An Analytical Study of
Thermo-mechanical Failure Mechanisms
of a Leadless Chip Resistor Solder Joint
by
Luke T. Orsini
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
In Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2011
i
© Copyright 2011
by
Luke Orsini
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
LIST OF SYMBOLS ...................................................................................................... viii
ACKNOWLEDGMENT .................................................................................................. xi
ABSTRACT .................................................................................................................... xii
1. Introduction.................................................................................................................. 1
2. Background .................................................................................................................. 3
2.1
Solder Microstructure......................................................................................... 3
2.2
Coarsening ......................................................................................................... 5
2.3
Coarsening During Thermo-Mechanical Fatigue .............................................. 7
2.4
Creep .................................................................................................................. 8
2.5
Crack Initiation and Growth............................................................................. 11
2.6
Effect of Solder Joint Thickness ...................................................................... 13
3. Modeling Stresses in a Leadless Chip Resistor Solder Joint ..................................... 14
3.1
Methodology .................................................................................................... 14
3.2
Governing Equation for Solder Deformation: The Anand Model ................... 19
4. Results........................................................................................................................ 21
4.1
Plastic Strain .................................................................................................... 21
4.2
Plastic Work ..................................................................................................... 30
4.3
Comparison Case 1 to Case 4........................................................................... 39
5. Conclusions................................................................................................................ 44
6. Recommendations for Further Evaluation ................................................................. 45
References........................................................................................................................ 46
APPENDIX A .................................................................................................................. 47
APPENDIX B .................................................................................................................. 88
iii
LIST OF TABLES
Table I: Microstructural coarsening model constants at 25OC [6]..................................... 7
Table II: Leadless Chip Resistor Dimensions ................................................................. 15
Table III: Material Properties .......................................................................................... 17
Table IV: Solder (Sn63Pb37) Constants for Anand (viscoplasticity) model [10] ........... 20
Table V: Plastic Strain Results ........................................................................................ 21
Table VI: Plastic Work Results ....................................................................................... 30
Table VII: Comparison of Case 1 and Case 4 Results..................................................... 39
Table B-1: Elastic Material Properties [9] ....................................................................... 89
Table B-2: Anand Model Material Parameters [9] .......................................................... 90
iv
LIST OF FIGURES
Figure 1: Chip Resistor Mounting ..................................................................................... 1
Figure 2: Leadless Chip Resistors Mounted to a Printed Circuit Board ............................ 2
Figure 3: Sn-Pb phase diagram [1] .................................................................................... 3
Figure 4: Sn63Pb37 eutectic solder showing colonies and colony boundaries [3] ........... 4
Figure 5: Eutectic solder showing fine microstructure developed by water quenching
from 250OC [3] .................................................................................................................. 5
Figure 6: Depiction of grain growth due to thermo-mechanical fatigue [7]...................... 8
Figure 7: Leadless chip resistor showing coarsened grain structure. ................................ 8
Figure 8: Leadless chip resistor showing crack along coarsened grain. ............................ 8
Figure 9: Typical creep curve for metals and alloys including solder ............................... 9
Figure 10: Log-Log plot of creep rate vs. applied shear stress for solder [3] .................... 9
Figure 11: Crack growth constituents C* (creep) and J-integral (elastic-plastic) [1]...... 12
Figure 12: Leadless Chip Resistor R1505 Dimensions ................................................... 14
Figure 13: Finite Element Model ..................................................................................... 17
Figure 14: Thermal Cycle Profile .................................................................................... 18
Figure 15a: Plastic Strain (Von Mises) – Case 1 – End of 1st cycle ............................... 22
Figure 15b: Plastic Strain (Von Mises) – Case 1 – End of 2nd cycle ............................. 22
Figure 15c: Plastic Strain (Von Mises) – Case 1 – End of 3rd cycle .............................. 23
Figure 15d: Plastic Strain (Von Mises) – Case 1 – End of 4th cycle .............................. 23
Figure 16a: Plastic Strain (Von Mises) – Case 2 – End of 1st cycle ............................... 24
Figure 16b: Plastic Strain (Von Mises) – Case 2 – End of 2nd cycle ............................. 24
Figure 16c: Plastic Strain (Von Mises) – Case 2 – End of 3rd cycle .............................. 25
Figure 16d: Plastic Strain (Von Mises) – Case 2 – End of 4th cycle .............................. 25
Figure 17a: Plastic Strain (Von Mises) – Case 3 - End of 1st Cycle ............................... 26
Figure 17b: Plastic Strain (Von Mises) – Case 3 - End of 2nd Cycle ............................. 26
Figure 17c: Plastic Strain (Von Mises) – Case 3 - End of 3rd Cycle .............................. 27
Figure 17d: Plastic Strain (Von Mises) – Case 3 - End of 4th Cycle .............................. 27
Figure 18a: Plastic Strain (Von Mises) – Case 4 - End of 1st Cycle ............................... 28
Figure 18b: Plastic Strain (Von Mises) – Case 4 - End of 2nd Cycle ............................. 28
Figure 18c: Plastic Strain (Von Mises) – Case 4 - End of 3rd Cycle .............................. 29
v
Figure 18d: Plastic Strain (Von Mises) – Case 4 - End of 4th Cycle .............................. 29
Figure 19: Change in Plastic Work as a Function of Cycles ........................................... 30
Figure 20a: Plastic Work – Case 1 - End of 1st Cycle .................................................... 31
Figure 20b: Plastic Work – Case 1 - End of 2nd Cycle ................................................... 31
Figure 20c: Plastic Work – Case 1 - End of 3rd Cycle .................................................... 32
Figure 20d: Plastic Work – Case 1 - End of 4th Cycle .................................................... 32
Figure 21a: Plastic Work – Case 2 - End of 1st Cycle .................................................... 33
Figure 21b: Plastic Work – Case 2 - End of 2nd Cycle ................................................... 33
Figure 21c: Plastic Work – Case 2 - End of 3rd Cycle .................................................... 34
Figure 21d: Plastic Work – Case 2 - End of 4th Cycle .................................................... 34
Figure 22a: Plastic Work – Case 3 - End of 1st Cycle .................................................... 35
Figure 22b: Plastic Work – Case 3 - End of 2nd Cycle ................................................... 35
Figure 22c: Plastic Work – Case 3 - End of 3rd Cycle .................................................... 36
Figure 22d: Plastic Work – Case 3 - End of 4th Cycle .................................................... 36
Figure 23a: Plastic Work – Case 4 - End of 1st Cycle .................................................... 37
Figure 23b: Plastic Work – Case 4 - End of 2nd Cycle ................................................... 37
Figure 23c: Plastic Work – Case 4 - End of 3rd Cycle .................................................... 38
Figure 23d: Plastic Work – Case 4 - End of 4th Cycle .................................................... 38
Figure 24a: Stress (Von Mises) – Case 1 - End of 1st Cycle .......................................... 40
Figure 24b: Stress (Von Mises) – Case 1 - End of 2nd Cycle ......................................... 40
Figure 24c: Stress (Von Mises) – Case 1 - End of 3rd Cycle .......................................... 41
Figure 24d: Stress (Von Mises) – Case 1 - End of 4th Cycle .......................................... 41
Figure 25a: Stress (Von Mises) – Case 4 - End of 1st Cycle .......................................... 42
Figure 25b: Stress (Von Mises) – Case 4 - End of 2nd Cycle ......................................... 42
Figure 25c: Stress (Von Mises) – Case 4 - End of 3rd Cycle .......................................... 43
Figure 25d: Stress (Von Mises) – Case 4 - End of 4th Cycle .......................................... 43
Figure B-1: Diagram of specimen [9] .............................................................................. 89
Figure B-2: Finite Element Model ................................................................................... 90
Figure B-3: Finite element model for constant strain rate ............................................... 91
Figure B-4: Constant Strain Behavior of Sn60Pb40 Solder Strain Rate = 1.0 x 10 -2 (1/s)
......................................................................................................................................... 91
vi
Figure B-5: Constant Strain Behavior of Sn60Pb40 Solder Strain Rate = 1.0 x 10-4 (1/s)
......................................................................................................................................... 92
Figure B-6: Distribution of inelastic shear strain in the solder joint at start of the -55oC
dwell of third cycle .......................................................................................................... 93
Figure B-7: Stress-strain hysteresis loop of selected element in the solder joint under
thermal cycling ................................................................................................................ 94
vii
LIST OF SYMBOLS
A
pre-exponential factor, (1/sec)
A
Weertman-Dorn constant, (dimensionless)
AII
Weertman-Dorn constant due to grain boundary sliding, (dimensionless)
AIII
Weertman-Dorn constant due to climb and glide, (dimensionless)
a
Strain rate sensitivity of hardening or softening, (dimensionless)
B
material constant
b
Burger’s vector (m)
c1
kinetic factor dependent on matrix composition, (in m3 K/hour)
c2
reference stress, (MPa)
Do
frequency factor (1/sec)
d
mean phase diameter at time t, (m)
d
grain size, (m)
do
mean phase diameter at time t=0, (m)
dγ s
dt
steady-state strain rate (1/sec)
E
elastic (Young’s) modulus, (lb/in2)
G
shear modulus, (lb/in2)
gp
gap between pads, (in)
Ho
Hardening / softening constant, (lb/in2)
hr
height, resistor, (in)
hs
height, solder joint fillet, (in)
ht
height, resistor termination, (in)
Im, In normalizing parameter
k
Boltzmann’s constant, (1.381x10-23 J/K)
lb
length, substrate/PCB, (in)
lp
length, PCB pad, (in)
lr
length, resistor, (in)
lt
length, resistor termination, (in)
m
strain rate sensitivity of stress, (dimensionless)
Nu
Nusselt number
viii
n
material constant (dimensionless)
n, nc
stress exponent (dimensionless)
n
Strain rate sensitivity of saturation (deformation resistance), (dimensionless)
p
grain size exponent (dimensionless)
Q
activation energy, (J/mol)
R
universal gas constant, (8.314 J/molK)
r, ϴ
polar coordinates at crack tip (length, radians)
Ŝ
Coefficient of deformation resistance saturation value, (lb/in2)
so
Initial value of deformation resistance (lb/in2)
s*
saturation value (lb/in2)
T
temperature, (OK)
TH
Homologous temperature (OC)
ts
thickness, solder joint fillet, (in)
tb
thickness, substrate/PCB, (in)
tp
thickness, PCB pad, (in)
wb
width, substrate/PCB, (in)
wp
width, PCB pad, (in)
wr
width, resistor, (in)
ws
width, solder joint fillet, (in)
wt
width, resistor termination, (in)
x
cavity spacing (um)

face centered cubic (FCC) form of tin (dimensionless)

body center tetragonal (BCT) form of tin (dimensionless)

