 
186 5.74 1.27 0.22 871.03 461.20 461.20 403.78 343.36 
187 4.15 1.27 0.32 911.42 328.90 328.90 283.68 343.36 
188 4.15 1.27 0.32 947.47 341.91 341.91 294.90 343.36 
189 4.15 1.27 0.32 903.30 325.97 325.97 281.15 343.36 
190 4.67 1.27 0.28 509.47 328.15 328.15 284.62 343.36 
131 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
191 5.47 1.27 0.23 682.29 378.13 378.13 330.35 343.36 
192 4.80 1.27 0.27 524.39 328.90 328.90 285.63 343.36 
193 1.54 1.04 1.06 409.30 352.03 352.03 312.63 343.36 
194 1.54 1.04 1.06 401.78 345.56 345.56 306.89 343.36 
195 1.54 1.04 1.06 407.53 350.51 350.51 311.28 343.36 
196 1.24 1.04 1.85 224.93 481.14 481.14 429.52 343.36 
197 1.24 1.04 1.85 225.74 482.86 482.86 431.06 343.36 
198 1.24 1.04 1.85 219.31 469.11 469.11 418.79 343.36 
199 1.65 1.04 0.92 407.84 327.93 327.93 292.05 343.36 
200 1.54 1.04 1.06 383.92 330.20 330.20 293.24 343.36 
201 1.59 1.04 0.99 371.59 308.90 308.90 274.67 343.36 
202 1.24 1.04 1.85 215.04 459.97 459.97 410.62 343.36 
203 1.24 1.04 1.85 220.90 472.52 472.52 421.83 343.36 
204 1.33 1.04 1.48 218.60 433.83 433.83 385.31 343.36 
205 0.90 0.83 3.06 481.68 616.87 616.87 574.81 343.36 
206 0.90 0.83 3.06 485.62 621.92 621.92 579.51 343.36 
207 0.90 0.83 3.06 484.12 619.99 619.99 577.72 343.36 
208 0.85 0.83 6.12 386.11 1073.38 1073.38 1023.92 343.36 
209 0.85 0.83 6.12 384.57 1069.09 1069.09 1019.83 343.36 
210 0.85 0.83 6.12 378.20 1051.39 1051.39 1002.94 343.36 
211 0.90 0.83 3.06 475.18 608.55 608.55 567.06 343.36 
212 0.90 0.83 3.06 464.18 594.46 594.46 553.92 343.36 
213 0.90 0.83 3.06 466.12 596.94 596.94 556.24 343.36 
214 0.85 0.83 6.12 369.71 1027.80 1027.80 980.44 343.36 
215 0.85 0.83 6.12 370.71 1030.56 1030.56 983.07 343.36 
216 0.85 0.83 6.12 371.23 1032.02 1032.02 984.47 343.36 
217 2.14 1.04 0.62 1218.59 769.92 769.92 698.09 519.18 
218 2.14 1.04 0.62 1314.23 830.34 830.34 752.87 519.18 
219 2.01 1.04 0.67 1260.38 842.36 842.36 760.03 519.18 
220 1.24 1.04 1.85 607.16 1298.73 1298.73 1159.40 519.18 
221 1.33 1.04 1.48 698.67 1386.58 1386.58 1231.51 519.18 
222 1.24 1.04 1.85 652.56 1395.84 1395.84 1246.09 519.18 
223 2.14 1.04 0.62 1256.85 794.08 794.08 720.00 519.18 
224 2.33 1.04 0.55 1362.79 795.04 795.04 726.23 519.18 
225 2.08 1.04 0.64 1164.56 756.51 756.51 684.24 519.18 
226 1.24 1.04 1.85 527.58 1128.51 1128.51 1007.44 519.18 
227 1.24 1.04 1.85 534.88 1144.12 1144.12 1021.38 519.18 
228 1.24 1.04 1.85 547.80 1171.76 1171.76 1046.05 519.18 
132 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
229 1.54 0.83 0.77 1154.97 894.81 894.81 861.43 519.18 
230 1.41 0.83 0.87 1052.24 879.92 879.92 837.12 519.18 
231 1.54 0.83 0.77 1136.33 880.37 880.37 847.52 519.18 
232 1.28 0.83 1.02 784.60 1421.84 1421.84 1337.58 519.18 
233 1.28 0.83 1.02 797.04 1444.39 1444.39 1358.78 519.18 
234 1.28 0.83 1.02 777.76 1409.44 1409.44 1325.91 519.18 
235 1.41 0.83 0.87 1113.68 931.30 931.30 886.01 519.18 
236 1.47 0.83 0.82 1111.34 894.08 894.08 855.62 519.18 
237 1.41 0.83 0.87 1108.22 926.73 926.73 881.66 519.18 
238 1.28 0.83 1.02 503.54 912.51 912.51 858.43 519.18 
239 1.28 0.83 1.02 421.50 763.83 763.83 718.56 519.18 
