A single crystal plasticity finite element formulation with embedded deformation twins

Jin, Tao; Mourad, Hashem Mohamed; Bronkhorst, Curt A.; Beyerlein, Irene J.

doi:10.1016/j.jmps.2019.103723

Title: A single crystal plasticity finite element formulation with embedded deformation twins

Full Record
Other Related Research

Abstract

Deformation twinning is an important plastic deformation mechanism in some polycrystalline metals such as titanium and magnesium. In this paper, we present a novel crystal plasticity finite element framework that accounts for deformation twinning explicitly, in addition to crystallographic slip. Within this computational framework, deformation twins are treated as weak discontinuities embedded within individual finite elements, such that a jump in the velocity gradient field is introduced (via the discretized gradient operator) between the twinned and untwinned crystalline regions, taking into account compatibility and traction continuity conditions at the interface between these two regions. The deformation gradient is multiplicatively split into elastic and plastic parts in the untwinned region, as is customary in finite-deformation crystal plasticity formulations. A different multiplicative decomposition of the deformation gradient into elastic, plastic (slip), and twinning parts is adopted in the twinned region, allowing deformation twinning to be accounted for as an additional mode of plastic deformation. Here, a stochastic model is used to predict twin nucleation at grain boundaries, and the evolution of the length and thickness of the twinned region under subsequent deformation is taken into account.

Authors:

Jin, Tao ^[1];

^[1]; Bronkhorst, Curt A. ^[2]; Beyerlein, Irene J. ^[3]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Wisconsin, Madison, WI (United States)
Univ. of California, Santa Barbara, CA (United States)

Publication Date:: Sat Sep 14 00:00:00 EDT 2019

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1569617

Alternate Identifier(s):: OSTI ID: 1564553

Report Number(s):: LA-UR-19-22568
Journal ID: ISSN 0022-5096; TRN: US2001354

Grant/Contract Number:: 89233218CNA000001; 20150431ER

Resource Type:: Accepted Manuscript

Journal Name:: Journal of the Mechanics and Physics of Solids

Additional Journal Information:: Journal Volume: 133; Journal Issue: C; Journal ID: ISSN 0022-5096

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Deformation twinning; Embedded weak discontinuity; Single-crystal elasto-viscoplasticity

Citation Formats


                    Jin, Tao, Mourad, Hashem Mohamed, Bronkhorst, Curt A., and Beyerlein, Irene J. A single crystal plasticity finite element formulation with embedded deformation twins.  United States: N. p., 2019. 
Web.  doi:10.1016/j.jmps.2019.103723.

Copy to clipboard


                    Jin, Tao, Mourad, Hashem Mohamed, Bronkhorst, Curt A., & Beyerlein, Irene J. A single crystal plasticity finite element formulation with embedded deformation twins.  United States.  https://doi.org/10.1016/j.jmps.2019.103723

Copy to clipboard


                    Jin, Tao, Mourad, Hashem Mohamed, Bronkhorst, Curt A., and Beyerlein, Irene J. Sat .  
"A single crystal plasticity finite element formulation with embedded deformation twins".  United States.  https://doi.org/10.1016/j.jmps.2019.103723.  https://www.osti.gov/servlets/purl/1569617.

Copy to clipboard


                    
@article{osti_1569617,

  title        = {A single crystal plasticity finite element formulation with embedded deformation twins},

  author       = {Jin, Tao and Mourad, Hashem Mohamed and Bronkhorst, Curt A. and Beyerlein, Irene J.},

  abstractNote = {Deformation twinning is an important plastic deformation mechanism in some polycrystalline metals such as titanium and magnesium. In this paper, we present a novel crystal plasticity finite element framework that accounts for deformation twinning explicitly, in addition to crystallographic slip. Within this computational framework, deformation twins are treated as weak discontinuities embedded within individual finite elements, such that a jump in the velocity gradient field is introduced (via the discretized gradient operator) between the twinned and untwinned crystalline regions, taking into account compatibility and traction continuity conditions at the interface between these two regions. The deformation gradient is multiplicatively split into elastic and plastic parts in the untwinned region, as is customary in finite-deformation crystal plasticity formulations. A different multiplicative decomposition of the deformation gradient into elastic, plastic (slip), and twinning parts is adopted in the twinned region, allowing deformation twinning to be accounted for as an additional mode of plastic deformation. Here, a stochastic model is used to predict twin nucleation at grain boundaries, and the evolution of the length and thickness of the twinned region under subsequent deformation is taken into account.},

  doi          = {10.1016/j.jmps.2019.103723},

  journal      = {Journal of the Mechanics and Physics of Solids},

  number       = C,

  volume       = 133,

  place        = {United States},

  year         = {Sat Sep 14 00:00:00 EDT 2019},

  month        = {Sat Sep 14 00:00:00 EDT 2019}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.jmps.2019.103723

