A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes

Abstract

A simple phenomenological constitutive model has been proposed to describe dynamic deformation behavior of various metals in wide strain rate, strain, and temperature regimes. The formulation of the model is, σ=[A+B{1−exp(−Cε)}][D ln(ε̇/ε̇0)+exp(E⋅ε̇/ε̇0)][1−(T−Tref)/(Tm−Tref)]m, where σ is the flow stress, ε is the strain, ε̇ is the strain rate, ε̇0 is the reference strain rate, T is the temperature, Tref is the reference temperature, Tm is the melting temperature, and A, B, C, D, E, and m are the material parameters. The proposed model successfully describes not only the linear rise of flow stress with logarithmic strain rate for many metals, but also the upturn of the flow stress at strain rate over about 104 s−1 for the case of copper. It can also describe the exponential increase in the flow stress with logarithmic strain rate for the case of tantalum, and is capable of predicting thermal softening of various metals at high as well as low temperature. The current model can be used for the practical simulation of many high-strain-rate events with improved precision and as a more rigorous comparison standard in the development of a physical model.

A simple constitutive model for predicting flow stress of medium carbon microalloyed steel during hot deformation

“…This dependency is in contrast to the hypothesis behind the JC model. This is a prevalent problem of the JC model and similar results have been also reported for other materials [6,[21][22][23].…”

High Temperature Flow Behavior and Microstructure of Al-Cu/Mg2Si Metal Matrix Composite

“…The obtained JC material constants have been summarized in Table 2, so the original JC model for the examined material can be summarized as follows: <r = (165 -123.70e2,3i)(1 + 0.053lne')(l -r 019) (8) The comparisons between the experimental and predicted flow stress by the original JC model are shown in Fig. 9.…”

“…The various constitutive models, which have been proposed to describe the high temperature flow behavior of the materials, can be generally classified into two main categories [7,8], These are known as phenomenological and physical based models, each of which possesses its own benefits and drawbacks. Although the physical based models may end to a more precise estimate of the flow behavior, these models are based on the kinematics and dynamics of dislocations, thereby requiring very clear understand ing of the mechanisms that control the material deformation and are hardly possible to apply in practical use.…”

Enhancement in the Modeling of Temperature and Strain Rate‐Dependent Plastic Hardening Behavior of a Sheet Metal

“…Modeling accuracy with respect to material difference is another important concern, and Shin et al [14] suggested constitutive model which can describe hardening behavior of various materials. The suggested model successfully applied to copper with strain rate up to 10 4 s À1 and showed reasonable prediction results for high strain rate deformation of other metallic materials including tantalum, beryllium, steel, uranium, and tungsten heavy alloys.…”