Reliability Assessment of Electronics Under Drop-Impact Using Cohesive Zone and 
XFEM Models 
 
by 
 
Mandar Nilkanth Kulkarni 
 
 
 
 
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 
August 6, 2011 
 
 
 
 
Keywords: XFEM, cohesive, line spring, drop, shock, SIF, reliability, Pb-free, solder, 
Electronic Packaging 
 
 
 
 
Approved by 
 
Pradeep Lall, Chair, Thomas Walter Professor of Mechanical Engineering 
 George T. Flowers, Professor of Mechanical Engineering 
Barton C. Prorok, Associate Professor of Materials Engineering 
 
 ii
Abstract 
 
 
The evolution of complexity in the handheld portable electronics accompanied 
with the miniaturization due to advancement in technology has contributed to their 
vulnerability under shock and drop conditions. Drop reliability of electronics has been 
addressed using various experimental and analytical techniques. Material characterization 
of Pb-free alloys at high strain rates typical of drop and shock is performed using these 
techniques. These transient dynamic phenomenons are addressed using advanced finite 
element methods such as extended finite element method, cohesive zone modeling and 
line spring element method to model crack/flaw initiation and propagation. The transient 
dynamic behavior of leadfree and leaded solder-interconnects have been studied in ball-
grid array, copper-reinforced solder column and high lead column package architectures. 
Four interconnect types have been modeled using XFEM including Sn3Ag0.5Cu, 
90Pb10Sn, Cu-Reinforced column, and 63Sn37Pb interconnects on ceramic ball-grid 
arrays. In addition, Sn3Ag0.5Cu on plastic ball-grid arrays has also been modeled. 
Extended finite element models have been correlated with cohesive-zone models along 
with experimental results. The board assemblies have been tested at 1,500g and 12,500g.  
The failed assemblies have been cross-sectioned and the failure modes correlated with 
model predictions.  The predicted failure modes for all four interconnect types correlate 
well with the observed locations for failure. In an initial part of this thesis, damage and 
 iii
life prediction of transient dynamics in electronics interconnects is presented using 
XFEM in conjunction with digital image correlation and explicit submodeling. 
The second part of this thesis deals with measurement of fracture properties of 
Pb-free alloys at high strain rate conditions using FE modeling techniques. For this 
purpose, bimaterial and single material copper-solder specimens are tested using uniaxial 
tensile testing machine. Models for crack/flaw initiation and propagation are developed 
using Line spring method and extended finite element method (XFEM). Critical stress 
intensity factor for leadfree alloys such as Sn3Ag0.5Cu and Sn1Ag0.5Cu are extracted 
from line spring models. Stress intensity factor at Copper pad and bulk solder interface is 
also evaluated in ball grid array packages. Specimens are tested at various strain rates and 
events are monitored using high speed data acquisition system as well as high speed 
cameras operating more than 50,000 fps. In this work, fracture properties such as SIF and 
J integral are measured using simulation techniques and correlated with experimental 
results. The solder deformation and damage thresholds at the copper-solder interface have 
been measured at strain-rates representative of shock and vibration. These high strain rate 
properties of solder alloys are used to define the material models in all finite element 
simulations which run based on a technique of node based sub-modeling.  
 iv
Acknowledgments 
 
 
 I would like to express my deep gratitude to my research advisor Dr. 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 (CAVE
3
) as a 
Graduate Research Assistant at Auburn University. I would also like to thank my other 
committee members, Dr. George T. Flowers and Dr. Barton C. Prorok, for their support 
and guidance while completing this thesis. 
I would like to thank my parents, Mr. Nilkanth M. Kulkarni and Mrs. Smita N. 
Kulkarni, as well as my elder brother Manoj and sister in law Pallavi, for having faith in 
me and providing endearing love, encouragement and moral support. I would also like to 
thank all my friends and colleagues for their priceless friendship and support. 
 
 v
Table of Contents 
 
 
Abstract ............................................................................................................................... ii 
Acknowledgments ............................................................................................................. iv 
List of Figures ................................................................................................................... vii 
List of Tables ................................................................................................................... xiv 
1 Introduction   .....................................................................................................................1 
 1.1 Electronic Packaging .........................................................................................1 
 1.2 Reliability Under Shock and Vibration..............................................................4 
            1.3 Finite Element Modeling of a Shock Phenomenon ...........................................5 
            1.4 Thesis Layout ...................................................................................................16 
2 Literature Review   ..........................................................................................................19 
            2.1 Shock Testing of Electronics ...........................................................................19 
            2.2 Digital Image Correlation (DIC) ......................................................................21 
            2.3 Finite Element Modeling for Transient Dynamic Loadings ............................22 
            2.4 Solder and Intermetallic Properties ..................................................................23 
3 Fracture Analysis using Finite Element Methods ...........................................................25 
 3.1 Extended Finite Element Method (XFEM) ......................................................25 
 3.2 Cohesive Zone Method ....................................................................................29 
 3.3 Line Spring Method .........................................................................................40
 vi
4 XFEM and CZM Based Shock-Reliability Models for Leadfree and Advanced 
Interconnects ...................................................................................................................44 
 
             4.1 Introduction  ....................................................................................................44 
              4.2 Test Vehicle  ..................................................................................................45 
              4.3 Experimental Set Up ......................................................................................52 
              4.4 Digital Image Correlation ..............................................................................57 
              4.5 Model Developement .....................................................................................59 
              4.6 Correlation of Model Predictions with Experimental Data  ..........................79 
 
5 SIF Evaluation using XFEM and Line Spring models under high strain rate 
environment for leadfree alloys ......................................................................................91 
 
              5.1 Introduction  ...................................................................................................91 
              5.2 Specimen Fabrication.....................................................................................93 
              5.3 High Speed Uniaxial Tensile Testing ............................................................98 
              5.4 Fracture Analysis of Bimaterial Specimen ..................................................100 
              5.5 Model Validation .........................................................................................113 
              5.6 Experimental SIF determination ..................................................................123 
              5.7 Use of Line Spring FE Models for BGA under Mechanical Shock ............126 
 
6 Summary and Future Work  ..........................................................................................142 
              6.1 Reliability Models for Pb-free alloys and Advanced Interconnects ............142 
              6.2 Scope for Future Work .................................................................................143 
Bibliography ....................................................................................................................145 
 
 vii
List of Figures 
 
 
Figure 1: I/O count increasing with respect to time resulting in enhanced system 
performance [Dally 2008 Page #12] ....................................................................................3 
Figure 2: Electronic packaging Hierarchy [Lau 1995 Page #2] ..........................................4 
Figure 3: Typical Linear Traction Separation behavior with failure mechanism ..............10 
Figure 4: General form of naming convention for cohesive element ................................12 
Figure 5: Thickness direction for three-dimensional cohesive elements.  .........................13 
Figure 6: Element near a crack tip showing state of stress ................................................14 
Figure 7: Crack in infinite plate subjected to a remote tensile stress .................................15 
Figure 8: Typical drop test apparatus and mounting scheme for PCB assembly ..............20 
Figure 9: Multiple Cohesive Segments in enrichment domain [Remmers 2008]  .............26 
Figure 10: Phantom nodes across a discontinuity in the structure. [Song 2006, Abaqus 
2009b]  ...............................................................................................................................27 
Figure 11: Four types of cohesive zone laws (a)  Polynomial (b) Piece-wise Linear (c) 
Exponential (d) Rigid Linear .............................................................................................33 
Figure 12: Quasi linear cohesive zone model in pure tension and pure shear [Falk 2001] 37 
Figure 13: Linear Traction-Separation response for cohesive elements ............................39 
Figure 14: Line spring element LS6 node numbering .......................................................41 
Figure 15: Configuration A Test Board (Ceramic Packages)  ...........................................46 
Figure 16: Interconnect array configuration for Test Board A, 400 I/O CBGA/CCGA ...47
 viii
Figure 17: Configuration B Test Board (Plastic Package)  ................................................48 
Figure 18: Interconnect array configuration for Test Board B, 324 I/O PBGA ................49 
Figure 19: Configuration C Test Board (Plastic Package)  ................................................50 
Figure 20: Interconnect array configuration for Test Board C, 100 I/O CABGA .............51 
Figure 21: Lansmont Drop Tower Model23 ......................................................................53 
Figure 22: Schematic of drop tower with high speed cameras for DIC .............................54 
Figure 23: Calibration images captured at different orientations.  ....................................55 
Figure 24: Acceleration for Test Boards ............................................................................56 
Figure 25: 3D-Digital Image Correlation Measurements in Printed Circuit Assembly ....57 
Figure 26: Speckle Coated Printed Circuit Board on Drop Tower and Bimaterial Copper-
Solder specimen during uniaxial tensile test.  ....................................................................59 
Figure 27: Explicit Global Model (Test Board ?A)  ..........................................................60 
Figure 28: Package nomenclature and Output locations for Explicit Global models at 
given orientation (Test Board-A)  ......................................................................................61 
Figure 29: Submodel created for PBGA 324 Sn3Ag0.5Cu of Configuration B test vehicle . 
............................................................................................................................................62 
Figure 30: Submodel created for CCGA solder column of Configuration A test vehicle .62 
Figure 31: Submodel created for CBGA Sn3Ag0.5Cu of Configuration A test vehicle ...63 
Figure 32: Submodel created for CBGA (Hi-Pb) of Configuration A test vehicle ...........63 
Figure 33: Submodel created for CBGA (63?Sn37Pb) of Configuration A test vehicle ...64 
Figure 34: Cut Section view of FE model for 90Pb10Sn Solder Joint on CBGA 
interconnect ........................................................................................................................65 
Figure 35: FE model for 90Pb10Sn Solder Joint on CBGA interconnect .........................66 
 ix
Figure 36: Cut Section view of FE model for Cu-Reinforced Solder Column on CCGA 
interconnect ........................................................................................................................67 
Figure 37: FE model for Cu-Reinforced Solder Column on CCGA interconnect .............68 
Figure 38: FE model for Sn3Ag0.5Cu Interconnect on CBGA interconnect ....................69 
Figure 39: FE model for Sn3Ag0.5Cu Interconnect on PBGA324 ...................................70 
Figure 40: Schematic of methodology in implementing XFEM for Drop event of PCB ..72 
Figure 41: Crack Initiation and Propagation in CCGA column solder joints at different 
time intervals after the occurrence of impact using XFEM ...............................................74 
Figure 42: Crack Initiation and Propagation in CBGA Sn3Ag0.5Cu solder joints at 
different time intervals after the occurrence of impact using XFEM ................................75 
Figure 43: Crack Initiation and Propagation in CBGA Eutectic Tin lead solder joints at 
different time intervals after the occurrence of impact using XFEM ................................76 
Figure 44: Crack Initiation and Propagation in CBGA Hi-Pb solder joints at different 
time intervals after the occurrence of impact using XFEM ...............................................77 
Figure 45: Crack Initiation and Propagation in PBGA Sn3Ag0.5Cu solder joints at 
different time intervals after the occurrence of impact using XFEM.  ..............................78 
Figure 46: Crack Initiation and Propagation in Test Board A CBGA Eutectic Tin lead 
solder joints at different time intervals after the occurrence of impact using Cohesive 
Zone Modeling ...................................................................................................................79 
Figure 47: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Left Top) ................................................................................80 
Figure 48: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Right Top) ..............................................................................81 
 x
Figure 49: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Left Bottom) ..........................................................................81 
Figure 50: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 ..................................................................................................82 
Figure 51: Strain Correlation between FE and DIC for 90Pb10Sn Solder Interconnect 
CBGA at U3 (Left Top) .....................................................................................................82 
Figure 52: Strain Correlation between FE and DIC for 90Pb10Sn Solder Interconnect 
CBGA at U3 (Right Top) ...................................................................................................83 
Figure 53: Strain Correlation between FE and DIC for 90Pb10Sn Solder Interconnect 
CBGA at U3 (Left Bottom) ...............................................................................................83 
Figure 54: Strain Correlation between FE and DIC for 90Pb10Sn Solder Interconnect 
CBGA at U3  ......................................................................................................................84 
Figure 55: Transient strain contour correlation on PCB between DIC with high-speed 
imaging and FE analysis at 2.5ms......................................................................................85 
Figure 56: Transient strain contour correlation on PCB between DIC with high-speed 
imaging and FE analysis at 6ms.........................................................................................86 
Figure 57: Transient strain contour correlation on PCB between DIC with high-speed 
imaging and FE analysis at 9ms.........................................................................................87 
Figure 58: Transient strain contour correlation on PCB between DIC with high-speed 
imaging and FE analysis at 12ms.......................................................................................88 
Figure 59: Bimaterial Cu-solder specimen preparation set-up with control valve of 
vacuum pump .....................................................................................................................93 
Figure 60: X-ray image of Bimaterial Copper Solder specimen for Sn3Ag0.5Cu ............94 
 xi
Figure 61: Schematic of Single Notched Bimaterial Specimen Geometry ........................94 
Figure 62: Schematic of Double Notched Bimaterial Specimen Geometry ......................94 
Figure 63: Schematic of typical Cu-Solder Interface in solder interconnect showing crack 
prone region .......................................................................................................................95 
Figure 64: Schematic of recording of cooling profile for bimaterial copper-solder 
specimen ............................................................................................................................97 
Figure 65: Comparison of recorded air cooling profile with industry recommended reflow 
cooling profile ....................................................................................................................98 
Figure 66: Schematic of uniaxial high strain rate tensile machine ....................................99 
Figure 67: Linear (a) and Quadratic (b) MPCs used in XFEM and Line Spring models 
respectively ......................................................................................................................102 
Figure 68: Line Spring model and XFEM Methodology for Bimaterial specimen tensile 
testing ...............................................................................................................................103 
Figure 69: FE models of Single Notch Bimaterial specimens with MPCs ......................105 
Figure 70: FE models of Double Notch Bimaterial specimens with MPCs ....................106 
Figure 71: Stress-Strain curve plotted for Sn1Ag0.5Cu for strain rates of 20s-1 and 55s-1 
[Lall 2011]  ......................................................................................................................107 
Figure 72: Stress-Strain curve plotted for Sn3Ag0.5Cu for strain rates of 20s-1 and 55s-1 
[Lall 2011]  ......................................................................................................................108 
Figure 73: Schematic of simulation elastic-plastic material model developed for 
Sn1Ag0.5Cu and Sn3Ag0.5Cu ........................................................................................109 
Figure 74: Crack Initiation and propagation in Bimaterial Cu-solder specimen of 
Sn3Ag.0.5Cu under 20 /sec strain rate.............................................................................110 
 xii
Figure 75: Critical SIF for Sn3Ag0.5Cu measured from line spring model with input from 
XFEM model under 20 per sec strain rate .......................................................................111 
Figure 76: SIF comparison for single notched bimaterial specimen of Sn3Ag0.1Cu and 
Sn1Ag0.5Cu .....................................................................................................................112 
Figure 77: SIF comparison for double notched bimaterial specimen of Sn3Ag0.5Cu and 
Sn1Ag0.5Cu .....................................................................................................................113 
Figure 78: Optical Microscopic image of solder region of bimaterial Sn3Ag0.5Cu 
specimen showing IMC at interface ................................................................................114 
Figure 79: Crack Initiation and propagation in bimaterial Cu-solder specimen of 
Sn3Ag0.5Cu under strain rate of 20 per sec captured using ultra high speed imaging at 
320,754 frames per second.  ............................................................................................116 
Figure 80: Transient strain contour correlation on Single notched Sn3Ag0.5Cu specimen 
between DIC with high speed imaging and FE at 0.00?s ................................................117 
Figure 81: Transient strain contour correlation on Single notched Sn3Ag0.5Cu specimen 
between DIC with high speed imaging and FE at 14.3?s ................................................118 
Figure 82: Transient strain contour correlation on Single notched Sn3Ag0.5Cu specimen 
between DIC with high speed imaging and FE at 24.0?s ................................................119 
Figure 83: Transient strain contour correlation on Single notched Sn3Ag0.5Cu specimen 
between DIC with high speed imaging and FE at 29.01?s ..............................................120 
Figure 84: Strain correlation at Point P1 between DIC and XFEM simulation...............121 
Figure 85: Strain correlation at Point P2 between DIC and XFEM simulation...............122 
Figure 86: State of stress in polar coordinates from crack tip .........................................124 
Figure 87: Displacement V plots at points near crack tip ................................................125 
 xiii
Figure 88: Correlation of opening mode stress intensity factor between line spring model 
and experimentally measured ..........................................................................................126 
Figure 89: Methodology implemented for defining boundary conditions to FE Models 128 
Figure 90: High speed camera snapshots of PCB showing full field strain distribution 
when dropped at high g loading .......................................................................................129 
Figure 91: Maximum principle stress distribution in PBGA324 interconnect with 
Sn1Ag0.5Cu alloy dropped at 12,500 g ...........................................................................130 
Figure 92: Flowchart of the procedures followed to evaluate fracture properties of most 
critical region in solder joints of BGA under mechanical shock .....................................132 
Figure 93: Second order FE model for PBGA324 with line spring elements .................133 
Figure 94: Cut section view of FE model for PBGA324 showing solder interconnects as 
B31 beam elements ..........................................................................................................134 
Figure 95: Section view of a critical interconnect showing location of line spring LS6 
elements in Line Spring model ........................................................................................135 
Figure 96: Zoomed-In view of interface showing LS6 line spring and other element types . 
..........................................................................................................................................136 
Figure 97: Maximum principle stress contours at critical solder location at different time 
interval after the impact ...................................................................................................138 
Figure 98: Stress intensity factor in 
? ?mmmmN /
 in contours in line spring elements at 
different time intervals after the impact at critical failure location .................................139 
Figure 99: SIF variation for PBGA234 package with Sn1Ag0.5Cu alloy .......................140 
Figure 100: J integral contours in line spring elements at different time intervals after the 
impact at critical failure location .....................................................................................141 
 xiv
List of Tables 
 
