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TECHNICAL PAPERS

# Constitutive Modeling of Metals Based on the Evolution of the Strain-Hardening Rate

[+] Author and Article Information
L. Durrenberger1

Laboratory of Physics and Mechanics of Materials, UMR CNRS 75-54, University Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz cedex, Francedurrenberger@lpmm.univ-metz.fr

J. R. Klepaczko

Laboratory of Physics and Mechanics of Materials, UMR CNRS 75-54, University Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz cedex, Franceklepaczko@lpmm.univ-metz.fr

A. Rusinek

Laboratory of Physics and Mechanics of Materials, UMR CNRS 75-54, University Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz cedex, Francerusinek@lpmm.univ-metz.fr

1

Corresponding author.

J. Eng. Mater. Technol 129(4), 550-558 (Jun 29, 2007) (9 pages) doi:10.1115/1.2772327 History: Received November 16, 2006; Revised June 29, 2007

## Abstract

The mechanical threshold stress (MTS) model is not commonly used in industrial applications due to its complexity. The Zener–Hollomon parameter $Z$ was utilized to develop a simplified and compact formulation similar to the MTS model. The predictions of the proposed formulation are compared to the results obtained by the original MTS model and experimental data. The flow stresses of three cold-rolled steels frequently used in automotive industries were analyzed for both formulations over a wide range of strain rates $(8.10−3s−1≤ε¯̇p≤103s−1)$.

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## Figures

Figure 1

Schematic evolution of the strain-hardening rate in a single crystal with respect to the true stress

Figure 2

Schematic evolution of the strain-hardening rate using Eqs. 8,9

Figure 3

Predictions of the modified model (thick lines) using the strain-hardening rate expressed by Eq. 8 and the MTS model (thin lines) compared to experimental data (square points) for BH260 (a) at three different strain rates (b) at three different strain levels; SP=Saturation Point

Figure 4

Predictions of the modified model (thick lines) using the strain-hardening rate expressed by Eq. 8 and the MTS model (thin lines) compared to experimental data (square points) for DP600 (a) at three different strain rates, (b) at three different strain levels; SP=saturation point

Figure 5

Predictions of the modified model (thick lines) using the strain-hardening rate expressed by Eq. 8 and the MTS model (thin lines) compared to experimental data (square points) for TRIP800 (a) at three different strain rates, (b) at three different strain levels

Figure 6

Predictions of the modified model (thick lines) using the strain-hardening rate expressed by Eq. 9 and the MTS model (thin lines) compared to experimental data (square points) for BH260 (a) at three different strain rates, (b) at three different strain levels

Figure 7

Predictions of the modified model (thick lines) using the strain-hardening rate expressed by Eq. 9 and the MTS model (thin lines) compared to experimental data (square points) for DP600 (a) at three different strain rates, (b) at three different strain levels

Figure 8

Predictions of the modified model (thick lines) using the strain-hardening rate expressed by Eq. 9 and the MTS model (thin lines) compared to experimental data (square points) for TRIP800 (a) at three different strain rates (b) at three different strain levels

Figure 9

Evolution of the strain-hardening rate using the fourth order Runge-Kutta method and the explicit form defined by Eq. 20 for the case of the TRIP800 steel; (b) Limit of strain calculated as a function of of the order n of the series in Eq. 20 for both steels at two strain rates 8.10−3s−1 and 103s−1)

Figure 10

Comparison of the stability and saturation conditions: (a) ultimate strain and (b) ultimate stress (with θmin=0.1MPa)

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