High Temperature Vibration Fatigue Life Prediction and High Strain Rate Material 
Characterization of Lead-Free Solders 
 
by 
 
Geeta Limaye 
 
 
 
 
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 
May 05, 2013 
 
 
 
 
Keywords: Pb-free, Vibration, Fatigue, Innolot, Temperature, High Strain Rate 
 
 
 
Approved by 
 
Pradeep Lall, Chair, T. Walter Professor of Mechanical Engineering 
Jeffrey Suhling, Quina Distinguished Professor and Chair of Mechanical Engineering 
George Flowers, Professor of Mechanical Engineering and Dean of the Graduate School 
ii 
 
Abstract 
 
 Current trends in the automotive industry warrant a variety of electronics for 
improved control, safety, efficiency and entertainment. Many of these electronic systems 
like engine control units, variable valve sensor, crankshaft-camshaft sensors are located 
under-hood. Electronics installed in under-hood applications are subjected 
simultaneously to mechanical vibrations and thermal loads. Typical failure modes caused 
by vibration induced high cycle fatigue include solder fatigue, copper trace or lead 
fracture. The solder interconnects accrue damage much faster when vibrated at elevated 
temperatures. Industry migration to lead-free solders has resulted in a proliferation of a 
wide variety of solder alloy compositions. Presently, the literature on mechanical 
behavior of lead-free alloys under simultaneous harsh environment of high-temperature 
vibration is sparse. In this research, a test vehicle representative of an engine control unit 
has been used. The reduction in stiffness of the PCB with temperature has been 
demonstrated by measuring the shift in natural frequencies with temperature. The test 
vehicle has been tested to failure by subjecting it to two elevated temperatures and 
harmonic vibrations at the corresponding first natural frequency. PCB deflection has been 
shown to increase with increase in temperature. The full field strain has been extracted 
using high speed cameras operating at 100,000 fps in conjunction with digital image 
correlation. Material properties of the PCB at elevated test temperatures have been 
measured using Dynamic Mechanical Analyzer (DMA).  
iii 
 
FE simulation using global-local finite element models is then correlated with the system 
characteristics such as modal shapes, natural frequencies and displacement amplitudes for 
every temperature. The solder level stresses have been extracted from the sub-models. 
Stress amplitude versus cycles to failure curves are obtained at all the three test 
temperatures. Temperature dependent terms have been added to the Basquin power law 
to predict the high cycle fatigue life of SAC305 solder at elevated temperatures.  
 In the second part of the thesis, the effect of aging and high strain rates on a newly 
developed high-temperature, high-performance lead-free substitute called Innolot by 
InnoRelTM targeting the automotive electronics segment has been studied. Innolot 
contains Nickel (Ni), Antimony (Sb) and Bismuth (Bi) in small proportions in addition to 
Sn, Ag and Cu. Recent studies have highlighted the detrimental effects of isothermal 
aging on the material properties of SAC alloys. This phenomenon has posed a severe 
design challenge across the industry and remains a road-block in the migration to Pb-free. 
This research includes the high strain rate material characterization of Innolot as the alloy 
ages at an elevated temperature of 500C. The strain rates chosen are in the range of 1-100 
per-second which are typical at second level interconnects subjected to drop-shock and 
vibration environments. The strain rates and elevated aging temperature have been 
chosen also to facilitate comparison with tests conducted on SAC105 and SAC305 alloys 
at CAVE3 by other researchers. Ramberg-Osgood non-linear model parameters have 
been determined to curve-fit through the experimental data. The parameters have been 
implemented in Abaqus FE model to obtain full-field stresses which correlates with 
contours obtained experimentally by Digital Image Correlation (DIC). 
iv 
 
Acknowledgments 
 
 I would like to express my deep gratitude to my research advisor Professor 
Pradeep Lall for giving me the opportunity to work under his guidance and mentorship at 
the NSF Center for Advanced Vehicle and Extreme Environment Electronics (CAVE3) 
as a Graduate Research Assistant at Auburn University. I would also like to thank my 
other committee members, Professor George Flowers and Professor Jeffrey Suhling, for 
their support and guidance while completing this research and thesis. 
 I would like to thank my parents, Mr. Shrikant Limaye and Dr. Mrs. Lalita 
Limaye, my elder sister Mukta Limaye, and all my family members for having faith in 
me and providing endearing love, encouragement and moral support. I gratefully 
acknowledge the support extended by the following people during my Masters program - 
Brad Palmer, John Marcell, Sandeep Shantaram, Ryan Lowe, Mahendra Harsha, Kewal 
Patel, Vikalp Narayan, Kazi Mirza, Shantanu Deshpande, Arjun Angral Mandar Kulkarni 
and Mayur Golatgaonkar.  
v 
 
Table of Contents 
 
Abstract ............................................................................................................................... ii 
Acknowledgments.............................................................................................................. iv  
List of Figures .................................................................................................................. viii  
List of Tables ................................................................................................................... xi i 
1 Introduction .......................................................................................................................1 
 1.1 Overview of Microelectronic Packaging ...........................................................1 
 1.2 Vibration Reliability of Electronics  ..................................................................8 
 1.3 FEA Procedures for Vibration Analysis ..........................................................16 
 1.4 Effect of High Temperature on the Reliability of Electronics .........................19 
 1.5 Thesis layout ....................................................................................................20 
2 Literature Review............................................................................................................23 
 2.1 Vibration Analysis of Electronics ....................................................................23 
 2.2 Digital Image Correlation (DIC) ......................................................................25 
 2.4 High Strain Rate Solder Characterization ........................................................28 
3 High Cycle fatigue Life Characterization of SAC305 Under Simultaneous exposure to 
High Temperature and Vibration Literature Review .........................................................31 
 3.1 Introduction ......................................................................................................31 
 3.2 Test Vehicle .....................................................................................................33 
 3.3 Harmonic Vibration at Elevated Temperature .................................................38
vi 
 
3.4 Approach to Solder High Cycle Fatigue Life Prediction at Elevated 
Temperature ...........................................................................................................40 
 3.5 Correlation of Test Vehicle with Global FE Model .........................................42 
 3.6 Failure Modes ..................................................................................................59 
 3.7 Solder Stress Estimation from Explicit Sub-models ........................................64 
 3.8 Summary and Conclusions ..............................................................................77 
4 Effect of High Strain Rate and Aging on Material Characterization of Innolot .............78 
 4.1 Introduction ......................................................................................................78 
 4.2 Test Specimen Preparation ..............................................................................81 
 4.3 Test Set-up .......................................................................................................83 
 4.4 Test Matrix .......................................................................................................88 
 4.5 Results and Discussion ....................................................................................88 
  4.5.1 High Strain Rate Tensile Testing ............................................................88 
  4.5.2 Effect of 1 day aging at 50C ...................................................................92 
  4.5.3 Effect of 30 days aging at 50C ................................................................93 
  4.5.4 Effect of 60 days aging at 50C ................................................................94  
.  4.5.5 Effect of Strain Rate on Material Properties of Innolot ..........................97 
  4.5.6 Comparison with SAC alloys..................................................................97 
  4.5.7 Ramberg-Osgood Non-linear models for Innolot .................................102 
  4.5.8 Digital Image Correlation .....................................................................110 
  4.5.9 FE Model for tensile specimen .............................................................111 
 4.6 Summary and Conclusions ............................................................................113 
5 Summary, Conclusions and Future Scope ....................................................................115 
vii 
 
Bibliography ..................................................................................................................119
viii 
 
List of Figures 
 
Error! Reference source not found. ............................... Error! Bookmark not defined. 
Figure 2: Hierarchy in Packaging of Electronic Systems ....................................................3 
Figure 3: Classification of Electronic Packages [Ref: 
http://am.renesas.com/products/package/variation/index.jsp] .............................................4 
Figure 4: Ball Grid Array Architecture ................................................................................5 
Figure 5: Lead strains due to relative motion between component and circuit board .......12 
Figure 6: Product form-factor test vehicle .........................................................................36 
Figure 7: X-ray images of components ..............................................................................37 
Figure 8: a) Cartoon of Tg measurement using DSC ........................................................38 
Figure 9: Differential Scanning Calorimeter from TA Instruments, model Q2000 ..........39 
Figure 10: DSC plot for PCB sample, Tg>140C ...............................................................39 
Figure 11:Test Matrix ........................................................................................................41 
Figure 12:Packages selected for test to failure ..................................................................40 
Figure 13:Test setup ...........................................................................................................41 
Figure 14: Approach to obtain elevated temperature S-N Curves .....................................43 
Figure 15:EMA setup .........................................................................................................44 
Figure 16: a) EMA Setup b) PCB inside the isothermal chamber .....................................45 
Figure 17:Acceleration response denoting natural frequencies .........................................46 
Figure 18: Change in 1st natural frequency as a function of temperature .........................47
ix 
 
Figure 19:Experimental mode shape at 1st natural frequency ...........................................48 
Figure 20:a) Global model for modal dynamic analysis to simulate board deflection ......50 
Figure 21:Linear Region of stress-strain curve of PCB .....................................................50 
Figure 22: DMA analysis of test vehicle ...........................................................................52 
Figure 23: Dependence of E on temperature a) Linear trend line b) Quadratic trend line 
............................................................................................................................................53 
Figure 24: Smeared property model ..................................................................................54 
Figure 25:Base excitation and PCB response ....................................................................58 
Figure 26:3D-Digital Image Correlation measurements in Printed Circuit Assembly ......59 
Figure 27:a) Experimental mode shape and full field out of plane displacement contour at 
1st natural frequency b)FE mode shape and full field out of plane displacement contour at 
1st natural frequency ..........................................................................................................60 
Figure 28: Correlation of PCB Out of plane displacement and in-plane strain .................62 
Figure 29: a)TSOP solder failure b)TSOP corner lead deformation c)Failure in BGA 
(corner solder failure) d)QFP lead failures ........................................................................65 
Figure 30: Resistance vs Cycles to failure .........................................................................67 
Figure 31: Difference in means of cycles to failure due to change in test temperature .....67 
Figure 32: a) BGA b) TSOP c) QFP d) SOL sub-models ..................................................70 
Figure 33: QFP high stresses in corner leads .....................................................................71 
Figure 34: Stress histories at 125C on a) TSOP corner solder b) BGA corner solder c) 
QFP corner lead .................................................................................................................71 
Figure 35: a) U19 Corner solder ball Mises stress distribution at 125C b)U19 corner 
solder stress distribution at 25C .........................................................................................73 
x 
 
Figure 36: a) U5 Corner solder Von Mises stress distribution 125C b) U5 corner stress 
distribution at 25C..............................................................................................................74 
Figure 37: Curve fitting through S-N data at 25C .............................................................75 
Figure 38: SAC305 phase growth [Lall 2012] ...................................................................76 
Figure 39: a)Fatigue coefficient as a function of temperature b)Fatigue exponent as a 
function of temperature ......................................................................................................78 
Figure 40: SAC305 S-N Curves at elevated temperature ..................................................79 
Figure 41: Setup for Innolot tensile specimen preparation ................................................85 
Figure 42: Innolot tensile specimen ...................................................................................85 
Figure 43: X-ray image of specimen .................................................................................85 
Figure 44: Reflow profile for specimen preparation ..........................................................86 
Figure 45: Implementation of slip joint mechanism to achieve constant cross-head 
velocity after impact ..........................................................................................................87 
Figure 46: Impact mechanism ............................................................................................88 
Figure 47: Position vs time plots of target points on the tester ..........................................89 
Figure 48: Cross-Head: a) Displacement b) Strain ............................................................90 
Figure 49: Stress-strain curves for Pristine Innolot ...........................................................92 
Figure 50: Stress-strain curves for Innolot aged at 50C for 1 day .....................................93 
Figure 51: Stress-strain curves for Innolot aged at 50C for 30 days .................................94 
Figure 52: Stress-strain curves for Innolot aged at 50C for 60 days .................................95 
Figure 53: Influence of aging on stress strain curves of Innolot at 10/s ............................98 
Figure 54: Influence of aging on stress strain curves of Innolot at 35/s ............................99 
xi 
 
Figure 55: Visual comparison of constitutive behavior of Innolot with SAC105 [Lall et. 
al. 2012] and SAC305 ......................................................................................................101 
Figure 56: Innolot, Pristine ..............................................................................................103 
Figure 57: Innolot, 30 days at 50C...................................................................................104 
Figure 58: Innolot, 60 days at 50C...................................................................................104 
Figure 59: Determination of secant yield strengt .............................................................107 
Figure 60: Family of curves for different values of n and m1=0.5 ..................................108 
Figure 61: Ramberg-Osgood model parameters and curve fit .........................................111 
Figure 62: Regression fit through strain-stress data of pristine Innolot at 35/s ...............113 
Figure 63: DIC analysis of Innolot, Pristine case at 35/s .................................................114 
Figure 64: Stress-strain response of a point at the center on FE model of tensile specimen115 
Figure 65: FE model of tensile specimen ........................................................................116 
Figure 66: Strain contours of tensile specimen at time steps of 0s, 1.75e-4s, 2.875e-4s and 
8.5714e-4s ........................................................................................................................117 
xii 
 
List of Tables 
 
Table 1: Thermal and mechanical properties of packaging materials .................................6 
Table 2: Innolot Composition [Miric et. al. 2010] .............................................................31 
Table 3:Package attributes .................................................................................................35 
Table 4: Comparison of actual and FE model mass ...........................................................53 
Table 5: Smeared Properties ..............................................................................................55 
Table 6: PCB Material properties at temperature ............... 56Table 7: RE at temperature 57 
Table 8: Solder material properties ....................................................................................68 
Table 9: Published values of Solder Fatigue constants ......................................................75 
Table 10: Fatigue strength coefficient and exponent at temperature .................................76 
Table 11: Innolot Composition ..........................................................................................83 
Table 12: Test Matrix for Innolot ......................................................................................91 
Table 13: Material Properties for Innolot, Pristine ............................................................92 
Table 14: Material Properties for Innolot, 1day aging at 50C ...........................................93 
Table 15: Material Properties for Innolot, 30 days aging at 50C.......................................94 
Table 16: Material Properties for Innolot, 60 days aging at 50C.......................................95 
Table 17: Aging effects on material properties of Innolot at 10/s .....................................98 
Table 18: Aging effects on material properties of Innolot at 35/s .....................................99 
xiii 
 
Table 19: Comparison of Elastic Modulus degradation in Innolot, SAC105 and SAC305 
due to aging ......................................................................................................................102 
Table 20: Comparison of UTS degradation in Innolot, SAC105 and SAC305 due to aging102 
Table 21: Ramberg-Osgood Parameters for Innolot ........................................................111 
Table 22: Comparison of Ramberg-Osgood parameters obtained using regression fit and 
closed form 2-point solution methods (Pristine, 35/s) .....................................................112 
1 
 
 
CHAPTER 1 
INTRODUCTION 
 
1.1. Overview of Microelectronic Packaging 
An integration of several circuits or components on a single chip is defined as an 
integrated circuit (IC). Packaging is the bridge that interconnects the ICs and other 
components into a system-level board to form electronic products. It is the portion of an 
electronic structure that protects an electronic/electrical element and its environment 
from each other [Ulrich 2006]. Traditionally defined as the back-end-of-the-line 
process that transforms ICs into functional assemblies, packaging brings together the 
fundamentals of Mechanical Engineering, Physics and Electronics towards the 
development of highly functional computing devices. The package must provide a 
structure to physically support the chip, a housing to protect the chip from the 
environment, some means to dissipate the  heat generated by the system, electrical 
connections to allow flow of signal and power to and from the chip, and a wiring 
structure to provide an interconnection between the chips of an electronic system. These 
four major functions of electronic packaging are illustrated in Figure 1 
2 
 
 
 
Figure 1: Functions of Electronic Packaging 
 
In addition to the basic functions described above an electronic package must be 
of high quality, reliable, safe and economical. In order to meet these requirements, a lot 
of emphasis has been laid on the development and characterization of reliable materials 
for packaging. Historically, packaging has always been a substantial fraction of the price 
of an IC (10 to 50%). In general, packaging costs are driven by the materials and 
fabrication requirements associated with the actual manufacturing and by the testing and 
rework associated with manufacturability. There are various levels of hierarchy in the 
packaging of electronic systems as shown in Figure 2. A chip housed in a chip carrier 
comprises of the first level of packaging. The chip is diced from a wafer of silicon and 
fabricated using a photolithographic process. Several packages or chip carriers mounted 
on a printed wire board or substrate constitute the second level of electronic packaging. 
Edge connectors on PCB which are inserted into back panel contacts form third level of 
packaging. 
3 
 
 
Figure 2: Hierarchy in Packaging of Electronic Systems [Adapted from 
?Mechanical Design of Electronic Systems? by Dally, Lall and Suhling 2008] 
Electronic Packaging Systems can be broadly classified either on the basis of the 
technology used for their assembly as: 
 1) Surface Mount Components  
2) Through Hole Components  
Alternatively, they can be classified based on the type of package as: 
1) Hermetically packaged 
2) Plastic encapsulated packages. 
The former classification of electronics packaging is the most widely accepted. The 
S i l i co n W a f e r
S i l i con C hi p
W i r e  bon ds
F l i p chi p s ol de r  bu m ps
1
st
Le ve l  I n t e r co n n e c t s  
Q ua d F l a t  P a ck  
B a l l  Gr i d Ar r a y
2
nd
Le ve l  In t e r c o n n e c t s  
( l e a d s  &  So l d e r  b a l l s )  
1
st
l e ve l  p a c k a ge  ( QF P ,  B G A )
P r i nt e d C i r cui t  B oa r d M ot he r  B oa r d
2
nd
Le ve l  p a c k a ge  ( P CB )
3
rd
Le ve l  p a c k a ge  ( M o t h e r b o a r d )
4 
 
through hole technology is more or less obsolete and the surface mount components are 
the most common packages in the electronics systems of the day. 
 
