Enhanced Polymer Passivation Layer for Wafer Level Chip Scale ...

creep deformation and time independent plastic deformation, it is not recoverable while the
elastic deformation is recoverable. A combination of plastic, elastic, viscoplastic, or
viscoelastic/creep models can be used to represent the constitutive behavior of materials.
In order to simulate correct solder stress-strain behavior under different loadings, the
selection of constitutive model for solder joints is very critical since it is one of the important
factors that can affect the accurate evaluation of the fatigue strength. Several creep and
viscoplastic models have been discussed in the past to describe the thermomechanical behavior
of SnAgCu solders.
Anand Viscoplastic Model: Anand [91] proposed a simple set of constitutive equations
for large, isotropic, viscoplastic deformations. There are two basic features of this model. First,
no explicit yield condition and no loading/unloading criterion are used. Second, this model
consists of single scalar internal state variable "s", called the deformation resistance, to measure
the isotropic resistance offered by the solder to the plastic flow. The Anand model can represent
the physical phenomena of strain-rate and temperature sensitivity, strain rate history effects,
strain-hardening and the restoration process of dynamic recovery. This model is broken down
into a flow equation and three evolution equations. The flow equation accommodates the strain
rate dependence on the stress at constant structure:
where p
Q
p Aexp
sinh
RT
s
100
1/ m
(5-1)
is the inelastic strain rate, A is a pre-exponential factor, Q is the activation energy, T is
the current absolute temperature, R is the universal gas constant,ξ is a multiplier of stress, σ is
the current tensile stress, s is the internal state variable (deformation resistance), and m is the