Table 1: Configuration A Package Architecture (Ceramic Packages) ...............................45 
Table 2: Configuration B Package Architecture (Plastic Package) ...................................51 
Table 3: Correlation of Model Predictions with Failure Modes from Experiment ............90 
Table 4: Element types used for FE models created for copper-solder bimaterial 
specimens .........................................................................................................................104 
Table 5: Statistical correlation matrix of strain vectors extracted at point P1 near crack 
initiation location .............................................................................................................121 
Table 6: Statistical correlation matrix of strain vectors extracted at point P2 away from 
crack .................................................................................................................................122 
Table 7: Package Architecture for PBGA324 ..................................................................127 
 1
CHAPTER 1 ?
 
INTRODUCTION 
 
1.1 Electronic Packaging 
Packaging of electronic systems refers to the placement and connection of many 
electronic and electro-mechanical components in an enclosure which protects the system 
from the environment and provides easy access for routine maintenance. It is an inter-
disciplinary field of study which begins at the first level where a chip is housed in its 
carrier and then extends to higher levels. To carry out the desired tasks with electronic 
systems, various mechanical aspects such as shock and vibration, thermo-mechanical 
deformation, reliability, cost, manufacturing, performance, thermal management, 
maintenance, connections, and ergonomics needs to be addressed. Analytical, 
experimental and numerical methods are used to assess the reliability of these electronic 
systems which are exposed to harsh environments such as shock, drop, and thermal 
loadings [Dally 2008].  
There are two main types of packaging techniques: through-hole technology and 
surface mount technology. Through-hole technology is no longer used because of its 
bulkiness. The electronic industry is trying to develop smaller chips with more dense 
circuits that require increasing amount of power. Semiconductor technology has been 
generally following Moore?s law. This law predicts the rate of scaling of the minimum 
 2
feature size on a semiconductor chip. With a smaller feature size, more devices and more 
functions can be fabricated on a specific chip for each succeeding generation of 
semiconductor. With this advancement there are several challenges faced by the 
packaging industry. Human scale peripheral devices must be able to handle numerous 
numbers of external input/output connections. Reduction in cross section of circuit lines 
increases the line resistance degrading the signal.  It increases the amount of heat that 
must be dissipated. More advanced I/O techniques such as flip chip solder balls need to 
be used, which increases overall packaging cost. To deal with these issues, electronic 
industry has come up with surface mount technology. Figure 1 shows the schematic, 
depicting the evolution of electronic packaging chip carriers over the years. 
 3
10000
2000
1000
400
300
200
100
?64 ?70 ?75 ?80 ?85 ?90 ?95 ?2000 ?2005
SCIM
Singlechip
5000
CSP
BGA
LLCC (320)
TBA (280)
PGA-50 Mil Grid
TBA (169) 
QFP 
PLCC (84) 
SLIM
CMOS Multichip
(100MM)
BiPolar1800 (90MM)
880 (64MM)
Multi Chip
361 (50MM)
(35MM)
196
D
I
P
 (
64)
 
MC
-
P
G
A
SO
P
 (
40)
D
u
a
l
 I
n
lin
e
M
S
T
 (
18)
To
 S
L
T
SLIM: Single Level Integrated Module
SCIM: Single Chip Integrated Module
Year 
N
u
m
b
e
r
 
o
f
 Pi
n
s
 Pe
r
 
Mo
d
u
l
e
 
 
Figure 1: I/O count increasing with respect to time resulting in enhanced system 
performance [Dally 2008 Page #12] 
There are various levels of hierarchy in the packaging of electronic systems as 
shown in Figure 2. A chip housed in a chip carrier comes under 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. 
 4
Wafer
Chip
First level package
(Multichip module)
Second level package
(PCB or card)
Third level package
(Motherboard)
First level package
(Single chip module)
 
Figure 2: Electronic packaging Hierarchy [Lau 1995 Page #2] 
 
1.2 Reliability Under Shock and Vibration 
Electronic systems may be subjected to shock environments during three times in 
its life cycle [Dally 2008].  
1. During manufacturing and assembly when the product is being transferred from 
one manufacturing station to another station 
2. Incorrect handling of an electronic system through the distribution chain until the 
installation location. 
3. Shock and vibration environment encountered during service of product. 
Abusive handlings of electronic devices are detrimental because very high 
accelerations will deform or may fracture the device. Use of a shock proof box will 
 5
limit the acceleration (g-levels) and transient forces (g-loads) transmitted through the 
box to the product. But for hostile conditions of operation such as military 
applications and modern handheld consumer electronics, products are exposed to 
severe vibrations and shocks on repeated occasions and for longer periods of time. 
Therefore, a design approach in such applications to construct stiff structures which 
sustain dynamic loadings is specified.  
During product development of microelectronic systems after completion of a 
prototype of a system, the product is subjected to controlled qualification testing 
where it is exposed to a specified shock and/or vibration environment. Failure modes 
investigated include solder joint failure due to fatigue, pin breakage in connectors, 
cable chafing and shear of bolts and pins due to shock loads. Thus, design of portable, 
military, automobile electronic hardware with demanding shock and/or vibration 
requirement is a challenging problem. 
During shock, transient input results in application of time dependent velocity to 
the body supporting electronic device. Shock is defined as a transient condition where 
a single impulse of energy is transformed to a system in a short period of time with 
large acceleration. 
 
1.3 Finite Element Modeling of a Shock Phenomenon 
Finite element modeling approach can be used to understand the dynamic 
phenomenon of electronic systems. It is an effective tool which is computationally 
efficient and its accuracy can be verified with data obtained from actual drop tests. 
 6
Various modeling approaches have been pursued previously to address these issues, 
including [Dally 2008]: 
1. Equivalent layer models to represent the solder joints and simulate their 
behavior under drop impact. 
2. Solid-to-solid sub-modeling techniques to analyze BGA reliability for 
drop impact using half the PCB board. 
3. Shell-to-solid sub-modeling using a beam-shell-based quarter symmetry 
model to reduce the computational time. 
4. Symmetry of load and boundary conditions used to obtain computational 
efficiency and decrease the model size. 
Transient dynamic deformation of PCBs is a wave propagation problem and 
hence an explicit time integration scheme can be implemented to simulate the drop 
phenomenon. The governing equation for a dynamic system can be expressed as: 
??? ? ??? ? ? ? ? ?
n
ext
n
int
nn
RRDCDM ???
???
     (1.1) 
For a linear problem, ? ? ? ?? ?
nn
int
DKR ? , where ? ?M , ? ?C  and ??K  are the mass, 
damping and stiffness matrices, respectively, and ? ?
n
D  is the nodal displacement 
vector as each time step. Methods of explicit direct integration calculate the dynamic 
response at the time step (n+1) from the equation of motion, the central difference 
formulation and known conditions at one or more preceding time steps as shown 
below: 
?? ???? ???? ??
1n
2
n
2
n
int
n
ext
1n
2
DC
t2
1
M
t
1
DM
t
2
RRDC
t2
1
M
t
1
??
?
?
?
?
?
?
?
?
?
?
?
???
?
?
?
?
?
?
?
?
?
 
          (1.2) 
 7
Equation (1.1) is combined with equation (1.2) at time step n. In the implicit method, 
the dynamic response at time step (n+1) has been calculated from known conditions 
at present time step, in addition to one or more preceding time-steps. 
 Element size in the explicit model is limited due to the conditional stability of the 
explicit time integration. Explicit time integration is well suited for propagation 
problems that occur in the impact events, because dynamic response of the board 
decays within a few multiples of its longest period. It is also better suited to 
accommodate material and geometric nonlinearity without any global matrix 
manipulation. Reduced integration elements are employed in modeling of printed 
circuit board assemblies, because they require fewer integration points to form 
element stiffness matrices. 
 The following crack/flaw analysis techniques can be used to analyze 
discontinuities in finite element approach [Abaqus 2009a,b,c]: 
(a) Extended Finite Element Method 
(b) Cohesive Zone Modeling 
(c) Line Spring Method 
XFEM is an extension of the conventional finite element method based on the 
concept of partition of unity. It allows presence of discontinuities in finite element by 
adding degrees of freedom with special displacement functions. It does not require the 
mesh to match the geometry of crack. Material and geometric nonlinear modeling is 
possible with XFEM analysis. XFEM can be used with the surface based cohesive 
behavior approach or the virtual crack closure technique, which are best suited for 
modeling interfacial delamination.  
 8
Enrichment definition *ENRICHMENT is associated with the possible region of 
failure in the model. Only degrees of freedom in elements within these regions are 
potentially enriched with special functions. The region should consist of elements which 
are presently intersected with crack or which are likely to be intersected by crack when 
crack propagates. Cohesive segment and phantom node based XFEM approach in FE tool 
simulates crack initiation and propagation. It simulates the crack nucleation and 
propagation along arbitrary solution dependent path in the bulk material, since the crack 
propagation is not tied to the element boundaries in a mesh. The formulae and laws that 
govern the crack propagation analysis using XFEM technique are very similar to those 
used for cohesive elements with traction separation behavior. For the linear elastic 
traction separation model, damage initiation criteria and damage evolution laws are 
defined. 
In Abaqus, the traction separation law assumes initially linear elastic behavior 
followed by the initiation and evolution of the damage. Elastic constitutive matrix is 
written for elastic behavior that relates the normal and shear stresses to normal and shear 
separations of a cracked element. 
If, 
t   Nominal traction stress vector 
n
t   Normal component of traction 
s
t  and  
t
t  Two shear components of traction 
n
?   Normal component of separation 
s
?  and  
t
?  Two shear components of separation 
The elastic behavior can be written as 
 9
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
Kt
K00
0K0
00K
t
t
t
t
t
t
s
n
tt
ss
nn
t
s
n
 
nn
K , 
ss
K  and 
tt
K  are calculated based on material properties of enriched 
elements.  
Damage modeling allows the simulation of the degradation and eventual failure of 
an enriched element. The failure mechanism consists of two ingredients, namely damage 
initiation criterion and damage evolution law. However, once a damage initiation 
criterion is met, damage can occur according to a user-defined damage evolution law. 
Figure 3 shows a typical linear traction separation response with failure mechanism.  
 10
 
T
max
?
max
Crack Opening ?
n
C
o
h
e
s
i
ve
 T
r
ac
ti
on
 T
n
 
Figure 3: Typical Linear Traction Separation behavior with failure mechanism 
 
Only first order solid continuum stress/displacement elements can be associated 
with the *ENRICHMENT definition. In the case of propagating cracks, these elements 
include bilinear plane strain and plane stress elements, linear brick elements, and linear 
tetrahedron elements. 
In case of cohesive zone modeling, cohesive elements can be used to model the 
behavior of adhesive interface, interfaces in composites and other cases where integrity 
and strength are of importance. Cohesive zone modeling involves the following steps for 
model building [Abaqus 2009a]: 
1. Choosing appropriate element type for a cohesive element set 
 11
2. Including these cohesive elements in the FE model and understanding 
typical modeling issues that arise 
3. Defining the initial geometry of cohesive elements 
4. Defining the mechanical properties and constitutive behavior of the 
cohesive elements 
The constitutive response of cohesive elements requires knowledge of the specific 
application and involves certain assumptions about the deformation and stress state that is 
applicable to this specific application. In abaqus, the available constitutive responses 
include: 
? A continuum description of the material (Continuum based constitutive 
model) 
? A traction separation description of the interface (Constitutive model 
specified directly in terms of traction versus separation) 
? A uniaxial stress state (Uniaxial stress based constitutive model useful in 
modeling gaskets and/or single adhesive patches) 
In the case of macroscopic material properties, the amount of energy released to create a 
new surface is used for fracture analysis. Based on the traction separation law, cohesive 
elements model the initial loading, initiation of damage, and the propagation of damage 
leading to eventual failure at the bonded interface. Prior to the initiation of damage, 
interface behavior is described as linear elastic. Cohesive elements are modeled in areas 
where the cracks are expected to develop. The model need not have any crack to begin 
with, because as a part of solution model locates precise location where crack initiates. 
Cohesive zone analysis can be carried out for two dimensional, three dimensional and 
 12
axisymmetric cases. Figure 4 shows the generalized form of naming convention for 
cohesive element. 
COH 3D 8 P
Pore 
Pressure
Number of 
Nodes
Two Dimensional (2D), Three 
Dimensional (3D), 
Axisymmetric (AX)
Cohesive 
Element
 
Figure 4: General form of naming convention for cohesive element 
 To define initial geometry of the cohesive elements, following aspects are taken 
into consideration: 
1. The nodal connectivity of elements and position of these nodes. 
2. Stack direction which identifies the top and bottom faces of cohesive elements 
independent of the nodal connectivity. 
3. The magnitude of the initial constitutive thickness which corresponds to the 
geometric thickness implied by the position of nodes and stack direction or be 
specified directly. 
 13
Element thickness direction is important because element behavior is different in the 
thickness and the in-plane direction. Default thickness direction of cohesive elements is 
as shown in Figure 5.  
Thickness
Direction
5
1
6
2
7
3
8
4
n
Top Face
Bottom Face
z
x
y
 
Thickness
Direction
4
1
5
2
6
3
Top Face
Bottom Face
z
x
y
 
Figure 5: Thickness direction for three-dimensional cohesive elements. 
 Using line spring models, fracture properties such as stress intensity factor and J 
integral are determined. Figure 6 shows an element near the tip of a crack in an elastic 
 14
material. Each stress component is proportional to a single constant K
I
. Entire stress 
distribution of the crack tip can be evaluated using equation given below if this single 
constant K
I
 in known. This constant is called as stress intensity factor which completely 
characterizes the crack-tip conditions in a material. If one assumes that the material fails 
locally at some critical combination of stress and strain, then it follows that fracture must 
occur at critical stress intensity K
IC
. Therefore K
IC
 is an alternate measure of toughness 
which is s size independent material property [Anderson 2005].  
?
x
y
r
?
xx
?
xy
?
yy
 
Figure 6: Element near a crack tip showing state of stress 
 
 15
2a
?
 
