Crystal plasticity simulation of the thermo-mechanical behavior in polycrystalline metals

Abstract

Metals and alloys play an important role in our society. Hence, understanding and further predicting their behavior, and in particular under machining processes, is of great scientific and industrial interest. Such an understanding will prove instrumental for the optimization of machining conditions, which will further lead to a reduction of cost and an increase of productivity. Under thermo-mechanical processes including the machining process, polycrystalline metals usually undergo large deformations, high strain rates and high temperatures. The response of metals in these processes is very complex since their mechanical behavior is often strongly coupled with thermal phenomena. Accurate simulations of such processes require a fully coupled modeling framework that can accurately describe both the mechanical and the thermal behavior of the material, as well as their interaction. Such a complex multi-physics nonlinear framework could be established with the commonly used finite element method (FEM). In FEM, the simulation accuracy is largely dependent on the constitutive model employed. Conventional constitutive models are usually phenomenological and lack the description of the plasticity anisotropy and microstructure heterogeneity that polycrystalline metals exhibit, limiting their simulation accuracy. To address this issue, in this research an elasto-visco-thermo-plastic constitutive model based on crystal plasticity theory is developed for single crystals, which could connect the macroscopic plastic deformation behavior with the dislocation glide along slip systems and crystal reorientation. Actual engineering metals and alloys are usually polycrystalline materials, made of numerous single crystals. Each macroscopic material point may represent a huge amount of grains, up to millions. For this reason it is difficult to precisely capture the detailed shapes and orientations of all the grains in a macroscopic point, and even more difficult to reproduce this microstructure in a finite element simulation due to the prohibitively computational cost. To link the macroscopic response of a material point and the underlying microstructure, homogenization approaches need to be constructed. In this research, the computational homogenization approach, which represents a macroscopic material point with a representative element volume (RVE) of the microstructure and obtains the macroscopic response and microscopic field distribution solving a boundary value problem on the RVE, is employed to study the response of polycrystalline metals during deformation. The modeling approach accounts for thermal strains, heat generation and conduction at the microscale, and the effect that this microscopic temperature field has on the crystal response through a temperature dependent crystal plasticity model. Machining is one of the most commonly used manufacturing operations. Due to its crucial importance in modern industry, an in-depth understanding of the mechanisms and an accurate predictive simulation framework that could link the machining parameters with output variables could optimize the machining conditions and finally lead to notable enhancement of product quality, improvement of manufacturing productivity and reduction of economical cost. A machining process is a complicated nonlinear multiphysics problem as it usually involves contact, large deformations, fracture, as well as heat generation and conduction. Such a complex problem is usually resolved with the finite element method. In this study, the orthogonal cutting process of low carbon steel C45, a typical ferrite-pearlite steel, under various machining conditions is simulated. As the accuracy of a finite element analysis is mainly dependent on the constitutive relation employed, to better describe the material behavior of ferrite-pearlite steel subjected to large strain, high strain rate and high temperature and account for its plastic anisotropy and microstructure heterogeneity features, a microstructure informed elasto-visco-thermo-plastic constitute model based on the crystal plasticity model is proposed and integrated into ABAQUS/Explicit as a user defined subroutine VUMAT. A pure Lagrangian method with element deletion technique is adopted. The numerical results show acceptable agreement with experimental data and it could also capture the heterogeneous distribution of stress in the contact face due to the use of microstructure based constitutive model, which could not be observed with other conventionally used models, such as Jonhson-Cook’s.