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Effect of Simulation Methodology on Solder Joint Crack Growth Correlation

Robert Darveaux

1900 South Price Road

Chandler, AZ 85248

rdarv@amkor.com

Ph. 480-821-2408 ext 5235

Fax. 480-821-6730

Abstract

A generalized solder joint fatigue life model for surface

mount packages was previously published in Refs [1,2]. The

model is based on correlation to measured crack growth data

on BGA joints during thermal cycling. It was subsequently

discovered by Anderson et.al. that the ANSYS

5.2 finite

element code used in the model had an error in its method for

calculating plastic work [3]. It was shown that significant

error in life prediction could result by using a recent version

of the code where the bug has been fixed. The error comes

about since the original crack growth constants were derived

based on plastic work calculations that had the bug.

In this paper, crack initiation and growth constants are re-

calculated using ANSYS

5.6. In addition, several other

model related issues are explored with respect to the crack

growth correlations. For example, 3D slice models were

compared to quarter symmetry models. Anand’s constitutive

model was compared with Darveaux’s constitutive model. It

was shown that the crack growth rate dependence on strain

energy density always had an exponent of 1.10 +/- 0.15. This

is in the range of the original correlation, so the accuracy of

relative predictions should still be within +/- 25%. However,

the accuracy of absolute predictions could be off by a factor

of 7 in the worst case, if the analyst uses a modeling

procedure that is not consistent with that used for the crack

growth correlation. The key to good accuracy is to maintain

consistency in the modeling procedure.

Introduction

Analytical models in engineering have several practical

uses: 1) rapid design optimization during the development

phase of a product, 2) predicting field use limits, and 3)

failure analysis of product returned from the field or failed in

a qualification test. The solder joint fatigue model presented

here was first published in Ref [1]. An outline of the

procedure to predict fatigue life is shown schematically in

Figure 1. The model utilizes finite element analysis to

calculate the inelastic strain energy density accumulated per

cycle during thermal or power cycling. The strain energy

density is then used with crack growth data to calculate the

number of cycles to initiate a cracks, and the number of cycles

to propagate cracks through a joint.

In reference [2], more work was presented regarding

sensitivity of the life prediction to the FEA procedure. As a

result, the procedure was modified slightly to include volume

averaging of the strain energy values near the joint interface.

The model has been successfully applied to TSOP, CQFP,

CBGA, PBGA, and power hybrid packages [1,2,4-9].

Calculate Strain Energy Density

Accumulated per Cycle

Calculate Number of Cycles

to Crack Initiation

Calculate Crack Growth Rate

Calculate Fatigue Life

Based on Joint Length

Figure 1. Solder joint fatigue life prediction method.

It was subsequently discovered by Anderson et.al. that

ANSYS 5.5.2 and earlier versions of the finite element code

had an error in their method for calculating plastic work [3].

Even though there had generally been good correlation to

measured results, it was shown that significant error in life

prediction could result by using a recent version of the code

where the bug has been fixed (e.g. ANSYS 5.5.3 and later

versions). The error comes about since the original crack

growth constants were derived based on plastic work

calculations that had the bug.

In this paper, crack initiation and growth constants are re-

calculated using ANSYS 5.6. In addition, several other

model related issues are explored with respect to the crack

growth correlations. Several recommendations are made so

the analyst can get accurate results more efficiently.

Constitutive Relations

Since solder is above half of its melting point at room

temperature, creep processes are expected to dominate the

deformation kinetics. Steady state creep of solder can be

expressed by a relationship of the form [10-12]

dε

= C

[sinh(ασ)]

exp(

-Q

) (1)

where dε

/dt is the steady state strain rate, k is

Boltzmann's constant, T is the absolute temperature, σ is the

applied stress, Qa is the apparent activation energy, n is the

stress exponent, α prescribes the stress level at which the

power law dependence breaks down, and C

is a constant.

Steady state creep data for 62Sn36Pb2Ag solder joints is

shown in Figure 2.

Figure 2. Steady state creep of 62Sn36Pb2Ag solder joints in

shear with Cr/Ni/Au pad metallization.

Figure 3. Typical creep strain plot for constant load test in

shear.