Figure 7: Crack in infinite plate subjected to a remote tensile stress 
For plate as shows in Figure 7, Stress intensity factor is given by, 
aK
I
???          (1.3) 
And stress field near the crack tip is, 
?
?
?
?
?
?
?
?
?
?
?
? ?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
??
2
3
sin
2
sin1
2
cos
r2
K
I
xx
     (1.4) 
?
?
?
?
?
?
?
?
?
?
?
? ?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
??
2
3
sin
2
sin1
2
cos
r2
K
I
yy
     (1.5) 
?
?
?
?
?
? ?
?
?
?
?
?
??
?
?
?
?
?
??
?
??
2
3
sin
2
sin
2
cos
r2
K
I
xy
      (1.6) 
 16
 Failure occurs when K
I
=K
IC
. In this case, K
I
 is the driving force for fracture and 
K
IC
 is a measure of material resistance. 
 
1.4 Thesis Layout 
 Chapter 1 starts with an introduction to electronic packaging stating important 
functions of packaging in microelectronic systems. Different types of packaging 
technologies are discussed with evolution from DIP to multi chip modules and grid arrays 
over the period of time.  Shock and drop related issues are described which are addressed 
during entire product life cycle. Finite element techniques for global models and various 
advanced fracture analysis techniques for submodels are explained. 
Chapter 2 encompasses literature survey on experimental and analytical methods 
which include FE methods used to simulate issues involved in drop and shock. Use of 
digital image correlation for various applications of full field strain measurements is 
discussed in this chapter. An overview of crack propagation models in FE such as 
extended finite element models, cohesive zone models has been provided. Theory and 
application of these methods in various other fields is explained. This chapter will give a 
better understanding of modeling recipes of PCB assemblies used for better 
computational output. IMC compound properties are very critical considering solder joint 
reliability. Past literature is discussed where fracture analysis of intermetallics is 
addressed using various test methods. 
 During the failure analysis and reliability assessment of electronic components, 
the thesis will enable (a) modeling of leadfree and advanced interconnects using sub-
modeling and global modeling approach (b) identification of exact crack location in the 
 17
enrichment domain (c) evaluation of stress intensity factor and J integral at critical 
location of failure. Several leadfree alloys will be investigated including SnAgCu alloys.  
Chapter 3 describes various crack and flaw initiation and propagation techniques 
used in this work for analysis of discontinuities in solder alloys during material 
characterization and actual drop conditions. These techniques include the extended finite 
element method, cohesive zone modeling and line spring method. XFEM have 
advantages over other fracture analysis methods including cohesive zone method as it 
models a crack in arbitrary solution dependent path and predicts the failure location. Line 
spring method introduces a local solution dominated by singularity at the crack tip which 
is predicted by XFEM. 
Chapter 4 addresses issues of drop/shock reliability of advanced and learfree 
electronics using these crack propagation techniques. Three test vehicles and 
experimental set up of shock tower is explained in this section. Nonlinear explicit and 
implicit models are created for global drop analysis and substructure drop analysis of 
printed circuit board assemblies. Analytical FE approach is validated with actual 
experimental testing and failure analysis. Sectioning, polishing and microscopic analysis 
of interconnects show good correlation with predicted failure locations. 
 Chapter 5 explains the SIF and J integral measurement procedure using line 
spring technique. Material characterization at strain rates representative of shock and 
drop of electronics is carried out using tensile testing of solder alloys. Section describes 
the detailed procedure of bimaterial copper-solder specimen fabrication with single and 
double notch at interface. Simulation and experimental results of these tests at two 
 18
different strain rates at 20 /sec and 55 /sec are presented. Findings of this study from 
analytical FE method show good correlation with experimental output. 
 19
CHAPTER 2 ?
 
LITERATURE REVIEW 
 
Considering mechanical aspects of electronic systems, the integrity of solder 
joints remains most important for ensuring quality of the product. A perfect joint is the 
one showing complete wetting of solder to pad and this is a universal requirement that 
applies to surface mount as well as through-hole components. Acceptable solder joint 
criterions are suggested for a perfect interconnect [Woodgate 1987]. In the pursuit of 
device shrinkage and circuit miniaturization, surface mount technology in itself has vastly 
evolved over the last couple of decades. 
2.1 Shock Testing for Electronics 
 Solder interconnects in handheld electronics are prone to accidental drops. 
Therefore, mechanical analysis of the devices is essential to improve their reliability 
against impact loadings. Standards established by JEDEC are most frequently used drop 
testing standards. The JEDEC standard JESD22-B111 specifies that the test vehicle 
should be mounted with the package side facing downwards to create a more critical 
loading condition [Yeh 2004]. JEDEC drop test is considered as a common ground for an 
assortment of semiconductor component manufacturers to compare the solder joint 
reliability under impact. This standard has been widely accepted and used by researchers 
to compare their reliability results. It also states that the drop orientation should be 
 20
horizontal or at zero degrees during the drop test. Figure 8 shows the schematic of drop 
test of a printed circuit assembly as per JEDEC JESD-B111. Product level drop tests are 
conducted on cell phones and other consumer electronics to show that angle of impact is 
a critical parameter in reliability of product [Liu 2005], [Seah 2002], [Lall 2006b]. 
 
Figure 8: Typical drop test apparatus and mounting scheme for PCB assembly 
(Source: Board Level Drop Test Method of Components for Handheld Electronic 
Products JESD22-B111)
 21
2.2 Digital Image Correlation (DIC) 
 In this thesis, area-array plastic and ceramic packages assembled with JEDEC 
form-factor printed circuit boards have been subjected to various g-loadings. Transient 
dynamic deformation of the board assemblies has been measured with strain gages in 
addition to optical measurements using high-speed cameras in conjunction with digital 
image correlation. DIC has been previously used to calculate full field displacement and 
deformation gradient in electronics [Lall 2007c, 2008b-d, 2009, Miller 2007, Park 
2007a,b, 2008]. High speed imaging has been used in the measurement of impact speed, 
force, deformation due to shock and thermal loading. Application of high speed 
photography includes quantitative evaluation of in-plane deformation characteristics of 
geo-materials [Watanabe 2005] and assessment of local failure of bone by implementing 
mechanical compression testing of bone samples in medical fields [Thurner 2005]. 
The application of digital speckle correlation in reliability of microelectronic 
packages and determination of mechanical properties of polyurethane foam plastics has 
been studied [Lu 1998, Zhang 1999]. Other optical methods used for optical 
measurement in electronic include speckle photography [Smith 1993], Moir? 
Interferometry [Ho 1997, Wang 2002], holographic [Petrov 1996] and speckle 
interferometry [Cote 2001]. 
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]. Digital image correlation also been used in printed circuit assemblies 
of mobile devices [Lall 2007, Miller 2007, Park 2007a], material characterization [Jin 
2007, Park 2007b, Thompson 2007], stresses and strain in flip-chip die under thermal 
 22
loading [Kehoe 2006], stresses in solder interconnects of BGA packages under thermal 
loading [Zhou 2001, Yogel 2001, Zhang 2004a, Zhang 2005, Sun 2006]. In this 
technique, displacement field quantities are obtained by tracking a geometric point before 
and after deformation [Zhou 2001, Amodio 2003, Srinivasan 2005, Kehoe 2006, Lall 
2007c, 2008c,d]. 
 
2.3 Finite Element Modeling for Transient Dynamic Loadings 
 In this work, the transient dynamic behavior of leadfree and leaded solder-
interconnects has been studied in ball-grid array and copper-reinforced solder column 
package architectures using advanced FE techniques such as extended finite element 
method (XFEM) and cohesive zone modeling (CZM) for ceramic and plastic packages. 
Previous researchers have used various modeling methods to simulate shock and 
vibration including smeared property models [Lall 2004, 2005], Timoshenko beam 
models with conventional and continuum shell [Lall 2006a,b, 2007a-e, 2008a-d], global-
local submodels [Tee 2003, Wong 2003, Zhu 2003, 2004], Implicit transient analysis 
with Input-G Method [Luan 2004]. [Yeh 2004] used an implicit solver by translating the 
input acceleration pulse into effective support excitation load on the test vehicle. 
Cohesive zone models are previously investigated to study failure at IMC layer [Lall 
2007f, 2009]. 
Previously, the authors have developed explicit finite element models, cohesive-
zone models, and global-local models for prediction of transient dynamics and life 
prediction of electronics [Lall 2004, 2005, 2006a-c, 2007a-e, 2008a-d]. Previous 
researchers have applied XFEM in various other fields such as concrete, composite 
 23
materials [Unger 2007, Hettich 2008]. XFEM technique has been previously used in 
various other applications including shock and detonation loaded thin walled structures 
[Cirak 2007], thin films and nanotubes [Oswald 2009]. Delamination of composites and 
brittle fracture in polycrystalline microstructures are studied using this enrichment 
approach of XFEM [Sun 2009, Sukumar 2003]. The use of XFEM to predict leadfree 
interconnect survivability in electronics subjected to dynamic environments is new. Finite 
element simulations of bimaterial copper-solder specimens under tensile testing 
conditions fetch fracture properties such as SIF, J integral suing line spring method.  
2.4 Solder and Intermetallic Properties 
Previously constitutive behavior of solder alloys has been studied under range of 
strain rates by use of Split Hopkinson Pressure Bar test and Double lap shear test. [Nie 
2008, Ong 2004]. Leadfree stress strain curves have been plotted at low to intermediate 
strain rates using nano-indentation tests where elastic modulus and yield stress is measure 
from hardness [Xu 2008]. Intermetallic compounds of Cu
6
Sn
5
 and Cu
3
Sn are commonly 
found at the interface of copper pad and solder in case of interconnects. These 
intermetallics affect the solder joint fatigue life and therefore the reliability of the system 
[Lall 2010
a
, Limaye 2008]. The viscoplastic constitutive behavior of Pb-free alloy versus 
leaded alloy has been studied where thin layer solder joint is constructed between two 
copper pads on thermo-mechanical-microscale test system. Intermetallic compound 
characterization is carried out at low strain loading conditions [Zhang 2004]. 
Sn3.8Ag0.7Cu solder has been tested using tensile test and shear test at low strain loading 
to study formation of needle rod like Ag
3
Sn intermetallics and complex intermetallic 
compound of (CuAuNi)
6
Sn
5
. Nickel and gold coating was provided as surface finish on 
 24
copper pads of FR4 test specimen. It was shown that mechanical properties of tensile and 
shear tests are highly strain rate dependent [Pang 2003]. Sn-Ag leadfree alloy system 
with pure copper wires is shear tested on MTS 858 MiniBionix microtester to investigate 
interfacial intermetallic compound. It was shown that fracture initiates and propagates 
within the Cu
6
Sn
5
 layer [Lee 2003]. Very minute size of these IMC layers in BGAs 
makes characterization of these compounds difficult. 
Fracture analysis of IMC compound has been addressed using FE methods. [Alam 
2008]. Fracture resistance of leadfree alloys has been studied at high strain rate 
conditions [Suha 2007]. [Lau 2002] studied crack propagation analysis of WLCSPs under 
thermal cycling condition. However, the use of line spring method to characterize Pb-free 
solder alloys for drop/shock environment is new. Mode I fracture analysis of Sn-Pb has 
previously been carried out to determine stress intensity factor using standard ASTM 
methods [Pratt 1994]. Cyclic dependent behavior of both Sn-Pb and leadfree materials 
has been investigated in servo-hydraulic fatigue testing machine in accord with ASTM 
standard test methods [Zhao 2003]. 
 
 25
CHAPTER 3 ?
 
FRACTURE ANALYSIS USING FINITE ELEMENT METHODS 
 
3.1 Extended Finite Element Method (XFEM) 
The extended finite element method was originally introduced by Belytschko and 
Black for solving the problems involving crack growth with minimum re-meshing 
[Belytschko 1999]. The method is implemented by addition of a discontinuous 
enrichment function to the standard approximation function using partition of unity. In 
classical finite element method crack tip singularity needs to be defined accurately by 
approximation function and discretization along the crack needs to conform the path of 
element edges. Remeshing of mesh topology which is done at each step affects the 
quality of the results and is computationally inefficient in FEM [Abdelaziz 2008]. XFEM 
allows the crack to propagate along an arbitrary solution dependent path with no 
requirement for remeshing of the mesh topology [Abaqus2009b]. The near-tip asymptotic 
singularity is not needed, and only the displacement jump across a cracked element is 
considered. For solder interconnects in portable electronics which are subjected to shock 
and impact conditions, additional degrees of freedom are provided to the nodes in the 
entire bulk corner solder because the corner interconnects are most vulnerable to failure 
under drop conditions [Lall 2009]. The Cohesive Segment method proposed by Remmers 
[2008] in conjunction with phantom nodes [Song 2006] has been used to address time 
 26
dependent dynamic fracture in the solder interconnects under a drop and shock 
environment. The method uses cohesive constitutive relationship to govern the debonding 
process enabling nucleation and growth of crack. Instead of embedding the crack tip in 
the bulk solder this method allows introduction of new cohesive segment when critical 
cohesive traction is reached. Cracks are introduced as jumps in the displacement fields. 
The magnitude of this jump is governed by the Cohesive Traction Separation Constitutive 
law. For domain with m discontinuities
dj
? , with each divided into 
?
?
j
 and 
?
?
j
 
[Remmers 2008] (Figure 9), 
m....2,1j
jj
???????
??
 
?
?
2
t
?
1,d
?
1,d
n
?
u
?
?
1
2,d
?
2,d
n
?
t
u
?
 
