Numerical Modeling and Simulations of Twinning-Induced Plasticity Using Crystal Plasticity Finite Element Method

Abstract

In the current work, a fully implicit numerical integration scheme is developed for modeling twinning-induced plasticity using a crystal plasticity framework. Firstly, the constitutive formulation of a twin-based micromechanical model is presented to estimate the deformation behavior of steels with low stacking fault energy. Secondly, a numerical integration scheme is developed for discretizing constitutive equations through a fully implicit time integration scheme using the backward Euler method. A time sub-stepping algorithm and the two-norm convergence criterion are used to regulate time step size and stopping criterion. Afterward, a numerical scheme is implemented in finite element software ABAQUS as a user-defined material subroutine. Finally, finite element simulations are executed for observing the validity, performance, and limitations of the numerical scheme. It is observed that the simulation results are in good agreement with the experimental observations with a maximum error of 16% in the case of equivalent stress and strain. It is also found that the developed model is able to estimate well the deformation behavior, magnitude of slip and twin shear strains, and twin volume fraction of three different TWIP steels where the material point is subjected to tension and compression.

Crystal Plasticity Elastic-Plastic Rate-Independent Numerical Analyses of Pollycrystalline Materials

“…The new twinning-induced crystal plasticity model in terms of the thermomechanical framework and with a new integration method, is developed by Khan and Alfozan (2019). The fully implicit integration procedure for a twinning-induced plasticity model based on the CP approach is also presented by Khan et al (2022). The propositions of other new models using the CP theory in order to simulate the behaviour of material in a microscopic scale are also available in literature (Li et al, 2022;Ibragimova et al, 2021;Li et al, 2020;Jeong & Voyiadjis, 2022).…”

An Elastic-Plastic Analysis of Polycrystalline Structure Using Crystal Plasticity Modelling – Theory and Benchmark Tests

“…In another model based on the selfconsistent approach [6], every grain is considered as an ellipsoidal heterogeneity which is placed in a uniform space representing the polycrystalline structure. The multiplicative decomposition of the total deformation gradient into elastic and plastic parts assuming also twinning is described by Khan et al [7]. Other more advance micromechanical models assume that some components of stress or strain states are the same or use the homogenization theory for the determination of stress and strain distributions in crystals [8][9].…”

Crystal Plasticity (Volume II)

“…Steels and iron-based alloys [2-9]; • Non-ferrous alloys with fcc-(Ni- [10,11] and Cu-based [12][13][14]), or hcp crystal structure (Mg- [15,16] and Ti-based [17,18]). Other examples include Zirconium [19], Bi-Sn alloy [20] or polycarbonate resins [21]; • Multicomponent and high-entropy alloys [22][23][24]; • General theoretical studies on crystal plasticity [25][26][27].…”