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A dislocation-based model for all hardening stages in large strain deformation

Identifieur interne : 000D36 ( Istex/Corpus ); précédent : 000D35; suivant : 000D37

A dislocation-based model for all hardening stages in large strain deformation

Auteurs : Y. Estrin ; L. S. T Th ; A. Molinari ; Y. Bréchet

Source :

RBID : ISTEX:46FC4FD19FD8F7CD06DE73DAEDC5CB309FB45AFC

English descriptors

Abstract

Abstract: A new model is presented to describe the hardening behaviour of cell-forming crystalline materials at large strains. Following previous approaches, the model considers a cellular dislocation structure consisting of two phases: the cell walls and the cell interiors. The dislocation density evolution in the two phases is considered in conjunction with a mechanical analysis for the cell structure in torsional deformation in which the cell walls are lying at 45° with respect to the macroscopic shear plane and are strongly elongated in the direction perpendicular to the applied shear direction. Guided by recent results on the volume fraction of cell walls [Müller, Zehetbauer, Borbély and Ungár, Z. Metallk. 1995, 86, 827], the cell-wall volume fraction is considered to decrease as a function of strain. Within a single formulation, all stages of large strain behaviour are correctly reproduced in an application for copper torsion. Moreover, strain rate and temperature effects are accounted for correctly and the predicted dislocation densities are in accord with experimental measurements. It is suggested that the factor responsible for the occurrence of hardening Stages IV and V is a continuous decrease of the volume fraction of the cell walls at large strains. A significant effect of the deformation texture variation on strain hardening is also discussed.

