Parameter Calibration of Anand Viscoplastic Model for Lead Free Solders
Calibrating Anand viscoplastic parameters for lead free solders demands isothermal tensile and relaxation testing across temperatures and strain rates.
State Variable
Constitutive Parameter
Mathematical representations of material behavior use internal parameters to capture the current microstructural condition of a solid during deformation. A state variable represents a physical property, such as dislocation density or grain size, that determines the future response of the material to mechanical loads. Unlike path-dependent quantities like total strain, this parameter depends only on the current state of the material.
Evolution Equation
Formulation of the evolution of these parameters is required to predict material behavior over complex loading histories. These equations describe how the variable changes with respect to plastic strain, temperature, and strain rate. This approach allows the modeling of transient behaviors like strain-rate sensitivity.
Physical Identification
Experimental validation of these internal variables is accomplished through indirect measurements like electrical resistivity or hardness testing. Transmission electron microscopy can also be used to measure dislocation densities directly. These measurements calibrate the evolution equations used in finite element models.
Model Integration
Integration of these microstructural parameters into finite element codes enables the simulation of complex forming processes where temperature and strain rate vary continuously. The model updates each state variable at every integration point, allowing the prediction of localized softening or hardening. This capability is useful for designing multi-step manufacturing processes where the material’s history affects the final properties of the component.