stress multiplier, (dimensionless)
a
incremental crack growth, (m)
ac
incremental crack growth due to creep, (m)
ap
incremental crack growth due to fatigue, (m)
Hg
activation energy, (kJ/mol)
τ
cyclic stress range, (MPa)
εy
yield strain
ix
εc
creep strain rate (1/sec)
ε ij
strain rate at crack tip (1/sec)
p
plastic strain rate (1/sec)
ε ij
dimensionless function
σe
Von Mises effective stress, (MPa)
σij
crack tip stress field
σy
yield stress, (stress)
σ ij
dimensionless function
τ
applied stress, (MPa)
μ
Poisson’s ratio (dimensionless)
x
ACKNOWLEDGMENT
Thank you to my wife and daughter for their continuous support and patience.
I would also like to thank Dr. Shun-Tien (Ted) Lin for his guidance and suggestions
throughout this project.
xi
ABSTRACT
This paper describes results of an analytical study of thermo-mechanical failure
mechanisms in a leadless chip resistor solder joint typically encountered in electronic
assemblies. Electronic assemblies for the commercial and military aircraft industry are
exposed to various environments that will affect their reliability. Fracturing of solder
joints is a common failure mode in these electronic assemblies. The solder used in
electronic assemblies is a tin-lead eutectic solder. The melting temperature of this type
of solder is 183OC (361OF). Under typical operating conditions temperatures as high as
120OC (248OF) are encountered (TH = 120/183 = 0.65). At this high temperature creep
deformation mechanisms become important. A review of literature on solder joint failure
is presented and it is apparent that a main cause of solder joint cracking is creep. A nonlinear Finite Element Model was created to determine the stresses and strain imposed on
a chip resistor solder joint as a result of thermal cycling. The FEM was also used to
show the effect of solder joint shape and size on the resulting stresses. The effect of
creep and other mechanisms that contribute to solder joint cracking were identified.
xii
1. Introduction
A leadless chip resistor is a leadless electronic device that is surface mounted to an
electronic assembly. The electrical connection is made by a solder joint connection
between the metalized termination on the resistor and metalized surface pad on the
printed circuit board (Figure 1 and 2)
Resistor
Termination
Solder Joint
Resistor
PCB Surface Pad
Printed Circuit Board (PCB)
Figure 1: Chip Resistor Mounting
Today tin-lead solder is used extensively in electronic assemblies. Tin-Lead solder (SnPb) has been used well over a millennium. The Romans used a Sn-Pb alloy to solder
pipes [1]. The solder plays an important role in the performance of a circuit card
assembly (CCA). For a leadless chip resistor the solder joint is not only used to make an
electrical connection. In surface mount technology, which leadless chip resistors are, the
solder also provides mechanical retention of the device.
Eutectic tin- lead solder
(Sn63Pb37) is widely used because of its good ability to wet to various metallic
substrates, high shear strength, and low processing temperature. This work focuses
exclusively on the Sn63Pb37 eutectic solder. Eutectic tin- lead solder (Sn63Pb37) has a
melting temperature (Tm) of 183OC (361.4OF). The environment that solder is being
used is continually becoming more demanding. In high reliability electronic assemblies
the solder typically operates above 0.65Tm (119OC, 246OF) and creep damage becomes
significant.
These assemblies are subjected to changes in temperature due to the operating
environment. The assemblies could be exposed to temperatures of -40OC to 125OC
(-40OF to -57OF). Any temperature change will induce stresses and strains due to
differences in coefficients of thermal expansion (CTE) between resistor and printed
1
circuit board; solder and resistor; solder and PCB surface pad. In addition to the CTE
differences the material stiffness of each element differs.
The failure of solder joints in electronics is often by low-cycle fatigue, the strains and
resultant stresses produced by the temperature cycles and the difference in coefficient of
thermal expansion [7].
Figure 2: Leadless Chip Resistors Mounted to a Printed Circuit Board
2
2. Background
2.1 Solder Microstructure
The microstructure of solder governs the deformation and failure of solder joints. As the
solder joint is aged, thermal cycled or deformed the microstructure (dislocation arrays,
grain size) evolves and the mechanical properties change over time. The mechanical
properties of a solder joint change with the evolving microstructure. Solder joints have a
complex microstructure are used at high homologous (similar in structure) temperatures
and deform at relatively low loads. This results in plastic deformation of the solder joint
that is rarely uniform. Common solders are typically micro structurally unstable. From
a macroscopic perspective solders often exhibits strain-softening [3].
From a
microscopic perspective it is unlikely to know the local properties of the solder and how
the deformation develops [3].
This paper will focus on Sn63Pb37 solder. Sn63Pb37 is a single eutectic binary solder
system. The phase diagram is shown in Figure 3.
Figure 3: Sn-Pb phase diagram [1]
3
The lowest melting point occurs at a eutectic composition where the liquid solidifies into
a mixture of two solids. The single eutectic point occurs at 183OC (361.4OF). Above
183OC there is the homogeneous liquid phase. Below 183OC the liquid transforms into
two (2) stable solid phases, a lead rich  phase and a tin rich  phase. The lead rich
phase has a face center cubic (FCC) and the tin rich phase has a body centered tetragonal
(BCT) structure. During cooling the microstructure forms from the liquid at constant a
constant temperature of 183OC. If the solder is slowly cooled the solid solutions grow
together parallel to each other in grain-like colonies. (See Figure 4) Faster cooling rates
results in a non-lamellar structure shown in Figure 5.
Figure 4: Sn63Pb37 eutectic solder showing colonies and colony boundaries [3]
4
Figure 5: Eutectic solder showing fine microstructure developed by water
quenching from 250OC [3]
The grain-like colony size as well as the interlamellar spacing is important to the
mechanical properties of the solder. It has been demonstrated that isothermal fatigue life
decreases with an increase in colony size [1]. Also, the tensile strength of unidirectional
solidified eutectic solder and tensile strength and ductility of random solidified eutectic
solder vary as a function of interlamellar spacing [1].
2.2 Coarsening
Coarsening occurs at room temperature over an extended period of time and is
accelerated at elevated temperatures. At room temperature Sn63Pb37 eutectic solder is
already at a relatively high homologous temperature. Therefore, the diffusion rate is
significant in the solder joint at room temperature and the microstructure of the solder is
not stable. Immediately after solidification the Pb-rich phase is supersaturated with Sn.
Within hours the Sn decomposes as precipitates within the Pb phase or as Sn grains if
the microstructure is very fine.
At room temperature over a period of approximately 30 days after solidification both the
eutectic solder grains and Sn-rich precipitates within the Pb phase undergo significant
coarsening. This coarsening (grain growth) results in the decrease of shear strength as
5
the coarsening occurs. Room temperature aging has been reported to reduce the shear
strength of Sn63Pb37 solder by 10% [1]. The grains will grow overtime as the grain
structure reduces the internal energy of a fine grain structure. After about 30 days, the
coarsening slows down and the change in material properties also slows down. This
microstructure change will continue until equilibrium is achieved.
[Hacke, Sprecher and Conrad, 1993] experimentally observed the solder microstructure
coarsens in accordance with cubic coarsening model [4] [6].
 Hg 
c1t
(1)
exp  

T
 RT 
Where d is the mean phase diameter at time t, (µm), d0 is the mean phase diameter (also
d3  t   d30 
referred to as the initial grain size @ t=0), (µm), c1 is the kinetic factor that depends on
the matrix composition in (µm3 K/hour), ΔHg is the activation energy for volume
diffusion of atoms, (KJ/mol), R is the universal gas constant (J/molK) and T is the
absolute temperature in OK.
As an example, using the coarsening model constants in Table I, a time of 720 hours (30
days) and at a temperature of 70OC (343OK) and substituting into the above equation the
grain size increases from an initial diameter of 8.3 µm to 8.5 µm and at 125OC (398OK)
the grain size increased to 16.0 µm.
The above equation neglects the effect of mechanical stress or strain. To include the
mechanical influence the more generalized equation [Arrowood, 1990; Nabarro, 1998]
has been proposed [8].
     
(2)
 1    
   c2  
Where c2 is the reference stress, (MPa), Δτ the cyclic stress range, (MPa) and n c is the
 Hg
ct
d  t   d  t   1 exp  
T
 RT
3
nc
3
0
stress exponent. Since the cubic coarsening model, equation 1 is the bulk (or volume)
diffusion of atoms a value of unity is selected for nc [6].
6
Table I: Microstructural coarsening model constants at 25OC [6]
Model Parameter
Temperature (T)
Activation energy for volume diffusion of
atoms (ΔHg)
Universal gas constant (R)
Matrix composition constant (c1)
Stress exponent (nc)
Initial grain size (d0)
Value
25OC (298OK)
94 KJ/mol
8.314 J/molK
4.2e15 µm3 K/hour
1
8.3 µm
2.3 Coarsening During Thermo-Mechanical Fatigue
Thermomechanical stresses caused by temperature in high temperature environments
also produce changes in the solder microstructure. The microstructure will change from
a fine grained mixture of Sn-Pb to a coarse grained structure along a thin band parallel to
the direction of strain. This coarsened region is weaker and is known to be the region
through which cracks propagate. As the grains grow due to thermo-mechanical fatigue
micro-voids develop at the grain boundary intersections; the micro-voids develop into
micro-cracks which develop into macro-cracks the lead to fracture. Figure 6 shows the
development of the coarsened grain and the effect on fatigue damage. When
approximately 25% of the fatigue life is consumed micro-voids are formed at the grain
boundary intersections and grow into micro-cracks after approximately 40% of the
fatigue life. The micro-cracks coalesce into macro-cracks leading to failure [7]. Figure
7 shows the coarsening of the grain structure under the resistor termination and
extending through the bulk solder fillet. Cracks can be seen to develop in this location.
Figure 8 shows a macro-crack has developed through the solder joint causing failure.
7
Figure 6: Depiction of grain growth due to thermo-mechanical fatigue [7]
Figure 7: Leadless chip resistor showing
coarsened grain structure.
Figure 8: Leadless chip resistor showing
crack along coarsened grain.
2.4 Creep
Solder is used at high operating temperatures therefore creep lays a major role in the
mechanical behavior of the solder and solder joint. Creep occurs when plastic
deformation in the solder due to stress and temperature over time leads to unacceptable
large displacements. There are three stages of creep; (I) primary, (II) secondary, and
(III) tertiary creep. A typical creep curve is shown in Figure 9. Region II, steady state
creep is generally used to describe the creep behavior of metals.
8
Strain
III
II
I
Time
Figure 9: Typical creep curve for metals and alloys including solder
The steady state creep behavior of solder can also be described as shown in Figure 10 as
a log-log plot of shear rate vs. shear stress.
The figure shows four regions. For
Sn63Pb37 solder grain (phase) size influences Region I and II. Regions III and IV are
Log shear rate (p)
independent of grain size.
IV n>10
III
n=3-7
II
I
n=2
n=3
Log shear stress ()
Figure 10: Log-Log plot of creep rate vs. applied shear stress for solder [3]
Steady state creep can be generally expressed by the Weertman-Dorn equation [3]
9
p
n
dγ s AGb  b   τ 

    Do exp   Q kT 
dt
kt  d   G 
dγ s
= steady-state strain rate
dt
(3)
Where G is the shear modulus, b is the Burgers vector, k is the Boltzmann’s constant, T
is the absolute temperature, d the grain size, τ is the applied shear stress, Do the
frequency factor, Q is the activation energy to cause deformation, n the stress exponent,
p the grain size exponent and A is a constant.
D. Grivas et al. [5] investigated the deformation process of Sn-Pb eutectic solder and
found the deformation in Region II is controlled by grain boundary sliding
(superplasticity) and in Region III deformation is controlled by dislocation climb and
glide (show example). Deformation in Region III is sometimes called matrix creep [3].
This suggests both superplastic and matrix creep deformation exists in Sn-Pb eutectic
solder. Based on the assumption that both these mechanisms occur at the same time and
independent of each other – superplastic deformation occurs at low stresses (Region II),
and dislocation climb and glide occur at higher stresses (Region III) the two deformation
mechanisms can be combined.
  Q a ,II  A III 7.1
  Q a ,III 
d s A II 1.96





exp


exp
 kT  T
dt
T d1.8


 kT 
(4)
In region III at intermediate stresses the strain rate depends on a power function of stress
and in region IV at higher stresses the strain rate is expressed as an exponential function
of stress. For these conditions the stress can be expressed as a hyperbolic sine function
where σe is the von-Mises effective stress,  represents the stress level where the power
law breaks down (transition from Region III to Region IV), Q is the activation energy, R
is the universal gas constant, T is absolute temperature, n stress power exponent, and A
is a constant.
n
 Q 
  A sinh  e   exp 

 RT 
ε = creep strain rate
10
(5)
2.5 Crack Initiation and Growth
Fatigue failures occur in solder joints due to cyclic loads and repeated reversal bending.
Failures in materials arise from crack initiation and propagating under these cyclic loads.
These fatigue failures can be thought of as a process of crack initiation and propagation.
In any material including solder there will be initiation sites. If the applied loads are
small the strength of the material is not affected. At higher loads irreversible changes in
the material takes place and a fatigue fracture will initiate at a discontinuity or other
stress riser in the material. Once the fracture is initiated it will grow or propagate until
the cross section is reduced until it can no longer support the loading and then the
material will crack. In practical applications vibration, thermal shock and mechanical
shock are possible, but the primary failure mechanism of concern in a surface mount
solder joint is cyclic differential thermal expansion. [2]
Cracks that develop in Sn63Pb37 eutectic solder joints exposed to thermal cycling are
intergranular, i.e. the cracks propagate along the grain boundaries that separate the Sn
rich and Pb rich phases. The crack growth mechanism at high homologous temperature
and low cycle frequency has been suggested to be nucleation, growth, and coalescence
of cavities along the grain boundaries.
During thermal cycling creep couples with the fatigue mechanism such that the creep
crack growth is enhanced by the fatigue mechanism. High temperature fatigue tests on
eutectic solder concluded that fatigue resulted in the development of cavities in the ascast and superplastic eutectic alloy.
The cavitations occurred at the intercolony
boundaries of the as-cast material (grain size = 50-80 m) and between the separate the
Sn rich and Pb rich phases in the superplastic eutectic (grain size = 5.8 m). Once the
initial crack is formed by one of the above mechanism the crack will propagate under the
applied stress until fracture occurs.
Numerically, fatigue crack growth for the solder can be described by the J (elasticplastic) integral. The J-integral characterizes the stress/strain field at the crack tip. The
C* integral is analogous to the J-integral. The C* integral accounts for the creep portion
of crack growth at the crack tip. See figure 11.
11
Creep
 C 
ij  

