A multi-mechanism model for cutting simulations based on the concept of generalized stresses

Abstract

In this work we extend an existing model for strain rate- and temperature-dependent asymmetric plastic material behavior accompanied by phase transformation with a gradient term of phase fraction based on the concept of generalized stresses as proposed by Gurtin and Forest. To this end a chemical variable, representing the austenite volume fraction, is treated as an extra degree of freedom, and the influence of its first gradient will be studied. A generalized principle of virtual power is postulated involving generalized stresses and used to derive the constitutive equations. The bulk model is formulated within a thermodynamic framework. For the scenario of a cutting process we have a martensite-austenite–martensite transformation. For the asymmetric visco-plastic part we use a modified strain rate form (Huh–Kang form) with a quadratic dependence of strength on the logarithm of the strain rate as a replacement for the linear dependence of the Johnson–Cook model. Furthermore, two numerical examples are given. Firstly, we identify the material parameters for the material DIN 100Cr6 in a hardened state by using experimental data under tension, compression and torsion taking the SD-effect into account. Secondly, a cutting simulation is investigated to test our model and the different mechanisms are illustrated.