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 11 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

Coupled elasticity, plastic slip, and twinning in single crystal titanium loaded by split-Hopkinson pressure bar

Journal Article Feng, B. ; Bronkhorst, C. A. ; Addessio, F. L. ; ... - Journal of the Mechanics and Physics of Solids

Here coupled elasticity, plastic slip, and twinning in high-purity single crystal titanium loaded by split-Hopkinson pressure bar (SHPB) are investigated, in the framework of large deformation and by utilizing the finite element method (FEM). A thermodynamically consistent system of equations for combined plastic slip and twinning is formulated. Novel kinematics is proposed to develop the driving forces for slip and twinning processes and to consider plastic slip in twins. Dislocation based crystal plasticity is proposed, with an emphasis on the interactions among all slip modes in multi-variant/multiphase heterogeneous materials. A mechanism for dislocation density evolution during twinning is proposed. The impact loading along the [0001] and [1more »« less
Cited by 13
https://doi.org/10.1016/j.jmps.2018.06.018

Full Text Available
Coupled nonlinear elasticity, plastic slip, twinning, and phase transformation in single crystal titanium for plate impact loading

Journal Article Feng, B. ; Bronkhorst, C. A. ; Addessio, F. L. ; ... - Journal of the Mechanics and Physics of Solids

High purity single crystal titanium (Ti) under shockwave loading in plate impact experiment is modelled and simulated, with help of the finite element. A thermodynamically consistent system of equations is formulated in the frame of large deformation to consider material anisotropy, rate dependence, and multi-physics including nonlinear elasticity, dislocation based plastic slip, deformation twinning, and phase transformation. A novel kinematics is proposed to consider phase transformation in the α twin variants and also to consider the dislocation based slip in all of components of parent material, primary twins and the ω phase. The thermodynamically consistent driving forces for plastic slip, twinning, and phase transformation are developed based upon the second law of thermodynamics. For nonlinear elasticity, the stiffness matrix is dependent on the volume fractions of all components, and the volumetric part of Cauchy stress is obtained from the nonlinear equation of state. Dislocation based plastic slip in multi-variant and multiphase heterogeneous materials is developed and interactions of dislocations among all slip modes are taken into account. A mechanism for dislocation density evolution during twinning and phase transformation is proposed. The shock loading along the [0001] and [10more »« less
Cited by 15
https://doi.org/10.1016/j.jmps.2019.03.019

Full Text Available
A finite element formulation for deformation twinning induced strain localization in polycrystal magnesium alloys

Journal Article Cheng, Jiahao ; Hu, Xiaohua ; Bong, Hyuk Jong ; ... - Computational Materials Science

Deformation twinning induces shear strain localization in hexagonal close-packed crystals and is critical for the material’s ductility and failure. Cracks often occur at twin-twin or twin-grain boundary intersections and propagate along twin bands. However, most crystal plasticity models for deformation twinning are based on a “pseudo-slip” approach and do not capture the localized deformation associated with the formation of each discrete twin band. The few exceptions are discrete twin models that involve very complex numerical algorithms and are often compromised in accuracy due to the numerical convergence. These factors make the discrete twin models hard to adopt. This paper proposesmore »« less
https://doi.org/10.1016/j.commatsci.2021.110323

Full Text Available
Single Crystal Plasticity Model with Deformation Twinning for the High Rate Deformation of β-HMX

Journal Article Zecevic, Milovan ; Addessio, Francis L. ; Cawkwell, Marc Jon ; ... - AIP Conference Proceedings

Deformation twinning is an active deformation mechanism during loading along certain crystallographic directions of β-cyclotetramethylene tetranitramine (β-HMX). In this work, a finite strain thermomechanical model is extended to include twinning as a deformation mechanism in addition to plastic slip. The stress is derived from the free energy expression including a term representing the equation of state. The crystal plasticity framework is used to divide the total strain into inelastic and elastic component, where the elastic part is used in the expression for the free energy. The twin systems are treated as pseudo slip systems and the shear rate on themore »« less
https://doi.org/10.1063/12.0001018

Full Text Available
Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

Journal Article Cheng, Jiahao ; Jong Bong, Hyuk ; Qiao, Hua ; ... - Computational Materials Science

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated withmore »« less
https://doi.org/10.1016/j.commatsci.2022.111480

Full Text Available

Similar Records