 BI n r 
 C 
ij  

 BI n r 
(6)
Elastic-Plastic
1
n
 n 1
 n 1
1
 m 1
ij    ,


J
ij  
 x y  y I m r 


ij    ,


J
ij  x 
 x y  y I m r 


m
ij   
 m 1
ij   
Where σij is the crack tip stress field, ε ij is the strain rate at the crack tip, B, m, and n are
material constants, In and Im are normalizing parameters, εy is yield strain, σy is the yield
stress, x represents the cavity spacing, r and ϴ are the polar coordinates at the crack tip,
σ ij , ε ij are dimensionless functions, and a is the incremental crack growth.
Figure 11: Crack growth constituents C* (creep) and J-integral (elastic-plastic) [1]
12
2.6 Effect of Solder Joint Thickness
An increase in solder joint thickness should decrease the strain and therefore increase the
fatigue life. However for eutectic or near eutectic Sn-Pb solder an increase in solder
joint thickness does not have a large effect on the microstructure. [1] Thicker solder
joints solidify at a slower rate. [3] This is attributed to the heterogeneous coarsened band
where the strain is concentrated, making the total thickness of the solder joint less
effective. An increase in the amount of shear strain imposed on a given solder joint
thickness results in a more rapid coarsening and leads to quicker failures.
13
3. Modeling Stresses in a Leadless Chip Resistor Solder Joint
There have been numerous articles confirming that the primary failure mechanism for
leadless chip resistors is thermo-mechanical fatigue and creep. The performance of the
resistor hence the electronic assembly is dependent on the reliability of the solder joint to
maintain an electrical connection. As discussed above, the failure mechanism of the
solder joint is complex. Finite element analysis is used extensively in industry to
determine the fatigue damage and creep behavior in solder joints.
3.1 Methodology
In this study ANSYS APDL is the finite element software was used to estimate the stress
and strain in a leadless chip resistor solder joint. ANSYS APDL is a commercially
available software package. The leadless chip resistor is a size R1505 resistor. The
device dimensions and the nominal solder joint geometry are shown in Figure 12 and
Table II.
Figure 12: Leadless Chip Resistor R1505 Dimensions
14
Table II: Leadless Chip Resistor Dimensions
hr
Height, resistor
Dimension
(in)
.024
lr
Length, resistor
.155
wr
Width, resistor
.050
hs
Height, solder joint fillet
.024*
ts
Thickness, solder joint
.002*
ws
Width, solder joint fillet
.050
ht
Height, resistor termination
.024
lt
Length, resistor termination
.015
wt
Width, resistor termination
.050
tp
Thickness, PCB pad
.0012
lp
Length, PCB pad
.0475
wp
Width, PCB pad
.060
tb
Thickness, substrate/PCB
.063
lb
Length, substrate/PCB
.310
wb
Width, substrate/PCB
.310
gp
Gap between pads
.105
Symbol
*
Description
Case 1: ts = .002, hs = .026
Case 2: ts = .001, hs = .025
Case 3: ts = .004. hs = .028
From the geometry shown, a two dimensional finite element model of the device was
created. A 2-D finite element model was selected to minimize computing time. The use
of the 2-D model was validated by simulating the model used in Wang, et al. [9]. See
Appendix B. By establishing symmetry boundary conditions (out-of-plane translations
and in-plane rotations are set to zero) [8] a half model can be used in the analysis and
still provide accurate results. The finite element model is created by running an ANSY
APDL macro. Four cases will be analyzed; Case 1 has a typical solder joint fillet. The
15
solder joint thickness between the resistor termination and solder pad is 0.002 inch thick,
Case 2 has a typical solder fillet with the solder joint thickness reduced to 0.001 inch;
Case 3 has a typical solder fillet with the solder joint thickness increased to 0.004 inch.
These first three cases were used to analyze the effect of solder joint thickness. Case 4
had a large bulbous solder fillet. The solder thickness between the resistor termination
and solder pad is 0.002 inch.
A macro was created for each of the four cases. The macro defines the geometry,
material properties including the Anand constants, mesh parameters, and boundary
conditions. The macro also defines the thermal cycle profile and initiates the solve
command. Appendix A contains the macros used for the various cases.
Figure 13 shows the finite element model created. The model is composed of a two
element types ANSYS Plane182 and Visco106. The Plane182 element is 2-D quad 4
node element with two degrees of freedom on each node: translation in the x, y
directions. The element supports plasticity, hyperelasticity, creep, stress stiffening, large
deflections and large strain. [8] The Visco106 element is a 2-D quad 4 node element
with three degrees of freedom at each node: translation in the x, y and z directions. The
element is used to represent highly nonlinear behavior. It is designed to solve rateindependent large strain plasticity problems. The Visco106 can also be defined as a 2-D
triangular 3 node element that makes it suited to modeling the irregular geometry of a
solder joint fillet.
16
Figure 13: Finite Element Model
In this analysis the resistor, resistor termination, and PCB pad are represented as
isotropic linear elastic solids. The substrate (PCB) is represented as an orthotropic linear
elastic solid and the solder is considered a visco-plastic material.
The material
properties used in the analysis are shown in Table III.
Table III: Material Properties
Resistor
Resistor
Termination
Ceramic
3.5E6
-
0.25
Coefficient
of
Thermal
Expansion
(1/OC)
40E-6
AgSnCu
1.2E7
-
0.37
18.9E-6
Substrate
(PCB)
Epoxy (GFG)
with Cu layers
(Ex) 2.5E6
(Ey) 1.0E6
(Ez) 2.5E6
18.7E6
3.6E6
(GxY) 0.4E6
(Gxz) 0.5E6
(Gyz) 0.4E6
-
(Nuxy) 0.26
(Nuxz) 0.14
(Nuyz) 0.26
0.35
0.39
(x) 18E-6
(y) 70E-6
(z) 18E-6
17.5E-6
23.4E-6
Description
Material
Young’s
Modulus,
E
(psi)
Shear
Modulus,
G
(psi)
Poisson’s
Ratio,

PCB Pad
Cu
Solder
Sn63Pb37
 Gravity (g) = 386.4 in/sec2
17
A cyclic thermal load condition is imposed in the analysis. The temperature will vary
from -40OC to 125OC (-40OF to 257OF). The transition rate from the minimum to
maximum temperature is 10OC per minute and a 20 minute dwell at the temperature
extremes. This thermal cycle profile based on JEDEC standards and used to represent
the environment encountered in the high reliability electronics industry to determine low
cycle fatigue limitations of a given device. The thermal cycle profile is shown in Figure
14. The purpose of thermal cycle load is to induce plastic work due to the mismatch in
the materials coefficients of thermal expansion.
140
120
Temperature (OC)
100
80
60
40
20
0
-20
-40
1st cycle
-60
0
50
2nd cycle
100
3rd cycle
150
200
Time (minutes)
Figure 14: Thermal Cycle Profile
18
4th cycle
250
300
3.2 Governing Equation for Solder Deformation: The Anand Model
In ANSYS there are various models available to simulate visco-plasticity. The Anand
model was originally developed for metal forming applications. It is however applicable
to applications that involve strain and temperature effect including solder joints and high
temperature creep [8]. The Anand model does not require any explicit yield condition
and loading /unloading criteria because it assumes that plastic flow occurs at all non-zero
stress values. The Anand model represents the non-linear rate dependent stress-strain
relation of solder. The model uses a single scalar internal variable (s), called the
deformation resistance that corresponds to the isotropic resistance of the solder to plastic
flow. The deformation resistance (s) is an average resistance and represents the
resistance of the plastic flow from such deformation mechanisms as dislocation density,
solid solution hardening and grain size effects [9]. Therefore the deformation resistance
(s) can be considered proportional to the equivalent stress.
σ = c  s; c < 1
And c is defined as:
m
 
1
 Q  
1  p
(7)
c  sinh  exp 
 

 RT   
 A
Where  p is the plastic strain rate, A is the pre-exponential factor, Q the activation
energy, m is the strain rate sensitivity,  is the stress multiplier, R is the universal gas
constant, and T is the absolute temperature. Rearranging the equation to have the strain
rate a function of stress and deformation resistance the equation is re-written as:
1m
 Q 
  
p  A exp  
 sinh    
 RT  
 s 
(8)
From the above equation
 p
 Q 
s  sˆ  exp 
(9)

 RT  
A
Where s* the saturation value of s, ŝ is the coefficient for deformation resistance
n
*
saturation value and n the strain rate sensitivity. From the development of the above
19
equations there are nine material parameters that need to be defined in the Anand model
See Table IV.
Table IV: Solder (Sn63Pb37) Constants for Anand (viscoplasticity) model [10]
Constant
so
Q/R
A

m
Ho
Ŝ
n
a
Description
Initial value of deformation
resistance
Activation energy / Universal gas
constant
Pre-exponential factor
Stress multiplier
Strain rate sensitivity of stress
Hardening / softening constant
Coefficient of deformation
resistance saturation value
Strain rate sensitivity of
saturation (deformation
resistance) value
Strain rate sensitivity of hardening
or softening
20
Value
Unit
1800
Stress (psi)
9400
(OK)
4E6
1.5
0.303
2E5
1 / time (1/sec)
Dimensionless
Dimensionless
Stress (psi)
2000
Stress (psi)
0.07
Dimensionless
1.3
Dimensionless
4. Results
4.1 Plastic Strain
The finite element model of a leadless chip resistor was conducted for the four cases
described below:

Case 1 has a typical solder joint fillet. The solder joint thickness between the resistor
termination and solder pad is 0.002 inch thick.

Case 2 has a typical solder fillet with the solder joint thickness reduced to 0.001
inch; Case 3 has a typical solder fillet with the solder joint thickness increased to
0.004 inch.