Figure 3: Classification of Electronic Packages [Ref: 
http://am.renesas.com/products/package/variation/index.jsp] 
 
5 
 
Driven by the trends towards miniaturization and increased functionality of 
electronic systems, there is a desire to make smaller and more complex electronic 
components. With the help of novel upcoming packaging technologies like System-on-
Chip (SoC), System-in-Package(SiP), Multi-Chip-Modules (MCM) and 3D packaging 
technologies like PoP and Stacked-Die components, the complexity of packaging 
architectures has exponentially increased. With the increase in the interconnect counts 
and decrease in the pitch between them, the susceptibility to failure has increased. 
Reliability of electronic packages has therefore gained a lot of significance and is of 
utmost importance in the highly competitive electronics market. A typical electronic 
package comprises of different materials that have vastly different material properties 
[Figure 4] 
 
 
Figure 4: Ball Grid Array Architecture
M o l d
S i l i co n D i e
D i e  A t t a c h
C u P a ds
B T  S ubs t r a t e
S ol de r
F i be r  E po x y  La m i na t e d P C B
6 
 
Table 1: Thermal and mechanical properties of packaging materials 
Material Elastic Modulus (GPa) 
Coefficient of 
Thermal Expansion 
(CTE) (10-6 1/K) 
Mold 23.5 15 
Silicon Die 162.7 2.5 
Die Attach 6.8 52 
Substrate 18 12.4 
Solder 30.5 24.5 
PCB 17 14.5 
 
For accurate reliability quantification, it is important to have a clear 
understanding of how all these constituent materials of a component interact with each 
other during the products operational life. For example, automotive electronic 
components such as Engine Control Unit (ECU) housed near the engine may experience 
harsh thermal cycling during their operational life. These extreme thermal conditions 
lead to severe expansion and contraction of the components. Due to a high degree of 
mismatch between the coefficients of thermal expansion (CTE) of the constituent 
materials in a package, high shear stresses will occur at the interface of two materials as 
one tries to expand and the other resists expansion. This can often lead to delamination 
between layers and shearing of interconnects.  
 The field of electronic packaging has been regularly evolving and adapting to 
meet the ever accelerating demands of the consumer electronics market. Electronic 
Packaging is development and characterization of reliable materials for packaging and 
7 
 
establishment of interconnections between different layers of an electronic 
component has remained the cornerstone of leading research in electronic packaging 
for the past few decades. In the light of growing environmental concerns, the Restriction 
of Hazardous Substances (RoHS) and the Environmental Preservation Agency have 
created stringent restrictions on the use of leaded solders. Disposed electronics often 
dumped as land-fills  likely to contaminate ground water resources due to the lead content 
in the solders. Lead-free and halogen-free solder alloy materials in particular have 
attracted great research attention. Industry migration to lead-free solders has resulted 
in a proliferation of a wide variety of solder alloy compositions. The most popular 
amongst these are the Tin-Silver-Copper (Sn-Ag-Cu or SAC) family of alloys like 
SAC105, SAC305 etc. Recent studies have highlighted the detrimental effects of 
isothermal aging on the material properties of these alloys. SAC alloys have shown up 
to 50% reduction in their initial elastic modulus and ultimate tensile strength within a 
few months of elevated temperature aging. This phenomenon has posed a severe design 
challenge across the industry and remains a road-block in the migration to Pb-free. 
Multiple compositions with additives to SAC have been proposed to minimize the effect 
of aging and creep while maintaining the melting temperatures, strength and cost at par 
with SAC. But, much waits to be explored as the reliability concerns associated with 
these novels materials have started to surface.  
 Electronic systems are present in all walks of life in today?s world. The 
applications of these systems range from communication, education, entertainment, 
transportation, research, health care, defense, manufacturing, finance etc. Electronic 
components thus enable core functionality of the devices that encompass them. With 
8 
 
electronic components residing at the heart of most of the mission-critical systems the 
reliability of these systems has gained tremendous significance. Unlike mechanical 
constituents, of any system, electrical components generally do not wear out. The failure 
of electrical systems is often undetectable prior to occurrence. The main reliability 
concerns associated with electronic components are associated with the following causes: 
1. Thermal stresses from exposure to elevated operating temperatures 
2. Mechanically stresses from transportation and handling  
3. Residual stresses from manufacturing processes 
4. Electro-migration, transient static discharge and other electrically induced failures 
 The solder interconnects are the most likely sites of occurrence of failure in 
case of thermo-mechanical and mechanical stresses. The primary reason for solders to 
be the site of failure under thermal stresses is the large CTE mismatch between solder 
and PCB or substrate. The solder interconnects are also amongst the most vulnerable 
sections under mechanical loading. As the failure of a solder interconnect can result in 
an open circuit, the failure of a single solder joint can result in drastic failure of the 
whole component and the electronic system leading to sudden downtime. Further, the 
electronics in certain applications like the underhood automotive electronics are 
simultaneously subjected to thermal and mechanical loads. This thesis researches the 
reliability of second level solder interconnects under this type of harsh environment. 
 
1.2. Vibration Reliability of Electronics [Steinberg 1998] 
 Electronic equipments get subjected to various forms of vibrations over their life 
cycle. The source of vibration can be the association with vibrating machinery during 
9 
 
usage or merely vibration loads associated with transportation or handling of the 
equipment. The form of vibration can range over a wide frequency band and acceleration 
levels. Many failures can occur due to vibrations and therefore it is necessary to 
understand the kind of vibration loads and the response of the electronic system to these 
loads. In automotive applications, the source of vibrations is mainly due to the rough 
surfaces over which the vehicles are used. In ships, submarines and airplanes, water 
buffeting and air buffeting as well as the engines are the main causes of vibration. In 
missiles in subsonic flight, the sound field developed by the rocket causes vibrations. 
 Electronic systems commonly make use of Printed Circuit Boards (PCB) which 
can easily be plugged in to or removed from modular type assemblies for service and 
replacement. There is a variety of PCB material and manufacturing processes in the 
industry. The most extensive are the PCBs made out of fiber glass reinforced epoxy with 
laminated layers of copper to form electrical conductors. PCB thickness varies from 
0.006 inch to 0.125 inch and the typical form factor in automotive application is 
rectangular. PCBs that have high power dissipating components, are often bonded to 
copper or aluminum heat sinks. The heat sink can be cast integrated with ribs that protect 
the PCB from severe vibration and shock. Ribs increase the stiffness of the circuit board 
and hence the resonant frequency. This reduces the PCB deflections and consequent 
component level stresses. Ribs can be made of aluminum, steel or epoxy fiberglass. 
Screws or quick release clamps are used to install the circuit boards onto modular 
assemblies. The way in which PCB is supported is an important factor that determines its 
response to the vibrations. A system subjected to severe vibrations and shock should not 
have a loose fit even if it eases the connector engagement. This is because a loose circuit 
10 
 
board will develop high acceleration and loads which will lead to deflections and stresses 
in the components of the PCB. Board edges are supported with guides made of beryllium 
copper or molded plastics. The grip of such guides prevents the rotation or translation of 
edges which increases the natural frequency of the board. A firm grip causes dissipation 
of energy due to vibration in the form of friction loss thus reducing the transmissibility of 
the PCB under resonant conditions. Other factors that affect the board transmissibility 
include board material, number and type of laminations, natural frequency, type of 
mounting, types of components on the board, acceleration levels, conformal coating, 
connectors and shape of board. When more energy is dissipated in the form of heat then 
there is less energy remaining and the transmissibility is lower. For rectangular PCB, the 
transmissibility will normally range from 0.5 to 2.0 times the square root of natural 
frequency. For resonant conditions, the dynamic bending stresses in a uniformly loaded 
circuit board can be determined by considering a sinusoidal load variation in the over the 
board surface when the edges are simply supported. This follows from the relative 
dynamic deflections which will be maximum at the center and zero at the edges. 
Sinusoidal vibrations often arise from rotating or oscillating machinery like engines, 
gears, wheels, motors etc. Sinusoidal vibrations are very useful for diagnostic purposes to 
evaluate the dynamic characteristics of electronic equipments like examining the resonant 
frequency, damping etc. The approximate fatigue life of a vibrating system can often be 
estimated from the fatigue characteristics of the various members that carry the major 
structural loads. These fatigue properties are usually obtained from controlled stress cycle 
tests performed on many parts that have been manufactured from the same material, with 
close dimensional tolerances. These parts are stress tested to failure, then the data points 
11 
 
are plotted on log-log paper, with stress on the vertical axis and number of cycles to 
failure on the horizontal axis. A straight line that represents the best average material 
properties is drawn through the scattered data points. The equation for the sloped portion 
of the curve can be expressed as follows [Steinberg 1998]:  
N1S1b=N2S2b 
 (1) 
where N = number of stress cycles to produce fatigue failure 
S = Stress level at which these failures occurred 
b = Fatigue exponent related to the slope of the line 
The exponent b is related to the fatigue life of the structure, and it is useful in predicting 
the fatigue life of other structures fabricated of the same material and exposed to the 
similar environments. In order to reflect the real structural properties of these materials, a 
stress concentration factor K must be included in the evaluation of exponent b. A typical 
stress concentration factor for an electronic box structure for a PCB within the box is 
about 2. For linear systems, the fatigue cycles will be directly related to time, so the time 
T can be used to replace the number of cycles (N). Also, the stress S will be directly 
related to the acceleration G and to the displacement Z. The dynamic can also be included 
if desired. These relations can be written as follows: [Steinberg 1998]  
T1G1b=T2G2b 
 (2) 
N1G1b=T2G2b 
 (3) 
N1Z1b=N2Z2b 
 (4) 
 The components mounted on electronic systems that are used in a vibration and 
shock environment often experience amplified or attenuated levels of vibrations 
depending the dynamic characteristics of the system. The resonant frequencies of PCB 
12 
 
may get excited and cause it to bend back and forth. The component level stresses depend 
on the geometry of the second level interconnects.  
 
Figure 5: Lead strains due to relative motion between component and circuit board 
 
For leaded packages, for a particular environment and particular PCB resonant frequency, 
the stresses on solder interconnects can be reduced by reducing the spring rate of the lead 
wires. This appears contradictory to the usual approach, where the failure of structure is 
prevented by making the structure more stiff. It can be explained as follows: 
F=kx 
 (5) 
 
Where F is the force, k is the stiffness and x is the displacement. If the displacement is 
constant, the only way to reduce the force can be reduced is by reducing k. This is the 
same condition that exists in the component lead wires for a specific dynamic 
displacement generated by the resonant frequency and acceleration level. Under resonant 
conditions, the stiffness of the lead wires that bend back and forth can be related to the 
following parameters: [Steinberg 1998] 
Kwire = EI/L3  
 
(6) 
 
S t r a i n ed  L ea d s
13 
 
This shows that to reduce the stiffness of the lead wire, the length has to be increased. 
When the wire length is doubled, the stiffness will reduce by a factor of 1/8 due to the 
inverse cubic relation. Likewise, the moment of inertia can be reduced to reduce the 
stiffness. This can be achieved by reducing the height or thickness of the lead wire. 
Coining the lead wire, i.e squeezing it into a flat metal strip reduces the thickness without 
changing the cross-sectional area. Thus the stiffness, force and stress in the lead wire can 
be reduced. In lead-less components like Ball Grid Arrays (BGA), the above relation 
applies to the shear stiffness of the solder that bonds the component to the PCB. The 
stiffness in this case can be expressed as: [Steinberg 1998] 
Kshear, solder = AG/L 
 
(7) 
where A = cross-sectional area of the solder in in2 
L=height of solder joint 
G=shear modulus of the solder. 
The shear stiffness can be decreased by reducing the cross-sectional area, reducing the 
shear modulus or increasing the height of the solder joint. In Steinberg?s work based on 
sinusoidal vibrations of a single component PCB, the fatigue life of 10 million stress 
reversal cycles can be achieved if the peak single amplitude displacement of the PCB is 
limited to the value below: [Steinberg 1998] 
 (8) 
where B=length of PCB edge parallel to component , in 
L=length of electronic component, in 
h=height or thickness of PCB, in 
LChr BZ 00022.0?
14 
 
C=constant for different types of components 
r=relative position factor for components 
The peak single-amplitude displacement expected at the center of a PCB can be estimated 
by assuming the PCB acts like a single-degree of freedom system at its resonant 
condition, [Steinberg 1998] 
 (9) 
The displacement value obtained from the above relation will be little less than the 
correct value obtained from the actual dimensions of the PCB plate geometry. Since PCB 
is approximated as a single degree of freedom system, the displacement will be of the 
centroid of PCB and not of the PCB itself.  
The size, location and orientation of a component on the PCB are important factors that 
affect the life of the component. The most critical location for large components is the 
center of PCB where the displacements are maximum. The curvature reduces as the 
component moves away from the center. This reduces the forces and stresses on solder 
joints.  
 In automotive applications, a combined harsh environment of high temperature 
and vibrations is prevalent at many locations. Current trends in the automotive electronics 
industry warrant the use of several electronic systems for safety, enhanced operator 
control and fuel efficiency and passenger entertainment. These include engine control 
units, crank-shaft / cam-shaft sensors, wheel speed sensors, exhaust gas sensors, cylinder 
pressure sensors, combustion sensors etc which are located underhood. The desire to 
place engine control units on the engine and transmission control units either on or in the 
transmission has pushed the ambient temperature above 125?C. High-temperature 
22 8.98.9 n inn f QGf GZ ??
15 
 
electronics used in automotive systems continue to grow, as fast as the cost and reliability 
issues are addressed. In the near future, hybrid electric vehicles and fuel cell vehicles will 
drive the demand for higher temperature power electronics. In the case of hybrid electric 
and fuel cell vehicles, the high temperature will be due to power dissipation. The use of 
lead (Pb) in solders for electronic connections is now extensively restricted in Europe, 
with its use likely to be phased out completely in the medium term. Although Pbfree 
solders have been the subject of much research, little investigation has been carried out 
into their reliability for applications exposed to vibration in service. Aerospace 
applications, which have service lives measured in decades, are of particular pertinence. 
The present work shows the development and validation of a method for testing small, 
model solder joints in high-cycle fatigue. The tests are conducted using common 
equipment yet provide fast results and objective comparisons between solders without the 
influence of PCBs or components, which typically obscure the solders? intrinsic 
contribution. S-N diagrams are presented which compare the performance of traditional 
Sn-Pb solder to that of Pb-free alloys at room and high temperatures and with copper and 
nickel substrates. It is found that in all situations the Pb-free alloys offer lower lifetimes 
to failure than the traditional Sn-Pb, an unexpected result when considering the inferior 
mechanical properties of the latter. The large disparity at room temperatures and with 
copper substrates is significantly reduced by elevated temperatures and by soldering to 
nickel substrates. In order to investigate these results, a number of techniques are 
employed. In addition to extensive fractography, the damping capacity of the solders is 
investigated and a scanning acoustic microscope is used in conjunction with resonant 
decay tracking of specimens to study the crack propagation paths prior to complete 
16 
 
failure. The analysis of results focuses on the possible causes for this performance 
difference, drawing on existing soldering literature and wider engineering principles. It is 
concluded that the overall pattern of results presents contradictory evidence for the 
contribution of various factors, such as yield strength or interfacial adhesion, which are 
hard to reconcile. It is thought likely that more numerous fatigue initiation sites in the Pb-
free alloys are responsible to some degree for their lower cycles to failure, although more 
research into the effect of substrate and interfacial intermetallics is necessary to 
determine the mechanism by which these influence the results, in the absence of relevant 
fractographic evidence. 
 
1.3. FEA Procedures for Vibration Analysis [Abaqus 6.10 Documentation] 
It is essential to be able to numerically extract the the eigenvalues and modes of 
an electronic system subjected to vibrations in order to evaluate the response of that 
system to the possible vibration loads. There are several response evaluation methods that 
are computationally inexpensive and provide useful insight into the structure?s dynamic 
behavior. Some of these methods provided in Abaqus/Standard and are described in this 
section. The eigenvalue problem for natural modes of small vibration of a finite element 
model is: [Abaqus 6.10 Theory Manual, Modal Dynamic Analysis] 
? ? ? ? ? ?? ? 0}{2 ??? ??? KCM  (10) 
 
where [M] is the mass matrix which is symmetric and positive definite in the problems of 
interest here [C] is the damping matrix, [K] is the stiffness matrix, which may or may not 
be positive definite or symmetric, ? is the eigenvalue and ? is the eigenvector or the 
17 
 
mode of vibration. The eigenvalues and eigenvectors of a system can be real or complex. 
But if [K] is assumed to be symmetric and [C] is neglected during the frequency 
extraction step, the system will have real squared eigenvalues ?2  and real eigenvectors 
only. For such symmetric eigenproblems, [K] is also assumed to be positive semidefinite. 
In this case ? becomes an imaginary eigenvalue, ?=i? where ? is the circular frequency, 
and the eigenvalue problem can be written as: [Abaqus 6.10 Theory Manual, Modal 
Dynamic Analysis] 
? ? ? ?? ? 0}{2 ??? ?? KM  (11) 
 
Lanczos eigensolver is a powerful method to solve this symmetrized eigenvalue problem. 
The Lanczos procedure in Abaqus/Standard consists of a set of Lanczos ?runs,? in each 
of which a set of iterations called steps is performed. For each Lanczos run the following 
spectral transformation is applied: [Abaqus 6.10 Theory Manual, Modal Dynamic 
Analysis] 
? ? ? ?? ? ? ? }]{[}{][ 1 ???? MMKMM ??? ? (12) 
 
where ? is the shift, ? is the eigenvalue and ? is the eigenvector. This transformation 
allows rapid convergence to the desired eigenvalues. The eigenvectors of the symmtrized 
problem and the transformed problem are identical, while the eigenvalues of the original 
problem and the transformed problem are related in the following manner: [Abaqus 6.10 
Theory Manual, Modal Dynamic Analysis] 
??? ?? 12  (13) 
 
18 
 
A Lanczos run will be terminated when its continuation is estimated to be inefficient. 
Followed by the frequency extraction procedure, is the modal dynamic analysis 
procedure. This procedure provides time history analysis of linear systems. The 
excitation to the system is input as a function of time by defining an amplitude curve. It is 
assumed that in between two points specified in the amplitude curve, the magnitude of 
excitation varies linearly. When the model is projected onto the eigenmodes used for its 
dynamic representation, the following set of equations at time t are obtained: [Abaqus 
6.10 Theory Manual, Modal Dynamic Analysis] 
ttfffqqCq ttt ???????? ???????? ? )(2...  (14) 
 
where ? and ? indices span the eigenspace, C?? is the projected viscous damping matix, 
q? is the generalized coordinate of mode ? (the amplitude of the response in this mode),  
???? mk? is the natural frequency of the undamped mode ? (obtained as the square 
root of the eigenvalue in the eigenfrequency step that precedes the modal dynamic time 
history analysis), (ft)? is the magnitude of the loading projected onto this mode (the 
?generalized load? for the mode) and ?f is the change in f over the time increment ?t. If 
the projected damping matrix is diagonal, this equation becomes the following uncoupled 
set of equations: [Abaqus 6.10 Theory Manual, Modal Dynamic Analysis] 
????????? ??? )(2 2
...
tfqqCq ???
 (15) 
 
where ?? is the critical damping ratio given by the relation [Abaqus 6.10 Theory Manual, 
Modal Dynamic Analysis]: 
19 
 
?
????? mc?2  (16) 
 
where c? is the modal viscous damping coefficient and m? is the modal mass in mode ?. 
The solution to the uncoupled equations is obtained readily as a particular integral for the 
loading and a solution to the homogeneous equation (with no right-hand side). These 
solutions can be combined and written in the general form: [Abaqus 6.10 Theory Manual, 
Modal Dynamic Analysis] 
??
?
??
??
?
??
?
??
??
??
?
????
?
??
?
??
??
??
?
???
????
??
tt
t
t
t
tt
tt f fbb bbqqaa aaqq
2221
1211.
2221
1211.  (17) 
 
where aij and bij are constants, since it is assumed that the loading only varies linearly 
over the time increment (that is ?f/?t is constant). Depending on whether the damping in 
the modal equilibrium equation is greater than, equal to, or less than critical damping this 
equation is solved using the corresponding aij and bij. 
 
