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1. 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.
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 Table XX figure XXX.
Leadless Chip Resistor R1505 Dimensions
Symbol
Description
hr
Height, resistor
lr
Length, resistor
wr
Width, resistor
hs
Height, solder joint fillet
ts
Thickness, solder joint fillet
ws
Width, solder joint fillet
ht
Height, resistor termination
lt
Length, resistor termination
wt
Width, resistor termination
tp
Thickness, PCB pad
lp
Length, PCB pad
wp
Width, PCB pad
tb
Thickness, substrate/PCB
lb
Length, substrate/PCB
wb
Width, substrate/PCB
gp
Gap between pads
* Case 1: ts = .002, hs = .026
Case 2: ts = .001, hs = .025
Case 3: ts = .004. hs = .028
Dimension
(in)
.024
.155
.050
.024*
.002*
.050
.024
.015
.050
.0012
.0475
.060
.063
.310
.310
.105
From the geometry shown a three dimensional 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.
INSERT FEA MODEL OF QUARTER SIZE
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. The thermal
cycle profile is shown in Figure XXX. The purpose of thermal cycle load is to induce plastic
work due to the mismatch in the materials coefficients of thermal expansion.
Thermal Cycle Profile
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 XX.
Material Properties
Resistor
Resistor
Termination
Ceramic
Young’s
Modulus,
E
(psi)
3.5E6
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
PCB Pad
Cu
Solder
Sn63Pb37
 Gravity (g) = 386.4 in/sec2
Shear
Modulus,
G
(psi)
-
Poisson’s
Ratio,

Coefficient of
Thermal Expansion
(1/OC)
0.25
40E-6
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
[ANSYS]. The Anand model does not require and explicit yield condition and loading
/unloading criteria. 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 [Anand article]. 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
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 
From the above equation
 p
 Q 
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.
n
*
Solder (Sn63Pb37) Constants for Anand (viscoplasticity) model
Constant Description
Value Unit
so
Initial value of deformation resistance
1800 Stress (psi)
Activation energy / Universal gas
energy/volume/
Q/R
9400
constant
energy/volume temperature (OK)
A
Pre-exponential factor
4E6 1 / time (1/sec)
Stress
multiplier
1.5
Dimensionless

m
Strain rate sensitivity of stress
0.303 Dimensionless
Ho
Hardening / softening constant
2E5 Dimensionless
Ŝ
n
a
Coefficient of deformation resistance
saturation value
Strain rate sensitivity of saturation
(deformation resistance) value
Strain rate sensitivity of hardening or
softening
2000
Dimensionless
0.07
Dimensionless
1.3
Dimensionless
USE POWER PROFILE IF ABLE TO GET MODEL TO RUN
The finite element model 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 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.