Figure 9: Multiple Cohesive Segments in enrichment domain [Remmers 2008] 
 27
 
Figure 10: Phantom nodes across a discontinuity in the structure. [Song 2006, 
Abaqus 2009b] 
Phantom nodes are superposed on the original real nodes to represent the 
discontinuity of the cracked elements. In an uncracked element, each phantom node is 
completely constrained to the corresponding real node. When the crack splits the element 
into two parts, each part is formed by a combination of some real and phantom nodes 
depending on the orientation of the crack. Each phantom node and its corresponding real 
node are no longer tied together and can move independantly (Figure 10) [Song 2006, 
Abaqus 2009b]. Displacement in the real domain is interpolated by using the degrees of 
freedom for the nodes in the phantom domain. The jump in the displacement field is 
accommodated by integrating over the area from the real nodes up to the crack. The 
displacement field (Equation (3.1)), strain (Equation (3.2)) and acceleration (Equation 
(3.3)) at material point are given by [Belytschko 1999; Daux 2000, Remmers 2008] 
???? ????t,xu
~
xHt,xu?t,xu
j
m
1j
dj?
?
?
??      (3.1) 
?? ?? ?? ??t,xu?xHt,xu?t,x
j
s
m
1j
dj
s
?????
?
?
?
,x
dj
??
    (3.2) 
 28
???? ????t,xu
~
xHt,xu?t,xu
j
m
1j
dj
????
??
?
?
?
??       (3.) 
?
?
?
?
?
??
??
?
?
?
?
j
j
dj
x
x
if
if
H
H
H          (3.4) 
where H is a jump function (heavyside, symmetric or unit symmetric), ? u
~
? is continuous 
displacement field for ?m? additional possible discontinuities. This displacement field 
corresponds to the enrichment nodes in enrichment domain. ?? ? ?t,xu
~
ht,xv
jj
?  is 
magnitude of jump in displacement 
??
?? HHh         (3.5) 
Thus the finite element form of the approximation field with cohesive segment approach 
is [Remmers 2008]: 
j
m
1j
dj
NbHNau
?
?
?
??       (3.6) 
where ?a? are the regular nodal degrees of freedom, and ?
j
b ? are the additional degrees of 
freedom associated with the discontinuity 
dj
? . The matrix N contains conventional finite 
element shape functions. Discretized acceleration is found by differentiating the 
differentiating the discretized displacement field: 
j
m
1j
dj
bNHaNu
??
????
?
?
?
??       (3.7) 
When the stress in the element reaches the critical value, the crack nucleates and crossing 
the integration point extends into neighboring element. Maximum principal stress 
criterion is used to represent damage initiation. Damage is said to initiate when the 
maximum principal stress ratio shown in expression below reaches unity. 
 29
?
?
?
?
?
?
?
?
?
0
max
max
f        (3.8) 
Crack travels until it reaches the boundaries of elements. High stresses occurred 
in the bulk material does not get reduced as soon as the crack is initiated. So in dynamic 
conditions such as drop and shock, stress in the vicinity of the crack is locally increased 
for small period of time and depending on the toughness of the solder material these 
stresses slowly fade away. 
 
3.2 Cohesive Zone Models 
 Electronic products may encounter damage during shock and vibration at various 
interfaces including solder ball and copper pad. Damage progression is accompanied by 
crack initiation and propagation. Modern day portable electronic products are subjected 
to shock loads during handling and operation. Miniaturization of electronic components 
increases their vulnerability to shocks and vibration. Thus, transient dynamics of their 
solder joints are difficult to capture in Impact loading. This leads to the requirement of 
Numerical prediction of failure and crack propagation through solder interconnects. In 
this chapter, cohesive zone based models for prediction of crack initiation and 
propagation are discussed. Cohesive zone models have been previously applied to various 
other applications involving concrete and cement based materials, glassy polymer, steels 
and so on [Elices 2002]. Crack path propagation and delamination are simulated in these 
applications. In electronics industry this methodology has been used to determine 
reliability of solder interconnects subjected to thermal loadings due to temperature 
fluctuations [Abdul-Baqi 2005]. 
 30
 Let A and B be the points on the opposite faces of an interface. Nominal traction 
field T  has both normal and tangential directional components. Consider u, t and b be 
three orthogonal directions. 
n
u  denotes the separation displacement in normal direction 
and 
t
u  and 
b
u  represent opening distances in two tangential directions. When object 
undergoes normal loading, the 
n
u  produced will be positive with increasing interfacial 
separation while negative with decreasing separation. The opening displacement at the 
interface be
AB
? , therefore at each point on the interface [Needleman 1987] 
ABn
.nu ??  
ABt
.tu ??  
ABb
.bu ??    (3.9) 
And corresponding nominal traction field in u,t and b direction is given by 
T.nT
n
?   T.tT
t
?  T.bT
b
?    (3.10) 
Therefore, displacement and traction vector be 
?
?
?
?
?
?
?
?
?
?
?
b
t
n
T
T
T
T   
?
?
?
?
?
?
?
?
?
?
?
b
t
n
u
u
u
u      (3.1) 
Constitutive relationship between traction and opening displacement field is 
described by potential function ?. 
?
?????
u
0
bbttnnbtn
]duTduTduT[)u,u,u(     (3.12) 
As normal loading is applied during impact loading, the magnitude of normal traction 
goes high. Fracture strength of the ductile solder material goes on increasing with 
increase in the strain rate but that of Inter-metallic compound decreases as strain rate goes 
high [Lall 2007]. When the traction force reaches its maximum value, the interface 
separation occurs as the material loses its stiffness completely and ultimately falls to zero 
 31
causing complete interfacial separation. Relative shearing across interface leads to the 
development of shear traction, but the dependence of the shear traction on opening 
displacements in u and b directions is taken as linear. Expression for specific potential 
function is obtained as: 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
????
2
nn
2
b
2
nn
2
t
2
nn
2
n
maxbtn
uu
21
u
2
1
uu
21
u
2
1
u
2
1u
3
4
1
u
2
1
4
27
)u,u,u(   (3.13) 
Here, 
max
?  is maximum traction at interface due to normal loading only. Opening 
displacements in b and t direction are assumed to be zero. ?  is characteristic length 
corresponding to maximum displacement of 
n
u  and ? specifies the ratio of shear to 
normal stiffness of the interface. The traction forces at the interface for ??
n
u , 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
???
1
uu
1
uuuu
21
u
4
27
T
n
2
b
n
2
t
2
nnn
maxn
 (3.14) 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
????
2
nnt
maxt
uu
21
u
4
27
T     (3.15) 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
??
?
?
?
?
?
?
????
2
nnb
maxb
uu
21
u
4
27
T     (3.16) 
And when the characteristic length at interface exceeds opening displacement
n
u , all 
traction forces go to zero. 
 32
0T
n
?  
0T
t
?         (3.17) 
0T
b
?  
Cohesive zone methodology can be used as a leading indicator of failure and in order 
to study crack propagation. To define the behavior of material and the crack formation at 
the failure location, four different types of cohesive laws can be used as shown in Figure 
11 [van den Bosch 2006]. 
a) Polynomial Cohesive Zone Law 
b) Piece-wise linear Cohesive Zone Law 
c) Exponential Cohesive Zone Law 
d) Rigid-linear Cohesive Zone Law 
These laws govern the constitutive relation of traction and characteristic opening 
length in both normal and tangential direction. ?
n
 and ?
t 
are opening displacements and 
n
T  and 
t
T  are traction forces in normal and tangential directions respectively.
 33
 
Figure 11: Four types of cohesive zone laws (a)  Polynomial (b) Piece-wise Linear (c) 
Exponential (d) Rigid Linear
 34
 ?n and ?t are the characteristic openings created when the normal and tangential 
tractions reaches maximum values of 
max,n
T  and 
max,t
T . Characteristic behavior of 
materials can be coupled or uncoupled depending on the relationship between normal 
traction and tangential opening displacement or tangential traction and normal opening 
displacement. For uncoupled cohesive law, normal traction force 
n
T  is independent of 
tangential displacement ?
t 
and the tangential traction force, 
t
T  does not depend on 
normal displacement, ?
n
 in the direction of applied impact loading. In case of coupled 
cohesive zone law, both displacement openings are controlled by both traction forces. 
The areas under tractions versus corresponding opening displacement curves physically 
represent separation work ?n and ?t [van den Bosch 2006]. 
 In uncoupled cohesive law, the failure is dominated by either normal loading or 
tangential loading. During drop event with JEDEC orientation, failure of the solder 
interconnect occurs mainly due to the normal loading caused by the shock wave. Normal 
traction T
n
 mainly produces the normal opening displacement ?
n.
 Debonding of the 
surfaces occurs thus due to Uncoupled cohesive zone law. 
For polynomial cohesive law, the partial coupling between normal and tangential 
direction is produced either by use of effective opening displacement and/or some 
coupling parameter (?). The general expression of effective opening parameter is given 
by 
2
t
t
2
n
n
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??       (3.18) 
And the tractions in normal and tangential directions are having general form, 
 35
???
?
?
? fTT
n
n
max,nn
 ?? ???
?
?
???
?
?
? fTfTT
t
t
max,n
t
t
max,tt
 (3.19) 
Here ? varies from 0
?
1. When traction exceeds its maximum value, ? becomes 
greater than 1. The piecewise linear cohesive zone law as shown in Figure 11 ((b) uses 
the coupling parameter ? to relate the traction forces. The curve of traction versus 
opening displacement shows the trapezoidal shape with middle flat region. In bilinear 
curve middle region is not present as proposed by [Geubelle 1998]. 
q and r  are the two parameters which control the exponential cohesive law proposed by 
Xu and Needleman. Normal and tangential tractions are functions of both normal and 
tangential opening displacements. 
),(TT
tnnn
???        (3.20) 
And in the same way, 
),(TT
tntt
???        (3.21) 
And  
n
t
q
?
?
?         (3.2) 
The expressions for both tractions are given as: 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
n
n
2
t
2
t
2
t
2
t
n
n
n
n
n
n
n
rexp1
1r
q1
expexpT  (3.23) 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
2
t
2
t
n
n
n
n
t
t
t
n
t
expexp
1r
qr
q2T    (3.24) 
[Falk 2001], [Rahulkumar 2000] and [Yuan 2003] have assumed the coupling 
parameter ? as unity, while [Araki 2005],[ Benzeggagh 1996],[ Dollhofer 2000],[ Pang 
1995],[ Warrior 2003],[ Yang 2001] have shown experimentally that potential energy 
 36
functions for normal and tangential directions are not equal. Several other authors have 
altered and extended the initial exponential cohesive law by Xu and Needleman. 
 37
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
max
?
n
T
?
n
?
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
t
?
max
?
t
T
?
 
Figure 12: Quasi linear cohesive zone model in pure tension and pure shear [Falk 
2001] 
 38
Bilinear cohesive zone law is shown in the above Figure 12 with linear increase 
followed by linear decrease in the traction. The dashed line shows the unloading and 
loading paths of traction. The model proposed by Xu and Needleman generates healing of 
the fracture surface during unloading.  
In this thesis, the results from XFEM have been benchmarked against cohesive zone 
models to study the predicted crack propagation path. Cohesive elements have been 
embedded at the solder ball and copper pad interface at the component side. The 
constitutive behavior of the cohesive elements is characterized by the traction-separation 
law which accounts for the amount of the energy required to create new surface or an 
interfacial crack. The CZM model simulates the initial loading, damage initiation, 
damage propagation of the crack at the layer between solder ball and copper pad leading 
to eventual failure. Progression of the stiffness degradation variable to unity causes 
failure of interconnects. The cohesive elements have been modeled to possess linear 
elastic traction and separation behavior, as shown in Figure 13. 
 39
 
0
?
0
t
f
?
Separation
Trac
tion
 
Figure 13: Linear Traction-Separation response for cohesive elements 
 
Softening behavior of cohesive zone after the damage initiation has been prescribed 
using the damage evolution law. Maximum nominal stress criterion is used to identify the 
locations for damage initiation: 
1
t
t
,
t
t
,
t
t
max
0
t
t
0
s
s
0
n
n
?
?
?
?
?
?
?
       (3.25) 
where 
n
t , 
s
t  and 
t
t  are the peak values of the nominal stress. The evolution of damage 
under a combination of normal and shear deformations can be expressed in terms of an 
effective displacement. Damage due to a combination of normal and shear deformations 
expressed in terms of 
n
? , 
s
?  and 
t
?  gives the displacement. 
 40
 
3.3 Line Spring Models 
Fracture properties of a material such as stress intensity factor and J integral can 
be calculated using Line spring models. Introduced by Rice and Levy [Rice 1972
a-b
], 
these models calculate SIFs computationally inexpensively. SIF for Pb-free alloys under 
high strain rate environment are measured using line spring elements attached to shell 
elements. Fracture properties are extracted at inter metallic component layer between 
bulk solder and copper in ball grid array packages. Variation of stress intensity factor at 
interface of Copper-Solder bimaterial specimen for different alloys under varying strain 
rates during tensile testing condition is plotted. 
Line spring elements are modeled as one dimensional elements LS6 in a series 
along the flaw edge. LS6 is a 6 node general second order line spring element. This 
element incorporates the local solution dominated by a singularity at the crack tip into 
shell elements in un-cracked state. Relative displacements and rotations are calculated 
across this interface section of bimaterial specimen for tensile test and IMC layer for 
BGA drop test. These properties are used to calculate local strain field, J integral and SIF 
at integration points of elements. In case of high speed uniaxial tensile test, Bimaterial 
copper-solder specimens are seem to fail at the notched interface. The crack initiates at 
the root of a 30? notch and propagates along the interface of two different materials. For 
this reason, line spring 1D elements are inserted at this interface. 
 41
4
1
5
2
6
3
LS6
t
q
Point A
Point B
Interface
n
 
Figure 14: Line spring element LS6 node numbering 
If q,n,t  represent orthonormal system with t  tangential to the specimen along the 
flaw, n  as normal to the specimen surface giving q  as [Gonalves 1999] 
ntq ??          (3.26) 
Figure 14 shows line spring modeling geometry of Bimaterial copper solder specimen 
with a LS6 element. Node 1, 2, 3 are on solder side of the specimen and node 4, 5, 6 are 
on copper side. As shown in the Figure 14, point A and B are placed at the same place 
but on opposite side of the flaw. The relative motion between these two points can be 
given by three displacement and three rotation strains for mode I, II and III. 
Mode 1 
Opening Displacement ? ? quu?u
ABI
???      (3.27) 
Opening Rotation ??t
ABI
???????       (3.28) 
Mode 2 ? Through thickness shear 
Relative Displacement ? ? nuuu
ABII
????      (3.29) 
Here, deformation does not take place due to relative rotation ??n
ABII
???????   
          (3.0) 
 42
Mode 3 
Relative Displacement ? ? tuuu
ABIII
????      (3.1) 
Relative Rotation ??q
ABIII
???????      (3.2) 
The compliance equation of mode I line spring model for a single notched specimen with 
far field loading is given as 
??
?
?
?
?
?
?
?
?
?
?
?
?
?
? M
N
G
u
         (3.3) 
N is axial force and M is bending moment. Energy compliance calibration gives matrix G 
[Tada 1973]. The compliance are obtained by modeling springs as plain strain single-
edge notched specimen of width t and crack depth a, subjected to axial force N and 
bending moment M per unit thickness. The additional displacement 
c
?  and rotation 
c
?  at 
the load points due to presence of crack are given by [Gonalves 1999] 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
M
N
PP
PP
2221
1211
c
c
        (3.4) 
The matrix P can be obtained from SIF calibration of single-edge notched 
specimen using energy compliance relations [Rice 1972c]. 
??
11
2
11
E
12
P ?
???
?         (3.5) 
??
12
2
2112
Et
12
PP ?
???
??        (3.6) 
??
22
2
22
E
12
P ?
???
?         (3.7) 
Therefore, at the interface stress intensity factor and J integral can be calculated by 
 43
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
I2I1
2
2/1
I
M
t
a
FtN
t
a
F
t
a
K       (3.8) 
G2
K
E
K
E
K
J
2
III
'
2
II
'
2
I
???         (3.9) 
1
F  and 
2
F  are approximate expressions given by [Tada 1973]. 
'
E  and ? are calculated as 
??
2
'
1
E
E
??
? , 
????
?
12
E
G        (3.40) 
 