Url:
DOI: 10.1016/S1359-6454(98)00196-7

Links to Exploration step

ISTEX:46FC4FD19FD8F7CD06DE73DAEDC5CB309FB45AFC

Le document en format XML

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<div type="abstract" xml:lang="en">Abstract: A new model is presented to describe the hardening behaviour of cell-forming crystalline materials at large strains. Following previous approaches, the model considers a cellular dislocation structure consisting of two phases: the cell walls and the cell interiors. The dislocation density evolution in the two phases is considered in conjunction with a mechanical analysis for the cell structure in torsional deformation in which the cell walls are lying at 45° with respect to the macroscopic shear plane and are strongly elongated in the direction perpendicular to the applied shear direction. Guided by recent results on the volume fraction of cell walls [Müller, Zehetbauer, Borbély and Ungár, Z. Metallk. 1995, 86, 827], the cell-wall volume fraction is considered to decrease as a function of strain. Within a single formulation, all stages of large strain behaviour are correctly reproduced in an application for copper torsion. Moreover, strain rate and temperature effects are accounted for correctly and the predicted dislocation densities are in accord with experimental measurements. It is suggested that the factor responsible for the occurrence of hardening Stages IV and V is a continuous decrease of the volume fraction of the cell walls at large strains. A significant effect of the deformation texture variation on strain hardening is also discussed.</div>
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<note type="content">Fig. 1: Three-dimensional TEM montage for a torsionally deformed copper sample near its outer surface (from Ref.[22]). Section (a) is parallel to both the radius and the axis, section (b) is in the plane of shear and section (c) is perpendicular to the radial axis.</note>
<note type="content">Fig. 2: Schematic picture of the dislocation cell structure in torsion.</note>
<note type="content">Fig. 3: Stress state along principal axes in simple shear.</note>
<note type="content">Fig. 4: A dislocation cell in torsion. The unit cell is shown by the broken line.</note>
<note type="content">Fig. 5: Simplified dislocation structure in a cell wall.</note>
<note type="content">Fig. 6: Variation of the volume fraction of the cell walls as a function of strain as measured by Müller et al.[19] for rolling of copper (stars) and as it is assumed in the present work for the case of torsion (solid line).</note>
<note type="content">Fig. 7: Strain hardening curve for copper as predicted by the present model (solid line). Stars are the data points taken from the paper of Zehetbauer[15] (torsional shear rate: γ ̇=10−2s−1). The Taylor factor evolution has been included.</note>
<note type="content">Fig. 8: Strain hardening rate curves as predicted by using a constant Taylor factor (M=1.65) as well as by including the variation of the Taylor factor obtained from polycrystal texture simulations. Triangles are the measurement data by Zehetbauer[15] in copper torsion (torsional shear rate: γ ̇=10−2s−1).</note>
<note type="content">Fig. 9: The relative hardening contributions of the cell walls (θw/θr) and cell interiors (θc/θr), as well as the softening caused by the decrease of the volume fraction of the cell walls (θf/θr) as a function of the resolved shear stress.</note>
<note type="content">Fig. 10: Predicted ratio (R) of the dislocation densities in the cell walls and the cell interiors as a function of strain.</note>
<note type="content">Fig. 11: The effect of strain rate on the rate of hardening. The symbols represent experimental points obtained by Zehetbauer[15] (+: γ ̇=10−4s−1; ×: γ ̇=10−2s−1).</note>
<note type="content">Fig. 12: The effect of temperature on the rate of hardening, simulated by varying the strain rate sensitivity parameter m (the corresponding n values for each curve are given by n=m/5).</note>
<note type="content">Fig. 13: The resolved shear stress as a function of the total dislocation density. Crosses and triangles are experimental data points obtained by Zehetbauer and Seumer[29] for torsion and rolling, respectively. The solid line shows the predicted curve with the Taylor factor evolution taken into account, while the dotted line is obtained for a constant value of the Taylor factor (M=1.65).</note>
<note type="content">Fig. 14: Predicted variation of the Taylor factor for simple shear as obtained using a Taylor-type viscoplastic polycrystal deformation texture model for m values in the range m=50–250.</note>
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<p>A new model is presented to describe the hardening behaviour of cell-forming crystalline materials at large strains. Following previous approaches, the model considers a cellular dislocation structure consisting of two phases: the cell walls and the cell interiors. The dislocation density evolution in the two phases is considered in conjunction with a mechanical analysis for the cell structure in torsional deformation in which the cell walls are lying at 45° with respect to the macroscopic shear plane and are strongly elongated in the direction perpendicular to the applied shear direction. Guided by recent results on the volume fraction of cell walls [Müller, Zehetbauer, Borbély and Ungár, Z. Metallk. 1995, 86, 827], the cell-wall volume fraction is considered to decrease as a function of strain. Within a single formulation, all stages of large strain behaviour are correctly reproduced in an application for copper torsion. Moreover, strain rate and temperature effects are accounted for correctly and the predicted dislocation densities are in accord with experimental measurements. It is suggested that the factor responsible for the occurrence of hardening Stages IV and V is a continuous decrease of the volume fraction of the cell walls at large strains. A significant effect of the deformation texture variation on strain hardening is also discussed.</p>