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

Shear Stress (psi)

Steady State Strain Rate (1/sec)

132C

67C

100C

27C

Steady state creep is not generally achieved immediately

when stress is applied. A certain amount of transient (or

primary) creep occurs before attaining steady state. For

normal decelerating transient creep, the strain rate starts high

and decreases to the steady state value as the material work

hardens. Transient creep at constant stress and temperature

can be described by [13]

dε

t + ε

( 1 - exp (-B

dε

t)) (2)

where ε

is the creep strain, dε

/dt is the steady state creep

rate, ε

is the transient creep strain, and B is the transient

creep coefficient. Taking the time derivative of both sides

yields

dε

= t))

dε

(-B exp

ε + 1 (

dε

(3)

where dε

/dt is the instantaneous creep rate and dε

/dt is

the steady state creep rate. Hence at t = 0, the instantaneous

creep rate is (1 + ε

B) times greater than the steady state

creep rate, and after a long time, the instantaneous rate is

equal to the steady state rate. A typical creep curve showing

this behavior for 62Sn36Pb2Ag solder joints is shown in

Figure 3 (γ is used to indicate shear strain, instead of ε for

tensile strain).

800006000040000200000

0.00

0.05

0.10

0.15

Time (sec)

Creep Strain

At high stresses, τ/G > 10

-3

, there is also a time-

independent plastic strain component to the deformation. The

following strain hardening law can be used to describe high

stress deformation

= C

(

)

(4)

where ε

is the time-independent plastic strain, G is the

shear modulus, and C

and m

are constants. The total

inelastic strain is given by the sum of creep strain and plastic

strain

= ε

+ ε

(5)

where ε

is the total inelastic strain.

Equations (1) - (5) were shown to fit the deformation

behavior of five different solder alloys in Ref [1]. The

constants for 62Sn36Pb2Ag solder are given in Table 1.

Unfortunately, these relations are not available in all

commercial finite element codes as standard options.

However, it is possible to input user defined constitutive

relations in most codes.

Table 1.

Darveaux Model Constitutive Constants

62Sn36Pb2Ag Solder, Tensile

Parameter Value Definition

(1/sec) 8.03E4 Steady State Creep

Prefactor

α (1/psi)

4.62e-4 Steady State Creep

Power Law Breakdown

n 3.3 Steady State Creep

Stress Exponent

Qa (eV) 0.70 Steady State Creep

Apparent Activation Energy

.023 Transient Creep Strain

263 Transient Creep Coefficient

3.35E11 Plastic Flow Prefactor

5.53 Plastic Flow Exponent

ANSYS does have viscoplastic elements as a standard

option, but they use Anand’s constitutive model [14,15]. The

use of these elements is convenient since the user does not

have to modify the source code. Anand’s model is broken

down into a flow equation, and three evolution equations:

Flow Equation

= A[sinh(ξσ/s)]

1/m

exp(

-Q

) (6)

Evolution Equations

= {h

(|B|)

|B|

}

(7)

B = 1 -

(8)

s* = s^ [

d / dt

exp (

) ]

(9)

In Ref[1], an approximate fit was made to the solder

deformation data using only the flow equation, Eq. (6). In

reference [2], a fit has been made using both the flow

equation, Eq. (6), and the evolution equations, Eq. (7-9). A

spreadsheet was set up to do 1-dimensional thermal cycle

simulations, with assembly stiffness and imposed strain as

inputs. Both the Anand model, Eqs. (6-9), and the Darveaux

model, Eqs. (1-5), were used. An iterative process was used

to determine the Anand constants that gave approximately the

same results as the Darveaux model. The recommended

Anand constants are listed in Table 2.

Table 2

Anand Constants for ANSYS

62Sn36Pb2Ag Solder

ANSYS Parameter Value Definition

C1 S

(psi) 1800 Initial Value of

Deformation Resistance

C2 Q/k (1/K) 9400 Activation Energy /

Boltzmann’s Constant

C3 A (1/sec) 4.0E6 pre-exponential factor

1.5 multiplier of stress

C5 m .303 stain rate sensitivity of

stress

C6 h

(psi) 2.0E5 hardening constant

C7 s^ (psi) 2.0E3 coefficient for deformation

resistance saturation value

C8 n .07 Strain rate sensitivity of

saturation (deformation

resistance) value

C9 a 1.3 strain rate sensitivity of

hardening

Non-linear Finite Element Analysis Method

Three-dimensional non-linear finite element modeling was

used to calculate the strain energy density accumulation in

solder joints. ANSYS 5.6 was used for all aspects: pre-

processing, solution, and post-processing. The solder

material was modeled as a viscoplastic solid, the printed

circuit boards as orthotropic linear elastic solids, and the rest

of the materials as linear elastic solids. The linear elastic

material properties are given in Refs [1,16].