240 1.28 0.83 1.02 515.21 933.65 933.65 878.31 519.18 
241 2.14 1.04 0.62 1262.52 797.67 797.67 723.25 638.45 
242 2.08 1.04 0.64 1279.96 831.47 831.47 752.04 638.45 
243 2.01 1.04 0.67 1233.38 824.31 824.31 743.74 638.45 
244 1.24 1.04 1.85 537.30 1149.28 1149.28 1025.99 638.45 
245 1.24 1.04 1.85 564.32 1207.08 1207.08 1077.59 638.45 
246 1.24 1.04 1.85 528.48 1130.43 1130.43 1009.16 638.45 
247 2.27 1.04 0.57 1287.51 770.90 770.90 702.44 638.45 
248 2.01 1.04 0.67 1184.51 791.66 791.66 714.28 638.45 
249 2.14 1.04 0.62 1217.31 769.11 769.11 697.35 638.45 
250 1.24 1.04 1.85 620.35 1326.94 1326.94 1184.59 638.45 
251 1.24 1.04 1.85 636.69 1361.88 1361.88 1215.78 638.45 
252 1.24 1.04 1.85 636.69 1361.88 1361.88 1215.78 638.45 
253 1.41 0.83 0.87 1218.02 1018.55 1018.55 969.02 638.45 
254 1.41 0.83 0.87 1102.38 921.85 921.85 877.02 638.45 
255 1.41 0.83 0.87 1128.67 943.83 943.83 897.93 638.45 
256 1.17 0.83 1.22 845.50 1666.20 1666.20 1552.27 638.45 
257 1.17 0.83 1.22 800.07 1576.68 1576.68 1468.86 638.45 
258 1.17 0.83 1.22 803.35 1583.13 1583.13 1474.88 638.45 
259 1.28 0.83 1.02 1135.14 1028.54 1028.54 967.58 638.45 
260 1.28 0.83 1.02 1085.23 983.32 983.32 925.04 638.45 
261 1.28 0.83 1.02 1160.01 1051.08 1051.08 988.78 638.45 
262 1.17 0.83 1.22 852.87 1680.73 1680.73 1565.80 638.45 
263 1.06 0.83 1.53 828.19 1780.00 1780.00 1647.19 638.45 
264 1.06 0.83 1.53 825.90 1775.09 1775.09 1642.65 638.45 
265 2.01 1.04 0.67 1190.88 795.91 795.91 718.12 719.12 
266 1.95 1.04 0.70 1147.12 789.28 789.28 710.42 719.12 
133 
Run 
Shear 
Strain ? 
Merchant 
Shear 
Strain 
? 
Payton 
Shear 
Strain ? 
Adjusted 
Resultant 
Force 
(newtons) 
Resultant 
Shear 
Stress 
Merchant 
(MPa) 
Resultant 
Shear 
Stress 
Payton 
(MPa) 
Resultant 
Shear 
Stress 
Adjusted 
(MPa) 
Measured 
Ultimate 
Stress 
(MPa) 
267 1.89 1.04 0.74 1208.35 856.53 856.53 769.13 719.12 
268 1.17 1.04 2.46 573.31 1323.32 1323.32 1194.28 719.12 
269 1.10 1.04 3.69 532.76 1326.54 1326.54 1220.78 719.12 
270 1.24 1.04 1.85 541.19 1157.61 1157.61 1033.42 719.12 
271 1.89 1.04 0.74 1179.52 836.09 836.09 750.78 719.12 
272 1.77 1.04 0.82 1153.66 869.71 869.71 777.52 719.12 
273 1.77 1.04 0.82 1107.64 835.02 835.02 746.50 719.12 
274 1.10 1.04 3.69 560.79 1396.34 1396.34 1285.02 719.12 
275 1.24 1.04 1.85 654.02 1398.95 1398.95 1248.87 719.12 
276 1.17 1.04 2.46 597.60 1379.39 1379.39 1244.89 719.12 
277 1.28 0.83 1.02 1205.20 1092.02 1092.02 1027.30 719.12 
278 1.17 0.83 1.22 1090.97 1074.97 1074.97 1001.46 719.12 
279 1.17 0.83 1.22 1088.56 1072.60 1072.60 999.25 719.12 
280 0.90 0.83 3.06 772.60 1978.90 1978.90 1843.97 719.12 
281 0.90 0.83 3.06 767.73 1966.40 1966.40 1832.33 719.12 
282 0.90 0.83 3.06 775.79 1987.05 1987.05 1851.57 719.12 
283 1.17 0.83 1.22 1110.60 1094.31 1094.31 1019.48 719.12 
284 1.17 0.83 1.22 1098.18 1082.08 1082.08 1008.09 719.12 
285 1.17 0.83 1.22 1079.74 1063.91 1063.91 991.16 719.12 
286 0.90 0.83 3.06 801.55 2053.04 2053.04 1913.06 719.12 
287 0.90 0.83 3.06 820.16 2100.71 2100.71 1957.48 719.12 
288 0.90 0.83 3.06 803.65 2058.40 2058.40 1918.06 719.12 
 