Case 4 had a large bulbous solder fillet. The solder thickness between the resistor
termination and solder pad is 0.002 inch.
Table V shows the maximum accumulated plastic strain observed. Figures 15-18 show
the Von Mises plastic strain distribution in the solder joint for all four cases at the end of
the 1st, 2nd, 3rd and 4th thermal cycle for all four cases The figures show the relatively
large strains are occurring in the solder below the chip resistor bottom termination
There is a plastic strain distribution that extends at from the bottom corner of the
termination and solder interface through the bulk solder fillet
The plastic strain
increases as the number of thermal cycles increases as shown in Table V. It should be
noted the majority of plastic strain occurs during the first cycle. Case 3 is shown to have
the lowest plastic strain.
Table V: Plastic Strain Results
1st Cycle
2nd Cycle
3rd Cycle
4th Cycle
Case 1 (nominal solder joint)
0.0101
0.0149
0.0201
0.0254
Case 2 (min solder joint)
0.0153
0.0150
0.0186
0.0228
Case 3 (max solder joint)
0.0059
0.0084
0.0113
0.0142
Case 4 (large fillet)
0.0112
0.0165
0.0222
0.0279
Plastic Strain, Von Mises (in/in)
21
Figure 15a: Plastic Strain (Von Mises) – Case 1 – End of 1st cycle
Figure15a shows largest strains occur in the solder at the interface of the chip resistor
bottom termination and solder.
Figure 15a also shows a strain distribution that
extends from the corner bottom of the termination and solder interface at
approximately 30O through the bulk solder fillet.
Figure 15b: Plastic Strain (Von Mises) – Case 1 – End of 2nd cycle
Figure 15b shows a similar distribution of plastic strain as Figure 15a with the largest
strains occurring in the same areas. There is a slight increase in the magnitude of the
strain.
22
Figure 15c: Plastic Strain (Von Mises) – Case 1 – End of 3rd cycle
The plastic strain distribution in Figure 15c is similar to Figure 15a and Figure 15b
with a slight increase in the magnitude of the strain. The rate of change in the
magnitude appears to increase slightly.
Figure 15d: Plastic Strain (Von Mises) – Case 1 – End of 4th cycle
Figure 15d again shows a similar distribution of plastic strain with a slight increase in
magnitude. The strain distribution that extends distribution from the corner bottom of
the termination and solder interface at approximately 30O through the bulk solder fillet
is still evident.
23
Figure 16a: Plastic Strain (Von Mises) – Case 2 – End of 1st cycle
Figure 16a shows two areas of higher plastic strain in the solder at the corners of the
bottom termination and solder interface. Similar to Case 1 there is a high strain
distribution that extends approximately 30O form the bottom right corner of the
termination through the bulk solder. The magnitude of the strain is larger than the
Case 1 model.
Figure 16b: Plastic Strain (Von Mises) – Case 2 – End of 2nd cycle
Figure 16b shows a similar distribution of plastic strain as Figure 16a with the largest
strains occurring in the same areas. There is a more pronounced gradient that extends
into the bulk solder. What is interesting is the magnitude of the strain has decreased
slightly.
24
Figure 16c: Plastic Strain (Von Mises) – Case 2 – End of 3rd cycle
Figure 16c shows the strain distribution at the bottom termination and solder interface
is becoming more uniform. The largest strains still occur in the same areas. The
distribution of strain extending into the bulk solder is similar as in Figure 16b. The
magnitude of the strain has increased slightly from the end of the 1st cycle (Figure
16a) and 2nd cycle (Figure 16b).
Figure 16d: Plastic Strain (Von Mises) – Case 2 – End of 4th cycle
Figure 16d shows the similar distribution of plastic strain with a slight increase in
magnitude. The strain distribution that extends distribution from the corner bottom of
the termination and solder interface through the bulk solder fillet is still evident.
25
Figure 17a: Plastic Strain (Von Mises) – Case 3 - End of 1st Cycle
You can see the very similar distribution of plastic strain in Figure 17a as in Case 1
(Figure 15a) with largest strain is occurring in the solder at the interface of the chip
resistor bottom termination and solder. The strain distribution that extends from the
corner bottom of the termination and solder interface at approximately 30O through the
bulk solder fillet is also present.
The magnitude of the strain has decreased
approximately 50% from the 1st case. This can be attributed to the increased solder
joint thickness under the termination.
Figure 17b: Plastic Strain (Von Mises) – Case 3 - End of 2nd Cycle
Figure 17b shows a similar distribution of plastic strain as Figure 17a with the largest
strains occurring in the same areas. There is a slight increase in the magnitude of the
strain.
26
Figure 17c: Plastic Strain (Von Mises) – Case 3 - End of 3rd Cycle
The plastic strain distribution in Figure 17c is similar to Figure 17a and Figure 17b
with a slight increase in the magnitude of the strain. The strain in the bulk solder
continues to grow as in the previous two cases.
Figure 17d: Plastic Strain (Von Mises) – Case 3 - End of 4th Cycle
Figure 17d continues to show the similar distribution of plastic strain with a slight
increase in magnitude. The strain distribution that extends distribution from the corner
bottom of the termination and solder interface through the bulk solder fillet is still
evident with an increase in the magnitude.
27
Figure 18a: Plastic Strain (Von Mises) – Case 4 - End of 1st Cycle
Figure18a shows largest strains occur in the solder at the interface of the chip resistor
bottom termination and solder. The distribution and magnitude of the strain is almost
identical to that of Figure 15a. What is evident in Case 4 is the strain distribution
extending into the bulk solder at approximately 30O is not as pronounced as the
previous cases.
Figure 18b: Plastic Strain (Von Mises) – Case 4 - End of 2nd Cycle
Figure 18b shows a similar distribution of plastic strain as Figure 18a with the largest
strains occurring in the same areas and a slight increase in the magnitude of the strain.
28
Figure 18c: Plastic Strain (Von Mises) – Case 4 - End of 3rd Cycle
The plastic strain distribution in Figure 18c is similar to Figure 18a and Figure 18b
with a slight increase in the magnitude of the strain. The plastic strain distribution in
the bulk solder appears to be more uniform.
Figure 18d: Plastic Strain (Von Mises) – Case 4 - End of 4th Cycle
Figure 18d again shows a similar distribution of plastic strain of Figures 18a, 18b, and
18c. The magnitude of the plastic strain continued to increase slightly.
29
4.2 Plastic Work
The plastic work is in indication of the damage that is occurring in the solder joint. Table
VI tabulates the accumulated plastic work.
Figure 19 is a plot of the change in plastic
work as a function of cycles. Figure 19 show that the plastic work or damage in the
solder joint becomes steady state after the first thermal cycle. The largest plastic work
occurs in the solder below the resistor termination as was indicated for the plastic strain
condition. Case 3 which has the lowest plastic work and the large fillet did not provide
any significant benefit. Figures 20-23 shows the plastic work that accumulates in the
solder joint for the four cases.
Table VI: Plastic Work Results
1st Cycle
2nd Cycle
3rd Cycle
4th Cycle
Case 1 (nominal solder joint)
166.201
320.116
474.076
628.040
Case 2 (min solder joint)
263.220
516.934
770.789
1024.646
Case 3 (max solder joint)
109.850
205.927
301.959
397.987
Case 4 (large fillet)
166.421
320.066
473.726
627.389
Plastic Work
Change in Plastic Work as a Function of Cycles or Time
Plastic Work
300.00
250.00
200.00
150.00
100.00
50.00
0.00
0
1
2
3
4
Cycle
Case 1 (nominal solder joint)
Case 2 (min solder joint)
Case 3 (max solder joint)
Case 4 (large fillet)
Figure 19: Change in Plastic Work as a Function of Cycles
30
Figure 20a: Plastic Work – Case 1 - End of 1st Cycle
Figure 20a shows the highest level of plastic work in the solder joint occurs in the area
of highest plastic strain. The highest level of plastic work is located at the bottom right
corner of the resistor solder interface.
Figure 20b: Plastic Work – Case 1 - End of 2nd Cycle
The distribution of plastic work shown in Figure 20b is the same as shown in Figure
20a at the end of the 1st cycle. The magnitude of the plastic work done during the 2nd
cycle is slightly higher than the plastic work during the 1st cycle.
31
Figure 20c: Plastic Work – Case 1 - End of 3rd Cycle
As in the previous figures the plastic work distribution is similar. The magnitude
continues to increase. The amount of the plastic work accomplished during the 3rd
cycle is approximately the same as plastic work accomplished during the 2nd cycle.
Figure 20d: Plastic Work – Case 1 - End of 4th Cycle
The plastic work distribution at the end of the 4th cycle is similar to the previous
figures or cycles. The amount of the plastic work accomplished during the 4th cycle is
approximately the same as plastic work accomplished during the previous cycle.
32
Figure 21a: Plastic Work – Case 2 - End of 1st Cycle
As in the case 1 results Figure 21a shows the highest level of plastic work in the solder
joint occurs in the area of highest plastic strain with the highest level of plastic work
located at the bottom right corner of the resistor solder interface. The magnitude of
plastic work is greater than case 1.
Figure 21b: Plastic Work – Case 2 - End of 2nd Cycle
The distribution of plastic work shown in Figure 21b is the same as shown in Figure
21a at the end of the 1st cycle. The accumulated magnitude of the plastic work at the
end of the 2nd cycle has doubled.
33
Figure 21c: Plastic Work – Case 2 - End of 3rd Cycle
The distribution of plastic work shown in Figure 21c is the same as the distribution at
the end of the 1st and 2nd cycle. The magnitude continues to increase. The amount of
the plastic work accomplished during the 3rd cycle is approximately the same as
plastic work accomplished during the 2nd cycle.
Figure 21d: Plastic Work – Case 2 - End of 4th Cycle
As in case 1 distribution at the end of the 4th cycle is similar to the previous figures or
cycles.
The amount of the plastic work accomplished during the 4th cycle is
approximately the same as plastic work accomplished during the previous cycle.
34
Figure 22a: Plastic Work – Case 3 - End of 1st Cycle
The plastic work distribution shown in Figure 22a is to the case 1 model (Figure 20a)
with largest plastic work occurring at the same location. As with the magnitude of the
plastic strain, the magnitude of the work has decreased approximately 50% from the
1st case. This can be attributed to the increased solder joint thickness under the
termination.
Figure 22b: Plastic Work – Case 3 - End of 2nd Cycle
Figure 22b shows a similar distribution of plastic strain as Figure 22a with the largest
strains occurring in the same areas. The accumulated magnitude of the plastic work at
the end of the 2nd cycle has doubled, as in the previous cases.
35
Figure 22c: Plastic Work – Case 3 - End of 3rd Cycle
The plastic work distribution in Figure 22c has not changed from Figure 22a and
Figure 22b. The amount of the plastic work accomplished during the 3rd cycle is
approximately the same as plastic work accomplished during the 2nd cycle.
Figure 22d: Plastic Work – Case 3 - End of 4th Cycle
The distribution at the end of the 4th cycle is similar to the previous cycles. The
amount of the plastic work developed during the 4th cycle is approximately the same
as plastic work accomplished during the previous cycle.
36
Figure 23a: Plastic Work – Case 4 - End of 1st Cycle
Figure 23a shows the largest amount of plastic work occurs in the solder at the
interface of the chip resistor bottom termination and solder with a concentration at the
bottom right corner. As in case 1, the highest levels are in an area of highest plastic
strain.
Figure 23b: Plastic Work – Case 4 - End of 2nd Cycle
Figure 23b shows a similar distribution of plastic work as Figure 23a with the largest
plastic work occurring in the same areas and a 2x increase in the magnitude of the
work.
37
Figure 23c: Plastic Work – Case 4 - End of 3rd Cycle
The plastic wok distribution in Figure 23c is similar to Figure 23a and Figure 23b. The
plastic work accomplished during the 3rd cycle is approximately the same as plastic
work accomplished during the 2nd cycle.
Figure 23d: Plastic Work – Case 4 - End of 4th Cycle
Figure 23d shows a similar distribution of plastic strain of Figures 23a, 23b, and 23c.
The amount of the plastic work developed during the 4th cycle is approximately the
same as plastic work accomplished during the previous cycle.
