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Solder Joint Cracking of Leadless Chip Resistors
in Electronic Assemblies
by
Luke T. Orsini
A 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
DRAFT
Approved:
_________________________________________
Ernesto Guitierrez-Miravete, Thesis Adviser
COPY
2011-08-15
Rensselaer Polytechnic Institute
Hartford, Connecticut
August, 2011
i
© Copyright 2011
by
Luke Orsini
All Rights Reserved
ii
CONTENTS
LIST OF TABLES............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
LIST OF SYMBOLS ........................................................................................................ vi
ACKNOWLEDGMENT .................................................................................................. ix
ABSTRACT ...................................................................................................................... x
1. Introduction.................................................................................................................. 1
2. Background.................................................................................................................. 3
2.1
Solder Microstructure......................................................................................... 3
2.2
Coarsening ......................................................................................................... 5
2.3
Coarsening During Thermo-Mechanical Fatigue .............................................. 6
2.4
Creep .................................................................................................................. 7
2.5
Crack Initiation and Growth............................................................................. 10
2.6
Effect of Solder Joint Thickness ...................................................................... 12
3. Modeling Stresses in a Leadless Chip Resistor Solder Joint..................................... 13
3.1
Methodology .................................................................................................... 13
3.2
Governing Equation: The Anand Model.......................................................... 17
4. Results........................................................................................................................ 20
5. Conclusions................................................................................................................ 21
6. Recommendations for Further Evaluation................................................................. 22
References........................................................................................................................ 23
APPENDIX A.................................................................................................................. 24
iii
LIST OF TABLES
Table 3.1-1: Leadless Chip Resistor Dimensions............................................................ 14
Table 3.1-2: Material Properties ...................................................................................... 15
Table 3.2-1: Solder (Sn63Pb37) Constants for Anand (viscoplasticity) model [10]....... 18
iv
LIST OF FIGURES
Figure 1-1: Chip Resistor Mounting.................................................................................. 1
Figure 1-2: Leadless Chip Resistors Mounted to a Printed Circuit Board ........................ 2
Figure 2-1: Sn-Pb phase diagram [1]................................................................................. 3
Figure 2-2: Sn63Pb37 eutectic solder showing colonies and colony boundaries [3] ........ 4
Figure 2-3: Eutectic solder showing fine microstructure developed by water quenching
from 250OC [3] .................................................................................................................. 5
Figure 2-4 Depiction of grain growth due to thermo-mechanical fatigue [7] ................... 7
Figure 2-5: Leadless chip resistor showing coarsened grain structure. ............................. 7
Figure 2-6: Leadless chip resistor showing crack along coarsened grain. ........................ 7
Figure 2-7: Typical creep curve for metals and alloys including solder ........................... 8
Figure 2-8: Log-Log plot of creep rate vs. applied shear stress for solder [3] .................. 8
Figure 2-9: Crack growth constituents C* (creep) and J-integral (elastic-plastic) [1] .... 11
Figure 3-1: Leadless Chip Resistor R1505 Dimensions.................................................. 13
Figure 3-2: Finite Element Model ................................................................................... 15
Figure 3-3: Thermal Cycle Profile................................................................................... 16
v
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 (µm)
c1
kinetic factor dependent on matrix composition, (in µm3 K/hour)
c2
reference stress, (MPa)
Do
frequency factor (1/sec)
d
mean phase diameter at time t, (µm)
d
grain size, (µm)
do
mean phase diameter at time t=0, (µm)
dγs
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/OK)
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)
n
material constant (dimensionless)
vi
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)
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)
α
face centered cubic (FCC) form of tin (dimensionless)
β
body center tetragonal (BCT) form of tin (dimensionless)
ζ
stress multiplier, (dimensionless)
∆a
incremental crack growth, (µm)
∆ac
incremental crack growth due to creep, (µm)
∆ap
incremental crack growth due to fatigue, (µm)
∆Hg
activation energy, (kJ/mol)
∆τ
cyclic stress range, (MPa)
εy
yield strain
εɺ c
creep strain rate (1/sec)
εɺ ij
strain rate at crack tip (1/sec)
vii
εɺ p
plastic strain rate (1/sec)
εɶ ij
dimensionless function
σe
von-Mises effective stress, (Mpa)
σij
crack tip stress field
σy
yield stress, (stress)
σɶ ij
dimensionless function
τ
applied stress, (MPa)
µ
Poisson’s ratio (dimensionless)
viii
ACKNOWLEDGMENT
Thank you to my wife and daughter for their support.
ix
ABSTRACT
Complex electronic assemblies for the commercial and military aircraft industry are
exposed to various environments that will affect the reliability of these assemblies.
Fracturing of solder joints is a common failure mode in these electronic assemblies.
This paper will investigate solder joint cracking of chip resistors in electronic
assemblies. There has been literature written that indicates a main cause of solder joint
cracking is creep. Typically, the solder used in electronic assemblies is a tin-lead
eutectic solder. The melting temperature of this type of solder is 183OC (361OF). The
effect of creep and other mechanisms that contribute to solder joint cracking will be
identified.
Mechanisms for solder joint cracks in resistors will be presented. A Finite
Element Analysis will be created to determine the stresses and strain imposed on a chip
resistor solder joint. The FEA model will also be used to show the effect of solder joint
shape and size.
x
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 1-1 and 1-2)
Resistor
Termination
Solder Joint
Resistor
PCB Surface Pad
Printed Circuit Board (PCB)
Figure 1-1: 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 paper will limit
itself to 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 service the solder will typically operate above
0.65Tm (119OC, 246OF) and then 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 change will induce stresses and strains due to differences in
coefficients of thermal expansion (CTE) between resistor and printed circuit board;
solder and resistor; solder and PCB surface pad. In addition to the CTE differences the
material stiffness of each element differs.
1
Figure 1-2: 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 evolves and the
mechanical properties change over time. The mechanical properties of a solder joint
change by dislocations and the grain growth.
Solder joints have a complex
microstructure and are used at high homologous (similar in structure) temperatures and
deform at relatively low loads. This results in plastic deformation of the solder joint and
is rarely uniform. Common solders are typically micro structurally unstable. From a
macroscopic perspective solder 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 needs to be understood [3].
This paper will focus on Sn63Pb37 solder. Sn63Pb37 is a single eutectic binary solder
system. The phase diagram is shown in Figure 2.1.
Figure 2-1: Sn-Pb phase diagram [1]
3
The lowest melting point falls at a eutectic point 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 α phase and a tin-β phase. The lead is face center
cubic (FCC) and the tin is body centered tetragonal (BCT) structure. During cooling the
microstructure forms. If the solder is slowly cooled the solid solutions grow together
parallel to each other in grain-like colonies. (See Figure 2-2) Faster cooling rates results
in a non-lamellar structure shown in Figure 2-3
Figure 2-2: Sn63Pb37 eutectic solder showing colonies and colony boundaries [3]
4
Figure 2-3: 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
at a 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].
 ∆H g 
c1t
exp  −