 44
CHAPTER 4 ?
 
XFEM AND CZM BASED SHOCK-RELIABILITY MODELS FOR LEADFREE AND 
ADVANCED INTERCONNECTS 
 
4.1 Introduction 
Electronic systems may often be subjected to drop and shock environments during 
manufacturing, shipping and operational conditions. The presented work helps in 
assessment of drop reliability of electronics in advanced and leadfree interconnects. 
Various experimental and finite element methods are implemented to study dynamic 
behavior of solder interconnects. Models for crack initiation and propagation in leadfree 
solder interconnects are developed. Implicit and explicit finite element methods are 
implemented to model non linear dynamic environment. Extended finite element method 
is used which enables the modeling the solder interconnect without explicitly meshing the 
crack surface. The crack propagated in crack domain along the solution dependent path 
with no requirement of remeshing the model.  Interface damage properties of the copper-
solder interface have been characterized at high strain rate on a bi-material specimen 
using high-speed imaging in conjunction with digital image correlation.  Damage 
properties have been used as input to the XFEM models.  The XFEM sub-models have 
been developed using node-based sub-modeling, transient displacement and velocity 
 45
histories from digital image correlation measurements with high-speed imaging of board 
assemblies during shock. 
4.2 Test Vehicle 
Three different configurations of test vehicles are used for this study. Test Board-
A has ceramic packages while Test Board-B is with plastic packages. All test vehicles are 
daisy chained. Test Boards A and C were subjected to JEDEC standard JESD-B211 drop 
test. Test Board-B was subjected to 12,500g, 0.2ms pulse.  Solder alloys include copper 
reinforced solder column grid array (CCGA), Eutectic tin lead solder (63Sn37Pb), high 
lead solder joint (90Pb10Sn), and SAC305 solder (Sn3Ag0.5Cu).  
Table 1: Configuration A Package Architecture (Ceramic Packages) 
Parameter 
CCGA 
Solder Colu
mns
 
CBGA 
63Sn37Pb 
CBGA 
(Hi-Pb Colu
mn)
 
CBGA 
Sn3Ag0.5Cu 
Length (mm) 21 21 21 21 
Width (mm) 21 21 21 21 
Thickness (mm) 2.4 2.4 2.4 2.4 
I/O 400 400 400 400 
Pitch (mm) 1 1 1 1 
Ball Diameter (mm) 0.6 0.6 0.6 0.6 
Joint Height 2 0.6 0.6 0.6 
 
Figure 15 shows test board A with copper reinforced solder column grid array 
packages. All the packages on this test board experience different strain pulse because of 
 46
the different geometric location. Figure 16 shows array configuration of the CBGA 
ceramic package with 400 I/Os. 
?
 
Figure 15: Configuration A Test Board (Ceramic Packages)
 47
 
 
Figure 16: Interconnect array configuration for Test Board A, 400 I/O 
CBGA/CCGA 
It has eight packages with same interconnect type on all the eight. These boards 
have ceramic packages with 400 I/O each. The board dimension are 106mm x173mm x 
2mm. Package Architecture is shown in Table 1. Test- Board B is a single package 
centrally located on board designed as per JEDEC specifications with dimensions as 
132mm x 77mm x 1.5mm as shown in Figure 17. Plastic package with 324 I/O is 
mounted on board for which array configuration is as shown in Figure 18. The solder 
interconnects are SAC305 solder (Sn3Ag0.5Cu).  
 48
 
 
Figure 17: Configuration B Test Board (Plastic Package)
 49
 
 
Figure 18: Interconnect array configuration for Test Board B, 324 I/O PBGA 
Figure 19 shows test Board-C which is a JEDEC test board with dimensions 
132mm X 77mm X 1mm. The test board has 15 chip-array ball-grid array packages 
(CABGA) populated on one side in a three-row, five-column format. The packages have 
an I/O count of 100 and pitch of 0.8mm full-array configuration as shown in Figure 20. 
The printed circuit board is made up of FR4-06. Package architecture of test board B and 
C are shown in Table 2. 
 50
 
1 10 15
14
13
12
11
92
83
74
65
 
Figure 19: Configuration C Test Board (Plastic Package)
 51
 
 
Figure 20: Interconnect array configuration for Test Board C, 100 I/O CABGA 
Table 2: Configuration B Package Architecture (Plastic Package) 
Parameter 19mm,PBGA 
(Test Board-B) 
10mm, CABGA 
(Test Board-C) 
Ball Count 324 100 
Ball Pitch (mm) 1 0.8 
Die Size (mm) 7.5 5.55 
Substrate Thickness (mm) 0.3 0.232 
Substrate Pad Type SMD NSMD 
Ball Diameter (mm) 0.65 0.48 
 
 52
4.3 Experimental Set-Up 
The Lansmont Model-23 drop tower has been used for shock testing of the board 
assemblies as shown in Figure 21. The drop height and pulse shape has been adjusted 
using pulse shaper between the impacting surfaces. The event has been monitored by two 
high speed cameras operating at 50,000 frames per second located as shown in schematic 
Figure 22. Two different high speed cameras mounted on tripods make an angle of 30? 
between them. Recommended angle for high accuracy is between 20? to 40? [Gu 2006, 
Helm 1996]. These synchronized cameras are externally triggered. Cameras are 
calibrated before recording the drop event which involves capturing the images of the 
target at different orientations as shown in Figure 23. Target specifications are 12 x 9 grid 
of black points on a white background with 9 mm pitch. 12 to 15 calibration images are 
recorded for good minimum error calibration results.  
 53
Guiding 
Rods
PCB Mounted via 
Standoffs on Base
Base
Pulse 
Shaper
 
Figure 21: Lansmont Drop Tower Model23 
Strain and continuity data is simultaneously acquired during a drop event using a 
high speed data acquisition system operating at a sampling frequency of 5 million 
samples per second. Failure is detected as an increase in the strain gage voltage. The 
board assemblies have been speckle-coated on both the board-side and package-side. 
 54
Different package locations on test boards exhibit different strain histories during the 
same drop and different number drops to failure. 
High Speed Cameras
30?
 
Figure 22: Schematic of drop tower with high speed cameras for DIC 
Test- Board A and C have been subjected to 1500G, 0.5ms pulse in accordance 
with JESD22-B111 while test Board-B has been subjected to ~12,500Gs, 0.2 ms pulse, as 
shown in Figure 24. 
 55
 
Figure 23: Calibration images captured at different orientations.
 56
0
2000
4000
6000
8000
10000
12000
14000
0 0.05 0.1 0.15 0.2 0.25
Acceleration(G)
Time (ms)
G- Loading
0
200
400
600
800
1000
1200
1400
1600
0 0.1 0.2 0.3 0.4 0.5 0.6
A
ccel
era
t
i
o
n
(
G
)
Time (ms)
G- Loading
 
Figure 24: Acceleration for Test Boards 
 57
4.4 Digital Image Correlation 
Digital image correlation (DIC) is an optical method to measure full field 
deformation and their derivatives of deformation on the surface of a loaded structure. 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. 
 
Figure 25: 3D-Digital Image Correlation Measurements in Printed Circuit 
Assembly 
The tracking is achieved using digital image processing of speckle pattern on the 
specimen surface. Figure 25 shows the principle of DIC in 3-dimensional case. The sub 
image before impact is referred as )r(I
1
 and the one after impact is referred as )r(I
2
 
respectively, which are related as follows: 
 58
)]r(Ur[I)r(I
12
??         (4.1) 
)]r(Ur[I)r(I
21
??         (4.2) 
where )r(U  is the displacement vector at pixel ? ?
T
y,xr ? . An algorithm based on the 
mutual correlation coefficient or other statistical functions are used to correlate the 
change in a reference pixel in the original image and the corresponding reference pixel in 
the deformed image. Three such typical correlations include absolute difference, least 
square and cross correlation. There are three typical correlation functions which are used 
and are defined as follows: 
Absolute difference: 
??
??
?
?
??
??
dr)r(
dr)r()'rr(
1)'r(
I
II
C
1
12
A
     (4.3) 
Least square: 
??
??
?
?
??
??
dr)r(
dr)]r()'rr([
1)'r(
2
1
2
12
L
I
II
C
     (4.) 
Cross-Correlation: 
??
2/1
2
2
2
1
2
1
C
dr)'rr(dr)r(
dr)'rr(
1)'r(
II
I)r(
I
C
?? ??
??
??
?
?
?
??
    (4.5) 
where ? (M x N) is the area of the sub image around reference pixel r, r` is the current 
pixel, 
)'r(
CA
 is the absolute correlation function, 
)'r(
CL
 is the least square correlation 
function, and 
)'r(
CC
 is the cross correlation function. In this research, digital image 
correlation has been used for material characterization of the solder under high strain rate 
as well as to determine the strain and deformation field on the entire PCB. Figure 26 
 59
shows the speckle coated PCB and Bimaterial Copper-Solder specimen during dynamic 
events of drop and high rate pull respectively. 
 
Figure 26: Speckle Coated Printed Circuit Board on Drop Tower and Bimaterial 
Copper-Solder specimen during uniaxial tensile test. 
4.5 Model Development 
Node based sub-modeling has been used to provide boundary conditions to the 
XFEM sub-model. Three versions of the explicit global models include Timoshenko 
Beam Elements, smeared property, and cohesive zone models. Here the global-output of 
the experimental data has been used to drive the attachment degree of freedom of the 
XFEM sub-model. These attachment degrees of freedom are the driven nodes and 
correspond to the DIC data output locations on speckle coated PCB. Digital image 
correlation has been used to extract displacement and velocity along with strain 
components at discrete speckle patterned location on PCB. Two model methodologies are 
 60
applied in this study namely extended finite element models and explicit finite element 
models with cohesive elements. 
X
Z
Y
P
R
I
N
T
E
D
 
C
I
R
C
U
I
T
 
B
O
A
R
D
B
A
S
ER
I
G
I
D
 
F
L
O
O
R
STANDOFF
PACKAGE 
(BELOW PCB)
 
Figure 27: Explicit Global Model (Test Board ?A) 
In explicit analysis, transient dynamic behavior of the populated printed circuit 
boards has been simulated after creating smeared property models as shown in Figure 27. 
Smeared packages are modeled with three dimensional C3D8R continuum reduced 
integration element to increase computational efficiency. Smeared property models are 
computationally efficient and structurally equivalent to the original structure [Lall 2004, 
2006]. PCB has been modeled with the S4R shell element and floor has been modeled as 
rigid element R3D4. Rayleigh damping has been used to model the damping behavior of 
the printed circuit assembly. Output from the global model is extracted at the cut-
boundary nodes. Corners of the cut-boundary nodes are shown in Figure 28.
 61
 
X
Y
Z
LB
LT
RT
RB
U
3
U
5
U
4
U
6
U
7
U
8
U
1
U
2
 
Figure 28: Package nomenclature and Output locations for Explicit Global models 
at given orientation (Test Board-A) 
Figure 35 to Figure 39 shows FE models for various types of interconnects used. 
Figure 34 and Figure 35 shows the high-lead interconnect with spherical ball of 
Sn10Pb90 solder component surrounded by eutectic 63Sn37Pb solder component. Figure 
36 and Figure 37 shows high lead Sn10Pb90 column wrapped with a copper spiral. The 
solder column and copper spiral are encased in a layer of eutectic 63Sn37Pb solder. The 
copper reinforcement is intended to enhance the interconnect reliability and provide 
redundancy in case of fracture of the solder column. Figure 29 to Figure 33 shows the 
submodels created for each kind of the package on the test board.  
 62
 
Figure 29: Submodel created for PBGA 324 Sn3Ag0.5Cu of Configuration B test 
vehicle 
 
Figure 30: Submodel created for CCGA solder column of Configuration A test 
vehicle 
 63
 
Figure 31: Submodel created for CBGA Sn3Ag0.5Cu of Configuration A test vehicle 
 
Figure 32: Submodel created for CBGA (Hi-Pb) of Configuration A test vehicle 
 64
 
Figure 33: Submodel created for CBGA (63?Sn37Pb) of Configuration A test 
vehicle 
 
 
 
 65
63Sn37Pb
Sn10Pb90
Cu Pad
 
Figure 34: Cut Section view of FE model for 90Pb10Sn Solder Joint on CBGA 
interconnect
 66
 
 
 
Figure 35: FE model for 90Pb10Sn Solder Joint on CBGA interconnect
 67
 
 
63Sn37Pb
Sn10Pb90 
column
Cu
Reinforcement
 
Figure 36: Cut Section view of FE model for Cu-Reinforced Solder Column on 
CCGA interconnect
 68
 
 
Figure 37: FE model for Cu-Reinforced Solder Column on CCGA interconnect
 69
 
 
 
 
Figure 38: FE model for Sn3Ag0.5Cu Interconnect on CBGA interconnect
 70
 
 
 
Figure 39: FE model for Sn3Ag0.5Cu Interconnect on PBGA324
 71
Figure 40 shows the schematic of the methodology implemented for XFEM 
approach. For test board-A with ceramic packages, enrichment domains are defined in the 
solder region of corner balls. For SAC305 solder (Sn3Ag0.5Cu) and Eutectic tin lead 
solder (63Sn37Pb) interconnects, entire solder ball is assigned with enrichment domain 
properties. While for CCGA and Hi-Pb solder, eutectic phase at top and bottom of the 
interconnect column is enriched with additional degrees of freedom. Similarly entire 
corner solder sphere is modeled as enrichment domain for plastic package of test board-
B. Enrichment domain creates the solution dependent region for XFEM analysis. Node 
based Submodeling approach is executed with velocity components from digital image 
correlation used as boundary conditions for all the sub-models. Damage thresholds 
derived from high rate test of bi-material specimen have been used in assigning the 
fracture strength of the solder material in the enrichment domain. Maximum principal 
stress criterion is used as damage initiation parameter. Damage behavior of the interface 
is governed by the traction separation laws. When this criterion is met, nucleation of the 
crack occurs and it travels to the adjacent element. 
 