38
4.3 Comparison Case 1 to Case 4
Figures 24 and 25 shows the Von Mises stress distribution in the solder joint for Case 1
and Case 4. The previous Figures show the plastic strain and plastic work results. Table
VII tabulates the results for Case 1 and Case 4. The larger stresses occur in the solder
underneath the chip resistor termination as did the plastic strain and work. Comparing
the results between Case 1 and Case 4 show no significant differences in the results
obtained.
Table VII: Comparison of Case 1 and Case 4 Results
1st Cycle
2nd Cycle
3rd Cycle
4th Cycle
Case 1 (nominal solder joint)
0.0101
0.0149
0.0201
0.0254
Case 4 (large fillet)
0.0112
0.0165
0.0222
0.0279
Case 1 (nominal solder joint)
166.201
320.116
474.076
628.040
Case 4 (large fillet)
166.421
320.066
473.726
627.389
Case 1 (nominal solder joint)
342.949
341.178
341.026
340.999
Case 4 (large fillet)
344.492
338.152
337.458
337.399
Plastic Strain, Von Mises (in/in)
Plastic Work
Stress, Von Mises (psi)
39
Figure 24a: Stress (Von Mises) – Case 1 - End of 1st Cycle
The distribution of Von Mises stress shown in Figure 24a reflects the plastic strain
distribution with the largest stresses occurring in the solder at the interface of the chip
resistor bottom termination and solder. Figure 23a also shows a stress distribution that
extends from the corner bottom of the termination and solder interface at
approximately 30O through the bulk solder fillet which was seen with plastic strain.
Figure 24b: Stress (Von Mises) – Case 1 - End of 2nd Cycle
Figure 24b shows a similar distribution of stress as Figure 24a with the largest stress
occurring in the same areas. There is a slight decrease in the magnitude of the stress
caused by stress relaxation.
40
Figure 24c: Stress (Von Mises) – Case 1 - End of 3rd Cycle
The plastic strain distribution in Figure 24c is similar to Figure 24a and Figure 24b
with the magnitude of stress decreasing slightly. The rate of change in the magnitude
appears to decrease slightly.
Figure 24d: Stress (Von Mises) – Case 1 - End of 4th Cycle
Figure 24d continues to show a similar distribution of Von Mises stress. The stress
level continues to decrease slightly. The stress distribution that extends from the
corner bottom of the termination and solder interface at approximately 30 O through the
bulk solder fillet is still evident as it was with plastic strain.
41
Figure 25a: Stress (Von Mises) – Case 4 - End of 1st Cycle
Figure 25a shows largest stress occurs in the solder at the interface of the chip resistor
bottom termination and solder as in case 1. The distribution and magnitude of the
strain is almost identical to that of Figure 24a. What is evident in Case 4 is the stress
distribution extends into the bulk solder approximately parallel to the x-direction.
Figure 25b: Stress (Von Mises) – Case 4 - End of 2nd Cycle
Figure 24b shows a similar distribution of Von Mises stress as Figure 25a with the
largest strains occurring in the same areas with a slight decrease in the stress level.
42
Figure 25c: Stress (Von Mises) – Case 4 - End of 3rd Cycle
The stress distribution in Figure 25c is similar to Figure 25a and Figure 25b with the
stress level decreasing.
Figure 25d: Stress (Von Mises) – Case 4 - End of 4th Cycle
Figure 25d again shows a similar distribution of plastic strain of Figures 25a, 25b, and
25c. The magnitude of the stress continued to decrease as a result of stress relaxation.
43
5. Conclusions
This report presents results of an analytical study of the thermo-mechanics of a leadless
chip resistor solder joint used in electronic assemblies. The mechanisms that can cause
cracking of the solder joints of leadless surface mount chip resistors under typical
operating conditions are reviewed and the resultant changes in the solder micro-structure
and properties were identified.
Because of the solder low melting temperature, it
undergoes significant microstructural changes that affect the reliability of the solder
joint. The cubic coarsening model showed how the grain size increased as a function of
time or temperature, with temperature having a greater influence.
A non-linear Finite Element Model was developed to estimate the strains and stresses
developed in the solder joint. The effects of temperature cycling, and solder joint shape
and size on the predicted stress field were quantified. The FEM predicted the highest
strains and stresses occur in the solder below the chip resistor bottom termination and
surface pad. It is therefore expected that cracks will most likely initiate at this location
and propagate thorough the bulk solder until failure. This is in qualitative agreement
with experimental findings (See Figures 7 and 8). This area is also where most
coarsening of the grain structure occurs.
It was found that the majority of solder damage occurs during the first thermal cycle, and
that the large solder joint fillet did not provide much benefit. However, solder joint
thickness will likely improve the reliability of the solder joint, since a thicker solder joint
reduces the plastic strain and plastic work at the joint.
44
6. Recommendations for Further Evaluation
Further work should include determining the solder joint life for the different cases by
calculating the number of cycles to failure. The effect of solder volume size should be
evaluated. A 3-D model can be developed and compared to the 2-D results. Apply the
thermal affect due to power disposition of device. Evaluate different resistor size.
Different temperature profiles as well as different ramp rates and dwell times can be
modeled and their effect on plastic work damage accumulation evaluated.
45
References
[1]
Frear D.R., Jones W.B., Kinsman K.R., Solder Mechanics A State of the Art
Assessment. The Minerals, Metals and Materials Society, 1990
[2]
Electronic Materials Handbook, Volume 1 Packaging, ASM International, 1989
[3]
Schubert A., Walter H., Dudek R., Michel B., Lefranc G., Otto J., Mitic G.,
“Thermo-Mechanical Properties and Creep Deformation of Lead-Containing and
Lead-Free Solders”, 2001 International Symposium on Advanced Packaging
Materials, pp. 129-134
[4]
Hacke P.L., Sprecher A.F., Conrad H., “Microstructure Coarsening During
Thermo-Mechanical Fatigue of Pb-Sn Solder Joints”, Journal of Electronic
Materials, Vol. 26, No. 7, 1997, pp. 774-782
[5]
Grivas, D., Murty, K.L., Morris, J.W. Jr., “Deformation of Pb-Sn Eutectic Alloys
at Relatively High Strain Rates”, Acta Metallurgica, 27 (1979), pp.731-737
[6]
Dasgupta A., Sharma P., Upadhyayula K., “Micro-Mechanics of Fatigue Damage
in Pb-Sn Solder Due to Vibration and Thermal Cycling”, International Journal of
Damage Mechanics, Vol. 10, 2001, pp. 101-132
[7]
Engelmaier W., “Solder Joints In Electronics: Design For Reliability”,
Engelmaier Associates
[8]
ANSYS, Inc, ANSYS Mechanical APDL and Mechanical Applications Theory
Reference. Release 13.0, November 2010, pp. 121-123
[9]
Wang G. Z., Cheng Z. N., Becker K., Wilde J., “Applying Anand Model to
Represent the Viscoplastic Deformation Behavior of Solder Alloys”, Journal of
Electronic Packaging, Vol. 123, September 2001, pp. 247-25
[10]
Yong Je Lee., “Viscoplastic Finite-Element Simulation to Predict the Solder
Joint Fatigue Life of Different Flash Memory Die stacking Architecture”,
University of Texas at Arlington, May 2006
46
APPENDIX A
47
!*
! CASE 1: .002 NOMINAL SOLDER JOINT MODEL
!*
/filname,Case1_nom,db
/title,Case 1 nominal solder joint
!*
*ABBR,kplot,kplot
*ABBR,lplot,lplot
*ABBR,aplot,aplot
*ABBR,nplot,nplot
*ABBR,eplot,eplot
!*
/PREP7
!*
! Define Element
ET,1,PLANE182,,,2
ET,2,VISCO106
!*
! Material Properties
!*
! 63Sn-37Pb solder - elasticity and viscoplastic properties
!MP,EX,1,3.6e6
MPTEMP,1,218,233,248
!Material temp table
MPTEMP,4,273,298,323
!continued
MPTEMP,7,348,373,398
!continued
MPDATA,EX,1,1,6.41E6,6.06E6,5.71E6
!Temp dependent modulus
MPDATA,EX,1,4,5.13E6,4.55E6,3.96E6
!continued
MPDATA,EX,1,7,3.38E6,2.79E6,2.21E6
!continued
MPDATA,PRXY,1,1,0.39,.39,.39
MPDATA,PRXY,1,4,0.39,.39,.39
MPDATA,PRXY,1,7,0.39,.39,.39
MP,ALPX,1,23.37e-6
!*
! Anand coefficients
TB,ANAND,1
TBDATA,1,1800,9400,4e6,1.5,0.303,2e5
TBDATA,7,2000,0.07,1.3
!*
! Chip Resister Termination
MP,EX,2,4e6
MP,PRXY,2,0.33
MP,ALPX,2,20e-6
!*
! Chip Resistor (Alumina oxide)
MP,EX,3,53E6
MP,PRXY,3,0.25
48
MP,ALPX,3,6e-6
!*
! Copper Surface Pad
MP,EX,4,19e6
MP,PRXY,4,0.35
MP,ALPX,4,17.5e-6
!*
!Pwb material (epoxy type GFG)
MP,EX,5,2.5E6
MP,EY,5,1.0E6
MP,EZ,5,2.5E6
MP,NUXY,5,.26
MP,NUXZ,5,.14
MP,NUYZ,5,.26
MP,GXY,5,.4E6
MP,GXZ,5,.50E6
MP,GYZ,5,.4E6
MP,ALPX,5,18E-6
MP,ALPY,5,70E-6
MP,ALPZ,5,18E-6
!*
! Geometric model
!*
lr=0.155/2
! Resistor half length
wr=.050/2
! Resistor half width
hr=0.024
! Resistor height
lt=0.015
! Termination length
tt=.001
! Termination thickness
tp=0.0012
! Cu pad thickness
wp=.060
! width of Cu pad
lp=0.0475
! length of Cu pad
gp=0.105/2
! 1/2 the total gap between pads
tb=0.063
! PWB thickness
lb=lr*2
! PWB length
!*
ts=0.002
! Solder joint thickness under resistor
ls=gp+lp
! solder pad
sf1=.25*ts
! keypoint location for solder fillet
sf2=.25*ts
! keypoint location for solder fillet
sf3=.25*ts
! keypoint location for solder fillet
sf4=.25*ts
! keypoint location for solder fillet
rf1=.025
! radius of fillet
rf2=.05
! radius of fillet
tol=1e-5
! tolerance
!*
! Define keypoints for geometry
49
k,1,0,0
k,2,gp,0
k,3,lr-lt,0
k,4,lr-tt,0
k,5,lr,0
k,6,gp+lp,0
k,7,lb,0
k,8,0,tb
k,9,gp,tb
k,10,lr-lt,tb
k,11,lr-tt,tb
k,12,lr,tb
k,13,gp+lp,tb
k,14,lb,tb
k,15,gp,tb+tp
k,16,lr-lt,tb+tp
k,17,lr-tt,tb+tp
k,18,lr,tb+tp
k,19,gp+lp,tb+tp
k,20,lr-lt-tt,tb+tp+ts
k,21,lr-lt,tb+tp+ts
k,22,lr-tt,tb+tp+ts
k,23,lr,tb+tp+ts
k,24,gp+lp-ts-tt,tb+tp+ts
k,25,0,tb+tp+ts+tt
k,26,lr-lt-tt/2,tb+tp+ts+tt
k,27,lr-lt,tb+tp+ts+tt
k,28,lr-tt,tb+tp+ts+tt
k,29,lr,tb+tp+ts+tt
k,30,gp+lp-2*ts-tt,tb+tp+ts+tt
k,31,0,tb+tp+ts+hr-tt
k,32,lr-lt-tt/2,tb+tp+ts+hr-tt
k,33,lr-lt,tb+tp+ts+hr-tt
k,34,lr-tt,tb+tp+ts+hr-tt
k,35,lr,tb+tp+ts+hr-tt
k,36,lr+tt,tb+tp+ts+hr-tt
k,37,lr-lt,tb+tp+ts+hr
k,38,lr-tt,tb+tp+ts+hr
k,39,lr,tb+tp+ts+hr
k,40,lr+tt/2,tb+tp+ts+hr
k,41,gp+lp-2*ts-tt,tb+tp+ts+hr-tt
k,42,gp+(lr-lt-tt-gp)/2,tb+tp+ts
!*
! Define lines using keypoints
L,1,2
L,2,3
!L1
!L2
50
L,3,4
L,4,5
L,5,6
L,6,7
L,8,9
L,9,10
L,10,11
L,11,12
L,12,13
L,13,14
L,1,8
L,2,9
L,3,10
L,4,11
L,5,12
L,6,13
L,7,14
L,15,16
L,16,17
L,17,18
L,18,19
L,9,15
L,10,16
L,11,17
L,12,18
L,13,19
L,20,21
L,21,22
L,22,23
L,23,24
Larc,15,20,42,rf2
L,16,21
L,17,22
L,18,23
L,19,24
L,25,26
L,26,27
L,27,28
L,28,29
L,29,30
L,20,26
L,21,27
L,22,28
L,23,29
L,24,30
L,31,32
!L3
!L4
!L5
!L6
!L7
!L8
!L9
!L10
!L11
!L12
!L13
!L14
!L15
!L16
!L17
!L18
!L19
!L20
!L21
!L22
!L23
!L24
!L25
!L26
!L27
!L28
!L29
!L30
!L31
!L32
!L33
!L34
!L35
!L36
!L37
!L38
!L39
!L40
!L41
!L42
!L43
!L44
!L45
!L46
!L47
!L48
51
L,32,33
L,33,34
L,34,35
L,35,36
L,25,31
L,26,32
L,27,33
L,28,34
L,29,35
LARC,30,36,41,rf1
L,37,38
L,38,39
L,39,40
L,33,37
L,34,38
L,35,39
L,36,40
!L,41,36
!*
! Define areas by lines
AL,23,37,32,36
AL,32,47,42,46
AL,42,58,52,57
AL,52,65,61,64
AL,21,35,30,34
AL,22,36,31,35
AL,20,34,29,33
AL,29,44,39,43
AL,30,45,40,44
AL,31,46,41,45
AL,41,57,51,56
AL,50,63,59,62
AL,51,64,60,63
AL,40,56,50,55
AL,39,55,49,54
AL,38,54,48,53
AL,8,25,20,24
AL,9,26,21,25
AL,10,27,22,26
AL,11,28,23,27
AL,4,17,10,16
AL,3,16,9,15
AL,2,15,8,14
AL,5,18,11,17
AL,1,14,7,13
AL,6,19,12,18
!L49
!L50
!L51
!L52
!L53
!L54
!L55
!L56
!L57
!L58
!L59
!L60
!L61
!L62
!L63
!L64
!L65
!L66
!A1-solder fillet
!A2-solder filler
!A3-solder fillet
!A4-solder fillet
!A5-solder
!A6-solder
!A7-solder fillet
!A8-solder fillet
!A9-termination
!A10-termination
!A11-termination
!A12-termination
!A13-termination
!A14-resistor
!A15-resistor
!A16-resistor
!A17-pad
!A18-pad
!A19-pad
!A20-pad
!A21-pwb
!A22-pwb
!A23-pwb
!A24-pwb
!A25-pwb
!A26-pwb
52
!*
allsel,all
!LOVLAP,all
LGLUE,all
!AOVLAP,all
AGLUE,all
!*
! Assign F.E. attributes, material to area
allsel,all
ASEL,s,area,,1,8,,
!solder
AATT,1,,2
allsel,all
ASEL,s,area,,9,13,,
!termination
AATT,2,,1
allsel,all
ASEL,s,area,,14,16,,
!resistor
AATT,3,,1
allsel,all
ASEL,s,area,,17,20,,
!pad
AATT,4,,1
allsel,all
ASEL,s,area,,21,26,,
!pwb
AATT,5,,1
allsel,all
!*
/VIEW,1,,,1
/ANGLE,1
/PNUM,MAT,1
/NUMBER,1
/COLOR,NUM,DGRA,1
/COLOR,NUM,MRED,2
/COLOR,NUM,CBLU,3
/COLOR,NUM,ORAN,4
/COLOR,NUM,GREE,5
/AUTO,1
/REPLOT,FAST
APLOT
!*
!Clear mesh if present
CLRMSHLN
! Define mesh size and mesh areas
ASEL,s,AREA,,5,6,,
!solder under termination
ESIZE,ts/3
MSHAPE,0,2D
!quads
MSHKEY,1
!mapped mesh
AMESH,all
!create mesh
53
allsel,all
!*
ASEL,s,AREA,,9,10, ,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,11,,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,14,15,,
ESIZE,2*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,12,13,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,16,,,