1.4. Effect of High Temperature on the Reliability of Electronics [Lall 1997] 
Reliability is the ability of a system to perform and maintain its functions under 
normal usage conditions as well as corner conditions. Reliability failures occur due to 
damage caused by internal or external stresses. Most of the times, one failure mechanism 
dominates leading to the failure of the system. Failure mechaniscm may be initialted due 
to operating conditions outside the prescribed specifications. Steady state temperature, 
temperature cycles, temperature gradients and time-dependent temperature changes all 
have the potential to affect the reliability of modern electronic devices and equipments 
[Lall 1997]. Current methodologies in reliability prediction under the influence of 
20 
 
temperature are derived from the activation energy based models proposed by Savante 
Arrhenius in which the steady state temperature dependence of the rate of chemical 
reaction was described in the form: [Lall 1997] 
TKErefrr Bch rtaerr /??? ??  (18) 
 
where rr is the reaction rate (moles/meter2second), rr-ref is the reaction rate at a reference 
temperature (moles/meter2second), Ea-chrt is the activation energy of the chemical reaction 
(eV), KB is the Boltzmann?s constant (8.617 x 10-5 eV/K) and T is the steady-state 
temperature (Kelvin). This model has been reformulated to predict the influence of steady 
state temperature on electronic device reliability. In this case, the MTF (hours), for a 
given steady state temperature is represented as: [Lall 1997] 
TKEr ef Bd evaeM TFM TF /????  (19) 
 
where MTFref is the mean time to failure at a specified reference temperature and Ea-dev is 
the device activation energy (eV). Often implicit in the test strategy is the assumption that 
the failure mechanism active at higher temperatures are also active in the equipment 
operating range, and that the Arrehenius relationship holds.  
 
1.5. Thesis Layout 
 This thesis presents the characterization of Pb-free solder alloys under various 
harsh environments that are particularly prevalent in the automotive electronics. The aim 
of this research is to develop a methodology to characterize the high cycle fatigue life of 
solders subjected to high temperature and vibrations. Using a combination of 
21 
 
experimental and FE based numerical methods, the S-N curve characterizing the high 
cycle fatigue life of SAC305 solder alloy has been obtained at various temperatures. 
Temperature dependent terms have been introduced in the Basquin Power law based 
fatigue life estimation for SAC305. It has been shown that the fatigue life of SAC305 
decreases as the temperature increases. Further, this research explores the fundamental 
material properties like the Elastic modulus and Ultimate Tensile strength of a newly 
developed Pb-free solder alloy called Innolot. This alloy has been developed targeting the 
automotive industry and is designed to resist the detrimental effects of exposure to 
elevated temperatures. In this study, the effect of elevated temperature aging and high 
strain rates has been studied on the material properties of Innolot and a comparison with 
SAC105 and SAC305 solders has been presented.  
 Chapter 2 presents literature survey on solder material characterization. 
Experimental and FE based methods used in studying the reliability of electronic 
packaging subjected to vibrations by prior researchers has been covered in this chapter. A 
major portion of this work deals with reliability of second level interconnects. This 
chapter highlights the state of art work that has been conducted by researchers till date in 
order to differentiate the work presented in this thesis. Board level reliability studies 
carried out on test vehicles have been emphasized. Previous work pertaining to the 
vibration for leaded and lead-free alloys has been presented. The later part of the 
literature review covers the work done by researchers in the field of investigation of 
solder constitutive behavior. The research on effect of isothermal aging, strain rates and 
solder alloy composition on the mechanical properties of Pb-free solders has been given 
special emphasis. This highlights the uniqueness of the research covered in the later part 
22 
 
of the thesis pertaining to the study of constitutive behavior of Innolot and the effects of 
high strain rate and isothermal aging on its constitutive behavior.  
 Chapter 3 presents a methodology development to evaluate the characteristic high 
cycle fatigue life S-N curve of solder at various test temperatures. The automotive harsh 
environment of high temperature and vibration levels has been simulated in the 
laboratory by mounting an isothermal chamber on the existing electrodynamic shaker. 
The chapter contains a detailed description of the test set-up, test vehicle and test cases 
used for this study. Further, the FE based simulation techniques and the correlation 
obtained with the experimental results have been covered. SAC305 high cycle fatigue 
characterization based on the Basquin Power law (S-N curve) is illustrated for every test 
temperature. The temperature dependence of the fatigue strength coefficient and the 
fatigue exponent has been evaluated and implemented in the power law. Thus the last 
section of this chapter presents a modified equation relating the SAC305 solder stress 
amplitude and the fatigue life at a given temperature.  
 In the next chapter, Chapter 4, the constitutive behavior of a newly developed Pb-
free substitute for high temperature and high performance applications has been 
evaluated. This alloys is called Innolot and is developed InnoRelTM targeting the 
automotive electronics segment. Innolot contains Nickel (Ni), Antimony (Sb) and 
Bismuth (Bi) in small proportions in addition to Sn, Ag and Cu. It is reported to perform 
better in thermal cycling as compared to the SAC alloys. In this research a novel test 
equipment capable of testing the solder material properties in the strain rate range of 1-
100 per second has been used to evaluate the constitutive behavior of Innolot. Further the 
effect of elevated temperature isothermal aging on the constitutive behavior of Innolot 
23 
 
has been studied. Finally a comparison of Innlot with SAC105 and SAC305 alloys 
conducted by other researchers has been presented. The last Chapter 5 summarizes the 
purpose and findings of the thesis and briefly discussed the scope for future work.   
24 
 
CHAPTER 2 
LITERATURE REVIEW 
 
2.1. Vibration Analysis of Electronics 
Electronic components in automotive applications get exposed simultaneously to 
high temperature and dynamic loads during their life cycles. Studies on automotive 
temperature extremes have recorded continuous maximum temperatures upto 140C and 
vibration level up to 10G RMS [Johnson et. al. 2004]. The significance of studying 
reliability under this type of environment is even more consequential for off-road 
automotives like construction and agricultural machinery. Both high temperature and 
vibrations contribute to the failures in such system [Barker et. al. 1990, 1992, Basaran et. 
al.  2002, Qi et. al. 2004]. The reliability of electronic products can be improved through 
a thorough understanding of the weakest link in the electronic systems which is the 
solder interconnects. There is a lack of fundamental understanding of reliability of 
electronic systems subjected to extended period of vibrations at elevated temperature. 
Most of the research is focused on reliability of solder interconnects subjected 
exclusively to vibrations [Steinberg 1988, Henderson et. al. 1995, Hu et. al. 1995, Wong 
et. al.  1997, Lall et. al.  2005, Lall et. al. 2007] or thermal cycling. Relatively few 
researchers have studied the reliability in the simultaneous environment of thermal 
cycling and vibration [Barker et. al. 1990, 1992, Basaran et. al.  2002, Qi et. al. 2004]. In 
this paper, the authors have characterized the high cycle fatigue S-N curves of
25 
 
lead-free solder at various constant temperatures. 
Most of the prior research in the area of reliability of solder joints is focused on 
thermal cycling which includes low cycle fatigue failure modes. Researchers have 
developed the theory and life prediction models for solder fatigue subjected to thermal 
cycling [Tavernelli 1962]. Similarly, the theory for life prediction and accelerated testing 
under random vibrations is also well formalized for leaded solders [Steinberg 1988, Hu 
1995, Henderson et al 1995].  Typical failures under vibration loads are due to high cycle 
fatigue occurring after several million cycles [Wong 1997] and may demonstrate 
multiple failure modes of solder fatigue, copper trace or lead fracture. Finite element 
modeling approaches for PCBs [Pittaresi 1990, Pittaresi et. al. 1991, 1993, Lall et. al. 
2004, 2005] and stress analysis for component and solder joint reliability under random 
vibration can also be found in current literature [Lau 1991, Upadhyayul et. al. 1997, Li 
1999, 2001]. Prior studies on the effect of concurrent thermal cycling and dynamic 
loading on electronic components have suggested incremental damage superposition 
approach for predicting solder joint reliability [Barker et. al. 1990, 1992, Basaran et. al. 
2002, Qi et. al. 2004].  The behavior of 63Sn/37Pb solder under in-plane vibration at 
high temperature has been studied [Zhao et. al. 1999].  
Second level solder interconnect stress investigation under dynamic loads has 
largely relied on FE based simulations. The purpose of the investigation presented in this 
paper is to study the behavior of SAC305 solder joints under out of plane vibration at 
elevated temperature. The test vehicle has been tested to failure subjecting it to out of 
plane harmonic vibrations at its first natural frequency inside an isothermal chamber. 
Digital Image Co-relation (DIC) has been used to measure full field displacement and 
26 
 
deformation gradient on the PCB. Previously, DIC has been used to accurately measure 
deformations in electronic assemblies subjected to drop and shock [Lall et. al. 2007b, 
Miller et. al. 2007, Park et. al. 2007a,b, 2008]. Global-local sub-modeling has been used 
to predict the solder joint stresses. The component deformation is governed by the PCB 
deflection. Material properties of PCB change with increase in the test temperature even 
below the glass transition temperature. This has been demonstrated by measuring the 
change in natural frequency as a function of temperature. In this study, modal analysis 
has been conducted at each elevated test temperatures and PCB material properties have 
been determined using Dynamic Mechanical Analyzer through each test temperature. 
Dynamic characteristics of the system including the natural frequencies, mode shapes 
and the out of plane displacement have been used to correlate the global model with the 
test vehicle. Prior researchers have plotted S-N curves for SAC alloys using a 
combination of experimental and finite element modeling techniques [Al-Yafawi et. al. 
2010]. In this paper the authors have developed a methodology to obtain the solder 
stresses at elevated test temperatures. Arrhenius theory has been used to develop a 
predictive model that would fit through the S-N curves at elevated temperature. Basquin 
power law for SAC305 solder has been modified by introducing temperature dependent 
fatigue coefficient and fatigue exponent terms. 
 
2.2. Digital Image Correlation 
Owing to the complexity of electronic assemblies, it is not feasible to place 
deformation measuring devices such as strain gages on them. Additionally, conventional 
deformation measuring techniques only evaluate localized values. With a multitude of 
27 
 
components on a single test assembly, it is beneficial to have an estimate of full field 
deformations for subsequent evaluation of individual component response. 
Digital Image Correlation (DIC) is a novel technique which works by tracking a 
geometric point on the specimen before and after deformation, thereby enabling full field 
strain and displacement measurement during a transient dynamic event. Geometric points 
on the test specimen are distinguished by speckle coating the surface of interest. Previous 
studies have established the effect of size, consistency and density of the speckle pattern 
on the accuracy of the method [Zhou et. al. 2001, Amodio et. al. 2003, Srinivasan et. al. 
2005]. The DIC method has its merits over strain measurement by using strain gage, 
which measure strain only at localized points on the specimen. Furthermore, the 
technique does not involve contact with the specimen during the monitored event and 
specimen preparation is very quick and easy. 
The Digital Image Correlation technique has been extensively used in this work 
to measure field quantities (deformation) and for subsequent calculation of their 
derivatives(strain). The technique has been employed in this work, in conjunction with 
high speed imaging systems to evaluate transient dynamic board response to JEDEC 
standard shock events as well as static bend tests. 
High speed photography has previously been used to measure deformations in 
sheet metal forming, Automotive crash testing, rail vehicle safety[Kirkpatrick et. al., 
2001], air- plane safety[Marzougui, 1999], modal analysis of turbine blades, high strain 
rate Split- Hopkinson bar tests, dynamic fracture phenomenon, and package hermiticity 
(MIL-STD- 883) tests. High-speed cameras measure impact speed, force, and 
deformation due to shock, and thermal loading. Previously, the measurement of 
28 
 
derivatives of field quantities, such as strains, was limited to a specific physical locations 
or discrete target points in an electronic structure. 
In the field of electronic packaging, DIC has been used to calculate full field 
deformations and deformation gradient in electronics [Lall et. al. 2007c, 2008b-d, 2009, 
Miller et. al. 2007, Park et. al. 2007a,b, 2008]. Previously, the DIC based strain 
measurements technique has been demonstrated to be useful for transient strain 
measurement in electronic assemblies, in the presence of rigid body motion Lall 2007 
2008]. Digital image correlation also been employed to study deformations in printed 
circuit assemblies for mobile devices [Lall et. al. 2007, Miller et. al. 2007, Park et. al. 
2007], material characterization [Park et. al. 2007] for evaluation of stresses and strain in 
flip-chip dies under thermal loading [Kehoe et. al. 2006] and for calculating stresses in 
solder interconnects of BGA packages under thermal loading conditions [Zhou et. al. 
2001]. DIC has also been used for evaluating elastic modulus of underfill materials at 
elevated temperatures during four-point bending tests [Park 2007a, Shi 2007]. In 
conjunction with high resolution SEM, the method has also been used to study the 
stresses released at the component surface before and after ion milling [Vogel 2007]. 
Although the technique has been widely used in thermal analysis of electronic 
packaging, it has recently gained a lot of attention in the field of transient dynamics as 
well. DIC algorithms in conjunction with high speed imaging systems are now widely 
used as tools for acquisition and analysis of deformation images. The technique has been 
extensively used in this study for evaluation of test vehicle deformation during transient 
dynamic as well as static mechanical events. 
 
29 
 
 
2.3. High Strain Rate Solder Characterization 
With the ROHS initiative on lead-free solder taking effect, the electronics 
industry has been presented with a wide array of lead-free options. Most of the Pb-free 
alloys in the industry today are plagued by aging and creep issues. Prior researchers have 
shown a deterioration of the material properties of SAC alloys with constant temperature 
aging [Lall 2012 et. al., Ma et. al. 2009, Zhang et. al. 2009, Darveaux 2005]. New 
developments in the Pb-free options have introduced small proportions of Ni, Zn, Co, Bi, 
Sb in the SAC alloys to increase resistance to aging and creep while maintaining the 
melting temperature and strength of the alloy comparable to SAC. Many researchers 
have shown enhanced material properties, microstructures and resistance to failures in 
thermal cycling due to the addition of rare earth elements in SAC alloys [Zhang et. al. 
2009, Liu et. al.]. InnoRelTM have introduced a new Pb-free alloy- Innolot, which 
consists of Ni, Sb and Bi in its composition (Table 2). This alloy has a melting range 
between 206C to 218C. Increased creep strength is a result of solid solution hardening 
and dispersion hardening mechanisms achieved by Bi, Sb dissolution in Sn crystal matrix 
and intermetallic phases by Ni. Prior studies have shown that Innolot is more reliable in 
thermal cycling as compared to SAC alloys [Miric et. al. 2010].  
The effects of aging on the microstructure and material properties of Pb-free 
alloys have been investigated at low strain rates less than 1/s [Chuang et. al. 2002, Coyle 
et. al. 2000, Darveaux 2005, Lee et. al. 2002, Pang et. al. 2004, Zhang et. al. 2009]. For 
high strain rate constitutive behavior investigation, researchers have relied on Split 
Hopkinson Pressure bar tests [Chan et. al. 2009, Siviour et. al. 2005]. The strain rates 
30 
 
achievable with this equipment, range from 500/s to 3000/s. In practice, the typical strain 
rates observed on second level interconnects in consumer electronics drop impacts are 
within 1/s to 100/s. Neither the Split Hopkinson Pressure bars nor conventional pull 
tester can be easily used to obtain these strain rates. Very few researchers have 
characterized Pb-free solder properties at strain rates of 1/s to 100/s [Lall et. al. 2011, 12, 
Meier et. al. 2009, Wong et. al. 2008]. The authors of this paper have explicitly 
demonstrated the capability of an innovative tensile tester to repeatably obtain constant 
strain rates of 10/s, 35/s and 50/s. The effect of strain rate and aging on the material 
properties of SAC105 and SAC305 has been established through this work [Lall et. al. 
2012]. In this paper, the same equipment and aging conditions have been used for two 
strain rates of 10/s and 35/s to characterize the constitutive behavior of Innolot. A 
comparison of the effects of strain rate and aging on Innolot and SAC alloys (SAC105 
and SAC305) has been presented.  
Non-linear Ramberg-Osgood model [Lall et. al. 2012, Nguyen et. al. 2011, 
Ohguchi et. al. 2006, Chen et. al. 2006, Muller et. al. 2005, Pang et. al. 2004, Park et. al. 
2002, Lee et. al. 1997, Knecht et. al. 1990] and Anand?s viscoplastic model [Mysore et. 
al. 2009, Bhate et. al. 2008, Yeo et. al. 2006, Pei et. al. 2005, Rodgers et. al. 2005, Wang 
et. al. 2005, Pang et. al. 2004, Wang et. al. 2001, Wilde et. al. 2000] are amongst the 
most popular models to describe solder stress-strain behavior. Prior researchers have 
used finite element analysis for modeling tensile tests [Lall et. al. 2012, Joun et. al. 2007, 
Niordson et. al. 2004, Cabezas et. al. 2004, Peng et. al. 2004, Koc et. al. 2004, Mirone 
2004, Tang et. al. 2003, Inal et. al. 2002, Komori 2002, Nilsson 2001]. This research, 
uses Ramberg-Osgood model for its implementation in Abaqus based FE codes. 
31 
 
In the past, Digital Image Correlation (DIC) has been used for material 
characterization at low strain rate testing of composites [Gershon et. al. 2010, Srinivasan 
et. al. 2005, Grytten et. al. 2009] and high strain rates for lead-free solder characterization 
[Lall et. al. 2012, 2011, 2010, Tiwari et. al. 2005] to investigate full-field displacement 
and strain contours as the test specimen deforms and fractures. DIC has been 
implemented in this work to correlate Ramberg-Osgood FE models with the 
experimental data.  
 
