The damage of the solder joint is defined as an exponential function of the nonlocal variable over the threshold .

and the local internal variable is defined as:

where:

= normalization constant of the equivalent inelastic strain rate

= power index representing the time-dependence of the lifetime fatigue behavior

= normalization constant of the von Mises equivalent effective (undamaged) stress

= stress-dependency exponent

= magnitude of the inelastic strain rate increment

The nonlocal variable is associated with the local internal variable by:

where:

= length-scale parameter

Referring to Figure 69.3: Finite Element Model of a Chip Resistor Assembly, the material properties for each component of the chip resistor assembly are defined as follows:

Cu-pad is modeled as isotropic plasticity:

MP,DENS,1,8942	
MP,EX,1,125e9	
MP,NUXY,1,0.345
MP,ALPX,1,1.77e-05
TB,PLAS,1,,,BISO
TBDATA,1,409.9e6,1.324e9

PCB is modeled as anisotropic elastic material:

MP,EX,3,14392
MP,EY,3,14393
MP,EZ,3,10719
MP,GXY,3,8032
MP,GXZ,3,4200
MP,GYZ,3,3567
MP,PRXY,3,0.2
MP,PRXZ,3,0.15
MP,PRYZ,3,0.15

MP,CTEX,3,13.7e-6
MP,CTEY,3,13.7e-6
MP,CTEZ,3,32.5e-6

Solder joint is modeled with kinematic hardening and generalized damage:

TB,ELAS,
TBDATA,1,8000E6,0.34
TB,CTE,,
TBDATA,1,2E-05

TB,RATE,,1,,EVH
TBDATA,1,8E4,0,0,0,0.125,6E6

TB,CHABOCHE,,1,2        
TBDATA,1,8E4
TBDATA,2,5E6,200
TBDATA,4,6E5,80

! DAMAGE PROFILE
C_ETA=32E-10
ETA_CR1=0
ZZ=10.0
! FATIGUE DAMAGE
M0=0.0
N0=1.0
P0=2.0
A0=100E6

TB,CDM,,,,GDMG
TBDATA,1,ETA_CR1,ZZ,M0,N0,P0,A0
TBDATA,7,C_ETA

Chip metallization is modeled as linear elastic:

MP,EX,14,200000
MP,NUXY,14,0.31
MP,ALPX,14,13e-6

Chip is modeled as linear elastic:

MP,EX,15,370000   
MP,NUXY,15,0.23
MP,ALPX,15,7e-6