 
 
134 
Appendix 5 
 
Program Files 
 
The figure below shows the LabVIEW file used to convert the force data from collection into an Excel file for further analysis. 
 
135 
The following MATLAB code was used to generate the average force tables. 
 
clear all 
close all 
clc 
  
xlsfiles = dir('C:\Users\Chase\Desktop\Post Process Data\Thesis 
Force Data\Saturday Files\*.xlsx'); 
ydatamean = zeros(length(xlsfiles),1); 
zdatamean = zeros(length(xlsfiles),1); 
  
for i = 1:length(xlsfiles) 
     
    xlsname = xlsfiles(i).name; 
     
    [num,txt,raw] = xlsread(fullfile('C:\Users\Chase\Desktop\Post 
Process Data\Thesis Force Data\Saturday Files\',xlsname),2); 
     
    ydata = num(:,2); 
    zdata = num(:,3); 
     
    plot(ydata,'LineWidth',2); 
    hold on 
    plot(zdata,'LineWidth',2,'color','red'); 
    hold off 
     
    disp(sprintf(['File name: ',xlsname])); 
    minpoint = input('Enter the min data point: '); 
    maxpoint = input('Enter the max data point: '); 
    %     minpoint = 250; 
    %     maxpoint = 500; 
    ydatamean(i) = mean(ydata(minpoint:maxpoint)); 
    zdatamean(i) = mean(zdata(minpoint:maxpoint)); 
     
    disp(sprintf([xlsname, ' mean: ',num2str(ydatamean(i))])); 
    disp(sprintf([xlsname, ' mean: 
',num2str(zdatamean(i)),'\n'])); 
     
end 
  
xlsdata = {xlsfiles(:).name}; 
xlsdata = xlsdata'; 
xlsdata(:,2) = num2cell(ydatamean); 
xlsdata(:,3) = num2cell(zdatamean); 
headers = {'Sample Name','Cutting Force','Thrust Force'}; 
  
%% 
xlswrite('C:\Users\Chase\Desktop\Post Process Data\Thesis Force 
Data\Saturday Files\Mean Results\Mean 
Results_Pick.xlsx',headers,'Sheet1','A1') 
xlswrite('C:\Users\Chase\Desktop\Post Process Data\Thesis Force 
Data\Saturday Files\Mean Results\Mean 
Results_Pick.xlsx',xlsdata,'Sheet1','A2') 
 
136 
The following MATLAB code was used to calculate the angles of interest as well 
as the uncut chip thickness and tool angles using text files generated from GIMP. 
 
clear all 
close all 
clc 
  
milpercmm = 0.393700787; 
  
scalefile = fopen('C:\Users\Chase\Desktop\Post Process Data\Scale 
Data\Scale.txt'); 
  
scalefull = textscan(scalefile,'%q'); 
scalefull = [scalefull{:}]; 
  
scaleremain = scalefull{20}; 
  
i = 1; 
while true 
    [scale{i}, scaleremain] = strtok(scaleremain); 
    if isempty(scaleremain),  break;  end 
    i = i+1; 
end 
  
[scalex1,scaley1] = strtok(scale{4},','); 
scaley1 = strtok(scaley1,','); 
  
scalex1 = str2double(scalex1); 
scaley1 = str2double(scaley1); 
  
[scalex2,scaley2] = strtok(scale{5},','); 
scaley2 = strtok(scaley2,','); 
  
scalex2 = str2double(scalex2); 
scaley2 = str2double(scaley2); 
  
pixpermil = abs(scaley2 - scaley1)/milpercmm; 
  
