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Title: Modeling elasto-viscoplasticity in a consistent phase field framework

Abstract

Existing continuum level phase field plasticity theories seek to solve plastic strain by minimizing the shear strain energy. However, rigorously speaking, for thermodynamic consistency it is required to minimize the total strain energy unless there is proof that hydrostatic strain energy is independent of plastic strain which is unfortunately absent. In this work, we extend the phase-field microelasticity theory of Khachaturyan et al. by minimizing the total elastic energy with constraint of incompressibility of plastic strain. We show that the flow rules derived from the Ginzburg-Landau type kinetic equation can be in line with Odqvist's law for viscoplasticity and Prandtl-Reuss theory. Free surfaces (external surfaces or internal cracks/voids) are treated in the model. Deformation caused by a misfitting spherical precipitate in an elasto-plastic matrix is studied by large-scale three-dimensional simulations in four different regimes in terms of the matrix: (a) elasto-perfectly-plastic, (b) elastoplastic with linear hardening, (c) elastoplastic with power-law hardening, and (d) elasto-perfectly-plastic with a free surface. The results are compared with analytical/numerical solutions of Lee et al. for (a-c) and analytical solution derived in this work for (d). Additionally, the J integral of a fixed crack is calculated in the phase-field model and discussed in the context ofmore » fracture mechanics.« less

Authors:
 [1];  [2];  [2]
  1. National Energy Technology Lab. (NETL), Albany, OR (United States); AECOM, Albany, OR (United States)
  2. National Energy Technology Lab. (NETL), Albany, OR (United States)
Publication Date:
Research Org.:
National Energy Technology Lab. (NETL), Albany, OR (United States)
Sponsoring Org.:
USDOE Office of Fossil Energy (FE)
OSTI Identifier:
1415563
Report Number(s):
A-CONTR-PUB-055
Journal ID: ISSN 0749-6419; PII: S0749641916301954
Grant/Contract Number:
ACI-1053575
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
International Journal of Plasticity
Additional Journal Information:
Journal Volume: 96; Journal Issue: C; Journal ID: ISSN 0749-6419
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Phase field method; Voids, cracks and inclusions; Elastic-viscoplastic material; Analytic functions; Variational calculus

Citation Formats

Cheng, Tian -Le, Wen, You -Hai, and Hawk, Jeffrey A. Modeling elasto-viscoplasticity in a consistent phase field framework. United States: N. p., 2017. Web. doi:10.1016/j.ijplas.2017.05.006.
Cheng, Tian -Le, Wen, You -Hai, & Hawk, Jeffrey A. Modeling elasto-viscoplasticity in a consistent phase field framework. United States. doi:10.1016/j.ijplas.2017.05.006.
Cheng, Tian -Le, Wen, You -Hai, and Hawk, Jeffrey A. Fri . "Modeling elasto-viscoplasticity in a consistent phase field framework". United States. doi:10.1016/j.ijplas.2017.05.006.
@article{osti_1415563,
title = {Modeling elasto-viscoplasticity in a consistent phase field framework},
author = {Cheng, Tian -Le and Wen, You -Hai and Hawk, Jeffrey A.},
abstractNote = {Existing continuum level phase field plasticity theories seek to solve plastic strain by minimizing the shear strain energy. However, rigorously speaking, for thermodynamic consistency it is required to minimize the total strain energy unless there is proof that hydrostatic strain energy is independent of plastic strain which is unfortunately absent. In this work, we extend the phase-field microelasticity theory of Khachaturyan et al. by minimizing the total elastic energy with constraint of incompressibility of plastic strain. We show that the flow rules derived from the Ginzburg-Landau type kinetic equation can be in line with Odqvist's law for viscoplasticity and Prandtl-Reuss theory. Free surfaces (external surfaces or internal cracks/voids) are treated in the model. Deformation caused by a misfitting spherical precipitate in an elasto-plastic matrix is studied by large-scale three-dimensional simulations in four different regimes in terms of the matrix: (a) elasto-perfectly-plastic, (b) elastoplastic with linear hardening, (c) elastoplastic with power-law hardening, and (d) elasto-perfectly-plastic with a free surface. The results are compared with analytical/numerical solutions of Lee et al. for (a-c) and analytical solution derived in this work for (d). Additionally, the J integral of a fixed crack is calculated in the phase-field model and discussed in the context of fracture mechanics.},
doi = {10.1016/j.ijplas.2017.05.006},
journal = {International Journal of Plasticity},
number = C,
volume = 96,
place = {United States},
year = {Fri May 19 00:00:00 EDT 2017},
month = {Fri May 19 00:00:00 EDT 2017}
}

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  • This study describes a theoretical and computational framework for the treatment of adiabatic shear band formation in rate-sensitive polycrystalline metallic materials. From a computational perspective, accurate representation of strain localization behavior has been a long-standing challenge. In addition, the underlying physical mechanisms leading to the localization of plastic deformation are still not fully understood. The proposed framework is built around an enhanced-strain finite element formulation, designed to alleviate numerical pathologies known to arise in localization problems, by allowing a localization band of given finite width (weak discontinuity) to be embedded within individual elements. The mechanical threshold strength (MTS) model ismore » used to represent the temperature and strain rate-dependent viscoplastic response of the material. This classical flow stress model employs an internal state variable to quantify the effect of dislocation structure evolution (work hardening and recovery). In light of growing evidence suggesting that the softening effect of dynamic recrystallization may play a significant role, alongside thermal softening, in the process of shear band formation and growth, a simple dynamic recrystallization model is proposed and cast within the context of the MTS model with the aid of the aforementioned internal state variable. An initiation criterion for shear localization in rate and temperature-sensitive materials is introduced and used in the present context of high-rate loading, where material rate-dependence is pronounced and substantial temperature increases are achieved due to the dissipative nature of viscoplastic processes. In addition, explicit time integration is adopted to facilitate treatment of the dynamic problems under consideration, where strain rates in excess of 10 4 s –1 are typically attained. Two series of experiments are conducted on AISI 316L stainless steel, employing the commonly used top-hat sample geometry and the Split-Hopkinson Pressure Bar dynamic test system. Axi-symmetric finite element simulation results are compared to cross-sectional micrographs of recovered samples and experimental load–displacement results, in order to examine the performance of the proposed framework and demonstrate its effectiveness in treating the initiation and growth of adiabatic shear banding in dynamically loaded metallic materials. These comparisons demonstrate that thermal softening alone is insufficient to induce shear localization behaviors observed in some materials, such as stainless steel, and support the hypothesis that dynamic recrystallization and/or other softening mechanisms play an essential role in this process.« less
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