Local and non-local thermomechanical modeling and finite-element simulation of high-speed cutting

Abstract

High-speed cutting is an important and widely-used process in modern production engineering. Considering the fundamental non-linear nature of this thermomechanical process, the finiteelement method is the numerical simulation tool of choice. In this context, a realistic numerical simulation of cutting processes places high demands on accuracy and efficiency. Since large deformation and deformation localization are involved, continual remeshing and mesh adaptation are required. In the context of a finite-element analysis, localized deformation patterns, as observed in experimental observations, can be modeled using thermo-viscoplastic material models including in particular the effect of thermal softening and in general damage as well. As is well-known, such softening effects result in a loss of solution uniqueness, resulting in socalled pathological mesh-dependence of the simulation results. In the last ten to fifteen years, a number of extensions to classical local modeling of softening, damage and failure have been proposed in order to account for the inherently non-local character of many processes contributing to such failure. For example, in the case of ductile failure in metal-matrix composites as based on void development, the process of void coalescence leading to failure is inherently non-local. From the mathematical / numerical point of view, many non-local models have the additional benefit of regularizing the boundary-value problem and alleviating mesh dependence. On this basis, the intention of the work presented in the following is to develop a general finite element framework to model and simulate the process of metal cutting and related processes. Here, we deal with two key issues. To resolve the complex deformation patterns, observed in context of metal cutting, we develop an adaptive finite element framework, based on a combination of error estimation and refinement indication. Further, we present an extended thermodynamic framework, with a general non-local description of several thermodynamic quantities. In this context we also discuss the effect of ductile damage. In the context of standard isochoric plasticity, the influence of hydrostatic pressure on the development of ductile damage is usually accounted for in an indirect fashion, by defining, e.g., a pressure-dependent formulation for the rate of damage. In contrast, the current work is based on both hydrostatic stress- and deviatoric stress-driven inelastic deformation, damage, and failure. The former drives for example primarily microvoid development, while the latter is related to micro-shear-band or microcrack development. The extended non-local description allows the modeling of lengthscale-effects, in general, but also the additional benefit of further reduction of mesh dependence is important and will be discussed.