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<ce:simple-para>A new model is presented to describe the hardening behaviour of cell-forming crystalline materials at large strains. Following previous approaches, the model considers a cellular dislocation structure consisting of two phases: the cell walls and the cell interiors. The dislocation density evolution in the two phases is considered in conjunction with a mechanical analysis for the cell structure in torsional deformation in which the cell walls are lying at 45° with respect to the macroscopic shear plane and are strongly elongated in the direction perpendicular to the applied shear direction. Guided by recent results on the volume fraction of cell walls [Müller, Zehetbauer, Borbély and Ungár,
<ce:italic>Z. Metallk. 1995</ce:italic>
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, 827], the cell-wall volume fraction is considered to decrease as a function of strain. Within a single formulation, all stages of large strain behaviour are correctly reproduced in an application for copper torsion. Moreover, strain rate and temperature effects are accounted for correctly and the predicted dislocation densities are in accord with experimental measurements. It is suggested that the factor responsible for the occurrence of hardening Stages IV and V is a continuous decrease of the volume fraction of the cell walls at large strains. A significant effect of the deformation texture variation on strain hardening is also discussed.</ce:simple-para>
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<abstract lang="en">Abstract: A new model is presented to describe the hardening behaviour of cell-forming crystalline materials at large strains. Following previous approaches, the model considers a cellular dislocation structure consisting of two phases: the cell walls and the cell interiors. The dislocation density evolution in the two phases is considered in conjunction with a mechanical analysis for the cell structure in torsional deformation in which the cell walls are lying at 45° with respect to the macroscopic shear plane and are strongly elongated in the direction perpendicular to the applied shear direction. Guided by recent results on the volume fraction of cell walls [Müller, Zehetbauer, Borbély and Ungár, Z. Metallk. 1995, 86, 827], the cell-wall volume fraction is considered to decrease as a function of strain. Within a single formulation, all stages of large strain behaviour are correctly reproduced in an application for copper torsion. Moreover, strain rate and temperature effects are accounted for correctly and the predicted dislocation densities are in accord with experimental measurements. It is suggested that the factor responsible for the occurrence of hardening Stages IV and V is a continuous decrease of the volume fraction of the cell walls at large strains. A significant effect of the deformation texture variation on strain hardening is also discussed.</abstract>
<note type="content">Fig. 1: Three-dimensional TEM montage for a torsionally deformed copper sample near its outer surface (from Ref.[22]). Section (a) is parallel to both the radius and the axis, section (b) is in the plane of shear and section (c) is perpendicular to the radial axis.</note>
<note type="content">Fig. 2: Schematic picture of the dislocation cell structure in torsion.</note>
<note type="content">Fig. 3: Stress state along principal axes in simple shear.</note>
<note type="content">Fig. 4: A dislocation cell in torsion. The unit cell is shown by the broken line.</note>
<note type="content">Fig. 5: Simplified dislocation structure in a cell wall.</note>
<note type="content">Fig. 6: Variation of the volume fraction of the cell walls as a function of strain as measured by Müller et al.[19] for rolling of copper (stars) and as it is assumed in the present work for the case of torsion (solid line).</note>
<note type="content">Fig. 7: Strain hardening curve for copper as predicted by the present model (solid line). Stars are the data points taken from the paper of Zehetbauer[15] (torsional shear rate: γ ̇=10−2s−1). The Taylor factor evolution has been included.</note>
<note type="content">Fig. 8: Strain hardening rate curves as predicted by using a constant Taylor factor (M=1.65) as well as by including the variation of the Taylor factor obtained from polycrystal texture simulations. Triangles are the measurement data by Zehetbauer[15] in copper torsion (torsional shear rate: γ ̇=10−2s−1).</note>
<note type="content">Fig. 9: The relative hardening contributions of the cell walls (θw/θr) and cell interiors (θc/θr), as well as the softening caused by the decrease of the volume fraction of the cell walls (θf/θr) as a function of the resolved shear stress.</note>
<note type="content">Fig. 10: Predicted ratio (R) of the dislocation densities in the cell walls and the cell interiors as a function of strain.</note>
<note type="content">Fig. 11: The effect of strain rate on the rate of hardening. The symbols represent experimental points obtained by Zehetbauer[15] (+: γ ̇=10−4s−1; ×: γ ̇=10−2s−1).</note>
<note type="content">Fig. 12: The effect of temperature on the rate of hardening, simulated by varying the strain rate sensitivity parameter m (the corresponding n values for each curve are given by n=m/5).</note>
<note type="content">Fig. 13: The resolved shear stress as a function of the total dislocation density. Crosses and triangles are experimental data points obtained by Zehetbauer and Seumer[29] for torsion and rolling, respectively. The solid line shows the predicted curve with the Taylor factor evolution taken into account, while the dotted line is obtained for a constant value of the Taylor factor (M=1.65).</note>
<note type="content">Fig. 14: Predicted variation of the Taylor factor for simple shear as obtained using a Taylor-type viscoplastic polycrystal deformation texture model for m values in the range m=50–250.</note>
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