Implicit Integration and Consistent Tangent Modulus of a Time-Dependent Non-Unified Constitutive Model.

Abstract

This paper is concerned with the implicit integration and consistent tangent modulus of a high-temperature constitutive model, in which time-dependent inelastic strain rate consists of the transient part affected by kinematic and isotropic hardenings and the steady part depending on stress and temperature. Such a model is useful for high-temperature structure analysis and is practical because of the ease in determining material constants. The implicit integration is shown to result in two scalar-valued equations, and the consistent tangent modulus is derived in a general form by introducing a set of fourth-rank constitutive parameters into discretized kinematic hardening. The constitutive model is, then, implemented in a finite element program and applied to lead-free solder joint analysis. It is demonstrated that the implicit integration is very accurate if the kinematic hardening model of Ohno and Wang is employed, and that the consistent tangent modulus affords parabolic convergence to the Newton-Raphson iteration for solving nodal force equilibrium equations.