ESIZE,4*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,17,20,,
ESIZE,2*ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,21,24,,
ESIZE,4*ts/3
!termination
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!Pad
!quads
!mapped mesh
!create mesh
!Pwb
!quads
54
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,25,26,,
ESIZE,8*ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,1,2,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,4,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,3,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
ASEL,s,AREA,,7,8,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
allsel,all
!*
! Create boundary conditions
LSEL,s,loc,x,0
CM,lsymm,line
DL,lsymm,,SYMM
NSEL,s,loc,x,0
!mapped mesh
!create mesh
!Pwb
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
55
NSEL,r,loc,y,0
D,all,all,0
allsel,all
!*
SAVE
!*
/solu
antype,static
allsel,all
nlgeom,on
LNSRCH,on
KBC,0
!*
!------------------------------!*
! Input temperature profile
!*
Tmx = 125
! Tmax (deg.C)
Tmx = Tmx+273
! convert degree C to Kelvin
Tmn = -40
! Tmin (deg.C)
Tmn = Tmn+273
! convert degree C to Kelvin
DWx = 20
! Dwell at Tmax (minutes)
DWx = DWx*60
! convert minute to seconds
DWn = 20
! Dwell at Tmin (minutes)
DWn = DWn*60
! convert minute to seconds
rdn = 10.0
! Ramp rate from hot to cold (deg.C/min)
tdn = 60*(Tmx-Tmn)/rdn
! ramp time (seconds)
rup = 10.0
! Ramp rate from cold to hot (deg.C/min)
tup = 60*(Tmx-Tmn)/rup
! ramp time
cycl = 4
! # of cycles
!*
*DO,ii,1,cycl
mm = 4*(ii-1)
NSUBST,100
TIME,tdn*ii+(DWn+tup+DWx)*(ii-1)
TREF,Tmx
!MPAMOD,1,298
BFUNIF,TEMP,Tmn
LSWRITE,mm+1
!*
NSUBST,50
TIME,(tdn+DWn)*ii+(tup+DWx)*(ii-1)
TREF,Tmn
BFUNIF,TEMP,Tmn
LSWRITE,mm+2
!*
56
NSUBST,100
TIME,(tdn+DWn+tup)*ii+DWx*(ii-1)
TREF,Tmn
BFUNIF,TEMP,Tmx
LSWRITE,mm+3
!*
NSUBST,50
TIME,(tdn+DWn+tup+DWx)*ii
TREF,Tmx
BFUNIF,TEMP,Tmx
LSWRITE,mm+4
*ENDDO
!------------------------------SAVE
LSSOLVE,1,16
finish
57
!*
! CASE 2: .001 MIN SOLDER JOINT MODEL
!*
/filname,Case2_min,db
/title,Case 2 min solder joint
!*
*ABBR,kplot,kplot
*ABBR,lplot,lplot
*ABBR,aplot,aplot
*ABBR,nplot,nplot
*ABBR,eplot,eplot
!*
/PREP7
!*
! Define Element
ET,1,PLANE182,,,2
ET,2,VISCO106
!*
! Material Properties
!*
! 63Sn-37Pb solder - elasticity and viscoplastic properties
!MP,EX,1,3.6e6
MPTEMP,1,218,233,248
!Material temp table
MPTEMP,4,273,298,323
!continued
MPTEMP,7,348,373,398
!continued
MPDATA,EX,1,1,6.41E6,6.06E6,5.71E6
!Temp dependent modulus
MPDATA,EX,1,4,5.13E6,4.55E6,3.96E6
!continued
MPDATA,EX,1,7,3.38E6,2.79E6,2.21E6
!continued
MPDATA,PRXY,1,1,0.39,.39,.39
MPDATA,PRXY,1,4,0.39,.39,.39
MPDATA,PRXY,1,7,0.39,.39,.39
MP,ALPX,1,23.37e-6
!*
! Anand coefficents
TB,ANAND,1
TBDATA,1,1800,9400,4e6,1.5,0.303,2e5
TBDATA,7,2000,0.07,1.3
!*
! Chip Resister Termination
MP,EX,2,4e6
MP,PRXY,2,0.33
MP,ALPX,2,20e-6
!*
! Chip Resistor (Alumina oxide)
MP,EX,3,53E6
58
MP,PRXY,3,0.25
MP,ALPX,3,6e-6
!*
! Copper Surface Pad
MP,EX,4,19e6
MP,PRXY,4,0.35
MP,ALPX,4,17.5e-6
!*
!Pwb material (epoxy type GFG)
MP,EX,5,2.5E6
MP,EY,5,1.0E6
MP,EZ,5,2.5E6
MP,NUXY,5,.26
MP,NUXZ,5,.14
MP,NUYZ,5,.26
MP,GXY,5,.4E6
MP,GXZ,5,.50E6
MP,GYZ,5,.4E6
MP,ALPX,5,18E-6
MP,ALPY,5,70E-6
MP,ALPZ,5,18E-6
!*
! Geometric model
!*
sr2=sqrt(2)
lr=0.155/2
wr=.050/2
hr=0.024
lt=0.015
tt=.001
tp=0.0012
wp=.060
lp=0.0475
gp=0.105/2
tb=0.063
lb=lr*2
!*
ts=0.001
ls=gp+lp
sf1=.25*ts
sf2=.25*ts
sf3=.25*ts
sf4=.25*ts
rf1=.025
rf2=.05
tol=1e-5
! Resistor half length
! Resistor half width
! Resistor height
! Termination length
! Termination thickness
! Cu pad thickness
! width of Cu pad
! length of Cu pad
! 1/2 the total gap between pads
! PWB thickness
! PWB length
! Solder joint thickness under resistor
! solder pad
! keypoint location for solder fillet
! keypoint location for solder fillet
! keypoint location for solder fillet
! keypoint location for solder fillet
! radius of fillet
! radius of fillet
! tolerance
59
!*
! Define keypoints for geometry
k,1,0,0
k,2,gp,0
k,3,lr-lt,0
k,4,lr-tt,0
k,5,lr,0
k,6,gp+lp,0
k,7,lb,0
k,8,0,tb
k,9,gp,tb
k,10,lr-lt,tb
k,11,lr-tt,tb
k,12,lr,tb
k,13,gp+lp,tb
k,14,lb,tb
k,15,gp,tb+tp
k,16,lr-lt,tb+tp
k,17,lr-tt,tb+tp
k,18,lr,tb+tp
k,19,gp+lp,tb+tp
k,20,lr-lt-tt,tb+tp+ts
k,21,lr-lt,tb+tp+ts
k,22,lr-tt,tb+tp+ts
k,23,lr,tb+tp+ts
k,24,gp+lp-ts-tt,tb+tp+ts
k,25,0,tb+tp+ts+tt
k,26,lr-lt-tt/2,tb+tp+ts+tt
k,27,lr-lt,tb+tp+ts+tt
k,28,lr-tt,tb+tp+ts+tt
k,29,lr,tb+tp+ts+tt
k,30,gp+lp-4*ts-tt,tb+tp+ts+tt
k,31,0,tb+tp+ts+hr-tt
k,32,lr-lt-tt/2,tb+tp+ts+hr-tt
k,33,lr-lt,tb+tp+ts+hr-tt
k,34,lr-tt,tb+tp+ts+hr-tt
k,35,lr,tb+tp+ts+hr-tt
k,36,lr+tt,tb+tp+ts+hr-tt
k,37,lr-lt,tb+tp+ts+hr
k,38,lr-tt,tb+tp+ts+hr
k,39,lr,tb+tp+ts+hr
k,40,lr+tt/2,tb+tp+ts+hr
k,41,gp+lp-2*ts-tt,tb+tp+ts+hr-tt
k,42,gp+(lr-lt-tt-gp)/2,tb+tp+ts
!*
! Define lines using keypoints
60
L,1,2
L,2,3
L,3,4
L,4,5
L,5,6
L,6,7
L,8,9
L,9,10
L,10,11
L,11,12
L,12,13
L,13,14
L,1,8
L,2,9
L,3,10
L,4,11
L,5,12
L,6,13
L,7,14
L,15,16
L,16,17
L,17,18
L,18,19
L,9,15
L,10,16
L,11,17
L,12,18
L,13,19
L,20,21
L,21,22
L,22,23
L,23,24
L,15,20
L,16,21
L,17,22
L,18,23
L,19,24
L,25,26
L,26,27
L,27,28
L,28,29
L,29,30
L,20,26
L,21,27
L,22,28
L,23,29
!L1
!L2
!L3
!L4
!L5
!L6
!L7
!L8
!L9
!L10
!L11
!L12
!L13
!L14
!L15
!L16
!L17
!L18
!L19
!L20
!L21
!L22
!L23
!L24
!L25
!L26
!L27
!L28
!L29
!L30
!L31
!L32
!L33
!L34
!L35
!L36
!L37
!L38
!L39
!L40
!L41
!L42
!L43
!L44
!L45
!L46
61
L,24,30
L,31,32
L,32,33
L,33,34
L,34,35
L,35,36
L,25,31
L,26,32
L,27,33
L,28,34
L,29,35
LARC,30,36,41,rf1
L,37,38
L,38,39
L,39,40
L,33,37
L,34,38
L,35,39
L,36,40
!L,41,36
!*
! Define areas by lines
AL,23,37,32,36
AL,32,47,42,46
AL,42,58,52,57
AL,52,65,61,64
AL,21,35,30,34
AL,22,36,31,35
AL,20,34,29,33
AL,29,44,39,43
AL,30,45,40,44
AL,31,46,41,45
AL,41,57,51,56
AL,50,63,59,62
AL,51,64,60,63
AL,40,56,50,55
AL,39,55,49,54
AL,38,54,48,53
AL,8,25,20,24
AL,9,26,21,25
AL,10,27,22,26
AL,11,28,23,27
AL,4,17,10,16
AL,3,16,9,15
AL,2,15,8,14
AL,5,18,11,17
!L47
!L48
!L49
!L50
!L51
!L52
!L53
!L54
!L55
!L56
!L57
!L58
!L59
!L60
!L61
!L62
!L63
!L64
!L65
!L66
!A1-solder fillet
!A2-solder filler
!A3-solder fillet
!A4-solder fillet
!A5-solder
!A6-solder
!A7-solder fillet
!A8-solder fillet
!A9-termination
!A10-termination
!A11-termination
!A12-termination
!A13-termination
!A14-resistor
!A15-resistor
!A16-resistor
!A17-pad
!A18-pad
!A19-pad
!A20-pad
!A21-pwb
!A22-pwb
!A23-pwb
!A24-pwb
62
AL,1,14,7,13
!A25-pwb
AL,6,19,12,18
!A26-pwb
!*
allsel,all
!LOVLAP,all
LGLUE,all
!AOVLAP,all
AGLUE,all
!*
! Assign F.E. attributes, material to area
allsel,all
ASEL,s,area,,1,8,,
!solder
AATT,1,,2
allsel,all
ASEL,s,area,,9,13,,
!termination
AATT,2,,1
allsel,all
ASEL,s,area,,14,16,,
!resistor
AATT,3,,1
allsel,all
ASEL,s,area,,17,20,,
!pad
AATT,4,,1
allsel,all
ASEL,s,area,,21,26,,
!pwb
AATT,5,,1
allsel,all
!*
/VIEW,1,,,1
/ANGLE,1
/PNUM,MAT,1
/NUMBER,1
/COLOR,NUM,DGRA,1
/COLOR,NUM,MRED,2
/COLOR,NUM,CBLU,3
/COLOR,NUM,ORAN,4
/COLOR,NUM,GREE,5
/AUTO,1
/REPLOT,FAST
APLOT
!*
!Clear mesh if present
CLRMSHLN
! Define mesh size and mesh areas
ASEL,s,AREA,,5,6,,
!solder under termination
ESIZE,ts/1.5
MSHAPE,0,2D
!quads
63
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,9,10,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,11,,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,14,15,,
ESIZE,2*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,12,13,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,16,,,
ESIZE,4*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,17,20,,
ESIZE,2*ts/1.5
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!Pad
!quads
!mapped mesh
!create mesh
64
ASEL,s,AREA,,21,24,,
ESIZE,4*ts/1.5
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,25,26,,
ESIZE,8*ts/1.5
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,1,2,,,
ESIZE,ts/1.5
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,4,,,
ESIZE,ts/1.5
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,3,,,
ESIZE,ts/1.5
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
ASEL,s,AREA,,7,8,,, !Solder fillet
ESIZE,ts/1.5
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
allsel,all
!*
!Create boundary conditions
LSEL,s,loc,x,0
!Pwb
!quads
!mapped mesh
!create mesh
!Pwb
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
!quads
!free mesh
!create mesh
65
CM,lsymm,line
DL,lsymm,,SYMM
NSEL,s,loc,x,0
NSEL,r,loc,y,0
D,all,all,0
allsel,all
!*
SAVE
!*
/solu
antype,static
allsel,all
nlgeom,on
LNSRCH,on
KBC,0
!*
!------------------------------!*
! Input temperature profile
!*
Tmx = 125
! Tmax (deg.C)
Tmx = Tmx+273
! convert degree C to Kelvin
Tmn = -40
! Tmin (deg.C)
Tmn = Tmn+273
! convert degree C to Kelvin
DWx = 20
! Dwell at Tmax (minutes)
DWx = DWx*60
! convert minute to seconds
DWn = 20
! Dwell at Tmin (minutes)
DWn = DWn*60
! convert minute to seconds
rdn = 10.0
! Ramp rate from hot to cold (deg.C/min)
tdn = 60*(Tmx-Tmn)/rdn
! ramp time (seconds)
rup = 10.0
! Ramp rate from cold to hot (deg.C/min)
tup = 60*(Tmx-Tmn)/rup
! ramp time
cycl = 4
! # of cycles
!*
*DO,ii,1,cycl
mm = 4*(ii-1)
NSUBST,100
TIME,tdn*ii+(DWn+tup+DWx)*(ii-1)
TREF,Tmx
!MPAMOD,1,298
BFUNIF,TEMP,Tmn
LSWRITE,mm+1
!*
NSUBST,50
TIME,(tdn+DWn)*ii+(tup+DWx)*(ii-1)
TREF,Tmn
66
BFUNIF,TEMP,Tmn
LSWRITE,mm+2
!*
NSUBST,100
TIME,(tdn+DWn+tup)*ii+DWx*(ii-1)
TREF,Tmn
BFUNIF,TEMP,Tmx
LSWRITE,mm+3
!*
NSUBST,50
TIME,(tdn+DWn+tup+DWx)*ii
TREF,Tmx
BFUNIF,TEMP,Tmx
LSWRITE,mm+4
*ENDDO
!------------------------------SAVE
LSSOLVE,1,16
finish
67
!*
! CASE 3: .004 MAX SOLDER JOINT MODEL
!*
/filname,Case3_max,db
/title,Case 3 max solder joint
!*
*ABBR,kplot,kplot
*ABBR,lplot,lplot
*ABBR,aplot,aplot
*ABBR,nplot,nplot
*ABBR,eplot,eplot
!*
/PREP7
!*
! Define Element
ET,1,PLANE182,,,2
ET,2,VISCO106
!*
! Material Properties
!*
! 63Sn-37Pb solder - elasticity and viscoplastic properties
!MP,EX,1,3.6e6
MPTEMP,1,218,233,248
!Material temp table
MPTEMP,4,273,298,323
!continued
MPTEMP,7,348,373,398
!continued
MPDATA,EX,1,1,6.41E6,6.06E6,5.71E6
!Temp dependent modulus
MPDATA,EX,1,4,5.13E6,4.55E6,3.96E6
!continued
MPDATA,EX,1,7,3.38E6,2.79E6,2.21E6
!continued
MPDATA,PRXY,1,1,0.39,.39,.39
MPDATA,PRXY,1,4,0.39,.39,.39
MPDATA,PRXY,1,7,0.39,.39,.39
MP,ALPX,1,23.37e-6
!*
! Anand coefficents
TB,ANAND,1
TBDATA,1,1800,9400,4e6,1.5,0.303,2e5
TBDATA,7,2000,0.07,1.3
!*
! Chip Resister Termination
MP,EX,2,4e6
MP,PRXY,2,0.33
MP,ALPX,2,20e-6
!*
! Chip Resistor (Alumina oxide)
MP,EX,3,53E6
68
MP,PRXY,3,0.25
MP,ALPX,3,6e-6
!*
! Copper Surface Pad
MP,EX,4,19e6
MP,PRXY,4,0.35
MP,ALPX,4,17.5e-6
!*
!Pwb material (epoxy type GFG)
MP,EX,5,2.5E6
MP,EY,5,1.0E6
MP,EZ,5,2.5E6
MP,NUXY,5,.26
MP,NUXZ,5,.14
MP,NUYZ,5,.26
MP,GXY,5,.4E6
MP,GXZ,5,.50E6
MP,GYZ,5,.4E6
MP,ALPX,5,18E-6
MP,ALPY,5,70E-6
MP,ALPZ,5,18E-6
!*
! Geometric model
!*
sr2=sqrt(2)
lr=0.155/2
! Resistor half length
wr=.050/2
! Resistor half width
hr=0.024
! Resistor height
lt=0.015
! Termination length
tt=.001
! Termination thickness
tp=0.0012
! Cu pad thickness
wp=.060
! width of Cu pad
lp=0.0475
! length of Cu pad
gp=0.105/2
! 1/2 the total gap between pads
tb=0.063
! PWB thickness
lb=lr*2
! PWB length
!*
ts=0.004
! Solder joint thickness under resistor
ls=gp+lp
! solder pad
sf1=.25*ts
! keypoint location for solder fillet
sf2=.25*ts
! keypoint location for solder fillet
sf3=.25*ts
! keypoint location for solder fillet
sf4=.25*ts
! keypoint location for solder fillet
rf1=.025
! radius of fillet
rf2=.020
! radius of fillet
tol=1e-5
! tolerance
69
!*
! Define keypoints for geometry
k,1,0,0
k,2,gp,0
k,3,lr-lt,0
k,4,lr-tt,0
k,5,lr,0
k,6,gp+lp,0
k,7,lb,0
k,8,0,tb
k,9,gp,tb
k,10,lr-lt,tb
k,11,lr-tt,tb
k,12,lr,tb
k,13,gp+lp,tb
k,14,lb,tb
k,15,gp,tb+tp
k,16,lr-lt,tb+tp
k,17,lr-tt,tb+tp
k,18,lr,tb+tp
k,19,gp+lp,tb+tp
k,20,lr-lt-tt/1.5,tb+tp+ts
k,21,lr-lt,tb+tp+ts
k,22,lr-tt,tb+tp+ts
k,23,lr,tb+tp+ts
k,24,gp+lp-ts-tt,tb+tp+ts
k,25,0,tb+tp+ts+tt
k,26,lr-lt-tt/2,tb+tp+ts+tt
k,27,lr-lt,tb+tp+ts+tt
k,28,lr-tt,tb+tp+ts+tt
k,29,lr,tb+tp+ts+tt
k,30,gp+lp-1.5*ts-tt,tb+tp+ts+tt
k,31,0,tb+tp+ts+hr-tt
k,32,lr-lt-tt/2,tb+tp+ts+hr-tt
k,33,lr-lt,tb+tp+ts+hr-tt
k,34,lr-tt,tb+tp+ts+hr-tt
k,35,lr,tb+tp+ts+hr-tt
k,36,lr+tt,tb+tp+ts+hr-tt
k,37,lr-lt,tb+tp+ts+hr
k,38,lr-tt,tb+tp+ts+hr
k,39,lr,tb+tp+ts+hr
k,40,lr+tt/2,tb+tp+ts+hr
k,41,gp+lp-2*ts-tt,tb+tp+ts+hr-tt
k,42,gp+(lr-lt-tt-gp)/2,tb+tp+ts
!*
! Define lines using keypoints
70
L,1,2
L,2,3
L,3,4
L,4,5
L,5,6
L,6,7
L,8,9
L,9,10
L,10,11
L,11,12
L,12,13
L,13,14
L,1,8
L,2,9
L,3,10
L,4,11
L,5,12
L,6,13
L,7,14
L,15,16
L,16,17
L,17,18
L,18,19
L,9,15
L,10,16
L,11,17
L,12,18
L,13,19
L,20,21
L,21,22
L,22,23
L,23,24
Larc,15,20,42,rf2
L,16,21
L,17,22
L,18,23
L,19,24
L,25,26
L,26,27
L,27,28
L,28,29
L,29,30
L,20,26
L,21,27
L,22,28
L,23,29
!L1
!L2
!L3
!L4
!L5
!L6
!L7
!L8
!L9
!L10
!L11
!L12
!L13
!L14
!L15
!L16
!L17
!L18
!L19
!L20
!L21
!L22
!L23
!L24
!L25
!L26
!L27
!L28
!L29
!L30
!L31
!L32
!L33
!L34
!L35
!L36
!L37
!L38
!L39
!L40
!L41
!L42
!L43
!L44
!L45
!L46
71
L,24,30
L,31,32
