Modeling very large plastic flows at very large strain rates for large-scale computation

Abstract

There are many important technological problems where accurate modeling of very large plastic deformations at very high strain rates is essential for effective and reliable design and manufacture of metal components. Examples are crashworthy vehicles, automated manufacturing, and automated metal forming and cutting. Another example is the understanding of the deformation field at the tip of a fast-running crack, where strain rates can easily exceed 10 5s −1 with local strains of several hundred percent. This paper summarizes some of the recent efforts by the authors and coworkers at the University of California, San Diego to develop physically-based constitutive models for mono- and polycrystalline solids, and to implement these models in large-scale finite element codes in the form of constitutive modules with efficient and robust computer algorithms. In the case of single crystal viscoplasticity, the constitutive integration is complicated by the fact that the essential set of ordinary differential equations is highly stiff for realistic levels of instantaneous rate-sensitivity. The algorithm that was developed for the integration of these equations in an explicit finite element environment is presented. Two example finite element solutions are given to demonstrate features of the overall finite element code. Also, a phenomenological viscoplasticity model that includes noncoaxiality between the stress and the plastic deformation rate is presented. This model is thought to be appropriate for high-strain-rate problems involving polycrystalline metals. Since the essential equation in this model is a single ordinary differential equation, numerical stiffness is not a factor; however, the integration is still complicated by an abrupt transition from the elastic regime to the plastic flow regime. A simple, robust “predictor-corrector” algorithm for the integration of this equation is presented.