A strain rate dependent thermo-elasto-plastic constitutive model for crystalline metallic materials

Cen Chen,Tzuchiang Wang

doi:10.1038/s41598-021-88333-1

Abstract

The strain rate and temperature effects on the deformation behavior of crystalline metal materials have always been a research hotspot. In this paper, a strain rate dependent thermo-elasto-plastic constitutive model was established to investigate the deformation behavior of crystalline metal materials. Firstly, the deformation gradient was re-decomposed into three parts: thermal part, elastic part and plastic part. Then, the thermal strain was introduced into the total strain and the thermo-elastic constitutive equation was established. For the plastic behavior, a new relation between stress and plastic strain was proposed to describe the strain rate and temperature effects on the flow stress and work-hardening. The stress–strain curves were calculated over wide ranges of strain rates (10–6–6000 s−1) and temperatures (233–730 K) for three kinds of crystalline metal materials with different crystal structure: oxygen free high conductivity copper for face centered cubic metals, Tantalum for body centered cubic metals and Ti–6Al–4V alloy for two phase crystal metals. The comparisons between the calculation and experimental results reveal that the present model describes the deformation behavior of crystalline metal materials well. Also, it is concise and efficient for the practical application.

Highlights

The strain rate and temperature effects on the deformation behavior of crystalline metal materials have always been a research hotspot
The strain rate and temperature effects on the flow stress are uncoupled in the JC model which is not in line with the case of most crystalline metals; the ZA model is not effective to predict the plastic behavior at temperatures above 0.6 Tm and lower strain rate, and it considers two different forms for fcc and bcc materials
The experimental results showed that the temperature effect on the elastic behavior should not be ignored due to the free thermal expansion of lattice and the thermal vibration of atoms[19]

Summary

Introduction

The strain rate and temperature effects on the deformation behavior of crystalline metal materials have always been a research hotspot. A strain rate dependent thermo-elasto-plastic constitutive model was established to investigate the deformation behavior of crystalline metal materials. The JC model was introduced to build a constitutive equation for the strain rate sensitivity and softening effect on the work-hardening behavior at different temperatures for crystalline m etals[2]. The KHL model was developed to describe the viscoplastic hardening behavior of polycrystalline materials and had successfully described the work-hardening behavior of copper (Cu) under cyclic shear straining and biaxial tension–torsion[18] These models mentioned above describe the strain rate and temperature effects on the flow softening and strain hardening behaviors, there are still some limitations for them. The comparison between the calculation and experimental results shows that the present model describes the thermo-elasto-plastic deformation at different strain rates and temperatures accurately. It is to applied in different crystalline metal materials

Methods

Results

Discussion

Conclusion