Anisotropic Materials Behavior Modeling Under Shock Loading

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Alexander A. Lukyanov

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 et al. (“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.

Author(s):  
Alexander A. Lukyanov

The objective of the work presented in this paper is to consider the thermodynamically consistent anisotropic plasticity model based on full decomposition of stress tensor into generalised deviatoric part and generalised spherical part of stress tensor. Two fundamental tensors αij and βij which represents anisotropic material properties are defined and can be considered as generalisations of the Kronecker delta symbol which plays the main role in the theory of isotropic materials. Using two fundamental tensors, αij and βij, the concept of total generalised “pressure” and pressure corresponding to the volumetric deformation are redefined. It is shown that the formulation of anisotropic plasticity in the case of incompressible plastic flow must be considered independently from the generalised hydrostatic “pressure”. Accordingly, a modification to the anisotropic Hill criterion is introduced. Based on experimental research which has been published, the modified Hill (1948, 1950) criterion for anisotropic elasto-plasticity is validated. The results are presented, discussed and future studies are outlined.


2021 ◽  
Vol 1157 (1) ◽  
pp. 012004
Author(s):  
J Friedlein ◽  
S Wituschek ◽  
M Lechner ◽  
J Mergheim ◽  
P Steinmann

SPE Journal ◽  
2018 ◽  
Vol 24 (02) ◽  
pp. 647-659 ◽  
Author(s):  
V. A. Torrealba ◽  
R. T. Johns ◽  
H.. Hoteit

Summary An accurate description of the microemulsion-phase behavior is critical for many industrial applications, including surfactant flooding in enhanced oil recovery (EOR). Recent phase-behavior models have assumed constant-shaped micelles, typically spherical, using net-average curvature (NAC), which is not consistent with scattering and microscopy experiments that suggest changes in shapes of the continuous and discontinuous domains. On the basis of the strong evidence of varying micellar shape, principal micellar curves were used recently to model interfacial tensions (IFTs). Huh's scaling equation (Huh 1979) also was coupled to this IFT model to generate phase-behavior estimates, but without accounting for the micellar shape. In this paper, we present a novel microemulsion-phase-behavior equation of state (EoS) that accounts for changing micellar curvatures under the assumption of a general-prolate spheroidal geometry, instead of through Huh's equation. This new EoS improves phase-behavior-modeling capabilities and eliminates the use of NAC in favor of a more-physical definition of characteristic length. Our new EoS can be used to fit and predict microemulsion-phase behavior irrespective of IFT-data availability. For the cases considered, the new EoS agrees well with experimental data for scans in both salinity and composition. The model also predicts phase-behavior data for a wide range of temperature and pressure, and it is validated against dynamic scattering experiments to show the physical significance of the approach.


1991 ◽  
Vol 7 (7) ◽  
pp. 693-712 ◽  
Author(s):  
Frédéric Barlat ◽  
Daniel J. Lege ◽  
John C. Brem

Author(s):  
Wei Tong

An accurate description of the directional dependence of uniaxial tensile yielding and plastic flow in advanced high-strength steel sheets may require either a nonassociated plasticity model with separate quadratic yield function and flow potential or an associated plasticity model with nonquadratic yield function. In this paper, Gotoh's fourth-order homogeneous polynomial yield function is applied to model two advanced high-strength steel sheets in an associated plasticity model. Both the parameter selection for calibrating Gotoh's yield function and its positivity and convexity verification are given in some detail. Similarities and differences between the associated plasticity model presented here and the nonassociated one appeared in the literature are discussed in terms of the directional dependence of yield stresses and plastic strain ratios under uniaxial tension and yield stresses under biaxial tension loading.


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