T
 RT 
d = mean phase diameter at time t, (µm)
d 3 ( t ) − d 30 =
d 0 = mean phase diameter (initial grain size @ t=0), (µm)
c1 = kinetic factor dependent on matrix composition, (in µm3 K/hour)
(2.2-1)
∆H g = activation energy, ( KJ / mol )
R= universal gas constant, ( J / mol ⋅ K )
T= temperature, (o K)
The above equation neglects the effect of mechanical stress or strain. To include the
mechanical influence the more generalized equation [Arrowood, 1990; Nabarro, 1998] is
used [8]
   ∆τ 
 1 +  
   c 2 
∆τ = cyclic stress range, (MPa)
 ∆H g
ct
d ( t ) − d ( t ) = 1 exp  −
T
 RT
3
3
0
nc



(2.2-2)
c2 = reference stress, (MPa)
n c = stress exponent
2.3 Coarsening During Thermo-Mechanical Fatigue
Thermomechanical stresses caused by temperature in high temperature environments the
microstructure of solder changes. 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
6
develop at the grain boundary intersections; the micro-voids develop into micro-cracks
which develop into macro-cracks the lead to fracture. (See Figure 2-4, 2-5 and 2-6)
Figure 2-4 Depiction of grain growth due to thermo-mechanical fatigue [7]
Figure 2-5: Leadless chip resistor showing
coarsened grain structure.
Figure 2-6: 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 2-7. Region II, steady state
creep is generally used to describe the creep behavior of metals.
7
Strain
III
II
I
Time
Figure 2-7: Typical creep curve for metals and alloys including solder
The steady state creep behavior of solder can also be described as shown in Figure 2-8 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 (γp)
independent of grain size.
IV n>10
III
n=3-7
II
I
n=2
n=3
Log shear stress (τ)
Figure 2-8: 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] where
G is the shear modulus, b is the Burgers vector, k is the Boltzmann’s constant, T is the
8
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.
p
n
dγs AGb  b   τ 
=
    Do exp ( − Q kT )
dt
kt  d   G 
dγs
= steady-state strain rate
dt
(2.4-1)
D. Gravis 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 
dγ s A II τ1.96
 +

exp
=
τ exp
1.8
dt
T d
 kT  T
 kT 
(2.4-2)
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, α 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 
εɺ = A sinh ( ασe )  exp 

