Stored Energy Predictions from Dislocation-Based Hardening Models and Hardness Measurements for Tensile-Deformed Commercial Purity Copper

Matjaž Čebron,Franc Kosel

doi:10.5545/sv-jme.2013.1569

Abstract

Stored energy analyses by differential scanning calorimetry (DSC) and indentation hardness measurement were performed on crosssectional samples cut from the gauge length of tensile-deformed copper specimens. The stress-strain curve was described using dislocationbased hardening models integrated into a visco-plastic Taylor-type model of polycrystal deformation. Three approaches in reproducing the experimental stress-strain curve were used to evaluate the differences in dislocation density predictions resulting from different modelling options. A good description of hardening was achieved by all three approaches and constitutive models and only negligible differences were found in the predicted dislocation density between assumed homogeneous and heterogeneous dislocation distribution throughout the polycrystal. Measured values of stored energy are somewhat lower than those published in research studies in which one-step and slow annealing methods were used. A simple model predicting a nearly linear increase of stored energy with dislocation density was found to adequately describe retained energy evolution. Since different dislocation arrangements result in different yield stress and energy predictions, both results can be used to determine values of parameters in two-internal-variable hardening models. Even though both measured quantities were satisfyingly described, uncertainties regarding material parameters and the applied polycrystal and stored energy models prevent us from claiming that the evaluated dislocation density distributions represent the actual dislocation structure in the material. As expected for strongly hardening materials, the relationship between yield stress and hardness could not be adequately approximated by a linear function. Instead, a linear combination of yield stress and hardening rate was used, finally providing a relation between hardness and stored energy through their mutual dependence on yield stress.

Highlights

In the last decades considerable effort has been dedicated to the development of hardening models based on the underlying physical mechanisms involved in plastic deformation of crystalline materials
This type of strain hardening behaviour can be explained in terms of constitutive models using a single internal variable related to the mean dislocation density [10]
Since ED machining causes a local increase of temperature and mechanical cutting induces further hardening in the surface layers, an opposite effect on hardness and stored energy was expected from the two cutting processes

Summary

Introduction

In the last decades considerable effort has been dedicated to the development of hardening models based on the underlying physical mechanisms involved in plastic deformation of crystalline materials. Earlier dislocation-based models of strain hardening, see [7] to [9], were mainly concentrating on explaining stage III of the hardening process and were able to describe a gradual decrease of the hardening rate, which in many cases is a nearly linear function of yield stress This type of strain hardening behaviour can be explained in terms of constitutive models using a single internal variable related to the mean dislocation density [10]. Stored dislocations in crystalline materials are rarely distributed homogeneously throughout the structure, implying that a satisfactory description of the mechanical state in terms of the mean dislocation density is inadequate To overcome this inconsistency and correctly describe the hardening behaviour following phase III, two-internal-variable models had to be invoked [11]

Methods

Results

Conclusion