Modeling elasto-viscoplasticity in a consistent phase field framework

Cheng, Tian -Le; Wen, You -Hai; Hawk, Jeffrey A.

doi:10.1016/j.ijplas.2017.05.006

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

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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:

Cheng, Tian -Le ^[1]; Wen, You -Hai ^[2]; Hawk, Jeffrey A. ^[2]

National Energy Technology Lab. (NETL), Albany, OR (United States); AECOM, Albany, OR (United States)
National Energy Technology Lab. (NETL), Albany, OR (United States)

Publication Date:: Fri May 19 00:00:00 EDT 2017

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:: 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.

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                    Cheng, Tian -Le, Wen, You -Hai, & Hawk, Jeffrey A. Modeling elasto-viscoplasticity in a consistent phase field framework.  United States.  https://doi.org/10.1016/j.ijplas.2017.05.006

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                    Cheng, Tian -Le, Wen, You -Hai, and Hawk, Jeffrey A. Fri .  
"Modeling elasto-viscoplasticity in a consistent phase field framework".  United States.  https://doi.org/10.1016/j.ijplas.2017.05.006.  https://www.osti.gov/servlets/purl/1415563.

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@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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