 RT 
εɺ = creep strain rate
(2.4-3)
9
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 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 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, which is 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 µm) and between the separate the
Sn rich and Pb rich phases in the superplastic eutectic (grain size = 5.8 µm). 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 and C* (creep) integral [1] where the J-integral controls crack growth
and the C*- integral controls the creep part. See figure 2-9.
10
Creep
 C∗ 
σij = 

 BI n r 
Elastic-Plastic
1
( n +1)
σɶ ij ( θ ) ,
n
 C∗  ( n +1)
εɺ ij = 
εɶ ij ( θ ) ,

 BIn r 
B, m, n = material constant


J
σij = 
 xε y σ y I m r 


1
( m +1)
σɶ ij ( θ )
m

 ( m +1)
J
εɶ ij ( θ )
εɺ ij = xε 
 xε y σ y I m r 


σ ij = crack tip stress field
I n , Im = normalizing parameter εɺ ij = strain rate at crack tip
ε y = yield stress
r, θ = polar coordinates at crack tip
σ y = yield strain
σɶ ij , εɶ ij = dimensionless functions
x = cavity spacing
∆a= incremetnal crack growth
(2.5-1)
Figure 2-9: Crack growth constituents C* (creep) and J-integral (elastic-plastic) [1]
11
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.
12
3. Modeling Stresses in a Leadless Chip Resistor Solder Joint
There have been numerous articles confirming 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 the failure mechanism of the solder joint
is complex. Finite element analysis is used extensively in the 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 used to determine 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 3-1 and
Table 3.1-1.
Figure 3-1: Leadless Chip Resistor R1505 Dimensions
13
Table 3.1-1: 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 fillet
.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 three dimensional solid model of the device is created using
Unigraphics. By establishing symmetry boundary conditions a quarter model can be
used in the analysis and provide accurate results. The quarter solid model is imported
into ANSY where the finite element analysis is performed.
The finite element model shown in Figure 3-2 is composed of a single element type
(ANSYS Solid 186). The Solid 186 element is 3-D quad 20 node element with three
degrees of freedom on each node: translation in the x, y and z directions. The element
14
supports plasticity, hyperelasticity, creep, stress stiffening, large deflections and large
strain. The Solid 186 can also be defined as a 3-D tetrahedral 20 node element that
makes it highly suited to modeling the irregular geometry of the solder joint fillet. [8]
Figure 3-2: 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 3.1-2.
Table 3.1-2: Material Properties
Description
Resistor
Resistor
Termination
Substrate
(PCB)
Young’s
Modulus,
E
(psi)
Shear
Modulus,
G
(psi)
Poisson’s
Ratio,
µ
Ceramic
3.5E6
-
0.25
Coefficient
of
Thermal
Expansion
(1/OC)
40E-6
AgSnCu
1.2E7
-
0.37
18.9E-6
(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
Material
Epoxy (GFG)
with Cu layers
PCB Pad
Cu
Solder
Sn63Pb37
• Gravity (g) = 386.4 in/sec2
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
15
extremes. The thermal cycle profile is shown in Figure 3-3.
The purpose of thermal
cycle load is to induce plastic work due to the mismatch in the materials coefficients of
thermal expansion.
Figure 3-3: Thermal Cycle Profile
16
3.2 Governing Equation: 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 and 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
 εɺ
1
 Q  
−1  p
c = sinh  exp 
(3.2-1)
 
ξ
 RT   
 A
Where εɺ p is the plastic strain rate, A is the pre-exponential factor, Q the activation
energy, m is the strain rate sensitivity, ζ 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 
 σ 
εɺ p = A exp  −
 sinh  ξ  
 RT  
 s 
(3.2-2)
From the above equation
n
 εɺ p
 Q 
(3.2-3)
s = sˆ  exp 

 RT  
A
Where s* the saturation value of s, ŝ is the coefficient for deformation resistance
*
saturation value and n the strain rate sensitivity. From the development of the above
equations there are nine material parameters that need to be defined in the Anand model.
17
Table 3.2-1: Solder (Sn63Pb37) Constants for Anand (viscoplasticity) model [10]
Constant
so
Q/R
A
ξ
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
18
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
19
4. Results
20
5. Conclusions
21
6. Recommendations for Further Evaluation
Evaluate model for effect of volume size.
Apply thermal affect due to power disposition of device.
Evaluate different resistor size.
Determine number of cycles to failure.
22
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”,
Emelmaier 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. 247-253
[10]
Islam, Mohd Nokibul., “Investigations on Damage Mechanics and Life
Prediction of Fine-Pitch Electronics in Harsh Environments”, Auburn University,
August 2005
23
APPENDIX A
24