Modeling of Inelastic Response of Metals with Emphasis on Cyclic Viscoplasticity

Doctoral thesis, 2000

This thesis is concerned with the continuum modeling of the macroscopic behavior of engineering metals, in particular as part of life prediction strategies. Focus is primarily placed on the formulation and numerics of models for cyclic rate-dependent response. A thermodynamically consistent viscoplastic model based on the Duvaut-Lions concept with coupling to damage is proposed and various aspects of it are discussed. To extend the application range of the model with respect to loading rates, the unconventional feature of a bounding dynamic yield surface is introduced by a particular choice of overstress function. The dynamic yield surface prevents the response of the model to become purely elastic for high loading rates; instead the response will be almost rate-independent and resembles elastic-plastic response. The Backward Euler rule is used to integrate the constitutive equations, and the efficiency of a multi-level iteration technique for solving the arising system of equations is demonstrated. Further, the algorithmic tangent stiffness is derived and the model is implemented in the commercial FE code Abaqus. A sensitivity analysis is performed and used within a gradient-based optimization method to determine the model parameters. An example showing the capability of the model to mimic cyclic and softening experimental data of stainless steel is given. The issue of thermo-elastic-viscoplastic modeling of the high-strength alloy IN792, used at high temperatures, is then addressed. Within the Perzynaviscoplasticity different overstress functions are examined. Among these, two functions are taken from the literature and one function, that includes the concept of dynamic yield surface, is proposed. Numerical issues such as integration, sensitivity analysis and parameter identification are discussed. Experimental data for step-relaxation tests and stationary creep for different temperatures are simulated and, finally, predicted. Elastic and plastic anisotropy at large inelastic strains, modeled within the framework of hyperelasto-plasticity, is also part of this thesis. A kinematic hardening rule is proposed, and its predictive capability is investigated. Numerical investigations of the consequences of anisotropy are presented. In addition, it is shown that truncation errors introduced by linearizations in the case of non-coaxiality may be significant.