Table 2: Innolot Composition [Miric et. al. 2010] 
Element Min % Max % 
Sn Balance (90.1-91.6) 
Ag 3.6 4.0 
Cu 0.6 0.8 
Ni 0.1 0.2 
Sb 1.3 1.7 
Bi 2.8 3.2 
 
 
 
32 
 
CHAPTER 3 
HIGH CYCLE FATIGUE CHARACTERIZATION OF SAC305 INTERCONNECTS 
UNDER SIMULTANEOUS EXPOSURE TO HIGH TEMPERATURE AND 
VIBRATION 
 
3.1  Introduction 
Electronic components in automotive applications get exposed simultaneously to 
high temperature and dynamic loads during their life cycles. Studies on automotive 
temperature extremes have recorded continuous maximum temperatures upto 140C and 
vibration level up to 10G RMS [Johnson, 2004]. The significance of studying reliability 
under this type of environment is even more consequential for off-road automotives like 
construction and agricultural machinery. Both, high temperature and vibrations 
contribute to the failures in such system. The reliability of electronic products can be 
improved through a thorough understanding of the weakest link in the electronic systems 
which is the solder interconnects. There is a lack of fundamental understanding of 
reliability of electronic systems subjected to extended period of vibrations at elevated 
temperature. Most of the research is focused on reliability of solder interconnects 
subjected exclusively to vibrations or thermal cycling. Relatively few researchers have 
studied the reliability in the simultaneous environment of thermal cycling and vibration. 
In this paper, the authors have characterized the high cycle fatigue S-N curves of lead-
free solder at various constant temperature. Most of the early research in the area of
33 
 
reliability of solder joints is focused on thermal cycling which includes low cycle fatigue 
failure modes. Researchers have developed the theory and life prediction models for 
solder fatigue subjected to thermal cycling [Tavernelli 1962]. Similarly, the theory for 
life prediction and accelerated testing under random vibrations is also well formalized 
[Steinberg 1988, Hu 1995, Henderson et al 1995].  Typical failures under vibration loads 
are due to high cycle fatigue occurring after several million cycles [Wong 1997] and 
include solder fatigue, copper trace or lead fracture. Finite element modeling approaches 
for PCBs [Pittaresi 1990, 1991, 1993, Lall 2004, 2005] and stress analysis for component 
and solder joint reliability under random vibration can also be found in current literature 
[Lau 1991, Upadhyayul 1997, Li 1999, 2001]. Prior studies on the effect of concurrent 
thermal cycling and dynamic loading on electronic components have suggested 
incremental damage superposition approach for predicting solder joint reliability [Barker 
1990, 1992, Basaran 2002, Qi 2004].  The behavior of 63Sn/37Pb solder under in-plane 
vibration at high temperature has been studied [Zhao 2000].  
Second level solder interconnect stress investigation under dynamic loads has 
largely relied on FE based simulations. Previously, global models have been 
investigated using equivalent layer models [Gu 2005], smeared property models [Clech 
1997, Lall 2004, 2005]. The purpose of the investigation presented in this paper is to 
study the behavior of SAC305 solder joints under out of plane vibration at elevated 
temperature. The test vehicle has been tested to failure subjecting it to out of plane 
harmonic vibrations at its first natural frequency inside an isothermal chamber. Digital 
Image Co-relation (DIC) has been used to measure full field displacement and 
deformation gradient on the PCB. Previously, DIC has been used to accurately measure 
34 
 
deformations in electronic assemblies subjected to drop and shock [Lall 2007b, Miller 
2007, Park 2007a,b, 2008]. Global-local sub-modeling has been used to predict the 
solder joint stresses. The component deformation is governed by the PCB deflection. 
Material properties of PCB change with increase in the test temperature even below the 
glass transition temperature. This has been demonstrated by measuring the change in 
natural frequency as a function of temperature. In this study, modal analysis has been 
conducted at each elevated test temperatures and PCB material properties have been 
determined using Dynamic Mechanical Analyzer (DMA) through each test temperature. 
Dynamic characteristics of the system including the natural frequencies, mode shapes 
and the out of plane displacement have been used to correlate the global model with the 
test vehicle. Prior researchers have plotted S-N curves for SAC alloys using a 
combination of experimental and finite element modeling techniques [Al-Yafawi 2010]. 
]. In this paper the authors have developed a methodology to obtain the solder stresses at 
elevated test temperatures. Arrhenius theory has been used to develop a predictive model 
that would fit through the S-N curves at elevated temperature. Basquin power law for 
SAC305 solder has been modified by introducing temperature dependent fatigue 
coefficient and fatigue exponent terms. 
 
3.2 Test Vehicle 
The test vehicle used for this study is a representative of engine control unit of an 
agricultural equipment. It has dimensions of 204mm x 129mm x 1.56mm. The test board 
has a variety of surface mount daisy chain packages including plastic ball grid array 
(PBGA), quad flat package (QFP), thin small outline package (TSOP), and small outline 
35 
 
package (SOL) mounted on a high glass transition printed circuit board as shown in 
Figure 6. Each daisy chained package is traced across two connector pins. Both, the 
leaded and BGA packages have SAC305 lead-free solder interconnects. The test board 
surface finish is immersion silver. The mass of the test vehicle is 133.46 gram. The 
attributes for each package are tabulated in Table 3. Die sizes are measured by scaling 
the known dimensions on the X-ray images in Figure 7. BGA configurations have been 
modeled as seen in the X-rays.  
Table 3:Package attributes 
Package Pitch (mm) 
Lead 
thickness 
or Ball 
diameter 
(mm) 
Solder 
alloy 
system 
I/O count 
 
 
Mass 
(gram) 
QFP 0.65 0.33 SAC305 144 5.86 
BGA 1.27 0.75 SAC305 46,272,388, 4.05 
TSOP 0.5 0.254 SAC305 48 0.54 
SOL 1.27 0.43 SAC305 16,24,32 0.85 
 
36 
 
 
 
Figure 6: Product form-factor test vehicle 
 
 
37 
 
 
BGA 272 
 QFP 144 
 
SOL 32 
 
TSOP 48 
Figure 7: X-ray images of components 
 
      
 
? 0 . 7 5 m m
2 4 . 8 8 m m
2 4 . 8 8 m m
5 . 0 6 m m
1 . 2 7 m m
( p i t c h )
5 . 0 6 m m
      
 
7  m m
3 0 . 6 m m
3 0 . 6 m m
0 . 3 m m
( l e a d  t h i c k n e s s )
0 . 6 5 m m
( p i t c h )
7  m m
      
 
1 . 2 7  m m
( p i t c h )
0 . 4 3  m m
5 . 7  m m
2 0 . 8  m m
7 . 5  m m
5 . 4 7  m m
 
 
 
 
 
 
 
0 . 2 5 4  m m
( p i t c h )
0 . 2 5 4  m m
3 . 4  m m
2 1  m m
1 2  m m
4 . 2  m m
38 
 
 
(a)      (b) 
Figure 8: a) Cartoon of Tg measurement using DSC [Adapted from: www.arlon-
med.com] b) Tg using DSC of cured epoxy resin 
[http://www.siint.com/en/documents/technology/thermal_analysis/application_
TA_008e.pdf] 
 
 
Differential Scanning Calorimetry (DSC) is often used to identify the Tg of a 
composite. [Figure 8] shows a cartoon of a typical DSC plot. A stepwise decrease in the 
heat capacity of a specimen marks the glass transition temperature (Tg).  
Differential Scanning Calorimetry (DSC) was conducted on a small sample of the 
PCB weighing 2.3mg. using the equipment shown in Figure 9 The heat flow vs 
temperature plot shown in Figure 10 does not show a sudden change in the heat flow 
through the sample during DSC which verifies that the glass transition temperature Tg of 
the PCB is well above the selected test temperatures.  This test vehicle has a 4-layer FR4 
laminated PCB designed for Pb-free components. 
39 
 
 
Figure 9: Differential Scanning Calorimeter from TA Instruments, model Q2000 
 
 
Figure 10: DSC plot for PCB sample, Tg>140C 
 
 
3.3 Harmonic Vibration Testing at Elevated Temperature 
The test vehicles have been randomly allotted to one of the case shown in the test 
matrix [Figure 11]. Baseline data is collected by setting the chamber temperature to 25C. 
Additionally, two elevated temperatures of 75C and 125C have been used. The test 
temperatures have been selected based on typical temperatures observed in automotive 
environment.  
40 
 
 
Figure 11:Test Matrix 
 
An isothermal oven is mounted on the shaker to enable temperature control. It has 
a glass window on top to acquire high speed video of the PBC deformation. In each case, 
the board is subjected to harmonic vibration dwelling at the corresponding first natural 
frequency with amplitudes of 10G. The wires connected on the PCB are taken out of the 
chamber and given as input to the high speed data logger. The resistance across daisy 
chained packages U4, U5, U17, U18, U19, U20, U21 [Figure 12] have been monitored 
using this high speed data logger.  
 
 
Figure 12:Packages selected for test to failure 
 
125 0 C
10G
C a se  2
1 st N F  ( 1 2 3 . 1 8 H z)
T
es
t 
te
m
p
er
a
tu
res
S tr es s  l ev el
25 0 C
7 5 0 C
C a se  3
1 st N F  ( 1 1 6 . 7 5 H z)
C a se  1
1 st N F  ( 1 2 9 . 9 6 H z)
41 
 
For a data logger, the electrical discontinuity is defined as a 20% resistance 
increase from the initial resistance value and the failure of a solder joint is defined as the 
first such event within five or more consecutive scans. Note that less than 3 seconds per 
scan is required for a data logger. The test is continued till all the aforementioned 
packages have failed. The time to failure is calculated based on the difference between 
the time stamp of the start of test and failure event for every package. Since a input 
vibration is at a constant frequency, the time to failure is easily converted to cycles to 
failure. Figure 13 shows the complete test setup.  
 
 
Figure 13:Test setup 
 
 
3.4 Approach to Solder High Cycle Fatigue Life Prediction at elevated 
Temperature 
The methodology used in this study is represented in the flow-chart depicted in 
D a t a  a c q u is it io n  s y s t e m  
f o r  c o n t in u it y  m o n it o r in g
H ig h  s p e e d  c a m e r a s  
a n d  l ig h t  f o r  D I C
O v e n  w it h  g l a s s  t o p
S h a k e r
S h a k e r  c o n t r o l l e r  
s y s t e m
42 
 
Figure 14. Experimental Modal Analyisis (EMA) is conducted on the test vehicle 
described in the previous section. Three temperatures: 25C, 75C and 125C have been 
used to conduct the EMA. The 1st natural frequency is located at each test temperature 
for subsequent tests to failure. Tests to failure have been conducted on the test vehicles 
by subjecting simultaneously to elevated temperature and sinusoidal vibrations at the 
corresponding 1st NF. High speed data acquisitions systems monitor the daisy chain 
resistance of each package to detect an increase in resistance leading to open event. 
Cycles to failure are counted based on time to failure. A smeared property global model 
of the test vehicle is constructed for FE based modal analysis. The PCB properties in this 
model are recursively updated to obtain a good correlation with EMA. Properties 
obtained by this technique are compared with PCB properties from conducting a 
dynamic mechanical analysis. Digital Image correlation is used to obtain full field 
displacement and strain contours of the board deformation. The deformations of the 
global model are correlated to further ensure good correlation between global model and 
the test vehicle. Dynamic explicit submodels of the failed components with temperature 
dependent PCB and solder properties give the solder level stresses at each temperature. 
S-N curve at the three test temperatures is obtained from cycles to failure and stress 
levels from sub models. Basquin power law is updated to incorporate the temperature 
dependence of the fatigue coefficient and exponent based on Arrhenius equation. 
43 
 
 
Figure 14: Approach to obtain elevated temperature S-N Curves 
 
3.5 Correlation of Test Vehicle with Global FE Model 
Solder stress characterization in dynamic analyses relies largely on finitely 
element analysis of well correlated FE models. However, a detailed model of the PCB is 
often very difficult to mesh and computationally inefficient to solve. In order to 
overcome this problem, it is necessary to build an equivalent FE model with equivalent 
material properties. Such a model is referred to as the global model. The detailed models 
of each component called sub-models, derive their boundary conditions at the local 
degrees of freedom from the global model. It is therefore essential to correlate the global 
model with the physical test vehicle.  
Modal analysis is the base to measure the response of the test vehicle to dynamic 
loads. The mode shapes, natural frequencies and structural damping have been obtained 
from this analysis. A light weight accelerometer of 2.05 gram is adhered to the PCB at 
two different locations. Figure 15 shows the setup with accelerometer located at the 
E x p e r i m e n t a l  Mo d a l  
A n a l y s i s
F r e q u e n c y  s w e e p  a t  2 5 C ,  7 5 C  
a n d  1 2 5 C  t o  l o c a t e  1
st
N F  a t  
e a c h  t e m p e r a t u r e
S i m u l t a n e o u s  H a r s h  
E n v i r o n m e n t
T e m p e r a t u r e  +  
V i b r a t i o n
Te s t s  t o  f a i l u r e  a t   2 5 C ,  7 5 C  a n d  
1 2 5 C  ( D w e l l  a t  c o r r e s p o n d i n g  
1
st 
N F ,  1 0 G  s i n u s o i d a l )
C y c l e  C o u n t
D a i s y  c h a i n  re s i s t a n c e  
m e a s u re d .  T i m e  t o  f a i l u re  
c o n v e rt e d  t o  c y c l e s  t o  
f a i l u re
E x p e r i m e n t a t i o n  &  A n a l y s i s
S - N  C u r v e s
F ro m  Cy c l e  c o u n t  a n d  s o l d e r l e v e l  
s t re s s e s ,  S - N  c u rv e s  a t  3  
t e m p e ra t u re s  a re  o b t a i n e d
S i m u l a t i o n
F E  M o d a l  A n a l y s i s
G l o b a l  m o d e l  c o rre l a t i o n  
w i t h  E M A  o b t a i n e d  a t  
e v e ry  t e m p e ra t u re  b y  
re c u rs i v e l y  u p d a t i n g  P CB  
m a t e ri a l  p ro p e r t i e s   
F E  V i b r a t i o n  A n a l y s i s
M o d a l  d y n a m i c  a n a l y s i s  o n  
g l o b a l  m o d e l  a n d  e x p l i c i t  
d y n a m i c  a n a l y s i s  o n  s u b -
m o d e l s  f o r fa i l e d  c o m p o n e n t s  
ru n  a t  3  t e m p e ra t u r e s  t o  o b t a i n  
s o l d e r s t re s s e s .  
D MA
F E  b a s e d  P CB p ro p e r t y  
d e g ra d a t i o n  c o rre l a t e d  t o  
a t  t e m p e ra t u re  E l a s t i c  
m o d u l u s  o b t a i n e d  f ro m  
e x p e ri m e n t  (D M A )
T e m p e r a t u r e  d e p e n d e n t  S -
N  C u r v e s
T e m p e ra t u re  d e p e n d e n c e  o f f a t i g u e  
c o n s t a n t s  b a s e d  o n  A rrh e n i u s  
e q u a t i o n  i n t ro d u c e d  i n   Ba s q u i n
P o w e r l a n
D I C
D i g i t a l  Im a g e  Co rre l a t i o n  
t o  o b t a i n  f u l l  f i e l d  
d i s p l a c e m e n t  s  a n d  s t ra i n s
44 
 
center. The board is mounted using standoffs at four corners on the shaker table with its 
packages facing down. The top side of the board is coated with a black random speckle 
pattern on a white background coat. A sine sweep profile from 5Hz to 500Hz with 
constant amplitude of 10G is entered in the shaker controller. Accelerometer mounted on 
the shaker measures the excitation signal and the other accelerometer mounted on the 
PCB measures the response. A transmissibility plot is obtained from this test. The 
excitation frequency corresponding to every peak in the transmissibility plot denotes the 
natural frequency of the board. The plots obtained from mounting the response 
accelerometer at the two locations are over-laid to find the first four natural frequencies 
[Figure 17].  
  
Figure 15:EMA setup 
 
P C B  w i t h  s p e c k l e  p a t t e r n
( p a c k a g e s  f a c i n g  d o w n )
A c c e l e r o m e t e r   2  ( r e s p o n s e )
A c c e l e r o m e t e r   1  ( c o n t r o l )
S h a k e r  t a b l e
B o u n d a r y  c o n d i t i o n
Lo c a t i on  1
Loc a t i on 0
45 
 
 
(a) 
 
 
(b) 
Figure 16: a) EMA Setup b) PCB inside the isothermal chamber 
 
46 
 
 
 
Figure 17:Acceleration response denoting natural frequencies 
 
Dynamic characteristics have been evaluated at elevated temperatures of 
50C, 75C, 100C and 125C. Figure 18 demonstrates the dependence of the first 
natural frequency of the test vehicle on the test temperature. The R2 value obtained 
for a straight line fit is 0.9978 which implies that the natural frequency decreases 
very linearly with increase in temperature.  
1 2 9 . 9 6
2 4 9 . 1 2
3 2 0 . 7 2
3 4 8 . 9 0
0
10
20
30
40
50
60
70
90 190 290 390 490
M
a
g
ni
t
ud
e
 
of
 r
e
s
po
ns
e
E xc i t a t i on Fr e que nc y  ( H z )
T r a n s m i s s i b i l i t y  P l ot
47 
 
 
 
Figure 18: Change in 1st natural frequency as a function of temperature 
 
For a system excited close to its resonant frequency, the damping ratio becomes a 
very critical dynamic characteristic. It enforces steady state of the response of the system. 
Half-power bandwidth method shown in Eq. (20) is used for lightly damped structures. 
Figure 19 shows the acceleration response from 100Hz to 150Hz. fn=129.96Hz and 
?fn=3.5Hz at 25C for clarity. From Eq. (20), the damping ratio is calculated to be 0.013 
n
nf2f???  (20) 
 
where ? is the damping coefficient, fn is the natural frequency and ?fn is the difference in 
half-power bandwidth frequencies. Figure 19 shows the acceleration response from 
100Hz to 150Hz. fn=129.96Hz and ?fn=3.5Hz at 25C for clarity. So the damping ratio is 
0.013.  
R ?  =  0 . 9 9 8 3
114
116
118
120
122
124
126
128
130
132
0 20 40 60 80 100 120 140
N
a
t
u
r
a
l
 F
r
eq
u
en
c
y
 (H
z
)
T e mp e r a t u r e  D e g  C
1 s t  N a t u r a l  Fr e q u e n cy  V S  T e m p e r a t u r e
48 
 
 
  
Figure 19:Experimental mode shape at 1st natural frequency 
 
The damping coefficient can further be split into Raleigh coefficients - mass damping 
coefficient and stiffness damping coefficient. [Papagiannaopoulos et. al.2011] 
21
212 ??? ?????  (21) 
 
where ? is the mass damping coefficient. Substituting for the terms on the RHS of Eq. 
(21): 
5.128132 )5.128132(22013.0 ? ?????  (22) 
 
64.10??  (23) 
 
The stiffness damping coefficient is given by: [Papagiannaopoulos et. al.2011] 
 
21
2??????  (24) 
49 
 
 
)5.128132(2 2013.0 ????
 (25) 
 
61059.1 ????  (26) 
 
It can be seen by comparing Eq.(23) and Eq.(26) that the mass damping is higher than 
the stiffness damping for this structure.  
The global model built for FE simulations is shown in Figure 20. The mass of 
this model is 134.3 gram and uses smeared properties for the packages. Table 4 shows 
the comparison of actual masses with simulation. Lanczos algorithm is used for Eigen 
frequency extraction of the global model.  
 
