Modelling Interfacial Package Creep in High Temperature Electronics
Interfacial package creep modeling requires viscoplastic constitutive equations and temperature-dependent stress mapping to prevent long-term field drift.
Anand Constitutive Model
Kinematic Formulation
Viscoplastic constitutive equations represent rate-dependent deformation and stress relaxation in metallic materials subjected to elevated temperatures. The anand constitutive model expresses plastic strain rate as a function of equivalent stress and internal state variables without requiring an explicit yield surface. Material parameters in the formulation include nine distinct constants governing stress sensitivity, thermal activation energy, and strain hardening saturation.
Non-linear differential equations govern the evolution of internal resistance during thermal cycling of microelectronic interconnects.
Hardening Representation
Deformation history alters internal state resistance through competing mechanisms of strain hardening and dynamic recovery. Finite element implementations of the anand constitutive model update the scalar internal state variable at each time step based on local temperature and strain increments. Saturation resistance limits the maximum dynamic hardening achievable during continuous mechanical shear.
The scalar representation omits directional anisotropy induced by mechanical pre-straining.
Parameter Determination
Uniaxial tensile tests conducted across multiple strain rates and isothermal temperatures provide the raw data required for curve fitting. Standard parameter extraction routines for the anand constitutive model use non-linear least squares optimization to minimize stress error across experimental datasets. Experimental testing of small scale solder joints requires precise displacement control to prevent compliance errors in load frames.
Discrepancies between bulk material properties and micro-scale solder ball geometry often degrade boundary condition predictions. Laboratory calibration requires temperature stability within half a degree Celsius during constant strain rate loading to prevent thermal expansion artifacts from confounding stress relaxation measurements.
Simulation Accuracy
Finite element thermal fatigue life predictions rely on accurate strain energy density calculations derived from stress-strain hysteresis loops. Numerical integration of the anand constitutive model exhibits time step sensitivity during rapid temperature transitions in power cycling simulations. Convergence failures occur when large strain increments exceed local stability limits of implicit solver algorithms.
Material qualification testing verifies that calculated creep rates match physical solder interconnect displacement within specified tolerance bands.