%% 
anglefiles = dir('C:\Users\Chase\Desktop\Post Process Data\Angle 
Data\*.txt'); 
  
for i = 1:length(anglefiles) 
     
    anglefile = anglefiles(i).name; 
     
    anglefilenum = fopen(['C:\Users\Chase\Desktop\Post Process 
Data\Angle Data\',anglefile]); 
     
    anglefull = textscan(anglefilenum,'%q'); 
    anglefull = [anglefull{:}]; 
     
    angleremain = anglefull{20}; 
 
137 
     
    j = 1; 
    while true 
        [angle{j}, angleremain] = strtok(angleremain); 
        if isempty(angleremain),  break;  end 
        j = j+1; 
    end 
     
    [planex1,planey1] = strtok(angle{4},','); 
    planey1 = strtok(planey1,','); 
     
    planex1 = str2double(planex1); 
    planey1 = str2double(planey1); 
     
    [planex2,planey2] = strtok(angle{5},','); 
    planey2 = strtok(planey2,','); 
     
    planex2 = str2double(planex2); 
    planey2 = str2double(planey2); 
     
    [toolx1,tooly1] = strtok(angle{9},','); 
    tooly1 = strtok(tooly1,','); 
     
    toolx1 = str2double(toolx1); 
    tooly1 = str2double(tooly1); 
     
    [toolx2,tooly2] = strtok(angle{10},','); 
    tooly2 = strtok(tooly2,','); 
     
    toolx2 = str2double(toolx2); 
    tooly2 = str2double(tooly2); 
     
    [onsetx1,onsety1] = strtok(angle{14},','); 
    onsety1 = strtok(onsety1,','); 
     
    onsetx1 = str2double(onsetx1); 
    onsety1 = str2double(onsety1); 
     
    [onsetx2,onsety2] = strtok(angle{15},','); 
    onsety2 = strtok(onsety2,','); 
     
    onsetx2 = str2double(onsetx2); 
    onsety2 = str2double(onsety2); 
     
    [shearx1,sheary1] = strtok(angle{19},','); 
    sheary1 = strtok(sheary1,','); 
     
    shearx1 = str2double(shearx1); 
    sheary1 = str2double(sheary1); 
     
    [shearx2,sheary2] = strtok(angle{20},','); 
    sheary2 = strtok(sheary2,','); 
     
 
138 
    shearx2 = str2double(shearx2); 
    sheary2 = str2double(sheary2); 
     
    %     [chipx1,chipy1] = strtok(angle{24},','); 
    %     chipy1 = strtok(chipy1,','); 
    % 
    %     chipx1 = str2double(chipx1); 
    %     chipy1 = str2double(chipy1); 
    % 
    %     [chipx2,chipy2] = strtok(angle{25},','); 
    %     chipy2 = strtok(chipy2,','); 
    % 
    %     chipx2 = str2double(chipx2); 
    %     chipy2 = str2double(chipy2); 
     
    planeangle(i) = atand((planey1-planey2)/(planex2-planex1)); 
     
    toolangle(i) = atand((toolx2-toolx1)/(tooly1-tooly2)) + 
planeangle(i); 
     
    phi(i) = atand((onsety2-onsety1)/(onsetx2-onsetx1)) + 
planeangle(i); 
     
    if shearx1 < shearx2 
        psi(i) = 90 + atand((shearx2-shearx1)/(sheary1-sheary2)) 
+ planeangle(i) - phi(i); 
    else 
        psi(i) = 90 - atand((shearx1-shearx2)/(sheary1-sheary2)) 
+ planeangle(i) - phi(i); 
    end 
     
    uncut(i) = (planey1 - onsety1)/pixpermil; 
     
    %     cut(i) = sqrt((chipx2-chipx1)^2 + (chipy2-
chipy1)^2)/pixpermil; 
end 
  
xlsdata = {anglefiles(:).name}; 
xlsdata = xlsdata'; 
xlsdata(:,2) = num2cell(toolangle'); 
xlsdata(:,3) = num2cell(phi'); 
xlsdata(:,4) = num2cell(psi'); 
xlsdata(:,5) = num2cell(uncut'); 
% xlsdata(:,6) = num2cell(cut'); 
  
headers = {'Sample Name','Tool Angle','Phi','Psi','Uncut Chip 
Thickness'}; 
  
xlswrite('C:\Users\Chase\Desktop\Post Process Data\Angle 
Data\Results\Results.xlsx',headers,'Sheet1','A1') 
xlswrite('C:\Users\Chase\Desktop\Post Process Data\Angle 
Data\Results\Results.xlsx',xlsdata,'Sheet1','A2') 
  
fclose('all');