(a) 
50 
 
 
(b) 
Figure 20:a) Global model for modal dynamic analysis to simulate board deflection 
 
 
Figure 21:Linear Region of stress-strain curve of PCB 
 
PCB deflections govern the component level stresses and strains. The deflection 
51 
 
of PCB for the same input vibration profile can change with change in temperature [Lall 
2011]. It is therefore essential to use accurate material properties of PCB at elevated 
temperatures and use them for the high temperature simulations. Tensile test is conducted 
to obtain the elastic modulus of PCB. Several samples along various in-plane directions 
have been used for tensile test. Figure 21 shows one of the representative stress-strain 
curves. Based on these tests, the PCB modeled as linear elastic isotropic with elastic 
modulus of 23.8GPa. The degradation in elastic modulus with temperature is assumed to 
be of the same rate as that obtained from DMA. A dynamic mechanical analysis has been 
run below the glass transition temperature of the PCB [Figure 22]. At 25C, the modulus 
is approximately 22GPa. It reduces to 21.1GPa at 75C. The room temperature values 
obtained in DMA is slightly higher than the value obtained in the average value in tensile 
test that is used in FE (23.8GPa). But the change in the elastic modulus with temperature 
is adapted from DMA. A 5.82% drop from 25C values is used for 75C and 14.28% drop 
from 25C elastic modulus is used for 125C. It should be noted that [Figure 23] for this 
test vehicle, the dependence of elastic modulus from DMA on temperature can be better 
described by a quadratic equation: y = -196099x2 + 459911x + 2E+10 (R2 = 0.9965) as 
compared to a linear equation (R2=0.9701). A quadratic dependence of the Elastic 
modulus on temperature is inline with the prior observation of linear dependence on 
temperature of the 1st natural frequency [Figure 18]. Table 7 compares shows the PCB 
elastic modulus values for FE simulation.   
 
52 
 
 
Figure 22: DMA analysis of test vehicle  
 
 
(a) 
53 
 
 (b) 
Figure 23: Dependence of E on temperature a) Linear trend line b) Quadratic trend line 
 
Table 4: Comparison of actual and FE model mass 
COMPONENT 
ACTUAL 
WEIGHT 
(GRAM) 
MODEL 
WEIGHT 
(GRAM) 
BGA 272 2.15 2.13 
BGA 388 4.05 3.94 
QFP 144 5.86 6.07 
TSOP 48 0.54 0.53 
SOL 32 0.85 0.85 
 
Smeared properties are used for the components on the global model. In this 
54 
 
approach, the component is modeled as block like structure omitting the geometric and 
material details. The component is then assigned equivalent material properties based on 
the multi-layer structure of the component.  
 
Figure 24: Smeared property model 
 
Eq.(27) gives the effective Poisson?s ratio based on the rule of mixtures widely applied in 
composite materials [Clech 1997]. The effective Young?s Modulus is obtained by Eq. 
(28) using the additive property of the bending property of individual layers of the 
component. The equivalent density in Eq. (29) is the volumetric average of the densities 
of the layers. Table 5 lists the calculated properties for the components. The temperature 
effect on the solder property deterioration has a noticeable impact on the effective 
Young?s Modulus of PBGAs. [Clech 1997] 
 
? ???? ni ni iiieff hh  (27) 
 
?eff is the effective Poisson?s ration of the component ?i and hi are the Poisson?s ratios 
and heights of the layers of the multi-layer stack. [Clech 1997] 
55 
 
n
nn
i i
3ii
e ff
e ff3e ff f2 f)1(12 hE)1(12 hE ?????? ? (28) 
 
Eeff and heff are the effective Elastic Modulus and height of the component Ei is the 
Elastic Modulus of each i layers of the multi-layer stack. [Clech 1997] 
? ???? ni ni iiieff VV  (29) 
 
?eff and is the effective density and Vi is the volume of each of the i layers of the multi-
layer stack.  
 
Table 5: Smeared Properties 
Component ?eff (kg/m3) ?eff Eeff (GPa) 
BGA 272 
U19 
2118.51 0.27 4.962 @ 25C 
4.96 @ 75C 
4.958 @ 
125C 
BGA 388 
U17, U18 
1987.34 0.39 4.366 @ 25C 
4.365 @ 75C 
4.364 @ 
125C 
QFP 144 
U1, U2, U3 
1976.42 0.25 12.706 
TSOP 48 
U4, U5, U2 
1962.12 0.27 8.294 
SOL 32 1997.76 0.26 9.3 
 
 
Eigen frequencies are extracted from the global model. The average error in the 
predicted natural frequency from FE and from EMA is given by Eq. (30). The average 
error is the mean of the absolute error in the first four natural frequencies obtained by 
EMA and FEA.  
56 
 
?? ??? n 1i E M A F E AE M A n)i(f )i(f)i(fRE  (30) 
 
where fEMA(i) is the ith NF from EMA and fFEA(i) is the ith NF from FEA and n=4 when 
considering first four NFs. This procedure is repeated for every test temperature: 25C, 
75C and 125C.  
Table 6 displays the material properties used for PCB. The PCB is modeled as linear 
elastic isotropic. Tensile test is conducted  at room temperature to measure the elastic 
modulus. The degradation in elastic modulus is assumed to be of the same rate as the the 
storage modulus obtained from dynamic mechanical analysis. Hence the percent 
reduction in modulus from the room temperatures values have been adapted from DMA. 
Table 7 displays the comparison between EMA and FE results using PCB properties 
from Table 6. There is a good correlation between natural frequencies obtained by FEA 
and EMA. Note that the error in 1st natural frequency for all three test temperatures is 
less than 4%, average error is less than 5% and maximum error is less than 7%.  
 
Table 6: PCB Material properties at temperature 
 
Temperature 
(deg C) 
E from 
tensile 
test  
E from 
DMA 
(GPa) 
D MA 
based % 
Drop in E 
wrt E @ 
25C  
E used 
in FE 
(GPa) 
25 23.8  22.4 0 23.8  
75 -  21.096 5.82 22.41  
125 -  19.2 14.28 20.4  
57 
 
Table 7: RE at temperature 
25C Properties EMA FEA %error 
E1 = 23.8 
129.96 129.19 0.59249 
249.12 247.7 0.570006 
320.72 305.68 4.689449 
348.9 327.75 6.061909 
  RE 2.978464 
     75C Properties EMA FEA %error 
E1 = 22.4 
123.18 125.66 2.013314 
237.94 241.53 1.508784 
309 297.37 3.763754 
338.38 318.97 5.736155 
  RE 3.255502 
     125C Properties EMA FEA %error 
E1 = 20.4 
116.75 120.39 3.117773 
225.52 232.32 3.015254 
299.37 285 4.80008 
328.17 305.86 6.798306 
  RE 4.432853 
 
 
 
The frequency extraction step normalizes the peak displacement. Therefore it 
cannot be used directly for displacement correlation. Instead modal dynamic procedure is 
used to obtain full field displacement histories of the global model. [Figure 25] shows 
that the displacement at a randomly selected point on the PCB changes from transient to 
steady state in about 0.5seconds. A phase shift of 90 degrees can be observed between 
the excitation and response.  
 
 
58 
 
 
  Figure 25:Base excitation and PCB response 
 
Digital Image correlation has been used in conjunction with high speed imaging 
to correlate the mode shape and the full field displacements of the FE model. Digital 
image correlation (DIC) is an optical method to measure full-field deformation and the 
derivatives of deformation on the surface of a loaded structure. Previously, the feasibility 
of using DIC for transient strain measurement in electronic assemblies, in the presence of 
rigid body motion has been demonstrated [Lall 2007a-e, 2008a-d]. The technique 
involves the application of speckle pattern on the surface of the printed circuit board 
assembly and tracking a geometric point on the speckle patterned surface before and after 
loading and using it to compute both in-plane as well as out-of-plane deformations in the 
structures.  
Displacement field quantities are obtained by tracking a geometric point before and 
59 
 
after deformation [Zhou 2001,Amodio 2003, Srinivasan 2005, Kehoe 2006, Lall 2007c, 
2008c,d]. The tracking is achieved using digital image processing of speckle pattern on 
the specimen surface. Figure 26 shows the principle of DIC in a three-dimensional case. 
The sub image before deformation is referred as I1 (r) and the one after impact is referred 
as I2 (r) respectively. 
 
 
Figure 26:3D-Digital Image Correlation measurements in Printed Circuit Assembly 
[Lall 2004a-d, 2005a-b, 2006a-f, 2007a-e, 2008a-f, 2009a-d, 2010a-j, 2011, 2012] 
 
60 
 
 
 
Figure 27:a) Experimental mode shape and full field out of plane displacement 
contour at 1st natural frequency b)FE mode shape and full field out of plane 
displacement contour at 1st natural frequency 
61 
 
Figure 27 compares the full field out of plane displacement from DIC and 
model, both conducted at 25C, 10G and first natural frequency. The mode shape in the 
two cases resembles closely. Displacement field ranges from -0.06mm to 2mm in DIC 
and -0.065mm to 2mm in modal dynamic analysis. PCB out of plane displacement and 
in-plane strain along the length captured by DIC correlate well with those predicted by 
FEA at the same point A(50,60) at all the test temperatures [Figure 28]. The FE 
predictions for displacement and strain are slightly lower in amplitude that the DIC 
values in all the cases. This can be attributed by the higher stiffness predict by FEA.   
  
  
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
0 0 . 0 0 5 0 . 0 1
D
is
p
la
c
e
m
e
n
t 
(m
m
)
T i m e  ( s )
D i s pl a c e m e nt C or r e l a ti on @  
125C
1 2 5 C _ D I C
1 2 5 C _ F E
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
0 0 . 0 0 5 0 . 0 1
D
is
p
la
c
e
me
n
t 
(mm
)
T i m e  ( s )
D i s pl a c e m e nt C or r e l a ti on @  
75C
7 5 C _ D I C
7 5 C _ F E
- 0 . 6
- 0 . 4
- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
0 0 . 0 0 5 0 . 0 1
D
i
s
p
l
a
c
e
m
e
n
t
 
(
m
m
)
T i m e  ( s )
D i s pl a c e m e nt C or r e l a ti on @  
125C
1 2 5 C _ D I C
1 2 5 C _ F E
- 0 . 0 0 2
- 0 . 0 0 1 5
- 0 . 0 0 1
- 0 . 0 0 0 5
0
0 . 0 0 0 5
0 . 0 0 1
0 . 0 0 1 5
0 . 0 0 2
0 0 . 0 0 5 0 . 0 1
E
x
x
 S
tr
a
in
 a
lo
n
g 
le
n
gt
h
 o
f 
P
C
B
T i m e  ( s )
E xx S tr a i n C or r e l a ti on @  2 5 C
e x x _ 2 5 C _ D I C
e x x _ 2 5 C _ F E
62 
 
 
Figure 28: Correlation of PCB Out of plane displacement and in-plane strain 
 
From the comparison of natural frequencies, mode shape out of plane 
displacements and in-plane strains, the global model can be said to correlate well with 
the test vehicle. 
3.6 Failure modes 
Typical failure modes observed on quad flat packages (QFPs) are lead 
deformation and lead cracking. This alludes to the fact that the weakest link in QFPs is 
the copper leads where the packages fail most frequently. FE results for QFP also 
indicate high stresses in the corner as well as mid-side leads [Figure 33]. The study is 
meant to investigate solder failures, therefore QFP failures have been disregarded. The 
TSOPS have failed at the solder joints without significant lead cracking though some 
lead deformation is observed in the corner leads. This indicates that TSOPs leads have 
high structural strength and the weakest link is the solder joint. Cross-sectioning of 
PBGAs reveals solder failure at corner balls. Figure 29 contains optical microscopic 
images of these failure modes. 
3 .4 8 E - 0 3 , 
6 .3 7 E - 04
0 . 0 0 4 6 4 6 , 
- 0 .0 0 0 4 4 7
33
- 0 . 0 0 2
- 0 . 0 0 1 5
- 0 . 0 0 1
- 0 . 0 0 0 5
0
0 . 0 0 0 5
0 . 0 0 1
0 . 0 0 1 5
0 . 0 0 2
0 0 . 0 0 5 0 . 0 1
E
x
x
 S
tr
a
in
 a
lo
n
g
 l
e
n
g
th
 o
f 
P
C
B
T i m e  ( s )
E xx S tr a i n C or r e l a ti on @  7 5 C
e x x _ 7 5 C _ D I C
e x x _ 7 5 C _ F E
- 0 . 0 0 2
- 0 . 0 0 1 5
- 0 . 0 0 1
- 0 . 0 0 0 5
0
0 . 0 0 0 5
0 . 0 0 1
0 . 0 0 1 5
0 . 0 0 2
0 0 . 0 0 5 0 . 0 1
E
x
x
 
S
t
r
a
i
n
 
a
l
o
n
g
 
l
e
n
g
t
h
 
o
f
 
P
C
B
T i m e  ( s )
E
xx
S tr a i n C or r e l a ti on @  
125C
e x x _ 1 2 5 C _ D I C
e x x _ 1 2 5 C _ F E
63 
 
 
 
(a) 
 
(b) 
64 
 
 
 
 
(c) 
65 
 
 
(d) 
Figure 29: a)TSOP solder failure b)TSOP corner lead deformation c)Failure in 
BGA (corner solder failure) d)QFP lead failures 
 
Cycles to failure differ for every package because it experiences different strain 
levels based on its location on the test board. The cycles to failure have been calculated 
by multiplying the time to failure by frequency of base excitation which is constant 
throughout the test. Typical resistance vs time plots are shown in Figure 30. Cycles to 
failure for each package as a function of test temperature are plotted in Figure 31. There 
is a difference in mean cycles to failure as the temperature is increased from 25C to 
125C. Since the test vehicles were assigned randomly to a test case, the difference in 
mean cycles to failure can be attributed to test temperature. 
66 
 
 
 
 
 
67 
 
 
Figure 30: Resistance vs Cycles to failure 
 
 
  
Figure 31: Difference in means of cycles to failure due to change in test temperature 
 
 
3.7 Solder Stress Estimation from Explicit Sub-models 
Explicit finite element models have been developed to model the vibration of the 
test boards. Model predictions have been used to determine the interconnect strain 
histories. Reduced integration elements have been used for computational efficiency, 
0
200000
400000
600000
800000
1000000
1200000
0 50 100 150
C
y
c
l
es
 t
o
 F
a
i
l
u
r
e
T es t  T emp er a t u r e (C el s i u s )
C y cl e s  t o  F a i l u r e  v s  T e m p e r a t u r e
T S O P  a t  U 2 1
T S O P  a t  U 5
B G A 2 8 8  a t  U 1 9
68 
 
since the internal load vector scales with the number of integration points. Computational 
time of the dynamic event is reduced by incorporating reduced integration elements in 
the analysis because these element types use fewer integration points to form the element 
stiffness matrices. Lower order elements have been implemented since they perform 
better when the strain is large or very high strain gradient is expected during vibration 
cycle. Three-dimensional continuum elements C3D8R have been used to model the 
components layers of printed circuit board, substrate, mold, leads, lead-frame, solder, 
corner solder balls, die, die paddle and copper pad. In PBGAs, except the four corner 
interconnects, all remaining interconnects have been modeled as Timoshenko beam 
elements. Displacement boundary conditions of the sub-models are derived from the 
global model. Explicit dynamic analysis is conducted to obtain solder stresses. Solder 
material properties at the three test temperatures are tabulated in Table 8. The 
degradation in material properties is assumed to be in-line with other SAC alloys. 
 
Table 8: Solder material properties 
TEMPERATURE 
(CELSIUS) 
ELASTIC 
MODULUS 
(GPA) 
UTS 
(MPA) 
25C 40 100 
75C 30 90 
125C 20 80 
 
The solder interconnects experience tension-compression as well as shear stress 
in a vibration test. For fatigue life prediction, an equivalent stress of the solder 
interconnects needs to be considered. Therefore an equivalent stress called Von Mises 
69 
 
stress is used for constructing the S-N curve. shows the stress contour in solder balls of 
BGA and TSOP. Volumetric average stress value is used in the region of solder/PCB 
interface so that mesh density does not have a significant effect on stress distribution. 
Solder stress levels for BGA and TSOP reduce with increase in temperature. High 
stresses are observed in corner solder ball at the PCB side. Similarly, high stresses are 
observed in corner leads and solder underneath these leads in TSOPs. The failure mode 
in BGA and TSOP obtained during tests is captured well in the simulation. [Figure 35, 
Figure 36]. is used to derive volume averaged stress. 
VVavg ??????  (31) 
 
 
 
 
(a) 
So l d e r (b e a m e l e me n t s)
Mo l d
D i e D i e  p a d d l e
Su b st ra t e
C o rn e r b a l l s
C u  p a d
S o l d e r
70 
 
 (b) 
 
(c) 
 
 
(d) 
Figure 32: a) BGA b) TSOP c) QFP d) SOL sub-models  
 
L e a d  fra m e
L e a d s
D i e
S o l d e r
M o l d
L e a d  f r a m eL e a d s
D i e
D i e  p a d d l e
S o l d e r
M o l d
71 
 
 
Figure 33: QFP high stresses in corner leads 
 
Solder stress levels for BGA and TSOP reduce with increase in temperature. High 
stresses are observed in corner solder ball at the PCB side. Similarly, high stresses are 
observed in corner leads and solder underneath these leads in TSOPs. The failure mode in 
BGA and TSOP obtained during tests is captured well in the simulation. [Figure 35, 
Figure 36]. 
   
