Development of Microstructure-Based Constitutive Model for Plastic Deformation Behavior of High-Entropy Alloys

Abstract

High-entropy alloys (HEAs) are solid solution alloys that are composed of various elements at almost the same ratio without principal elements. The characteristic of the chemical composition of the alloy induces severe lattice distortion, which improves the mechanical properties by interfering with the dislocation movement and enhancing the strain hardening rate. Because of excellent strength, ductility and toughness of HEAs reported in earlier studies, they have been getting spotlight in the world of academia and industry. Also, HEAs having superior mechanical properties to that of commercial materials have been actively developed for industrial applications. The manufacturing of industrial HEAs products additionally requires plastic forming to make the desired shape, so fundamental understanding of plastic deformation behavior of HEAs is important to realize the application of HEAs to industry. However, theoretical understanding of plastic deformation behavior of HEAs has not been thoroughly explored by researchers. Here, in the present study, the plastic deformation behaviors of HEAs is reported by constitutive modeling and simulation techniques reflecting the microstructural components such as dislocation glide, deformation twinning, accumulation of geometrically necessary dislocation from strain gradient and atomic size misfit. The constitutive modeling was performed based on the Kocks-Mecking-Estrin model with modification to account for the twinning effect of HEAs, in which the total dislocation density is a single internal variable, while the evolution equation describing its variation during plastic deformation is governed by the twin volume fraction. This model assumes that the materials follow isotropic hardening rule. However, the material is subjected to combined hardening involving isotropic and kinematic hardening caused by back-stress due to local misorientation and accumulation of geometrically necessary dislocations. Therefore, a model describing the variation of geometrically necessary dislocation density was developed to improve the accuracy of the plastic deformation analysis. CrMnFeCoNi HEA and two layered materials bonded with stainless steel and high manganese steel respectively were chosen as testbeds of the developed constitutive modeling and analyzed. As an experimental verification step of the modeling, twin volume fraction, total dislocation density, and back-stress were measured through electron backscatter diffraction, x-ray diffraction pattern with convolutional multiple whole profile analyses, and loading-unloading-reloading test, respectively. The present study confirms that the microstructural changes predicted by the theoretical analyses are in good agreement with those measured by the experimental methods. Therefore, the developed model successfully describes the plastic deformation behavior of the HEAs, showing its analytical and predictive ability and accuracy. The present research demonstrates that outstanding mechanical properties of HEAs are originated from the severe lattice distortion induced by multi-principal elements. Dynamic recovery and dislocation movement are effectively prohibited by high strain field around dislocations, so that strain hardening rate increases. Meanwhile, in this study, in order to utilize HEAs as industrial materials, the effect of back-stress due to GNDs is increased by forming heterogeneous structure through laminating with conventional alloys. Based on the analysis using the proposed constitutive equations, it is quantitatively confirmed that the contribution of kinematic hardening due to GNDs to the total flow stress of the material is about 50 %, and that it increases as the straining progresses. In addition, it is understood that deformation twinning and deformation-induced phase transformation contribute to work hardening by promoting GND accumulation through increasing the density of boundary at which the incompatibility interaction between adjacent grains occurs.