L,32,33
L,33,34
L,34,35
L,35,36
L,25,31
L,26,32
L,27,33
L,28,34
L,29,35
LARC,30,36,41,rf1
L,37,38
L,38,39
L,39,40
L,33,37
L,34,38
L,35,39
L,36,40
!L,41,36
!*
! Define areas by lines
AL,23,37,32,36
AL,32,47,42,46
AL,42,58,52,57
AL,52,65,61,64
AL,21,35,30,34
AL,22,36,31,35
AL,20,34,29,33
AL,29,44,39,43
AL,30,45,40,44
AL,31,46,41,45
AL,41,57,51,56
AL,50,63,59,62
AL,51,64,60,63
AL,40,56,50,55
AL,39,55,49,54
AL,38,54,48,53
AL,8,25,20,24
AL,9,26,21,25
AL,10,27,22,26
AL,11,28,23,27
AL,4,17,10,16
AL,3,16,9,15
AL,2,15,8,14
AL,5,18,11,17
!L47
!L48
!L49
!L50
!L51
!L52
!L53
!L54
!L55
!L56
!L57
!L58
!L59
!L60
!L61
!L62
!L63
!L64
!L65
!L66
!A1-solder fillet
!A2-solder filler
!A3-solder fillet
!A4-solder fillet
!A5-solder
!A6-solder
!A7-solder fillet
!A8-solder fillet
!A9-termination
!A10-termination
!A11-termination
!A12-termination
!A13-termination
!A14-resistor
!A15-resistor
!A16-resistor
!A17-pad
!A18-pad
!A19-pad
!A20-pad
!A21-pwb
!A22-pwb
!A23-pwb
!A24-pwb
72
AL,1,14,7,13
!A25-pwb
AL,6,19,12,18
!A26-pwb
!*
allsel,all
!LOVLAP,all
LGLUE,all
!AOVLAP,all
AGLUE,all
!*
! Assign F.E. attributes, material to area
allsel,all
ASEL,s,area,,1,8,,
!solder
AATT,1,,2
allsel,all
ASEL,s,area,,9,13,,
!termination
AATT,2,,1
allsel,all
ASEL,s,area,,14,16,,
!resistor
AATT,3,,1
allsel,all
ASEL,s,area,,17,20,,
!pad
AATT,4,,1
allsel,all
ASEL,s,area,,21,26,,
!pwb
AATT,5,,1
allsel,all
!*
/VIEW,1,,,1
/ANGLE,1
/PNUM,MAT,1
/NUMBER,1
/COLOR,NUM,DGRA,1
/COLOR,NUM,MRED,2
/COLOR,NUM,CBLU,3
/COLOR,NUM,ORAN,4
/COLOR,NUM,GREE,5
/AUTO,1
/REPLOT,FAST
APLOT
!*
!Clear mesh if present
CLRMSHLN
! Define mesh size and mesh areas
ASEL,s,AREA,,5,6,,
!solder under termination
ESIZE,ts/6
MSHAPE,0,2D
!quads
73
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,9,10,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,11,,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,14,15,,
ESIZE,2*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,12,13,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,16,,,
ESIZE,4*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,17,20,,
ESIZE,2*ts/6
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!Pad
!quads
!mapped mesh
!create mesh
74
ASEL,s,AREA,,21,24,,
ESIZE,4*ts/6
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,25,26,,
ESIZE,8*ts/6
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,1,2,,,
ESIZE,ts/6
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,4,,,
ESIZE,ts/6
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,3,,,
ESIZE,ts/6
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
ASEL,s,AREA,,7,8,,,
ESIZE,ts/6
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
allsel,all
!*
!Create boundary conditions
LSEL,s,loc,x,0
!Pwb
!quads
!mapped mesh
!create mesh
!Pwb
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
75
CM,lsymm,line
DL,lsymm,,SYMM
NSEL,s,loc,x,0
NSEL,r,loc,y,0
D,all,all,0
allsel,all
!*
SAVE
!*
/solu
antype,static
allsel,all
nlgeom,on
LNSRCH,on
KBC,0
!*
!------------------------------!*
! Input temperature profile
!*
Tmx = 125
! Tmax (deg.C)
Tmx = Tmx+273
! convert degree C to Kelvin
Tmn = -40
! Tmin (deg.C)
Tmn = Tmn+273
! convert degree C to Kelvin
DWx = 20
! Dwell at Tmax (minutes)
DWx = DWx*60
! convert minute to seconds
DWn = 20
! Dwell at Tmin (minutes)
DWn = DWn*60
! convert minute to seconds
rdn = 10.0
! Ramp rate from hot to cold (deg.C/min)
tdn = 60*(Tmx-Tmn)/rdn
! ramp time (seconds)
rup = 10.0
! Ramp rate from cold to hot (deg.C/min)
tup = 60*(Tmx-Tmn)/rup
! ramp time
cycl = 4
! # of cycles
!*
*DO,ii,1,cycl
mm = 4*(ii-1)
NSUBST,100
TIME,tdn*ii+(DWn+tup+DWx)*(ii-1)
TREF,Tmx
!MPAMOD,1,298
BFUNIF,TEMP,Tmn
LSWRITE,mm+1
!*
NSUBST,50
TIME,(tdn+DWn)*ii+(tup+DWx)*(ii-1)
TREF,Tmn
76
BFUNIF,TEMP,Tmn
LSWRITE,mm+2
!*
NSUBST,100
TIME,(tdn+DWn+tup)*ii+DWx*(ii-1)
TREF,Tmn
BFUNIF,TEMP,Tmx
LSWRITE,mm+3
!*
NSUBST,50
TIME,(tdn+DWn+tup+DWx)*ii
TREF,Tmx
BFUNIF,TEMP,Tmx
LSWRITE,mm+4
*ENDDO
!------------------------------SAVE
LSSOLVE,1,16
finish
77
!*
! CASE 4: .002 NOMINAL SOLDER JOINT, LARGE FILLET MODEL
!*
/filname,Case4_big,db
/title,Case 4 large fillet
!*
*ABBR,kplot,kplot
*ABBR,lplot,lplot
*ABBR,aplot,aplot
*ABBR,nplot,nplot
*ABBR,eplot,eplot
!*
/PREP7
!*
! Define Element
ET,1,PLANE182,,,2
ET,2,VISCO106
!*
! Material Properties
!*
! 63Sn-37Pb solder - elasticity and viscoplastic properties
!MP,EX,1,3.6e6
MPTEMP,1,218,233,248
!Material temp table
MPTEMP,4,273,298,323
!continued
MPTEMP,7,348,373,398
!continued
MPDATA,EX,1,1,6.41E6,6.06E6,5.71E6
!Temp dependent modulus
MPDATA,EX,1,4,5.13E6,4.55E6,3.96E6
!continued
MPDATA,EX,1,7,3.38E6,2.79E6,2.21E6
!continued
MPDATA,PRXY,1,1,0.39,.39,.39
MPDATA,PRXY,1,4,0.39,.39,.39
MPDATA,PRXY,1,7,0.39,.39,.39
MP,ALPX,1,23.37e-6
!*
! Anand coefficients
TB,ANAND,1
TBDATA,1,1800,9400,4e6,1.5,0.303,2e5
TBDATA,7,2000,0.07,1.3
!*
! Chip Resister Termination
MP,EX,2,4e6
MP,PRXY,2,0.33
MP,ALPX,2,20e-6
!*
! Chip Resistor (Alumina oxide)
MP,EX,3,53E6
78
MP,PRXY,3,0.25
MP,ALPX,3,6e-6
!*
! Copper Surface Pad
MP,EX,4,19e6
MP,PRXY,4,0.35
MP,ALPX,4,17.5e-6
!*
!Pwb material (epoxy type GFG)
MP,EX,5,2.5E6
MP,EY,5,1.0E6
MP,EZ,5,2.5E6
MP,NUXY,5,.26
MP,NUXZ,5,.14
MP,NUYZ,5,.26
MP,GXY,5,.4E6
MP,GXZ,5,.50E6
MP,GYZ,5,.4E6
MP,ALPX,5,18E-6
MP,ALPY,5,70E-6
MP,ALPZ,5,18E-6
!*
! Geometric model
!*
sr2=sqrt(2)
lr=0.155/2
! Resistor half length
wr=.050/2
! Resistor half width
hr=0.024
! Resistor height
lt=0.015
! Termination length
tt=.001
! Termination thickness
tp=0.0012
! Cu pad thickness
wp=.060
! width of Cu pad
lp=0.0475
! length of Cu pad
gp=0.105/2
! 1/2 the total gap between pads
tb=0.063
! PWB thickness
lb=lr*2
! PWB length
!*
ts=0.002
! Solder joint thickness under resistor
ls=gp+lp
! solder pad
sf1=.25*ts
! keypoint location for solder fillet
sf2=.25*ts
! keypoint location for solder fillet
sf3=.25*ts
! keypoint location for solder fillet
sf4=.25*ts
! keypoint location for solder fillet
rf1=.075
! radius of fillet
rf2=.05
! radius of fillet
tol=1e-5
! tolerance
79
!*
! Define keypoints for geometry
k,1,0,0
k,2,gp,0
k,3,lr-lt,0
k,4,lr-tt,0
k,5,lr,0
k,6,gp+lp,0
k,7,lb,0
k,8,0,tb
k,9,gp,tb
k,10,lr-lt,tb
k,11,lr-tt,tb
k,12,lr,tb
k,13,gp+lp,tb
k,14,lb,tb
k,15,gp,tb+tp
k,16,lr-lt,tb+tp
k,17,lr-tt,tb+tp
k,18,lr,tb+tp
k,19,gp+lp,tb+tp
k,20,lr-lt-tt,tb+tp+ts
k,21,lr-lt,tb+tp+ts
k,22,lr-tt,tb+tp+ts
k,23,lr,tb+tp+ts
k,24,gp+lp-ts/2,tb+tp+ts
k,25,0,tb+tp+ts+tt
k,26,lr-lt-tt/2,tb+tp+ts+tt
k,27,lr-lt,tb+tp+ts+tt
k,28,lr-tt,tb+tp+ts+tt
k,29,lr,tb+tp+ts+tt
k,30,gp+lp-ts/1.5,tb+tp+ts+tt
k,31,0,tb+tp+ts+hr-tt
k,32,lr-lt-tt/2,tb+tp+ts+hr-tt
k,33,lr-lt,tb+tp+ts+hr-tt
k,34,lr-tt,tb+tp+ts+hr-tt
k,35,lr,tb+tp+ts+hr-tt
k,36,lr+tt,tb+tp+ts+hr-tt
k,37,lr-lt,tb+tp+ts+hr
k,38,lr-tt,tb+tp+ts+hr
k,39,lr,tb+tp+ts+hr
k,40,lr+tt/2,tb+tp+ts+hr
k,41,gp+lp-2*ts-tt,tb+tp+ts+hr-tt
k,42,gp+(lr-lt-tt-gp)/2,tb+tp+ts
!*
! Define lines using keypoints
80
L,1,2
L,2,3
L,3,4
L,4,5
L,5,6
L,6,7
L,8,9
L,9,10
L,10,11
L,11,12
L,12,13
L,13,14
L,1,8
L,2,9
L,3,10
L,4,11
L,5,12
L,6,13
L,7,14
L,15,16
L,16,17
L,17,18
L,18,19
L,9,15
L,10,16
L,11,17
L,12,18
L,13,19
L,20,21
L,21,22
L,22,23
L,23,24
Larc,15,20,42,rf2
L,16,21
L,17,22
L,18,23
L,19,24
L,25,26
L,26,27
L,27,28
L,28,29
L,29,30
L,20,26
L,21,27
L,22,28
L,23,29
!L1
!L2
!L3
!L4
!L5
!L6
!L7
!L8
!L9
!L10
!L11
!L12
!L13
!L14
!L15
!L16
!L17
!L18
!L19
!L20
!L21
!L22
!L23
!L24
!L25
!L26
!L27
!L28
!L29
!L30
!L31
!L32
!L33
!L34
!L35
!L36
!L37
!L38
!L39
!L40
!L41
!L42
!L43
!L44
!L45
!L46
81
L,24,30
L,31,32
L,32,33
L,33,34
L,34,35
L,35,36
L,25,31
L,26,32
L,27,33
L,28,34
L,29,35
LARC,30,36,29,rf1
L,37,38
L,38,39
L,39,40
L,33,37
L,34,38
L,35,39
L,36,40
!L,41,36
!*
! Define areas by lines
AL,23,37,32,36
AL,32,47,42,46
AL,42,58,52,57
AL,52,65,61,64
AL,21,35,30,34
AL,22,36,31,35
AL,20,34,29,33
AL,29,44,39,43
AL,30,45,40,44
AL,31,46,41,45
AL,41,57,51,56
AL,50,63,59,62
AL,51,64,60,63
AL,40,56,50,55
AL,39,55,49,54
AL,38,54,48,53
AL,8,25,20,24
AL,9,26,21,25
AL,10,27,22,26
AL,11,28,23,27
AL,4,17,10,16
AL,3,16,9,15
AL,2,15,8,14
AL,5,18,11,17
!L47
!L48
!L49
!L50
!L51
!L52
!L53
!L54
!L55
!L56
!L57
!L58
!L59
!L60
!L61
!L62
!L63
!L64
!L65
!L66
!A1-solder fillet
!A2-solder filler
!A3-solder fillet
!A4-solder fillet
!A5-solder
!A6-solder
!A7-solder fillet
!A8-solder fillet
!A9-termination
!A10-termination
!A11-termination
!A12-termination
!A13-termination
!A14-resistor
!A15-resistor
!A16-resistor
!A17-pad
!A18-pad
!A19-pad
!A20-pad
!A21-pwb
!A22-pwb
!A23-pwb
!A24-pwb
82
AL,1,14,7,13
!A25-pwb
AL,6,19,12,18
!A26-pwb
!*
allsel,all
!LOVLAP,all
LGLUE,all
!AOVLAP,all
AGLUE,all
!*
! Assign F.E. attributes, material to area
allsel,all
ASEL,s,area,,1,8,,
!solder
AATT,1,,2
allsel,all
ASEL,s,area,,9,13,,
!termination
AATT,2,,1
allsel,all
ASEL,s,area,,14,16,,
!resistor
AATT,3,,1
allsel,all
ASEL,s,area,,17,20,,
!pad
AATT,4,,1
allsel,all
ASEL,s,area,,21,26,,
!pwb
AATT,5,,1
allsel,all
!*
/VIEW,1,,,1
/ANGLE,1
/PNUM,MAT,1
/NUMBER,1
/COLOR,NUM,DGRA,1
/COLOR,NUM,MRED,2
/COLOR,NUM,CBLU,3
/COLOR,NUM,ORAN,4
/COLOR,NUM,GREE,5
/AUTO,1
/REPLOT,FAST
APLOT
!*
!Clear mesh if present
CLRMSHLN
! Define mesh size and mesh areas
ASEL,s,AREA,,5,6,,
!solder under termination
ESIZE,ts/3
MSHAPE,0,2D
!quads
83
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,9,10,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,11,,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,14,15,,
ESIZE,2*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,12,13,,
ESIZE,tt/2
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,16,,,
ESIZE,4*tt/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,17,20,,
ESIZE,2*ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!termination
!quads
!mapped mesh
!create mesh
!Resistor
!quads
!mapped mesh
!create mesh
!Pad
!quads
!mapped mesh
!create mesh
84
ASEL,s,AREA,,21,24,,
ESIZE,4*ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,25,26,,
ESIZE,8*ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,1,2,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,4,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,1
AMESH,all
allsel,all
!*
ASEL,s,AREA,,3,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
ASEL,s,AREA,,7,8,,,
ESIZE,ts/3
MSHAPE,0,2D
MSHKEY,0
AMESH,all
allsel,all
!*
allsel,all
!*
! Create boundary conditions
LSEL,s,loc,x,0
!Pwb
!quads
!mapped mesh
!create mesh
!Pwb
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!mapped mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
!Solder fillet
!quads
!free mesh
!create mesh
85
CM,lsymm,line
DL,lsymm,,SYMM
NSEL,s,loc,x,0
NSEL,r,loc,y,0
D,all,all,0
allsel,all
!*
SAVE
!*
/solu
antype,static
allsel,all
nlgeom,on
LNSRCH,on
KBC,0
!*
!------------------------------!*
! Input temperature profile
!*
Tmx = 125
! Tmax (deg.C)
Tmx = Tmx+273
! convert degree C to Kelvin
Tmn = -40
! Tmin (deg.C)
Tmn = Tmn+273
! convert degree C to Kelvin
DWx = 20
! Dwell at Tmax (minutes)
DWx = DWx*60
! convert minute to seconds
DWn = 20
! Dwell at Tmin (minutes)
DWn = DWn*60
! convert minute to seconds
rdn = 10.0
! Ramp rate from hot to cold (deg.C/min)
tdn = 60*(Tmx-Tmn)/rdn
! ramp time (seconds)
rup = 10.0
! Ramp rate from cold to hot (deg.C/min)
tup = 60*(Tmx-Tmn)/rup
! ramp time
cycl = 4
! # of cycles
!*
*DO,ii,1,cycl
mm = 4*(ii-1)
NSUBST,100
TIME,tdn*ii+(DWn+tup+DWx)*(ii-1)
TREF,Tmx
!MPAMOD,1,298
BFUNIF,TEMP,Tmn
LSWRITE,mm+1
!*
NSUBST,50
TIME,(tdn+DWn)*ii+(tup+DWx)*(ii-1)
TREF,Tmn
86
BFUNIF,TEMP,Tmn
LSWRITE,mm+2
!*
NSUBST,100
TIME,(tdn+DWn+tup)*ii+DWx*(ii-1)
TREF,Tmn
BFUNIF,TEMP,Tmx
LSWRITE,mm+3
!*
NSUBST,50
TIME,(tdn+DWn+tup+DWx)*ii
TREF,Tmx
BFUNIF,TEMP,Tmx
LSWRITE,mm+4
*ENDDO
!------------------------------SAVE
LSSOLVE,1,16
finish
87
APPENDIX B
88
Validation
Wang, Cheng, Becker, and Wilde [9] concluded the Anand model can be used to
represent the inelastic deformation behavior of solder at high homologous temperature
and can be used for finite element simulation of the stress/strain responses of a solder
joint.
To verify the Anand finite element analysis was working correctly a finite element
model was created to simulate the model used in Wang, et al. [9] Figure B-1 shows the
geometry of the model. Tables B-1 and B-2 presents the elastic material properties and
Anand parameters, respectively, used in the analysis.
Sn60Pb40 solder joint
2 PL
1.2
Al2O3
ceramic
FR4
0.381
3.0
substrate
28
2
32
Dimensions are in mm
Figure B-1: Diagram of specimen [9]
Table B-1: Elastic Material Properties [9]
Elastic Material Properties
Young’s Modulus
(MPa)
3.447(104) - 151T(oC)
Poisson’s
Ratio
0.316
Coefficient of thermal
expansion (ppm/oC)
25
Al2O3 ceramic
2.76(104)
0.3
6.7
FR4 Substrate
1.6(104)
0.3
16
Material
Sn60Pb40 solder
89
Table B-2: Anand Model Material Parameters [9]
Anand Model Material Parameters
Constant
so
Q/R
Description
Value
Unit
Initial value of deformation
resistance
56.33
MPa
Activation energy / Universal gas constant
10830
K
1.49(107)
(1/sec)
11
Dimensionless
A
Pre-exponential factor