(a)    (b)    (c) 
(b) Figure 34: Stress histories at 125C on a) TSOP corner solder b) BGA corner 
solder c) QFP corner lead 
 
 
 
Hi g h  s tr es s  l ev el s  i n
l ea d s  o f  Q FP
- 1 .0 0 E + 0 8
- 8 .0 0 E + 0 7
- 6 .0 0 E + 0 7
- 4 .0 0 E + 0 7
- 2 .0 0 E + 0 7
0 .0 0 E + 0 0
2 .0 0 E + 0 7
4 .0 0 E + 0 7
6 .0 0 E + 0 7
8 .0 0 E + 0 7
1 .0 0 E + 0 8
0 0 .0 0 5 0 .0 1Str
es
s P
a
T im e  ( s )
S tr e s s  H is tor y  (  C or ner  s ol der  
inter c onn e c t T S O P )
- 1 .0 0 E + 0 8
- 8 .0 0 E + 0 7
- 6 .0 0 E + 0 7
- 4 .0 0 E + 0 7
- 2 .0 0 E + 0 7
0 .0 0 E + 0 0
2 .0 0 E + 0 7
4 .0 0 E + 0 7
6 .0 0 E + 0 7
8 .0 0 E + 0 7
1 .0 0 E + 0 8
0 0 .0 0 5 0 .0 1Str
es
s P
a
T im e  ( s )
S tr e s  H is tor y  (  C or ner  s ol der  B G A  2 7 2 )
- 1 .0 0 E + 0 8
- 7 .5 0 E + 0 7
- 5 .0 0 E + 0 7
- 2 .5 0 E + 0 7
0 .0 0 E + 0 0
2 .5 0 E + 0 7
5 .0 0 E + 0 7
7 .5 0 E + 0 7
1 .0 0 E + 0 8
0 0 .0 0 5 0 .0 1Str
es
s P
a
T im e  ( s )
S tr e s s  H is tor y  (  C or ner  le a d Q FP  1 4 4 )
72 
 
 
High cycle fatigue failure is characterized by Basquin power law relation: 
bffa )N2(???  (32) 
 
where ?a is the stress amplitude (MPa), ?f  is the fatigue strength coefficient (MPa), b is 
the fatigue strength exponent and (2Nf) are stress  cycles to failure. The constants ?f  and b 
have been determined by substituting ?a calculated from FE analysis and Nf from average 
cycles to failure for a component. For the 25C case, a value of ?f =65.193MPa and b=-
0.071 fits the data points with the R2 value of 0.997. Prior researchers have published a 
value of ?f =64.80622?50.16874 MPa and b=-0.14425?0.05501 [Yu 2011] for SAC305. 
These researchers have used a specially designed test vehicle with two daisy chained, 
symmetrically placed Amkor ball grid array (CTBGA 288) packages using SAC305 
solder. The test vehicle is a 100mm by 50mm rectangle with two thicknesses of 0.6mm 
and 1mm. The test vehicle is subjected to sinusoidal vibration over a limited frequency 
band centered at the 1st natural frequency and Von-Mises stresses from FEA. The scope of 
this study is limited to room temperature tests.  
Table 9 lists the fatigue coefficients published in literature for various solder alloys.  
S-N curve obtained in this study is plotted on a log-log scale as shown in Figure 37. 
The procedure is repeated for all test temperatures to obtain two additional S-N curves. 
While the cycles to failure reduce with increase in temperature, the failure threshold also 
decreases with increase in temperature due to degradation of material properties [Figure 
40]. 
73 
 
 
 
Figure 35: a) U19 Corner solder ball Mises stress distribution at 125C b)U19 corner 
solder stress distribution at 25C 
74 
 
 
  
Figure 36: a) U5 Corner solder Von Mises stress distribution 125C b) U5 corner 
stress distribution at 25C 
 
 
 
75 
 
Table 9: Published values of Solder Fatigue constants 
Author Alloy ?f (MPa) b R2 
Yu 2011 SAC305 64.8 -0.1443 0.77 
Yu 2011 SAC405 152.2 -0.2079 0.97 
Mason 1964 63Sn37Pb 66.3 -0.12 - 
Yao 1999 63Sn37Pb 177.15 -0.2427 - 
Steinberg 2001 63Sn37Pb 109.6 -0.1 - 
 
 
Figure 37: Curve fitting through S-N data at 25C 
 
 
 
y  = - 0 . 0 7 1 x +1 . 8 1 4 2
R?  = 0 . 9 9 7
O n  l i n e a r  s c a l e  t h e  p o w e r  r e l a t i o n  i s :  y  = 6 5 . 1 9 3 x
- 0 . 0 7 1
1 0 . 0 0
1 0 0 . 0 0
1 . 0 E + 0 4 1 . 0 E + 0 5 1 . 0 E + 0 6 1 . 0 E + 0 7
St
r
e
s
s
 
a
m
p
l
i
t
u
d
e
 
(
M
P
a
)
 
Lo
g
-
Sc
a
l
e
N u m b e r  o f s t r e s s  r e ve r s a l  cycl e s  (Lo g - Sca l e )
S A C 3 0 5  S - N  C u r v e s  a t  T e m p e r a t u r e
76 
 
Table 10: Fatigue strength coefficient and exponent at temperature 
Temperature 
(Celsius) ?f (MPa) b 
25 65.193 -0.071 
75 47.797 -0.1 
125 36.02 -0.113 
 
 
Figure 38: SAC305 phase growth [Lall 2012] 
 
The coefficients ?f and b evolve with temperature as shown in the table above. 
The fatigue coefficient and the fatigue exponent decrease with increase in temperature. 
The reduction in ?f and b causes a shift in the S-N curves with increase in temperature as 
shown in Figure 40. This change can be attributed to the evolution of microstructure of 
SAC305. Figure 38 shows the evolution of phase structure as seen in SEM within just 
one day of aging at 75C and 125C [Lall 2004a-d, 2005a-b, 2006a-f, 2007a-e, 2008a-f, 2009a-
d, 2010a-j, 2011, 2012]. Based on Arrhenius theory, the relation between the fatigue 
strength coefficient and temperature is assumed to be of the form given by Eq. (33)  
KTE0,fT,f f,Ae ?????  (33) 
 
where ?f,T  is the fatigue strength coefficient at temperature T Kelvin, K is the 
Boltzmann?s constant and Ea, ?f is the activation energy in eV. Taking natural log of 
77 
 
both sides of Eq. (33) and then substituting the slope and intercept values from Figure 39 
a: 
KTElnln f,A0,fT,f ?????  
(34) 
 
T 39.7008352.1ln T,f ???  (35) 
 
Taking antilog: 
T39.700T,f e8352.1 ???  (36) 
 
 
(a) 
y  =  7 0 0 . 3 9 x  +  1 . 8 3 5 2
R ?  =  0 . 9 9 6 9
S l ope  =  E
A, ? f
/K
E
A, ? f
=  7 0 0 . 3 9 * 8 . 6 1 7 e - 5
E
A, ? f 
=  0 . 0 6 e V
3 . 5
3 . 6
3 . 7
3 . 8
3 . 9
4
4 . 1
4 . 2
4 . 3
0 . 0 0 2 0 . 0 0 2 5 0 . 0 0 3 0 . 0 0 3 5l
n
(
F
a
t
i
gu
e
 
c
o
e
ffi
c
i
e
n
t
 
(
M
P
a
)
)
1 / T e m p e r a t u r e  ( K e l v i n
- 1
)
F a t i g u e  S t r e n g t h  C o e ff i c i e n t  v s  T e m p e r a t u r e
F a t i gu e  s t r e ng t h 
coe f f i ci e nt
78 
 
 
(b) 
Figure 39: a)Fatigue coefficient as a function of temperature b)Fatigue exponent as 
a function of temperature 
 
Similarly, considering the magnitude of fatigue coefficient b as a function of 
absolute temperature: 
 
KTE0T b,Aebb ??  (37) 
 
Taking natural logarithm of both the sides,  
KTEblnbln b,A0T ??  (38) 
 
Substituting slope and intercept from Figure 39b: 
?????? ??? T 82.5597447.0bln T  (39) 
 
Taking into account the negative sign of the exponent,  
y  =  5 5 9 . 8 2 x  +  0 . 7 4 4 7
R ?  =  0 . 9 6 6 4
S l ope  =  E
A ,b
/K
E
A ,b
=  5 5 9 . 8 2 * 8 . 6 1 7 e - 5
E
A ,b  
=  0 . 0 4 8 e V
1
1 . 5
2
2 . 5
3
0 . 0 0 2 0 . 0 0 2 5 0 . 0 0 3 0 . 0 0 3 5
|l
n
|F
a
t
i
gu
e
 
e
x
p
o
n
e
n
t
||
1 / T e m p e r a t u r e  ( K e l v i n
- 1
)
F a t i g u e  E x p o n e n t  v s  T e m p e r a t u r e
79 
 
? ?T82.559T e475.0b ????  (40) 
 
Activation energy for the fatigue coefficient is 0.06eV. The activation energy for 
Sn-Pb solder creep found in literature is about 0.5eV for grain boundary creep and 0.84 
eV for matrix creep [Knecht 1990]. To account for the effect of temperature in predicting 
the fatigue life of SAC305, Eq.(36) and Eq.(40) that give the temperature dependence of 
these parameters can be substituted in the Basquin power law relation given by Eq.(32) 
? ? TbfT,fa )N2(????  (41) 
 
Thus the high cycle fatigue life of SAC305 as a function of temperature can be expressed 
in terms of Basquin power relation as follows: 
?????? ?? ???
?
??
?
? ??? T82.559e475.0
fT
39.700
a )N2(e8352.1
 (42) 
where ?a is the stress amplitude in MPa, T  is the test temperature in Kelvin and 2Nf is 
cycles to failure.  
 
 
Figure 40: SAC305 S-N Curves at elevated temperature 
y  =  - 0 . 0 7 1 x + 1 . 8 1 4 2
R?  =  0 . 9 9 7
y  = - 0 . 1 x +1 . 6 7 9 4 0 1
R?  = 0 . 9 6 1 3
y  = - 0 . 1 1 3 x +1 . 5 5 6 5 4
R?  = 0 . 9 6 4 4
1 . 0 0
1 0 . 0 0
1 0 0 . 0 0
1 . 0 E + 0 3 1 . 0 E + 0 4 1 . 0 E + 0 5 1 . 0 E + 0 6 1 . 0 E + 0 7
St
r
e
s
s
 
a
m
p
l
i
t
u
d
e
 
(
M
P
a
)
 
Lo
g
-
Sca
l
e
N u m b e r  o f s t r e s s  r e ve r s a l  cyc l e s  ( Lo g - Sca l e )
S A C 3 0 5  S - N  C u r v es  a t  T em p er a t u r e
S - N  cur v e  a t  2 5 C
S - N  C ur v e  a t  7 5 C
S - N  C ur v e  a t  1 2 5 C
80 
 
 
3.8 Summary and Conclusions 
First natural frequency of the test vehicle has been determined at three 
temperatures: 25C, 75C and 125C. It is observed to reduce linearly with increase in 
temperature. The material properties of the PCB have been investigated by tensile tests 
and DMA at elevated temperatures for FE simulation of global model. The FE based 
natural frequencies are compared with EMA. PCBs are tested to failure by subjecting to 
harmonic vibration, dwelling at the natural frequency for each test temperature. Cycles to 
failure are derived from the experiments for BGAs and TSOPs that fail at the solder. A 
reduction in mean cycles to failure is observed with increase in temperature for each 
component. The global FE model is correlated with the test vehicle using natural 
frequencies, mode shapes and out of plane displacement fields. Global model drives the 
detailed explicit sub-model of the components to output solder Von Mises stresses with 
material property degradation at temperature. Volume averaged solder stresses at high 
stress location of every component is plotted against its experimentally obtained cycles to 
failure. S-N curves for SAC305 are obtained based on Basquin power law relation 
between stress amplitude and stress reversal cycles. S-N curves at 25C, 75C and 125C 
are thus obtained for SAC305. The temperature dependence of the fatigue strength 
coefficient and fatigue exponent have been implemented in the SAC305 S-N curve 
relation using Arrhenius theory. The temperature dependent fatigue coefficient and 
fatigue exponent are implemented in Basquin power relation. This study assumes that the 
effect of change of strain rate due to different temperature dependent test frequency 
(difference of 12Hz) does not have any effect on the fatigue life of the solder.  
81 
 
CHAPTER 4 
EFFECT OF HIGH STRAIN RATE AND AGING ON MATERIAL 
CHARACTERIZATION OF INNOLOT 
 
4.1 Introduction 
With the ROHS initiative on lead-free solder taking effect, the electronics industry has 
been presented with a wide array of lead-free options. Most of the Pb-free alloys in the 
industry today are plagued by aging and creep issues. Prior researchers have shown a 
deterioration of the material properties of SAC alloys with constant temperature aging 
(Lall 2012, Ma 2009, Zhang 2009, Darveaux 2005). New developments in the Pb-free 
options have introduced small proportions of Ni, Zn, Co, Bi, Sb in the SAC alloys to 
increase resistance to aging and creep while maintaining the melting temperature and 
strength of the alloy comparable to SAC. Many researchers have shown enhanced material 
properties, microstructures and resistance to failures in thermal cycling due to the addition 
of rare earth elements in SAC alloys [Zhang 2009, Liu 2007, Wu 2004, Kim 2003, Huang 
2000]. InnoRelTM have introduced a new Pb-free alloy- Innolot, which consists of Ni, Sb 
and Bi in its composition (Table 2). This alloy has a melting range between 206C to 218C. 
Increased creep strength is a result of solid solution hardening and dispersion hardening 
mechanisms achieved by Bi, Sb dissolution in Sn crystal matrix and intermetallic phases 
by Ni. Prior studies have shown that Innolot is more reliable in thermal cycling as 
compared to SAC alloys [Miric 2010].  
82 
 
The effects of aging on the microstructure and material properties of Pb-free alloys have 
been investigated at low strain rates less than 1/s [Chuang 2002, Coyle 2000, Darveaux 
2005, Lee 2002, Pang 2004, Tsui 2002, Zhang 2009]. For high strain rate constitutive 
behavior investigation, researchers have relied on Split Hopkinson Pressure bar tests 
[Chan 2009, Siviour 2005]. The strain rates achievable with this equipment, range from 
500/s to 3000/s. In practice, the typical strain rates observed on second level interconnects 
in consumer electronics drop impacts are within 1/s to 100/s. Neither the Split Hopkinson 
Pressure bars nor conventional pull tester can be easily used to obtain these strain rates. 
Very few researchers have characterized Pb-free solder properties at strain rates of 1/s to 
100/s [Lall 2011, 12, Meier 2009, Wong 2008]. The authors of this paper have explicitly 
demonstrated the capability of an innovative tensile tester to repeatably obtain constant 
strain rates of 10/s, 35/s and 50/s. The effect of strain rate and aging on the material 
properties of SAC105 and SAC305 has been established through this work [Lall 2012]. In 
this paper, the same equipment and aging conditions have been used for two strain rates of 
10/s and 35/s to characterize the constitutive behavior of Innolot. A comparison of the 
effects of strain rate and aging on Innolot and SAC alloys (SAC105 and SAC305) has 
been presented.  
Non-linear Ramberg-Osgood model [Lall 2012, Nguyen 2011, Ohguchi 2006, Chen 2006, 
Muller 2005, Pang 2004, Park 2002, Lee 1997, Knechet 1990] and Anand?s viscoplastic 
model [Mysore 2009, Bhate 2008, Yeo 2006, Pei 2005, Rodgers 2005, Wang 2005, Pand 
2004, Wang 2001, Wilde 2000] are amongst the most popular models to describe solder 
stress-strain behavior. Prior researchers have used finite element analysis for modeling 
tensile tests [Lall 2012, Joun 2007, Niordson 2004, Cabezas 2004, Peng 2004, Koc 2004, 
83 
 
Mirone 2004, Tang 2003, Inal 2002, Komori 2002, Nilsson 2001]. This research, uses 
Ramberg-Osgood model for its relatively simple implementation in Abaqus based FE 
codes. 
In the past, Digital Image Correlation (DIC) has been used for material characterization at 
low strain rate testing of conposites [Gershon 2010, Srinivasan 2005, Grytten 2009] and 
high strain rates for lead-free solder characterization [Lall 2012, 2011, 2010, Tiwari 2005] 
to investigate full-field displacement and strain contours as the test specimen deforms and 
fractures. DIC has been implemented in this work to correlate Ramberg-Osgood FE 
models with the experimental data.  
Table 11: Innolot Composition [Miric et. al. 2010 ] 
Element Min % Max % 
Sn Balance (90.1-91.6) 
Ag 3.6 4.0 
Cu 0.6 0.8 
Ni 0.1 0.2 
Sb 1.3 1.7 
Bi 2.8 3.2 
 
 
 
84 
 
4.2 Test specimen preparation 
The test specimens used for the high strain rate tensile tests are thin rectangular bars 
40mm (length) X 5mm (width) X 0.5mm (thickness). The cross-sectional thickness of 
0.5mm is selected to corresponding to the height of second level solder interconnects 
specifically in BGAs. To prepare the test specimen, small pieces of bulk solder are molten 
in a glass crucible kept in a soldering pot. Rectangular, hollow glass tubes with very high 
dimensional precision are fabricated in advanced glass-shops to form the solder 
specimens. One end of the glass tubes is dipped in the molten solder and a suction 
pressure upto 600mm Hg is applied at the other end. As a result of capillary action and 
suction pressure, the molten solder from the crucible rises in the glass tube. Once the 
solder rises upto the desired level, the control valve of the pump is cut off and the glass-
tube is quenched in water to allow the specimen to solidify [Figure 41]. The specimens in 
the glass tube are reflowed using the profile shown is Figure 44. Thermocouples attached 
to the glass tubes mapped this reflow temperature profile using a radio-frequency KIC 
temperature profiling system. This profile is typical for commercial lead-free solders 
across the industry. Figure 42 and Figure 43 show a typical tensile specimen and its X-ray 
image. X-ray and optical microscopic images of every sample have been taken to ensure 
the absence of voids and premature cracks in the gage length of specimens. After reflow, 
the specimens are stored in isothermal chamber ovens for a desired length of aging time. 
Prior to the test, the glass tube is gently broken using a vice to take out the solder 
specimen. A thin white coat of paint is applied to the solder specimen and a random black 
speckle pattern is created to enable Digital Image Correlation. For pristine cases, tests are 
85 
 
conducted within five hours after reflow to minimize the effects of room temperature 
aging.  
 
