# Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model

## TL;DR

This paper proposes a new method to estimate heating caused by plastic deformation using strain data and a thermal model.

## Contribution

A novel approach combining strain data and a thermal finite element model to estimate plasticity-induced heating is introduced.

## Key findings

- The energy-based variational model shows inconsistencies in estimating plasticity-induced heating.
- A thermal finite element approach using strain data and the Johnson–Cook model provides a more reliable estimation.
- The Taylor–Quinney coefficient is integrated to model the fraction of plastic work converted to heat.

## Abstract

Temperature evolution during plastic deformation is of great importance for the design of manufacturing processes, as well as for the analysis and prediction of tool wear. However, the results from experimental- and numerical-type research are still often contradictory. In this paper, we analyze methods for estimating plasticity-induced heating directly from displacement fields that can be recorded during experiments or extracted from simulation results. In terms of computational methodology, the thermodynamically motivated energy-based variational formulation of the coupled thermo-mechanical boundary-value problem is adapted to the problem at hand. Since an analysis of this variational formulation exhibits challenges and distinct inconsistencies with respect to the problem at hand, an alternative approach is proposed. This alternative approach is essentially a purely thermal finite element simulation, and it is conducted using a heat source term that is empirically based on the fraction of irreversible deformation work converted to heat. Our approach estimates plasticity-induced heating based on the strain and strain rate data derived from displacement fields. We therefore incorporate thermo-visco-plastic constitutive behavior (Johnson–Cook) with a thermodynamically motivated model that specifies the fraction of plastic work converted to heat (the Taylor–Quinney coefficient).