 72
BCs: DIC 
velocity vectors
JEDEC Drop
Solder Properties from 
High Rate Test
Mold
PCB
 
Figure 40: Schematic of methodology in implementing XFEM for Drop event of 
PCB 
The extended finite element sub-models have been created for all the packages on 
both test vehicles. The corner interconnects have been modeled with 8-node hexahedral 
element C3D8 elements. The remaining solder interconnects have been created with 
Timoshenko beam B31 elements. The Timoshenko beam element has six degrees of 
freedom at each node including, three translational and three rotational degrees of 
freedom. Rotational degrees of freedom have been constrained to model the interconnect 
behavior. All remaining package components including the chip, mold compound, 
substrate and printed circuit board have been modeled with C3D8 elements. Gravity 
loading has been added in the model to account for the inertia forces occurring during the 
drop event. 
 73
For CCGA column, location U3, initiation and propagation of crack at various 
times after the impact during the transient shock-event, is shown in Figure 41. Model 
predictions indicate crack initiation at 1.55 ms after the impact. Failure initiates in 
interconnects right above the fillet region. Figure 42 and Figure 43 show crack initiation 
and propagation in bulk solder for Sn3Ag0.5Cu and 63Sn37Pb configurations. Figure 44 
shows the crack initiation in the 90Pb10Sn solder interconnect through the 63Sn37Pb 
wetted attachment layer. Figure 45 shows a crack that has initiated in solder layer on PCB 
side of the element for Plastic package with SAC305 interconnect. Average stress state 
has been used to determine the instances and extension of the crack through the solder 
component of the package. 
 74
 
 
T=0.00ms T=0.26ms T=1.44ms
T=1.54ms T=1.55ms
X
X
X-X
 
Figure 41: Crack Initiation and Propagation in CCGA column solder joints at 
different time intervals after the occurrence of impact using XFEM
 75
 
 
T=0.00ms T=0.75ms
X
X
T=0.84ms
X-X
X
-
X
 
Figure 42: Crack Initiation and Propagation in CBGA Sn3Ag0.5Cu solder joints at 
different time intervals after the occurrence of impact using XFEM
 76
 
 
T=0.00ms
T=1.36ms
X
X
X
-X
T=1.66ms
X-X
 
Figure 43: Crack Initiation and Propagation in CBGA Eutectic Tin lead solder 
joints at different time intervals after the occurrence of impact using XFEM
 77
 
T=0.00ms
T=1.23ms
X
X
T=1.30ms
X-X
 
Figure 44: Crack Initiation and Propagation in CBGA Hi-Pb solder joints at 
different time intervals after the occurrence of impact using XFEM
 78
 
Figure 46 shows the crack initiation and progression in the 63Sn37Pb solder joint 
of the ceramic package using the cohesive zone model. The model predictions from CZM 
correlate well with XFEM models. 
T=0.00ms
T=0.93ms
X
X
X-X
T=1.16ms X-X
 
Figure 45: Crack Initiation and Propagation in PBGA Sn3Ag0.5Cu solder joints at 
different time intervals after the occurrence of impact using XFEM.
 79
 
T=0.00ms
T=1.19ms
T=2.39ms
T=2.69ms
 
Figure 46: Crack Initiation and Propagation in Test Board A CBGA Eutectic Tin 
lead solder joints at different time intervals after the occurrence of impact using 
Cohesive Zone Modeling 
 
4.6 Correlation of Model Predictions with Experimental Data 
The results extracted from these models have been compared with the high-speed 
measurement of strains from digital image correlation. Figure 47 to Figure 50 shows the 
correlation between experimentally measured strain and simulation strain along the PCB 
length for package location U4 for 90Pb10Sn Solder Interconnect Ceramic Package in 
test board-A. Model predictions show good correlation with experimental data in both 
 80
magnitude and phase. Figure 51 to Figure 54 shows the correlation for package location 
U3 with 90Pb10Sn Solder Interconnect Ceramic Package in test board-A. 
Hi-Pb Package U4 (LEFT TOP)
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0.004
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 al
ong B
oar
d L
e
ngt
h
DIC Strain
Simulation Strain
 
Figure 47: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Left Top)
 81
Hi-Pb Package U4 (RIGHT TOP)
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 al
ong B
oar
d L
e
ngt
h
DIC Strain
Simulation Strain
 
Figure 48: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Right Top) 
Hi-Pb Package U4 (LEFT BOTTOM)
-0.003
-0.002
-0.001
0.000
0.001
0.002
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 al
ong B
oar
d 
L
e
ngt
h
DIC Strain
Simulation Strain
 
Figure 49: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Left Bottom)
 82
Hi-Pb Package U4 (RIGHT BOTTOM)
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 al
ong B
oar
d L
e
ngt
h
DIC Strain
Simulation Strain
 
Figure 50: Strain Correlation between FE model and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U4 (Right Bottom) 
Hi-Pb Package U3 (LEFT TOP)
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 a
l
ong B
oar
d L
e
ng
t
h
Simulation Strain
DIC Strain
 
Figure 51: Strain Correlation between FE and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U3 (Left Top)
 83
Hi-Pb Package U3 (RIGHT TOP)
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 al
ong B
oar
d L
e
ngt
h
Simulation Strain
DIC Strain
 
Figure 52: Strain Correlation between FE and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U3 (Right Top) 
Hi-Pb Package U3 (LEFT BOTTOM)
-0.004
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 al
ong B
oar
d L
e
ngt
h
Simulation Strain
DIC Strain
 
Figure 53: Strain Correlation between FE and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U3 (Left Bottom)
 84
Hi-Pb Package U3 (RIGHT BOTTOM)
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0 0.002 0.004 0.006 0.008 0.01 0.012
Time (sec)
St
r
a
i
n
 
a
l
o
n
g B
o
ar
d L
e
ngt
h
DIC Strain
Simulation Strain
 
Figure 54: Strain Correlation between FE and DIC for 90Pb10Sn Solder 
Interconnect CBGA at U3 (Right Bottom) 
Explicit finite element model predictions have been validated by full-field 
correlation of board strains with experimental measurements from digital image 
correlation. Figure 55 to Figure 58 show the transient mode-shapes and measured strain 
magnitudes during the drop event from simulation and experiment. Comparison shows 
that the similarity of the transient mode shape and strain distribution over the entire board 
assembly. Figure 55 to Figure 58 shows the full field strain distribution on PCB at 
different instances just after the impact. 
 85
 
T=2.25 ms
 
s
 
Figure 55: Transient strain contour correlation on PCB between DIC with high-
speed imaging and FE analysis at 2.5ms 
 86
 
T=6.00 ms
 
 
Figure 56: Transient strain contour correlation on PCB between DIC with high-
speed imaging and FE analysis at 6ms 
 87
 
T=9.00 ms
 
 
Figure 57: Transient strain contour correlation on PCB between DIC with high-
speed imaging and FE analysis at 9ms 
 88
 
T=12.0 ms
 
 
Figure 58: Transient strain contour correlation on PCB between DIC with high-
speed imaging and FE analysis at 12ms 
 89
 
Board assemblies have been cross-sectioned after failure to understand the failure 
modes. Table 3 the correlation between the model predictions and the observed failure 
modes in board assemblies after failure in the shock test. The location of the failure 
modes correlate well with the experimental data. Copper columns fail close to the 
package interconnect interface. Sn3Ag0.5 Cu interconnects on the CBGA package fail 
close to the package-solder interface. Sn3Ag0.5 Cu interconnects on PBGA package fail 
close to board interface. 90Pb10Sn interconnects fail close to the board interface in the 
eutectic solder. 
 90
Table 3: Correlation of Model Predictions with Failure Modes from Experiment 
Type Model Predictions Experimental Data 
Cu-Column 
CBGA 
T=1.55ms
X
X
X-X
  
Sn3Ag0.5Cu 
CBGA 
X
X
T=0.84ms
 
90Pb10Sn 
CBGA 
X
X
T=1.30ms
X-X
 
Sn3Ag0.5Cu 
PBGA 
X
X
X-X
T=1.16ms
 
 91
CHAPTER 5 ?
 
SIF EVALUATION USING XFEM AND LINE SPRING MODELS UNDER HIGH 
STRAIN RATE ENVIRONMENT FOR LEADFREE ALLOYS 
 
5.1 Introduction 
Transition to Pb-free solder alloy system has brought many challenges in 
electronic industry. Behavior of these new alloys under dynamic conditions of shock and 
drop is not completely known. Intermetallic compounds of Cu
6
Sn
5
 and Cu
3
Sn are 
commonly found at the interface of copper pad and solder in case of interconnects. These 
intermetallics affect the solder joint fatigue life and therefore the reliability of the system 
[Lall 2010
a
, Limaye 2008]. Very minute size of these IMC layers in BGAs makes 
characterization of these compounds difficult. Therefore in this work, bimaterial copper 
solder specimens are tested using tensile tester with notch near interface where 
intermetallic compounds are formed. Stress intensity factor at this critical failure location 
is determined using both finite element models and experimental techniques. Finite 
element approach along with experimental testing methods is implemented to assess the 
reliability of leadfree solder alloys under range of strain rate conditions. Boundary 
conditions derived from experimental procedures are used to drive finite element models 
of crack propagation. Bimaterial copper-solder specimens are ?V? notched at the center 
typical of bulk solder and copper pad of package interconnect. These specimens are 
 92
tested on uniaxial tensile tester. Finite element simulations of these specimens under 
tensile testing conditions fetch fracture properties such as SIF, J integral. This thesis 
addresses the need of testing leadfree alloys at strain rates similar to field applications. 
Here, specimens are tested for crack propagation study using a uniaxial tensile testing 
machine which allows high strain rates. Displacement fields in front of crack extracted 
using ultra high speed imaging are used to evaluate SIF at crack nucleation. This 
experimental SIF is well correlated with the SIF value determined using line spring finite 
element model. Bimaterial copper-solder specimens are fabricated with single notch and 
double notch of 30? at center interface. These specimens are tested at two high strain rate 
conditions of 20 per sec and 55 per sec. Stress-strain properties acquired during testing 
are used to build material models in line spring models and extended finite element 
models. In this paper, solder deformations and critical stress intensity factors are 
measured at strain rates representative of shock and vibration. Also, JEDEC form factor 
printed circuit board is tested on a shock tower at high g-level. Stress intensity factor at 
copper pad solder ball interface is studied in centrally mounted package on this board. 
Transient deformation of the board is studied with high speed cameras and high speed 
data acquisition systems. In this study DIC has been used to study crack propagation in 
single notch and double notch specimens under dynamic loadings. It has also been used 
to extract velocity vectors on PCBs subjected to drop testing. Relative motion of two 
ends of bimaterial specimens has been monitored during tensile testing using high speed 
cameras. The displacements and velocities tracked during these transient events are used 
to drive FE models. Attachment degrees of freedom of Line spring and XFEM models 
use these displacements and velocities as boundary conditions for simulation. 
 93
5.2 Specimen Fabrication 
For the purpose of this study, bimaterial copper solder specimens are prepared using a 
novel procedure where solder uniaxial test specimens are formed in high precision 
rectangular cross-section glass tubes using a vacuum suction process. The solder is 
melted in a quartz crucible using a melting pot maintained at 242?C. Figure 59 shows the 
set-up for preparing the specimen. 
 
Figure 59: Bimaterial Cu-solder specimen preparation set-up with control valve of 
vacuum pump
 94
 
Solder
Copper
 
Figure 60: X-ray image of Bimaterial Copper Solder specimen for Sn3Ag0.5Cu 
30?
30?
40 mm
5mm COPPER SOLDER
 
Figure 61: Schematic of Single Notched Bimaterial Specimen Geometry 
30?
40 mm
5mm
COPPER SOLDER
 
Figure 62: Schematic of Double Notched Bimaterial Specimen Geometry
 95
Cu Pad
Solder
PCB
Crack 
Prone 
Region
 
Figure 63: Schematic of typical Cu-Solder Interface in solder interconnect showing 
crack prone region 
 Figure 63 shows the X ray image of fabricated specimen showing homogenous 
interface of copper and solder. Parameters are controlled to avoid formation of voids in 
solder material. Figure 61 and Figure 62 shows schematic of fabricated single notched 
and double notched specimen. Bimaterial specimens are fabricated because this interface 
geometry resembles with the actual copper pad and bulk solder interface in solder 
interconnects as shown in Figure 63. Intermetallic compound is formed at this region 
which is a critical for a crack to nucleate and propagate [Lall 2010
a
]. 
Oxidized Copper material with 0.4mm thickness was inserted into glass tube up to 
half of its length. Specimen thickness is chosen to be representative of an actual joint. 
Other end of the glass tube was inserted into the molten solder which rises in the tube by 
capillary action, and additionally suction was applied to the other end via a rubber tube 
connected to the house vacuum system. The suction force was controlled through a 
regulator on the vacuum line. When desired amount of solder was drawn into the tube, 
 96
the glass tube is drawn out of solder pot and is held in a vertical position for cooling of 
solder. In this holding position cooling solder is on top of the copper strip where bottom 
end of copper strip is connected to vacuum pump. Therefore the weight of solder and the 
suction pressure act in the same direction avoiding formation of voids due to opposing 
forces. The tube was then cooled to room temperature (25?C) by air cooling. Temperature 
of specimen solder is recorded during cooling stage to study the cooling of solder during 
fabrication. Figure 64 shows the schematic of method implemented to record the 
temperature of solder specimen during cooling. Thermocouple is connected to a 
multimeter with data logging system.  
 97
Thermo couple
Cooling
Solder
Glass tube
Multimeter 
with Data 
Logger
Computer
Oxidized
Copper
Interface
Suction
 
Figure 64: Schematic of recording of cooling profile for bimaterial copper-solder 
specimen during cooling stage 
Figure 65 shows the comparison of recommended and actual observed cooling profile 
of specimen. Cooling part of the recommended reflow oven profile suitable for Pb-free 
alloys is compared with cooling profile of specimen. It can be seen that the rate of 
cooling of the specimen after fabrication is identical to the rate of cooling of solder 
interconnects during actual reflow of printed circuit boards. This plays an important role 
 98
in achieving similar grain structure and therefore material properties as observed in actual 
solder interconnects.  
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0
50
100
150
200
250
0 50 100 150
Ra
t
e
 o
f
 Co
o
l
i
n
g
 
(
 
o
C/
s
e
c
)
T
e
m
p
era
tu
re (
o
C)
Time (second)
Cooling Profile (Air Cooling)
Room 
Temperature
Cooling 
Portion of 
Reflow Profile
Recorded 
Temperature
Rate of 
cooling 
 
Figure 65: Comparison of recorded air cooling profile with industry recommended 
reflow cooling profile 
The overlapped solder was then removed from the oxidized copper surface area. 
The solder-copper interface is purely edge-to-edge. ?V? notches were made along the 
interface using wire electronic discharge machine (EDM). The notch opening angle 
selected was 30
0
. A flux was applied on copper in order to make a good joint during the 
casting process. These specimens were speckle coated from one side to capture DIC. 
5.3 High speed Uniaxial Tensile testing 
Bi-material copper solder specimens have been subjected to high strain rate 
tensile testing. Specimens are tested to a strain rate typical of shock and vibration. 
Uniaxial tensile testing machine as shown in Figure 66 is employed for this purpose. The 
bimaterial specimens were notched with a 30? ?V? notch at the interface typical of solder-
copper interface in package interconnects. Two types of specimen are fabricated with 
 99
single notch and double notch. Single edge notched tension (SENT), double edge notched 
tension (DENT) specimens have been tested for steels to study effect of specimen 
geometry J integral [Landes 1972, Gross 1965]. Specimen is gripped between two 
crossheads using screws. A range of strain rates 1-100 s
-1
 has been achieved by 
controlling the impact hammer. Testing is continuously monitored by high speed cameras 
and high speed data acquisition systems.  
FIXED
MOVING BASE
Top
Crosshead
Bottom
Crosshead
Slip Joint
Bi-material
Specimen
Target
 