Figure 41: Setup for Innolot tensile specimen preparation [Lall et. al. 2012] 
 
 
Figure 42: Innolot tensile specimen 
 
 
Figure 43: X-ray image of specimen 
 
86 
 
 
Figure 44: Reflow profile for specimen preparation [Lall et. al. 2012] 
 
4.3 Test setup 
An innovative tensile tester manufactured in-house has been used to facilitate cross-head 
strain rates in the range of 1/s to 100/s. It incorporates an impact hammer-like action 
where the hammer can have variable mass and drop height to achieve the desired cross-
head strain rate. The specimen is mounted between two cross-heads. The top cross-head is 
rigidly fixed and houses the piezoelectric load sensor. The bottom crosshead is mounted 
on a slip-joint.  
0
50
100
150
200
250
300
0 100 200 300 400
T
e
m
p
e
r
a
t
u
r
e
 (
0
C)
T i m e  ( s e c )
S p e c i m e n  R e fl o w  P r o fi l e
Ai r  i ns i de  r e f l ow  ov e n
O n Gl a s s  T ube
87 
 
 
Figure 45: Implementation of slip joint mechanism to achieve constant cross-
head velocity after impact [Lall, P., Shantaram, S., Suhling, J., Locker, D., 
ECTC, 2012] 
 
The slip joints extends non-linearly due to the impact of the hammer and subsequently 
causes a linear (constant velocity and constant strain rate) extension of the bottom cross-
head. The solder specimen thus experiences a constant strain rate extension. High speed 
cameras capture the specimen deformation upto failure to obtain full field strain contours 
T
0
= 0 s e c  
( A t  r e s t  )
T
1
> T
0
( z e r o s pe c i m e n 
e l ong a t i on up t o 
c om pl e t e  s l i p 
j oi nt  e xt e ns i on)
T
2
> T
1
( s pe c i m e n 
pul l e d  a t  
c ons t a nt  hi gh 
ve l oc i t y)
F or c e  
s e ns or
G a uge  
l e ngt h 
0.040m
F ul l  r od  
e xt e ns i on 
0. 02 54 m
S pe c kl e d  
s ol d e r  j oi nt
88 
 
using DIC. Very high speed oscilloscope records the force data from the load sensor 
during the specimen failure. Figure 45 illustrates the initial configuration of the tester. In 
the second image of Figure 45 the impact hammer has hit the intermediate plate. This 
impact initiates the extension of the slip join as shown. Note that the bottom crosshead is 
still at the initial position and there is no deformation of the specimen. After the complete 
extension of this slip joint of 25.4mm, the bottom cross-head moves downwards pulling 
the solder specimen attached on top of it [Figure 45].  
Figure 46 illustrates the initiation of slip-joint motion due to the impact hammer. Point 1 is 
a point on the fixed reference datum. Point 2 is on the impact hammer that drops and hits 
the intermediate plate labeled ?Contact?. Point 3 is on the base of the slip joint.  
 
Figure 46: Impact mechanism [Lall et. al. 2012] 
To illustrate that constant strain rate is obtained at the slip joint repeatedly, the motion of 
the targets is captured and analyzed for the 35/s case. The plot in Figure 47 is obtained 
P o i n t  1  
( F i x e d )
P o i n t  2  
( I m p a c t  H a m m e r )
P o i n t  3  
( S l i p  J o i n t )
0 . 1 2 0 m
D a t u m
0 . 8 9 m
C o n t a c t
89 
 
using high speed imaging in conjunction with motion tracking software to obtain the 
displacement histories of these target points on the tensile tester. The continuous green 
line plot in Figure 47, corresponds to the relative position of the impact hammer. As 
expected, the initial section of this is parabolic due to the near-free-fall of the impact 
hammer. As the hammer hits the intermediate plate, the motion of the slip-joint below the 
bottom cross-head is initiated. The dotted line denotes the motion of the slip joint. Figure 
48a, shows that though the initial section of slip joint extension was non-linear, the cross-
head displacement, which initiates only after the complete (0.0254m) extension of slip 
joint, is very linear. Figure 48b gives the cross-head strain as a function of time. It can be 
seen that a constant strain rate of 35/s is achieved at the cross-head. For every test, the 
specimen gets pulled at the same desired strain rate. Similar plots and repeatability is 
observed for 10/s strain rate achieved by altering the mass and drop height of impact 
hammer.  
 
Figure 47: Position vs time plots of target points on the tester [Lall et. al. 2012 ] 
 
- 1
- 0 . 8
- 0 . 6
- 0 . 4
- 0 . 2
0
0 0 . 0 5 0 . 1 0 . 1 5 0 . 2 0 . 2 5 0 . 3
P
o
s
it
io
n
 w
rt
 t
o
 P
o
in
t 
1
 (m
)
T i m e  (s e c o n d )
R e l a ti v e  D i s p l a c e m e n t V s  Ti m e  
(S tr a i n  R a te  = 3 5 / s )
P o s i t i o n  o f Im p a c t  h a m m e r 
(P o i n t  2 ) w rt  F i x e d  D a t u m  
(P o i n t  1 )
P o s i t i o n  o f S l i p  J o i n t  (P o i n t  
3 ) w rt  t o  P o i n t  1 (fi x e d  
D a t u m )
I ns t a nce of  
I m pac t  
90 
 
 
(a) 
 
(b) 
Figure 48: Cross-Head: a) Displacement b) Strain [Lall, et. al. 2011] 
 
 
 
 
0
0 . 0 0 1
0 . 0 0 2
0 . 0 0 3
0 . 0 0 4
0 . 0 0 5
0 . 0 0 6
0 . 0 0 7
0 . 0 0 8
0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6
D
o
w
n
w
a
r
d
 
d
i
s
p
l
a
c
e
m
e
n
t
 
(
m
)
T i m e  ( s e c o n d )
C r o s s - H ea d  D o w n w a r d  D i s p l a cem ent
C r os s - H e ad 
D o wnw ar d 
D i s pl ac e m e nt
V e l o c i ty  =  1 . 4 0 8  m / s
0
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
0 . 1
0 . 1 2
0 . 1 4
0 . 1 6
0 . 1 8
0 . 2
0 0 . 0 0 5 0 . 0 1
St
r
a
i
n
T i m e  ( s e c o n d )
C r o s s - H e a d  St r a i n  V s  T i m e
C r o s s - H e ad  
S tr ai n V s  
T i m e
S tr ai n r at e  =  3 5 / s
91 
 
4.4 Test matrix 
Table 12 shows the test matrix. Two strain rates 10/s and 35/s have been used for the 
tensile tests. Along with this isothermal aging at 50C for three durations has been 
employed ? 1day, 30days and 60day. Table 12 illustrates the test cases. All the tests were 
conducted at room temperature which is maintained at 25C. The test temperature and 
strain rates are selected to facilitate comparisons with SAC105 and SAC 305 alloys 
conducted previously by these authors.  
Table 12: Test Matrix for Innolot 
Aging duration at 50C Strain rate 10/s Strain rate 35/s 
1day X X 
 30 days X X 
60 days X X 
Pristine  
(no aging, within 5 hours after 
reflow) 
X X 
 
4.5 Results and Discussion 
4.5.1. High Strain Rate Tensile Testing 
Thin rectangular bars of 40mm (length), 5mm (width), 0.5mm (thickness) are prepared 
from Innolot by the procedure described earlier in this paper. Reflow profile is 
maintained similar to commercial reflow profile used for Pb-free components. Data 
92 
 
measured from multiple samples for every case is averaged to obtain the material 
response under every condition.   
 
 
Figure 49: Stress-strain curves for Pristine Innolot 
 
 
Table 13: Material Properties for Innolot, Pristine 
Strain Rate 
 (per second) 
E  
(GPa) 
UTS  
(MPa) 
10 39.3 73.8 
35 43.5 98 
 
 
0
10
20
30
40
50
60
70
80
90
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 (
MP
a)
S tr a i n
I n n o l o t  C o n s t i t u t i v e  B e h a v i o r  ( P r i s t i n e )
I nno l ot ,  P r i s ti ne  at 
1 0 / s
I nno l ot ,  P r i s ti ne  at 
3 5 / s
93 
 
 
 
Figure 50: Stress-strain curves for Innolot aged at 50C for 1 day 
 
 
 
Table 14: Material Properties for Innolot, 1day aging at 50C 
 
Strain Rate 
 (per second) 
E  
(GPa) 
UTS  
(MPa) 
10 38.4 71.2 
35 42.1 96 
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 
(
MP
a)
S tr a i n
I n n ol ot  C on s t i t u t i v e  B e h a v i or  
( 1 d a y  a g i n g  @  5 0 C )
I nno l ot ,  1 day  at  
5 0 C ,  1 0 / s
I nno l ot ,  1 day  at  
5 0 C ,  3 5 / s
94 
 
 
 
Figure 51: Stress-strain curves for Innolot aged at 50C for 30 days 
 
 
 
Table 15: Material Properties for Innolot, 30 days aging at 50C 
 
Strain Rate 
 (per second) 
E  
(GPa) 
UTS  
(MPa) 
10 36.01 70.4 
35 41.7 93.2 
 
 
 
 
0
20
40
60
80
100
0 0 . 0 5
S
tr
e
s
s
 
(
M
P
a)
S tr a i n
I n n ol ot  C on s t i t u t i v e  B e h a v i or  
( 3 0 d a y s  a g i n g  @  5 0 C )
I nn o l o t,  3 0 da y s  a t 
5 0 C ,  1 0 / s
I nn o l o t,  3 0 da y s  a t 
5 0 C ,  3 5 / s
95 
 
 
 
Figure 52: Stress-strain curves for Innolot aged at 50C for 60 days 
 
 
Table 16: Material Properties for Innolot, 60 days aging at 50C 
Strain Rate 
 (per second) 
E  
(GPa) 
UTS  
(MPa) 
10 35.63 70.02 
35 41 91.7 
 
4.5.2. Effect of 1 day Aging at 50C 
The specimens are prepared and reflowed as discussed previously. After reflow, the 
specimens are aged by storing in an isothermal chamber set at 50C. Randomly selected 
specimens are taken out of the isothermal chamber after 1 day and tested at strain rates of 
10/s and 35/s. Figure 50 shows the stress-strain curves of Innolot aged at 50C for 1 day. It 
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 (
MP
a)
S tr ai n
I n n o l o t  C o n s t i t u t i v e  B e h a v i o r  
( 6 0 d a y s  a g i n g  @  5 0 C )
I nn o l o t,  6 0  da y s  a t 
5 0 C ,  1 0 / s
I nn o l o t,  6 0  da y s  a t 
5 0 C ,  3 5 / s
96 
 
can be seen that the mean elastic modulus and ultimate tensile strength of the specimens 
reduce from pristine values tabulated in Table 13. However, at 10/s, the elastic modulus 
reduces by 0.9GPa and the UTS reduces by 2.6MPa. Likewise at 35/s the elastic modulus 
reduces by 1.4GPa and UTS by 2MPa. The small reductions in both elastic modulus and 
UTS may be attributed to reduced stiffness of the material due to 1 day exposure to 50C. 
Table 19 compares the reduction of elastic modulus due to 1 day aging at 50C in Innolot, 
SAC105 and SAC305. Considering the elastic modulus in the pristine cases as baseline, it 
can be noted that the percent reduction in the elastic modulus of Innolot is 2.29% and 
3.22% for the two strain rates which is much less than SAC305 (11.44% and 13.28%) 
and SAC105 (6.15% and 3.88%) for the same pre-conditions.    
4.5.3. Effect of 30 days Aging at 50C 
Figure 51 shows the stress-strain curve of Innolot after 30 days exposure to isothermal 
aging at 50C. Comparing the properties in Table 15 with the pristine properties in Table 
13 and 1 day aged properties from Table 14, it can be inferred that aging continues to 
degrade the properties of Innolot after 30 days at 50C for both the strain rates. The 
pristine elastic modulus at 10/s is 39.3GPa and reduces to 36.01 GPa while the pristine 
elastic modulus at 35/s is 43.5GPa and reduces to 41.7GPa after 30 days at 50C. The 
pristine UTS at 10/s is 73.8MPa and reduces to 70.4MPa while the pristine UTS at 35/s is 
98MPa and reduces to 93.2MPa after 30 days at 50C. Although there is considerable 
degradation in the material properties of Innolot under these conditions, a comparison 
with SAC alloys shows that the effect of isothermal aging on Innolot is much less 
pronounced. Table 19 shows that the elastic modulus of Innolot reduces by 8.37% and 4.14% at 
the two strain rates after 30 days at 50C. For the same aging, the reduction in elastic modulus of 
SAC105 is 35.4% and 31.94% and for SAC305 is all the way up to 40.3% and 39.41%. Table 20 
97 
 
shows that the UTS of Innolot reduces by 4.6% and 4.9% at the two strain rates after 30days at 
50C. For the same aging, the reduction in UTS of SAC105 is 11.71% and 17.47% and for 
SAC305 is 8.51% and 12.5% 
4.5.4. Effect of 60 days Aging at 50C 
Figure 52 shows the stress-strain curves of Innolot after 60 days of isothermal aging at 
50C. Table 16 lists the elastic modulus and UTS corresponding to the two curves in 
Figure 52. Comparing Table 15 and Table 16, there is only a small reduction in the elastic 
modulus and UTS for both strain rates. This implies that there is not much difference in 
the material properties of Innolot after 30 days of aging at 50C and 60 days of aging at 
50C. Comparing with SAC alloys (Table 19), after 60 days of aging the elastic modulus 
of Innolot reduces by 9.34% and 5.75% for 10/s and 35/s respectively. For the same 
conditions, the elastic modulus of SAC105 reduces by 37.5% and 36.42% and SAC305 
reduces by 43.28% and 41.08%. Table 20 shows that the UTS of Innolot reduces by 
5.12% and 6.43% at the two strain rates after 60 days at 50C. For the same aging, the 
reduction in UTS of SAC105 is 14.99% and 20.39% and for SAC305 is 9.7% and 13.9% 
 
 
 
 
 
98 
 
 
 
 
Figure 53: Influence of aging on stress strain curves of Innolot at 10/s 
 
 
 
Table 17: Aging effects on material properties of Innolot at 10/s 
 
Aging E  (GPa) UTS  (MPa) 
Pristine 39.3 73.8 
30 days at 50C 36.01 70.4 
60 days at 50C 35.63 70.02 
 
 
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 (
MP
a)
S tr ai n
I n n o l o t  C o n s t i t u t i v e  B e h a v i o r  
( E f f e ct  o f  I s o t h e r m a l  a g i n g  a t  1 0 / s )
I nno l ot ,  P r i s ti ne ,  
1 0 / s
I nno l ot ,  3 0  day s  at 
5 0 C ,  1 0 / s
I nno l ot ,  6 0  day s  at 
5 0 C ,  1 0 / s
99 
 
 
 
Figure 54: Influence of aging on stress strain curves of Innolot at 35/s 
 
 
Table 18: Aging effects on material properties of Innolot at 35/s 
Aging E  (GPa) UTS  (MPa) 
Pristine 43.5 98 
30 days at 50C 41.7 93.2 
60 days at 50C 41 91.7 
 
 
 
 
 
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 (
MP
a)
S tr ai n
I n n o l o t  C o n s t i t u t i v e  B e h a v i o r  
( E f f e ct  o f  I s o t h e r m a l  a g i n g  a t  3 5 / s )
I nno l ot ,  P r i s ti ne ,  
3 5 / s
I nno l ot ,  3 0  day s  at 
5 0 C ,  3 5 / s
I nno l ot ,  6 0  day s  at 
5 0 C ,  3 5 / s
100 
 
4.5.5. Effect of strain rate on material properties of Innolot 
Figure 49 through Figure 52 show the response of Innolot for each of the test 
case. Each of these plots contain two stress-strain curves one of which is obtained at a 
constant strain rate of 10/s and the other at a constant strain rate of 35/s. It can be seen 
that at every precondition, the stress-strain curve at 10/s lies below the stress-strain curve 
at 35/s. Correspondingly, the elastic modulus and the UTS have lower values at the lower 
strain rate. Table 13 through Table 16 contain the numerical values of the effective elastic 
modulus and ultimate tensile strength. This response can be attributed to the fact that 
Innolot is a highly strain rate dependent material. The higher the strain rate, the more stiff 
the material behaves thus yielding a higher value of elastic modulus and UTS. 
 
4.5.6. Comparison with SAC alloys 
These authors have previously published data on SAC105 and SAC305 using the same 
test setup, strain rates and aging conditions [Lall 2012]. Figure 55 compares the 
constitutive behavior of the three alloys in all the test cases. It can be seen that while the 
elastic modulus of Innolot is comparable with SAC305, the UTS of Innolot is much 
higher than both SAC105 and SAC305. Table 19 and Table 20 compares the percent 
decrease in the material properties of the three alloys due to aging at the strain rate of 
10/s. The elastic modulus of Innolot reduces by 9.34% where as that of SAC105 and 
SAC305 reduces by 37.5% and 43.28% respectively. Likewise, the UTS of Innolot 
reduces by 5.12% where as that of SAC105 and SAC305 reduces by 14.99% and 9.7% 
respectively.  
101 
 
 
   
Figure 55: Visual comparison of constitutive behavior of Innolot with SAC105 [Lall 
et. al. 2012] and SAC305 [Lall et. al. 2012] 
  
  
  
  
  
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 
(
MP
a
)
S tr ai n
C o mp a r i s o n  o f  C o n s t i t u t i v e  
B e h a v i o r  ( P r i s t i n e ,  1 0 / s )
I nno l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
e
s
s
 
(
MP
a)
S tr ai n
C o mp a r i s o n  o f  C o n s t i t u t i v e  
B e h a v i o r  ( P r i s t i n e ,  3 5 / s )
I nno l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
r
e
s
s
 
(
MP
a
)
S tr ai n
C o m p a r i s o n  o f  C o n s t i t u t i ve  
B e h a vi o r  ( 1 d a y a gi n g a t  5 0 C ,  1 0 / s )
I nn o l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
r
e
s
s
 
(
M
P
a)
S tr ai n
C o mp a r i s o n  o f  C o n s t i t u t i v e  
B e h a v i o r  ( 1 d a y a gi n g a t  5 0 C ,  3 5 / s )
I nn o l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
r
e
s
s
 
(
MP
a)
S tr ai n
C o m p a r i s o n  o f  C o n s t i t u t i v e  B e h a v i o r  
( 3 0  d a ys  a gi n g a t  5 0 C ,  1 0 / s )
I nn o l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
r
e
s
s
 
(
MP
a)
S tr ai n
C m p a r i s o n  o f  C o n s t i t u t i v e  B e h a v i o r  
( 3 0  d a ys  a gi n g a t  5 0 C ,  3 5 / s )
I nn o l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
r
e
s
s
 
(
MP
a)
S tr ai n
C o m p a r i s o n  o f  C o n s t i t u t i v e  B e h a v i o r  
( 6 0  d a ys  a gi n g a t  5 0 C ,  1 0 / s )
I nn o l o t
S A C 3 0 5
S A C 1 0 5
0
20
40
60
80
100
0 0 . 0 5
S
tr
r
e
s
s
 
(
MP
a
)
S tr ai n
C m p a r i s o n  o f  C o n s t i t u t i v e  B e h a v i o r  
( 6 0  d a ys  a gi n g a t  5 0 C ,  3 5 / s )
I nn o l o t
S A C 3 0 5
S A C 1 0 5
102 
 
Table 19: Comparison of Elastic Modulus degradation in Innolot, SAC105 and 
SAC305 due to aging 
Pre-
condition 
% Reduction in elastic modulus with Pristine as baseline 
Innolot E(GPa) SAC105 E(GPa) [Lall et. al. 2012] SAC305 E(GPa) [Lall et. al. 2012] 
10/s 35/s 10/s 35/s 10/s 35/s 
Pristine 0 0 0 0 0 0 
1day at 50C 2.29 3.22 6.15 3.88 11.44 13.28 
30 days at 
50C 8.37 4.14 35.4 31.94 40.3 39.41 
60 days at 
50C 9.34 5.75 37.5 36.42 43.28 41.08 
 
Table 20: Comparison of UTS degradation in Innolot, SAC105 and SAC305 due to 
aging 
Pre-condition 
% Reduction in UTS with Pristine as baseline 
Innolot UTS (MPa) SAC105 UTS (MPa) [Lall et. al. 2012] SAC305 UTS (MPa) [Lall et. al. 2012] 
10/s 35/s 10/s 35/s 10/s 35/s 
Pristine 0 0 0 0 0 0 
1day at 50C 3.52 2.04 4.17 6.02 4.95 4.69 
30 days at 
50C 4.6 4.9 11.71 17.47 8.51 12.5 
60 days at 
50C 5.12 6.43 14.99 20.39 9.70 13.9 
103 
 
Innolot thus exhibits much higher resistance to aging that these SAC alloys. Compared 
with SAC105 and SAC305 alloys, Innolot material properties exhibit a higher strain rate 
dependence. On the other hand, the influence of aging at a given strain rate in Innolot, is 
much less pronounced. The microstructure of a pristine sample of Innolot is shown in  
Figure 56. Although some evolution in the microstructure is observed after 30 days aging 
(Figure 57), between 30 days and 60 days (Figure 58) there is very little change in the 
microstructure. This is in line with the small changes in the elastic modulus and UTS 
values of 30 days aged samples and 60 days aged samples tabulated in Table 19 and 
Table 20. 
 
