Physical Framework
Mathematical constitutive equations describe the rate-dependent deformation of electronic interconnects under thermal cycling. The anand viscoplasticity model defines the relationship between stress and plastic strain rate by using a single internal state variable. This framework omits the traditional yield surface and allows for a continuous transition between elastic and inelastic behavior.
It applies to lead-free solder alloys where creep and plasticity occur simultaneously at elevated temperatures.
Deformation Analysis
The model calculates the accumulation of inelastic strain over time. Because the internal state variable evolves with deformation, the software accounts for the hardening and softening of the solder joint during the entire thermal dwell period. The mathematical structure relies on several parameters that characterize the rate sensitivity and the activation energy of the alloy.
Engineers use these values to simulate the stress relaxation that occurs when a circuit board sits at high temperature. Accurate simulation prevents the failure of fine pitch components.
Numerical Limitation
Mechanical behavior prediction depends on the precision of the input constants derived from tensile tests. The anand viscoplasticity model loses accuracy when the material undergoes very low strain rates or stays below half of its melting temperature. The scalar state variable represents the resistance to plastic flow.