Figure 66: Schematic of uniaxial high strain rate tensile machine 
Two targets are placed on a machine as shown in Figure 66. Top target is attached 
on a fixed plate while bottom target on a moving plate. Using high speed imaging 
 100
cameras motion of these targets is recorded. Slip joint is inserted between bottom 
crosshead and bottom plate in order to remove any noise and sudden jerk due to hammer 
impact. Displacement of bottom target with respect to top target gives the deformation of 
the specimen. Two different leadfree alloys with two strain rates are tested. 
The load was monitored using ICP force sensor in conjunction with a high speed 
data acquisition system. The ICP force sensor uses a built-in MOSFET microelectronic 
amplifier to convert the high impedance charge output into low impedance voltage signal 
for recording. The low impedance voltage signal is not affected by tribo-electric cable 
noise or contaminations. The ICP sensor is powered from a separate constant current 
source. It is well suited for continuous, unattended force monitoring in harsh environment 
such as drop/impact conditions. Sensor is designed to measure impact force. The flat 
sensing surface is located on top of the sensor and is designed to measure force as it is 
applied axially. In this application of impact testing, as the impact hammer contacts the 
moving base of uniaxial tensile tester metal to metal impact produces high frequency 
ringing. Polyimide film tape covers cap surface of the sensor to reduce this effect. These 
sensors are constructed with compression mode quartz crystals preloaded in a rigid 
housing. These designs give the sensors microsecond response time and resonant 
frequencies in hundreds of KHz, with minimal overshooting or ringing. Small diaphragm 
diameter ensures spatial resolution of narrow shockwaves. Therefore, use of these sensors 
is perfectly suited for such high speed high strain rate loading application [PCB 2009].  
5.4 Fracture Analysis of bimaterial Specimens 
Line spring and XFEM models are used for determination of stress intensity 
factor and J integral at interface between copper and solder of bimaterial specimens. 
 101
Variation of SIF with solder alloys and strain rate has been measured. Single notched and 
double notched XFEM and line spring models are built. This stress intensity factor 
defines amplitude of crack tip singularity. It is one of the most important concepts in 
fracture analysis. J integral which is nonlinear energy release rate can be viewed as both 
energy parameter and a stress intensity parameter. It is a path independent contour 
integral for analysis of crack. J integral is a more general version of the energy release 
rate. For case of bimaterial tensile testing condition with linear elastic material [Anderson 
2005], 
'
2
I
E
K
J ?         (5.1) 
Node based modeling technique has been implemented to provide boundary 
conditions to these models. Here global output extracted from experimentation has been 
used to drive attachment degree of freedom of FE models. These attachment degrees of 
freedom are the driven nodes in the simulation. Figure 68 shows the methodology used 
while simulating these models. Relative displacement vectors measured from 
experimentation are given at the bottom edge of the solder part of model. Top edge in 
copper region is constrained which resembles the fixed base of the uniaxial tensile tester. 
In order to achieve sufficient element density at the expected crack region, multipoint 
constraints are implemented. MPCs help in defining fine mesh at the interface region. 
Central interface of Cu-solder bimaterial specimens is critical from failure point of view. 
Therefore, maximum number of elements is needed in this region of possible failure. 
With use of MPC, it is possible to achieve finer discretization of elements at desired 
region resulting optimum mesh density. Coarse mesh is acceptable in the region away 
from interface. This method is computationally efficient and memory economical. 
 102
Multipoint constraints (MPC) allow constraints to be imposed between different degrees 
of freedom of the model. Linear and quadratic type multi-point constraints are used here 
to achieve higher element density near interface of two materials [Abaqus 2009c]. 
CPS4
CPS4
CPS4
CPS4 CPS4
CPS4
ap
b
Solder
Copper
S8R
S8R
S8R
S8R S8R
S8R
a
b
c
Solder
Copper
p1 p2
En
r
i
c
h
me
n
t
 R
e
gi
on
LS6
(a) (b)
 
Figure 67: Linear (a) and Quadratic (b) MPCs used in XFEM and Line Spring 
models respectively 
Figure 67 (a) shows linear MPCs used for plane stress CPS4 elements of XFEM 
model. Each degree of freedom at point p is interpolated linearly from the corresponding 
degrees of freedom at nodes a and b. Entire solder region of bimaterial specimen is 
modeled as enrichment domain. In case of line spring models, second order shell 
elements S8R are used to construct the models. Quadratic mesh refinement is 
implemented for these second order elements. Here, as shown in Figure 67 (b) each 
degree of degree of freedom at node p1 and p2 are alternately interpolated quadratically 
from corresponding degrees of freedom at nodes a, b and c. Line spring elements are 
 103
modeled near the root of a notch at interface. Element types used for every part of both 
Line spring and XFEM models is given is Table 4. As 2
nd
 order line spring LS6 needs to 
be aligned with shell element, therefore line spring models are constructed with S8R shell 
elements. Figure 69 and Figure 70 show the detailed zoomed in view of these models for 
single notched and double notched geometry.  
Relative
Displacement
Vectors from
Experimentation
at Solder End
Constrained at
Copper End
Co
ppe
r
So
l
d
e
r
 
Figure 68: Line Spring model and XFEM Methodology for Bimaterial specimen 
tensile testing 
 104
 
Table 4: Element types used for FE models created for copper-solder bimaterial 
specimens 
Element Types Copper Solder 
Line Spring Model S8R S8R 
XFEM Model CPS4 CPS4 
 
 105
20mm
5mm
20mm
 
Figure 69: FE models of Single Notch Bimaterial specimens with MPCs 
 
 106
5mm
20mm
20mm
 
Figure 70: FE models of Double Notch Bimaterial specimens with MPCs 
 
For these simulations, classical metal plasticity material models are used in 
conjunction with linear elastic models. These models use Mises yield surfaces which 
allows isotropic yield. The Mises yield surfaces assume that yielding of the metal is 
independent of the equivalent pressure stress [Abaqus 2009d]. Yielding of the solder 
 107
material is observed at the crack tip of notched specimen under high strain rate condition. 
Material model is defined by giving the value of uniaxial yield stress as a function of 
uniaxial equivalent plastic strain. Uniaxial yield stress and uniaxial equivalent plastic 
strain is measured from stress-strain curves shown in Figure 71 for Sn1Ag0.5Cu and 
Figure 72 for Sn3Ag0.5Cu plotted for corresponding strain rates (20 per sec and 55 per 
sec) using uniaxial tensile tester [Lall 2011]. Figure 73 shows the representative 
constitutive model of elastic-plastic material defined for Sn1Ag0.5Cu and Sn3Ag0.5Cu 
under experimentally tested strain loading conditions. Total strain in solder is composed 
of plastic strain and elastic strain. 
0
10
20
30
40
50
0 0.02 0.04 0.06
St
r
e
ss M
P
a
Strain
Sn1Ag0.5Cu
20 / sec 55 / sec
 
Figure 71: Stress-Strain curve plotted for Sn1Ag0.5Cu for strain rates of 20s
-1
 and 
55s
-1
 [Lall 2011] 
 108
 
0
10
20
30
40
50
0 0.02 0.04 0.06
St
r
e
ss M
P
a
Strain
Sn3Ag0.5Cu
20  / sec 55 / sec
 
Figure 72: Stress-Strain curve plotted for Sn3Ag0.5Cu for strain rates of 20s
-1
 and 
55s
-1
 [Lall 2011] 
 109
 
 
St
r
e
ss
Strain
?pl ?el
?t
 
Figure 73: Schematic of simulation elastic-plastic material model developed for 
Sn1Ag0.5Cu and Sn3Ag0.5Cu 
To evaluate fracture properties of solder, two crack/flaw models of extended finite 
element and line spring models are simulated for each case as described below: 
(a) Extended Finite Element Model: 
Initially XFEM model is simulated until the crack initiates and starts propagating. 
Entire solder region is enriched with additional degrees of freedom as specimen is 
expected to fail in weak solder portion. Instead of embedding the discontinuity/crack at 
experimentally observed location, damage criterion is defined for model. As this criterion 
is met crack nucleates and travels to the neighboring elements. For both cases of single 
 110
notch and double notch geometry, failure has been observed at root of the notch. This 
region is same as experimentally observed location of crack. Critical time at which crack 
starts initiating and opening is extracted for each alloy and each strain loading condition 
using XFEM models. Crack opening displacement is also measured for this critical time. 
This crack domain is defined with material models developed from experimentation. For 
a case Sn3Ag0.5Cu alloy with single notched bimaterial specimen, Figure 74 shows that 
crack initiates at 29?s after pull and later propagates in the neighboring elements. 
Initiation of deformation shows a stress concentration at the root of notch. Critical time 
duration and critical crack opening displacement is recorded for these conditions. These 
XFEM models use displacement boundary conditions derived from experimentation. 
T=00.0?s
T=33.7?s
T=29.0?s
T=33.8?s
 
Figure 74: Crack Initiation and propagation in Bimaterial Cu-solder specimen of 
Sn3Ag.0.5Cu under 20 /sec strain rate 
 
 
 
 111
(b) Line Spring Model: 
Line Spring models are built with second order shell elements. Second order 1D LS6 
element is given a flaw depth as critical crack opening displacement measured from 
XFEM simulation. Line spring model is simulated for a critical time duration extracted 
from XFEM models. Therefore critical SIF can be evaluated from these line spring 
models. Figure 75 shows line spring model output for Sn3Ag0.5Cu specimen under 20 
per sec strain rate. LS6 elements at crack tip show critical value of SIF at tip of crack. 
)/( mmmmN
 
Figure 75: Critical SIF for Sn3Ag0.5Cu measured from line spring model with input 
from XFEM model under 20 per sec strain rate 
 Similar models are constructed and analyzed for both single notched and double 
notched bimaterial specimens. Stress-strain properties obtained from experimentation of 
Sn3Ag0.5Cu and Sn1Ag0.5Cu alloy systems are fed to extended finite element models 
and then to line spring models. Figure 76 and Figure 77 show that at strain rate of 55 per 
sec SIF value for double notched and single notched bimaterial specimen does not show 
much difference. This is expected because [Gross 1965], SIF measurement capacity for 
single edge notch and off center pin loaded specimens in tension is not sensitive to the 
eccentricity of loading. It can be seen that SIF value does not show much variation 
 112
between Sn1Ag0.5Cu and Sn3Au0.5Cu alloys for lower values of strain rate of 20 per 
sec. SIF increases with increase in strain rate. For both cases of single notch and double 
notch cases Sn3Au0.5Cu has higher SIF compared to Sn1Au0.5Cu at 55 per sec strain 
rate. 
Stress Intensity Factor for Bimaterial Specimen with 
Single Notch
0
10
20
30
40
50
60
70
80
20 55
Strain Rate (per sec)
SIF
SAC305
SAC105
)/( mmmmN
 
Figure 76: SIF comparison for single notched bimaterial specimen of Sn3Ag0.1Cu 
and Sn1Ag0.5Cu 
 113
Stress Intensity Factor for Bimaterial Specimen with 
Double Notch
0
10
20
30
40
50
60
70
80
90
20 55
Strain Rate (per sec)
SI
F
SAC305
SAC105
)/( mmmmN
 
Figure 77: SIF comparison for double notched bimaterial specimen of Sn3Ag0.5Cu 
and Sn1Ag0.5Cu 
5.5 Model Validation 
Failed specimens have been studied using optical microscope after the tensile test. 
Interface region of the Sn3Ag0.5Cu solder shows formation of intermetallic compound 
due to bond with copper region of bimaterial specimen as shown in Figure 78. All 
bimaterial specimens failed at the interface as crack initiated at the root of the V notch 
and propagated along the intermetallic layer of interface. 
 114
Intermetallic Compound
 
Figure 78: Optical Microscopic image of solder region of bimaterial Sn3Ag0.5Cu 
specimen showing IMC at interface 
Digital image correlation enables measurement of full field strain, displacement 
and velocity on the entire area of the specimen. High speed imaging at 320,754 makes 
study of crack nucleation and travel of crack possible. Displacement of bottom crosshead 
is tracked with respect to fixed top crosshead using motion analysis of targets on tensile 
tester. After complete displacement of slip joint deformation of specimen initiates. Closer 
look at images of interface shows (Figure 79) nucleation and development of crack with 
time. Final frame of this experimental high speed imaging in Figure 79 shows copper and 
solder parts are completely separated. Strain along the length of the specimen extracted 
from both experimentation and XFEM simulation has been compared to validate the 
 115
accuracy of the approach. Strain values with respect to time are extracted at number of 
locations on the specimen. Along with contours, these strain magnitudes are compared 
statistically between experimentation and simulation. Figure 80 to Figure 83 shows the 
transient strain magnitudes and FE predicted strain at various time steps after impact on 
moving base of uniaxial tensile tester. Comparison shows similarity of strain contours 
over entire specimen area. The strain induced in copper part of the specimen is lower 
compared to solder region during entire event. At the root of the crack plastic behavior of 
solder material is observed. Therefore, strain contours near notch shows higher strain 
along length of the specimen. This plastic region starts growing as the bottom crosshead 
moves downwards and material starts deforming. DIC contours in Figure 83 shows that 
the interface is on the verge of separation resulting in the failure of specimen. Strain 
extracted in the plastic region shown in Figure 84 indicates nonlinear behavior of the 
material. 
 116
Co
ppe
r
So
l
d
e
r
Frame 1 Frame 2 Frame 3 Frame 4
Frame 5 Frame 6 Frame 7 Frame 8
 
Figure 79: Crack Initiation and propagation in bimaterial Cu-solder specimen of 
Sn3Ag0.5Cu under strain rate of 20 per sec captured using ultra high speed imaging 
at 320,754 frames per second. 
Figure 84 shows correlation between strain at the crack location extracted during 
simulation and DIC for bimaterial specimen of Sn3Ag0.5Cu with single notch pulled at 
20 per sec. This strain Eyy is variation of strain magnitude along length of specimen with 
time. Correlation matrix in Table 5 shows strong statistical correlation (0.5<<0.9915) 
between strain vectors from simulation and DIC at crack location. Figure 85 and Table 6 
give strain magnitude correlation at point P2 away from cracked notch on the same 
specimen in the solder region. 
 117
 
T=0.00?s
 
Figure 80: Transient strain contour correlation on Single notched Sn3Ag0.5Cu 
specimen between DIC with high speed imaging and FE at 0.00?s 
 118
 
T=14.3?s
 
Figure 81: Transient strain contour correlation on Single notched Sn3Ag0.5Cu 
specimen between DIC with high speed imaging and FE at 14.3?s 
 119
 
T=24.0?s
 
Figure 82: Transient strain contour correlation on Single notched Sn3Ag0.5Cu 
specimen between DIC with high speed imaging and FE at 24.0?s 
 120
 
T=29.01?s
 
Figure 83: Transient strain contour correlation on Single notched Sn3Ag0.5Cu 
specimen between DIC with high speed imaging and FE at 29.01?s 
 121
0
0.005
0.01
0.015
0.02
0.025
0.03
0 0.05 0.1 0.15 0.2
St
r
a
i
n
 E
y
y
Time (ms)
Correlation between DIC strain and FE Simulation strain for 
Bimaterial Specimen of Sn3Ag0.5Cu with Single Notch under 
20 /sec Strain Rate at P1
Simulation Strain
Experimental Strain
P1
 
Figure 84: Strain correlation at Point P1 between DIC and XFEM simulation 
 
Table 5: Statistical correlation matrix of strain vectors extracted at point P1 near 
crack initiation location 
Correlation Matrix 
For Point P1 
Strain Eyy 
Simulation Experimental 
Strain 
Eyy 
Simulation 1.0000 0.9915 
Experimental 0.9915 1.0000 
 122
0
0.002
0.004
0.006
0.008
0.01
0 0.03 0.06 0.09 0.12 0.15 0.18 0.21
St
r
a
i
n
 Eyy
Time (ms)
Correlation between DIC strain and FE Simulation strain for 
Bimaterial Specimen of Sn3Ag0.5Cu with Single Notch under 
20 /sec Strain Rate at P2
Simulation Strain
Experimental Strain
P2
 