Figure 56: Innolot, Pristine 
104 
 
 
Figure 57: Innolot, 30 days at 50C 
 
 
Figure 58: Innolot, 60 days at 50C 
 
 
105 
 
Table 19, Table 20compare the percent decrease in the material properties of the three 
alloys due to aging at the strain rate of 10/s. The elastic modulus of Innolot reduces by 
9.34% where as that of SAC105 and SAC305 reduces by 37.5% and 43.28% respectively. 
Likewise, the UTS of Innolot reduces by 5.12% where as that of SAC105 and SAC305 
reduces by 14.99% and 9.7% respectively. Innolot thus exhibits much higher resistance to 
aging that these SAC alloys. 
4.5.7. Ramberg-Osgood Non-linear models for Innolot 
Non-linear relationship between stress-strain curves of solder are often described using 
Ramberg-Osgood model. The model can represent strain hardening effects well, is simple 
to implement in Abaqus based FE codes and the parameters required for the model can be 
estimated easily if the constitutive behavior is available. In this model, the axial strain in a 
tensile sample strain at a stress level is considered to consist of elastic (e) and plastic (p) 
parts given by the equation below: [Ranberg et. al. 1943, Lall et. al. 2012] 
p
n
e E
KE ???????? ?????????????? ???
 
(43) 
 
where ? is the stress along the axial direction, E is the elastic modulus and K and n are the 
shape parameters. To estimate K and n, the following closed form approach can be used. 
Dimensionless variables ? and ? are defined as [Lall et. al. 2012]: 
E
1?
???
 
(44) 
 
106 
 
1?
???
 
(45) 
 
where ?1 is the secant yield strength. Multiplying both sides of equation (43) by (E/ ?1) 
[Lall et. al. 2012] 
???
?
???
? ?
?
??
?
???
?
??
?
?? n
E
EK
E
EE ?
?
?
??? 111  
(46) 
 
Substituting Eq. (44) and Eq. (45) in Eq. (46) [Lall et. al. 2012] 
???
?
???
? ?
?
??
?
??? ?1n
EK
????
 
(47) 
 
Substitute ?1=?, [Lall et. al. 2012] 
???
?
???
? ?
?
??
?
??? ?1nn
EK
????
 
(48) 
 
The abscissa of the secant yield strength for stress strain curve in Figure 59 is given by 
modifying Eq.(43) and substituting ?1=?, [Lall et. al. 2012] 
n
EKEEm ??
??
?
?????
?
???
?
?? 11
1
11 ????
 
(49) 
 
107 
 
where m1E=?1/?1 as shown in Figure 59. Multiply Eq. (49) by E/?1 
 
 
Figure 59: Determination of secant yield strength [Adapted from Lall et. al. 2012 ] 
 
11
1
11 ????????? nEKm ?  (50) 
 
 
Rearranging Eq. (50), [Lall et. al. 2012] 
n
EmmK
??
?????
?? 11
1
11 ?
 
(51) 
 
S l ope  =  E
S l ope  =  m
1
E
S l ope  =  m
2
E
1
?
1
?
2
?
2
?
108 
 
???
?
???
? ?
?
??
?
??? ?11 nn EK ????
 
(52) 
 
???
?
???
? ?
?
??
?
??
?
??
?
???
?
???
?
? ??? ?? 1111
1
11
nnn
EEm
m ?????
 
(53) 
 
nmm ??? ???????? ???
1
11
 
(54) 
 
Related stress-strain curves that may be described by equation (54) have the same value of 
n. Figure 60 shows a family of curves for m1=0.75 and different values of n. The stress 
deviation curve has been obtained by plotting stress against the difference between the 
measured strain and elastic strain according to Hooke?s law. [Lall et. al. 2012] 
 
 
Figure 60: Family of curves for different values of n and m1=0.5 [Adapted from Lall 
et. al. 2012]  
 
0
0 . 4
0 . 8
1 . 2
0 50 100
m = 0 . 5 ,  n= 1
m = 0 . 5 ,  n= 4
m = 0 . 5 ,  n= 8
m = 0 . 5 ,  n= 1 0 0
0  <  n <  i nf i ni t y
?
?
109 
 
nn
EKEEKEEd ?????????????????
?
???
? ?
?
??
?
???
?
??
?
???? ??????
 
(55) 
 
???????? EnKd ?lo glo glo g  (56) 
 
m1 is chosen such that the secant yield strength 1 would approximately be the yield 
strength for 0.002 offset strain. Thus Eq. (55) can be written as: [Lall et. al. 2012] 
EEmE ???? ???????????? 1 1002.0
 (57) 
 
m1 is solved for using this equation: [Lall et. al. 2012] 
1E002.01E002.0m1
2.011
??????  (58) 
 
The shape parameter is derived using the second secant yield strength ?2 corresponding to 
second secant modulus m2E [Lall et. al. 2012] 
n
EKEEm ???????????
???
?
?? 22
2
22 ????
 
(59) 
 
12
2
11 ????????? nEKm ?  (60) 
The equations for K and n gives [Lall et. al. 2012]: 
110 
 
n
EmmK
??
???????
12
2
21 ?
 
(61) 
 
???
?
???
?
???
?
???
?
?
??
??
2
1
10
2
1
1
2
10
lo g
1
1lo g
1
?
?
m
m
m
m
n
 
(62) 
 
shape parameter is derived using the second secant yield strength ?2 corresponding to 
second secant modulus m2E 
Figure 61 shows the Ramberg-Osgood model fit through the experimental data on Innolot 
for the Pristine case. The model fits well through the data for all the cases considered in 
this study. The values of the parameters n and K obtained for each of the cases is tabulated 
below. By using these parameters, the response of solder interconnects can be modeled 
very accurately in component or PCB level drop-shock or vibration simulations using 
commercial FE codes.  
111 
 
 
Figure 61: Ramberg-Osgood model parameters and curve fit 
 
Table 21: Ramberg-Osgood Parameters for Innolot 
Aging 
Strain 
rate 
(/s) 
E 
(GPa) n K 
Pristine 10 39.3 20.54175 6.41265E53 
1day @ 
50C 10 38.4 26.17152 1.21237E+70 
30 days 
@ 50C 10 36.01 33.38179 1.09736E+89 
60 days 
@50C 10 35.63 24.80184 5.11964E+65 
Pristine 35 43.5 22.22059 1.84915E57 
1day @ 
50C 35 42.1 24.47599 1.27544E+63 
30 days 
@ 50C 35 41.7 22.65212 2.8671E+58 
60 days 
@50C 35 41 23.05484 3.56932E+59 
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 (
MP
a)
S tr a i n
I n n o l o t  C o n s t i t u t i v e  B e h a v i o r  ( P r i s t i n e )
In n o l o t  P r i s t i n e @  
1 0 / s
In n o l o t  P r i s t i n e @  
3 5 / s
n =2 0 . 5 4 1 7 5 , 
K =6 .4 1 2 6 5 E 5 3
n =2 2 . 2 2 0 5 9 2 , 
K =1 .8 4 9 1 5 E 5 7
112 
 
 
Another method for obtaining K, n and E is by using a regression fit through the 
experimental data. As a sample case, the regression fit for pristine data at strain rate of 
35/s has been obtained. Non-linear least-square based regression technique called 
Levenberg-Marquardt algorithm has been used for regression. Equation (43) is solved for 
K, n and E such that the error between the actual and regressed value of the response 
variable (i.e. strain) is minimized. The R2 of regression fit is 0.9575 and the sum of 
squared errors is 0.0001404. The values of the three parameters obtained after regression 
are tabulated in Table 22. It can be observed that the closed form 2-point solution method 
given by Equation (61) and Equation (62) predicts the Ramberg-Osgood model 
parameters n, K and E almost as accurately as a regression fit through the entire stress-
strain data. This method also has the advantage of being computationally efficient.  
Table 22: Comparison of Ramberg-Osgood parameters obtained using regression fit 
and closed form 2-point solution methods (Pristine, 35/s) 
Parameter 
Regression 
R2=0.9575 
rmse = 0.01185 
2-point solution 
R2=0.8814 
rmse = 13.3516 
E (Pa) 43e+9 43.5e+9 
n 22.31 22.22059 
K 1.8e57 1.84915E+57 
 
113 
 
 
Figure 62: Regression fit through strain-stress data of pristine Innolot at 35/s 
 
4.5.8. Digital Image Correlation 
Digital image correlation (DIC) is an optical method to measure full-field deformation and 
the derivatives of deformation on the surface of a loaded structure. For 2D DIC analysis of 
the specimens, a thin layer of white pain is coated on the surface of the specimen. Random 
black speckle pattern is created on the white background. As the specimen deforms due to 
loading, the geometric positions of the speckles change with respect to the initial position 
when the specimen is un-deformed.  High speed cameras capture the deformation of the 
specimen to failure at about 80000 frames per second. The motion of every speckle in all 
the frames is tracked using sum of squared difference correlation. This gives the full field 
displacement contour. Gradients of the displacement contour are calculated to obtain the 
full field strains. In this study, Digital image correlation has been used to correlate the FE 
model of the tensile specimen with Ramberg-Osgood material model. A representative 
114 
 
case of this correlation is presented here. DIC analysis has been conducted for a Pristine 
specimen tested at 35/s. From the red curve in Figure 61, plastic deformation corresponds 
to strains exceeding 1.97e-3. Since the strain rate is constant, this should occur after 
(1.97e-3/35)s i.e after 0.00005629s, the strain should be 1.97e-3. Likewise UTS occurs at 
strain = 0.003 which would occur in 0.008571s. This is demonstrated in Figure 63.     
 
Figure 63: DIC analysis of Innolot, Pristine case at 35/s 
 
4.5.9. FE model for tensile specimen 
A FE model of the tensile specimen is shown in Figure 63. This model uses 3D solid 8-
noded continuum elements (C3D8I). Displacement BC corresponding to a strain rate of 
115 
 
35/s is applied in the negative y direction at the bottom end of the specimen. The top end 
is fully constrained. The Ramberg-Osgood material model derived for this case is 
implemented for simulation in Abaqus. The stress-strain response of this model correlates 
well with the experimental behavior. This is demonstrated in  
Figure 64 and  
Figure 65. Strain time histories of the model are close to the expected strain time histories 
given the constant strain rate of 35/s used for the tensile test. The full field strain contours 
also correlate with DIC to a good extent. 
 
Figure 64: Stress-strain response of a point at the center on FE model of tensile 
specimen 
0
20
40
60
80
100
0 0 . 0 2 0 . 0 4 0 . 0 6
S
tr
e
s
s
 (
MP
a)
S tr ai n
I n n o l o t  C o n s t i t u t i v e  B e h a v i o r  ( P r i s t i n e )
In n o l o t  P r i s t i n e  
@  3 5 / s
n =2 2 .2 2 0 5 9 2 , 
K = 1 .8 4 9 1 5 E 5 7
F E _ M o d e l
116 
 
 
Figure 65: FE model of tensile specimen 
117 
 
 
Figure 66: Strain contours of tensile specimen at time steps of 0s, 1.75e-4s, 2.875e-4s 
and 8.5714e-4s 
 
4.6 Summary and Conclusions 
Stress-strain curves for Innolot were experimentally obtained for strain rates of 10/s and 
35/s. Effect of isothermal aging on the material properties of Innolot was studied by aging 
specimens at 50C for three durations of 1day, 30days and 60days. The constitutive 
118 
 
behavior of Innolot and material property degradation due to aging was compared with 
SAC105 and SAC305 data collected previously by these authors. While Innolot is more 
strain rate dependent than the two SAC alloys, it is much better at resisting material 
property degradation due to aging. There is very little degradation in the material 
properties and the microstructure of Innolot as it ages from 30 days to 60 days at 50C. 
Ramberg-Osgood model is used to fit the experimental data. A two point closed form 
solution method to predict the Ramberg-Osgood parameters, is compared with regression 
fit. The three parameters required for implementing this model have been derived for all 
the test cases. FE simulation of the tensile test correlates well with the tensile test in terms 
of the specimen stress-strain response. The full field strain contours occurring at various 
points in time match well with the experimentally obtained contours using Digital Image 
Correlation.
119 
 
CHAPTER 6 
SUMMARY, CONCLUSIONS AND FUTURE SCOPE 
 
 The initial part of this study is to develop a methodology for creating a model for 
high cycle fatigue life reliability of Pb-free solders subjected to the combined 
environment of high temperature and vibration has been proposed. A combination of 
experimental and numeric techniques have been employed for creating this model. The 
simultaneous harsh environment of high temperature and vibration is observed to have 
wide application for automotive electronics. To simulate this environment in the lab, the 
existing shaker system was updated by coupling it with an isothermal chamber, so that 
the PCB under test would simultaneously experience elevated temperature and vibration 
levels. Following is a brief discussion of the underlying assumptions. 
This model fits the failure data on the test vehicle under consideration to a good 
extent. The model assumes that the high cycle fatigue failures in SAC305 occur due to 
repeated loading less than the elastic limit. The Basquin power law relating the stress 
amplitude level to fatigue life in terms of stress reversal cycles to failure is assumed to 
hold true. It is assumed that the S-N relations hold true even at elevated temperatures 
lest with evolved fatigue strength coefficients and fatigue exponents. Further, the 
evolution of these two parameters with temperature is considered to be governed by the 
adaptated form of Arrhenius equation used to predict the influence of steady state 
temperature on electronic device reliability. In this study, a test vehicle representative of 
120 
 
an engine control unit containing SAC305 components has been tested to failure 
subjecting it to its first natural frequency. The first natural frequency is chosen to 
accelerate the lab tests. However, it was observed that there is a significant shift in the 
first natural frequency with increase in the temperature. Therefore the PCB is subjected 
to slightly different frequencies depending on the selected test temperature. It is 
assumed that within this range of frequencies (~15Hz) the solder high cycle fatigue life 
remains constant. First natural frequency of the test vehicle has been determined at three 
temperatures: 25C, 75C and 125C. It is observed to reduce linearly with increase in 
temperature. The test vehicles are tested to failure by subjecting to harmonic vibration, 
dwelling at the natural frequency for each test temperature. Cycles to failure are derived 
from the experiments for BGAs and TSOPs that fail at the solder. A reduction in mean 
cycles to failure is observed with increase in temperature for each component. Tensile 
tests, DMA and DSC analyses are conducted to determine the actual material properties 
of the PCB experimentally. These have been used as inputs to the PCB in the global 
model. Smeared properties for components are calculated for components in the global 
model. The global FE model is then correlated with the test vehicle using natural 
frequencies, mode shapes and out of plane displacement fields. Global model drives the 
detailed explicit sub-model of the components to output solder Von Mises stresses with 
material property degradation at temperature. Volume averaged solder stresses at high 
stress location of every component is plotted against its experimentally obtained cycles 
to failure. Curve-fitting based on Basquin power law relation between stress amplitude 
and stress reversal cycles yields the S-N curve at that temperature. S-N curves at 25C, 
75C and 125C are thus obtained for SAC305. The temperature dependence of the 
121 
 
fatigue strength coefficient and fatigue exponent have been implemented in the SAC305 
S-N curve relation. It can be observed that for the same stress level, this model predicts 
lesser cycles to failure at higher test temperatures. 
In the later part of this research work, a newly developed solder alloy called 
Innolot, targeting the automotive industry is characterized to obtain its uniaxial tensile 
stress-strain characteristic  stress-strain curves at high strain rates and elevated 
temperature aging. Stress strain curves for Innolot were experimentally obtained for 
strain rates of 10/s and 35/s. Effect of isothermal aging on the material properties of 
Innolot was studied by aging specimens at 50C for three durations of 1day, 30days and 
60days. The constitutive behavior of Innolot and material property degradation due to 
aging was compared with SAC105 and SAC305 data collected previously by these 
authors. While Innolot is more strain rate dependent than the two SAC alloys, it is much 
better at resisting material property degradation due to aging. There is very little 
degradation in the material properties and the microstructure of Innolot as it ages from 30 
days to 60 days at 50C. Ramberg-Osgood model is used to fit the experimental data. A 
two point closed form solution method to predict the Ramberg-Osgood parameters, is 
compared with regression fit. The three parameters required for implementing this model 
have been derived for all the test cases. FE simulation of the tensile test correlates well 
with the tensile test in terms of the specimen stress-strain response. The full field strain 
contours occurring at various points in time match well with the experimentally obtained 
contours using Digital Image Correlation. 
In the future, the high cycle fatigue model for SAC305 needs to be tested and 
improvised if needed for a larger dataset preferably conforming to Weibull failure 
122 
 
distribution. Similar predictive models can be created for other solder alloys. In the high 
strain rate material characterization,  Innolot needs to be tested under additional strain 
rates in the range of 1-100 per second. The effect of additional aging temperatures and 
duration on the material properties of Innolot can also be studied.  
 
 
123 
 
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