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Research Papers

Anisotropic Materials Behavior Modeling Under Shock Loading

[+] Author and Article Information
Alexander A. Lukyanov

Abingdon Technology Center, Schlumberger, Research & Development, Abingdon, Oxfordshire OX14 1UJ, UKaaluk@mail.ru

J. Appl. Mech 76(6), 061012 (Jul 27, 2009) (9 pages) doi:10.1115/1.3130447 History: Received February 09, 2008; Revised February 04, 2009; Published July 27, 2009

In this paper, the thermodynamically and mathematically consistent modeling of anisotropic materials under shock loading is considered. The equation of state used represents the mathematical and physical generalizations of the classical Mie–Grüneisen equation of state for isotropic material and reduces to the Mie–Grüneisen equation of state in the limit of isotropy. Based on the full decomposition of the stress tensor into the generalized deviatoric part and the generalized spherical part of the stress tensor (Lukyanov, A. A., 2006, “Thermodynamically Consistent Anisotropic Plasticity Model,” Proceedings of IPC 2006, ASME, New York; 2008, “Constitutive Behaviour of Anisotropic Materials Under Shock Loading,” Int. J. Plast., 24, pp. 140–167), a nonassociated incompressible anisotropic plasticity model based on a generalized “pressure” sensitive yield function and depending on generalized deviatoric stress tensor is proposed for the anisotropic materials behavior modeling under shock loading. The significance of the proposed model includes also the distortion of the yield function shape in tension, compression, and in different principal directions of anisotropy (e.g., 0 deg and 90 deg), which can be used to describe the anisotropic strength differential effect. The proposed anisotropic elastoplastic model is validated against experimental research, which has been published by Spitzig and Richmond (“The Effect of Pressure on the Flow Stress of Metals,” Acta Metall., 32, pp. 457–463), Lademo (“An Evaluation of Yield Criteria and Flow Rules for Aluminium Alloys,” Int. J. Plast., 15(2), pp. 191–208), and Stoughton and Yoon (“A Pressure-Sensitive Yield Criterion Under a Non-Associated Flow Rule for Sheet Metal Forming,” Int. J. Plast., 20(4–5), pp. 705–731). The behavior of aluminum alloy AA7010 T6 under shock loading conditions is also considered. A comparison of numerical simulations with existing experimental data shows good agreement with the general pulse shape, Hugoniot elastic limits, and Hugoniot stress levels, and suggests that the constitutive equations perform satisfactorily. The results are presented and discussed, and future studies are outlined.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Contour plots of the proposed yield surface at constant shear stress for the AA2008 T4 and AA2090 T3 alloys, respectively. The numbers in the legend refer to the magnitude of the shear stress in megapascal. The experimental data used to define the proposed yield surface at zero shear stress are also present.

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Figure 2

Distribution of the yield stress versus angle in uniaxial tension for the AA7108 T1 and AA6063 T1 alloys (proposed model). The experimental data used to define the yield surface at zero shear stress are also present.

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Figure 3

Schematic of the experimental target assembly

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Figure 4

Back-surface gauge stress traces from plate-impact experiments versus numerical simulation of stress (PMMA) waves for plate-impact test (impact velocity 450 m/s)—target AA7010 T6 for longitudinal and transverse directions, respectively

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Figure 5

Back-surface gauge stress traces from plate-impact experiments versus numerical simulation of stress (PMMA) waves for plate-impact test (impact velocity 895 m/s)—target AA7010 T6 for longitudinal and transverse directions, respectively

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