The goal of the simulations was to calculate the plastic

work per unit volume (or viscoplastic strain energy density)

accumulated per thermal cycle. Either two or three complete

thermal cycles were simulated in order to establish a stable

stress-strain hysteresis loop. The plastic work accumulated

during the last cycle was used for all crack growth

correlations. A typical slice model is shown in Figure 4, and

a quarter symmetry model is shown in Figure 5. A solder

joint model is shown in Figure 6.

Figure 4. Slice model of CBGA assembly

Figure 5 Quarter symmetry model of CBGA assembly

Figure 6. Model of solder joint. Three layers near substrate

interface are .0005” thick each.

The slice model (Figure 4) has a symmetry boundary

condition along the centerline of the joints. The boundary

condition along the opposite edge (centerline between rows)

is coupled in the y-direction.

It was shown in Ref [2] that the calculated strain energy

density increases as element size in the solder joint decreases.

Hence, a volume averaging technique was used to reduce this

sensitivity to meshing.

The strain energy value of each

element is normalized by the volume of the element.

∆W

ave

∆WV

•

∑

(10)

where ∆W

ave

is the average viscoplastic strain energy density

accumulated per cycle for the interface elements, ∆W is the

viscoplastic strain energy density accumulated per cycle of

each element, and V is the volume of each element. This

technique helps make the analysis more robust, but it was

found that there was still some dependency on the thickness

of the interface elements. For the models in the present study,

the thickness of the first three layers of elements was set to

0.0005 inches each.

Regarding time step size, sub-steps that result in a 10C

temperature change during the ramps, and an increasing time

step during the dwells were used. For example, considering a

-40C <-> 125C thermal cycle with 900 sec ramps and 900 sec

dwells, sixteen load steps were used during the ramps, and 4

load steps during the dwells (60, 120, 240, and 480 sec).

Linear + Non-linear Analysis Method

A second method was employed to calculate the strain

energy density accumulation in solder joints. In this method,

linear finite element analysis is used to calculate the assembly

stiffness and imposed strain on the solder joints. Then a 1-

dimensional nonlinear analysis is used to calculate strain

energy density accumulated per cycle. The non-linear

simulation can be performed in a spreadsheet. This method

was used to analyze flip chip assemblies in Ref [17].

Two finite element simulations are required. The

reference temperature is set to the high temperature of the

cycle, and the final temperature is set to the average

temperature of the cycle. For example, for a –40C Ù 125C

cycle, the reference temperature would be 125C and the final

temperature is 42.5C. A linear analysis is used to calculate

the equivalent stress and strain distribution in the solder

joints. This simulation is then repeated using a 100X lower

elastic modulus for the solder material. The results of these

two simulations are used to estimate the effective assembly

stiffness, S

, and imposed strain per degree temperature

change, ε

, as indicated in Figure 7.

= −(σ

−σ

.01

)/(ε

−ε

.01

) (11)

= (ε

.01

+ σ

.01

)/∆T (12)

where σ

and ε

are the equivalent stress and strain

calculated using the full elastic modulus of solder, and σ

.01

and ε

.01

are calculated using 1/100 the elastic modulus of

solder.

The advantage of this method is that it is at least 30 times

faster than doing a full non-linear finite element analysis. The

disadvantages are 1) the full effect of temperature dependent

properties cannot be captured, and 2) the stress distribution in

the solder joints is probably not exactly equal to that of a full

non-linear method.

Crack Growth Measurement

A series of tests were run using 4 assemblies, 2 alloys, and

8 thermal cycle conditions. All of the assemblies used

ceramic chip carriers and eutectic ball grid array joints, but

there were variations in the PC boards, chip carrier structures,

and joint array patterns. Details of the Ceramic BGA

assemblies are given in Table 3. Thermal cycling conditions

are given in Table 4. All of the tests were conducted using

62Sn36Pb2Ag, and 3 additional tests were done using

60Sn40Pb.

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