Figure 85: Strain correlation at Point P2 between DIC and XFEM simulation 
 
Table 6: Statistical correlation matrix of strain vectors extracted at point P2 away 
from crack 
Correlation Matrix 
For Point P2 
Strain Eyy 
Simulation Experimental 
Strain 
Eyy 
Simulation 1.000 0.993 
Experimental 0.993 1.000 
 123
5.6 Experimental SIF determination 
 [Limtrakarn 2010] proposed a method to compute stress intensity factor in 
opening mode and shearing mode.For linear elastic fracture mechanics (LEFM), stresses 
are related to stress intensity factor by following relations [Williams 1957], 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
? ??
?
?
?
?
?
?
?
?
? ??
?
?
?
??
2
3
cos
2
cos2
2
sinK
2
3
sin
2
sin1
2
cosK
r2
1
II
I
x
     (5.2) 
?
?
?
?
?
?
?
?
?
?
?
?
???
?
?
?
?
?
?
?
??
?
?
?
??
2
3
cos
2
cos
2
sinK
2
3
sin
2
sin1
2
cosK
r2
1
II
I
y
    (5.3) 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
???
?
??
2
3
sin
2
sin1
2
cosK
2
3
cos
2
cos
2
sinK
r2
1
II
I
xy
   (5.4) 
Here, 
K
I
:  Stress intensity factor for opening mode (Mode I) 
K
 II
: Stress intensity factor for tearing mode (Mode II) 
r and ? Distance and angle in polar coordinate system as shown in Figure 86. 
?
x
 Normal stress in X direction 
?
y
 Normal stress in Y direction 
?
x
 Shearing stress 
 124
L
?
x, u
y, v
r
?
x
?
xy
?
y
d
b
c
e
Crack Tip
 
Figure 86: State of stress in polar coordinates from crack tip 
Generalized form of stress intensity factor at the crack tip is given by [Limtrakarn 
2005], 
aFK ???
?
         (5.) 
Here, F is the geometry factor which depends on dimensions, ?
?
 is far-field stress and a 
is the crack length. 
 The opening stress intensity factor K
I
 can be computed from displacement 
extrapolation at points b, c, d and e as shown in Figure 86 [Limtrakarn 2010]. Points b, c, 
d, e are location near crack tip. Using high speed imaging technique of DIC, 
displacements u and v along x and y directions can be measured. These displacement 
vectors are extracted till nucleation of crack.  
 125
 
????
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
???
?
2
VV
VV4
L
2
k113
E
K
ec
dbI
    (5.6) 
where,  E is modulus of elasticity 
  ? is poisson?s ratio 
  k= (3- ?)/(1+ ?) for plane stress condition. 
Figure 87 shows the ?v? displacement plots for point b, c, d and e along ?y? direction for 
bimaterial single notched case tested with 20 per sec strain rate. 
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.00000 0.00001 0.00002 0.00003 0.00004 0.00005
D
i
sp
l
a
cem
en
t
 V
 a
l
o
n
g
 Y
 d
i
rect
i
o
n
 
(
m
m
)
Time (sec)
Ve Vd Vc Vb
 
Figure 87: Displacement V plots at points near crack tip 
Form equation (5.6) stress intensity factor for opening mode I for Sn3Ag0.5Cu 
alloy under strain rate of 20 per sec, K
I 
is calculated to be 19.82 ? ?mmmm/N . For identical 
conditions of simulation line spring models predict SIF K
I 
as 17.93 ? ?mmmm/N . Thus, it 
can be seen that simulation method shows strong correlation with experimentally 
measured value as shown in Figure 88 with error of 9.5%. 
 126
0
5
10
15
20
25
Simulation Experiment
S
t
ress In
t
e
n
s
i
t
y
 
F
a
ct
o
r
Method of Measurement
)/( mmmmN
 
Figure 88: Correlation of opening mode stress intensity factor between line spring 
model and experimentally measured 
 
5.7 Use of Line Spring FE Models for BGA Under Mechanical Shock 
Finite elements models are created for plastic packages with two different alloy 
systems namely SAC105 and SAC305. Line spring element technique discussed 
previously has been implemented in order to extract fracture properties at interconnect 
failure region. Time dependent Stress intensity factor and J integral values at interface 
between solder ball and copper pad region are measured in drop simulation at high g 
loading conditions. Test vehicle used for this purpose has a centrally mounted single 
package of PBGA324. Package attributes are shown in Table 7. 
 127
Table 7: Package Architecture for PBGA324 
Parameter PBGA324 
Ball Count 324 
Ball Pitch (mm) 1 
Die Size (mm) 7.5 
Substrate Thickness (mm) 0.3 
Substrate Pad SMD 
Ball Diameter (mm) 0.65 
DIC velocity data at four corner locations of package on PCB side of speckle 
coated board is measured.  DIC has been used to extract displacement and velocity along 
with full field strain contours on speckle pattern coated PCB. These velocity drive 
attachment degrees of freedom of PBC components of line spring as shown in Figure 89. 
Contour plot of full filed strain histories is measured on entire printed circuit board 
during complete drop event. Board is coated with speckle pattern similar to bimaterial 
specimens. Figure 90 shows high speed camera snapshots at different time intervals after 
board is dropped at 12,500g. As central region of the board undergoes maximum 
deflection, maximum strain is observed at this location during flexing.  
 128
-8
-6
-4
-2
0
2
4
6
8
10
0 0.001 0.002 0.003
V
e
lo
c
i
ty
 (
m
/s
e
c
)
Time (sec)
Velocity Vectors for Simulation
Left Top Right Top
Right Bottom Left Bottom
DIC Velocity to Simulation
Line Spring Model
 
Figure 89: Methodology implemented for defining boundary conditions to FE 
Models
 129
 
Figure 90: High speed camera snapshots of PCB showing full field strain 
distribution when dropped at high g loading 
It has been shown previously that bulk solder crack at the interface is a 
predominant mode of failure for printed circuit board assemblies under drop environment 
[Lall 2010
a
]. Therefore line spring elements LS6 are inserted in this region of a critical 
solder interconnect at most critical region. Figure 92 explains the procedures 
implemented in order to identify the most critical region on critical solder interconnect. 
Transient dynamic behavior of this centrally located package is simulated for 6ms 
at high loading of 12,500g. Global model is created with smeared packages mounted on 
PCB. In this explicit analysis, critical high stress region is identified as four corners of the 
package. To carry out detailed investigation of this critical region, submodels are created 
 130
with all four corner solder interconnects as spherical solder balls. Remaining 320 
interconnects are modeled as Timoshenko beam elements. B31 beam element has six 
degrees of freedom including three rotational and three translational dof. Rotational 
degrees of freedom have been constrained to model the interconnect behavior of the 
beam elements. This explicit model is given experimental boundary conditions as 
explained earlier. Corner solder joint with maximum stress if found as shown in Figure 
91 and modified as enrichment domain for XFEM analysis.  
 
Figure 91: Maximum principle stress distribution in PBGA324 interconnect with 
Sn1Ag0.5Cu alloy dropped at 12,500 g 
 In XFEM analysis entire solder region of this corner interconnects is modeled 
with enriched degrees of freedom. This enrichment domain creates solution dependent 
region for XFEM analysis. Damage thresholds derived from high strain tests are used to 
 131
build constitutive damage model for quasi-static analysis. Damage behavior of this model 
is governed by traction separation law. When maximum principal stress criterion is met, 
crack nucleates at the critical location and travels to the adjacent elements. This critical 
location is recorded and used at flaw region for Line Spring models.  
 132
 
Simulate Global model with Smeared Packages 
for drop phenomenon at 12,500g Loading
Indentify Critical High Stress Locations 
Simulate Sub-model with detailed corner solder 
interconnects
Simulate XFEM Models with corner solder 
interconnect as enrichment domain 
Identify the crack location and critical time at 
which crack opens
Create Line Spring Model to evaluate fracture 
properties with LS6 elements at Critical Location
Identify Critical Corner Solder Interconnect
 
Figure 92: Flowchart of the procedures followed to evaluate fracture properties of 
most critical region in solder joints of BGA under mechanical shock 
In quasi-static analysis of Line Spring model second order elements are used to 
model all the components of sub-model. Figure 93 shows this 2
nd
 order sub-model for 
 133
PBGA324 package on the test board. Four corner interconnects are modeled in detail as 
spherical solder ball with copper pad. Remaining interconnects are modeled with beam 
B1 elements. 
 
Figure 93: Second order FE model for PBGA324 with line spring elements 
All remaining package components such as mold, substrate, PCB, copper pad, 
bulk solder region of corner interconnects are modeled with 20 node C3D20 solid 
elements. Cut section view of the package is shown in Figure 94. 
 134
SUBSTRATE
CHIP
SOLDER 
INTERCONNECTS
 
Figure 94: Cut section view of FE model for PBGA324 showing solder interconnects 
as B31 beam elements 
Figure 95 and Figure 96 shows the detailed view of critical region where LS6 
elements are inserted. Remaining region of this layer of solder is modeled with small 
Timoshenko beams with solder properties. Line spring elements are modeled adjacent to 
2D shell elements with element type S8R. This 2D shell element and line spring elements 
are given properties of solder material. Experimentally observed crack thickness is 
assigned as surface flaw for line spring element.  
 135
LINE SPRING 
ELEMENTS 
(LS6)
SHELL & 
BEAM WITH 
SOLDER 
PROPERTIES
 
Figure 95: Section view of a critical interconnect showing location of line spring LS6 
elements in Line Spring model 
 136
C3D20
S8R
LS6
C3D20
B31
 
Figure 96: Zoomed-In view of interface showing LS6 line spring and other element 
types 
A 12,500 g mechanical shock in JEDEC configuration was simulated. High 
stresses are observed in the corner solder joints.  Models are simulated for a total of 6ms 
after the impact in order to capture first few high amplitude peaks of displacement. Stress 
contours in the solder interconnect is shown in Figure 97. It shows maximum principal 
stress distribution in critical solder interconnect at critical location at different time 
intervals after the impact of the test board on a drop table. As expected from XFEM 
prediction it can be seen that stresses are higher in the interface region and goes on 
increasing at different time interval after the impact. Total area of small beam elements 
added together accounts for the area of solder layer at the interface. Failure of solder 
interconnect is caused due to flexing of the board during drop event. Corner solder 
interconnect undergoes maximum tensile loading state. As tensile loading is predominant 
 137
cause of failure, opening mode stress intensity factor is investigated at critical failure 
location. Opening mode (Mode 1) SIF variation with respect to time under simulated 
condition is shown in figure Figure 98. SIF contours on line spring LS6 elements shows 
maximum value of K
I
 at crack initiation location predicted using XFEM analysis. It can 
be seen that K
I
 goes on increasing from periphery towards the center of interconnect. It 
indicated that the damage starts at periphery and this crack travels towards center of 
solder joint. Figure 99 shows stress intensity factor plotted against time. It can be seen 
that SIF crosses the critical value evaluated by high strain rate tensile testing of bimaterial 
specimen. This bimaterial specimen has been tested at strain rate of 55s
-1
. This critical 
SIF is reached when package is dropped at 12,500g loading. Figure 100 shows time 
varying J integral contours of line spring elements at different time intervals after the 
impact. J integral contours also indicate the trend of damage progression from periphery 
towards center of the solder. 
 
 
 138
T=1.2 ms
T=2.4 ms
T=4.8 ms T=6.1 ms
 
Figure 97: Maximum principle stress contours at critical solder location at different 
time interval after the impact 
 139
 
Time=6.1 ms
Time=1.2 ms
Time=4.8 ms
Time=2.4 ms
 
Figure 98: Stress intensity factor in 
? ?mmmmN /
 in contours in line spring elements at 
different time intervals after the impact at critical failure location 
 140
 
0
10
20
30
40
50
60
70
01234567
S
t
ress In
t
e
n
s
i
t
y
 F
a
cto
r
 
Time (ms)
SIF Variation in PBGA324
Critical Stress Intensity Factor
? ?mmmmN /
 
Figure 99: SIF variation for PBGA234 package with Sn1Ag0.5Cu alloy 
 141
 
Time=6.1 ms
Time=1.2 ms
Time=4.8 ms
Time=2.4 ms
 
Figure 100: J integral contours in line spring elements at different time intervals 
after the impact at critical failure location 
 142
CHAPTER 6 ?
 
SUMMARY AND FUTURE WORK 
 
6.1 Reliability Models for Pb-free alloys and Advanced Interconnects 
In this work, extended finite element has been used with explicit time integration 
for transient dynamic reliability prediction of electronic under 1500g and 12,500g shock 
loads. Several interconnect structures have been studied including Sn3Ag0.5Cu, Cu-
reinforced Column, 63Sn37Pb, 90Pb10Sn on Ceramic ball grid array and plastic ball grid 
array devices. Interface fracture strength for the copper solder interface has been 
measured from high-strain rate tests of the bi-material specimen. XFEM model 
predictions based on measured values of interface strength have been correlated for all 
the interconnect technologies studied. The model predictions correlate well with the 
observed failure modes.  
Using line spring technique critical stress intensity factors have been evaluated 
based on extended finite element method. Evaluated properties are correlated with 
experimentally determined SIF values. Crack nucleation and propagation in single and 
double notched bimaterial specimen has been studied experimentally and analytically. 
Simulation strain vectors at crack tip and away from crack tip have been correlated with 
strain extracted using ultra high speed imaging technique. Along with strain contour 
correlation for bimaterial specimens, strong statistical agreement between experimental 
 143
and FE results has been presented. A new approach to address high strain rate events is 
explained which allows material characterization of leadfree solder alloys over range of 
strain rates. Method for fabrication of bimaterial copper-solder specimen is described 
which allows preparation of homogenous test samples with no void formation. In case of 
ball grid arrays, critical solder interconnect which is located using extended finite 
element method is simulated for line spring analysis. A technique for determination of 
fracture properties in this critical solder interconnect is developed using line spring 
method at high g shock loads. 
 
6.2 Scope for Future Work 
Linear elastic finite element models are simulated in this current work. It would 
be interesting to built material models which are nonlinear in nature. Constitutive models 
which are elastic-plastic or viscoplastic in behavior can be used to define solder alloy in 
FE models of drop and tensile tests. New crack propagation techniques similar to 
extended finite element method, cohesive zone method and line spring method can be 
implemented to address the issues of bulk solder crack and IMC cracks. 
Other failure modes observed in failure of electronics such as pad cratering, chip 
delamination, underfill cracking, material fracture in capacitors, resisters, lead fracture 
can be analyzed using these crack propagation techniques XFEM and CZM to find out 
critical failure region. Cohesive zone modeling can be used to asses the 
thermomechanical reliability of BGA interconnects also. 
Extended finite element analysis presented in this thesis addresses the event as 
quasistatic dynamic event. It would be a valuable study to carry out explicit dynamic 
 144
analysis of leadfree interconnects under drop and shock conditions. Strains fields 
measured from these global models and submodels can be used in life prediction models 
based on various higher order learning algorithms. 
 145
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