Stress multiplier
m
Strain rate sensitivity of stress
0.303
Dimensionless
Ho
Hardening / softening constant
2640.75
MPa
s^
Coefficient of deformation
resistance saturation value
Strain rate sensitivity of saturation
(deformation resistance) value
Strain rate sensitivity of hardening
or softening
80.42
MPa
0.0231
Dimensionless
1.34
Dimensionless
n
a
Using symmetry boundary conditions a half model was used and meshed with 2-D plane
strain elements ANSYS Plane182 and Visco106 elements. The finite element model is
shown in Figure B-2.
Figure B-2: Finite Element Model
90
The first method of validation the Anand model was tested for constant strain rate
behavior. Two cases were run. Case 1 was a constant strain rate of 1.0 x 10-2 1/s and
case 2 was a constant strain rate of 1.0 x 10-4 1/s. The finite element model used to
simulate the solder is shown in Figure B-3. Figure B-4 and B-5 show the correlation
between the results obtained form Wang et al. [9] and the stress-strain obtained from the
finite element model.
The results show good correlation between the finite element model and results
presented in Wang et al. [9] especially in the range of steady-state plastic flow.
BC’s
UX = 0
Line of Symmetry
BC’s
Initial Condition
Corner Node
UX = Strain rate/time
UX, UY = 0
Figure B-3: Finite element model for constant strain rate
(a) [9]
(b) Anand Model
Figure B-4: Constant Strain Behavior of Sn60Pb40 Solder
Strain Rate = 1.0 x 10-2 (1/s)
91
(a) [9]
(b) Anand Model
Figure B-5: Constant Strain Behavior of Sn60Pb40 Solder
Strain Rate = 1.0 x 10-4 (1/s)
The second method of validation a cyclic thermal load condition was imposed in the
analysis. The temperature varied from -55OC to 125OC (-67OF to 257OF). The transition
rate from the minimum to maximum temperature is 36OC per minute and a 10 minute
dwell at the temperature extremes. The inelastic shear strain distribution in the solder is
plotted and compared with Wang et al. [9] as shown in Figure B-6. When compared, the
distribution of strain is similar. The maximum value of the strain from the model is
within 8% of that presented in Wang et al. [9] with the maximum strain occurring at the
lower left hand corner of the solder joint. Any variation between Wang et al. [9] and the
finite element model can be attributed to the mesh size and/or the boundary conditions,
both were not defined, applied to the model.
The third method of validation is a cyclic strain range is created from a stress-strain
hysteresis loop. The loop is created by plotting the inelastic strain verse the shear stress
for a given element over the four thermal cycles as shown in Figure B-7. Figure B-7
shows the hysteresis loop based on the model follows a similar cyclic pattern as Wang et
al. [9]. Any variation can be attributed to the element selected for creating the loop. The
element used in the model can be different than the element selected by Wang et al. [9].
92
(a) [9]
(b) Based on the Anand model
Figure B-6: Distribution of inelastic shear strain in the solder joint
at start of the -55oC dwell of third cycle
93
(a) [9]
(b) based on Anand model
Figure B-7: Stress-strain hysteresis loop of selected element in
the solder joint under thermal cycling
94