On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

Abstract

The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e., an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid-solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress-strain response in good agreement

The mechanism of twinning activation and variant selection in magnesium alloys dominated by slip deformation

“…Here, the twins are isolated inside one grain and did not propagate into the neighboring grain. For this case, the activation of twinning may be induced by the activity of dislocation slips in neighboring grains [7]. Recent studies revealed that whether the occurrence of slip-induced twin or twin induced twin was related to grain boundary misorientation [22].…”

“…However, Mg alloys have relatively bad workability at room temperature [3]. Therefore, to expand their applications it is desirable to have an in-depth understanding of the strain accommodation mechanisms in Mg alloys [4][5][6][7][8][9][10][11].…”

A variational constitutive model for slip-twinning interactions in hcp metals: Application to single- and polycrystalline magnesium

“…Both slip and twinning contribute to the plastic deformation and the specific order of these two mechanisms is not obvious. Therefore, we adopt the approach of Kalidindi (2001) and work with a single inelastic deformation gradient F in to incorporate both relaxation schemes rather than further splitting F in multiplicatively into plastic slip and twinning components (Homayonifar and Mosler, 2011Mosler, , 2012. This further implies that no kinematic interactions between slip an twinning are built into this decomposition but will be accounted for by the specific constitutive model presented below.…”

“…The exponential law mimics Voce hardening (Agnew et al, 2001;Graff et al, 2007) and is well suited to describe the high-resistance of non-basal slip systems in hcp metals (Homayonifar and Mosler, 2011). σ ∞ α is the ultimate stress on each system, and h α captures the corresponding hardening rate.…”

“…(Proust et al, 2009;Homayonifar and Mosler, 2011). For illustrative purposes, we include compression twinning (and suppress tensile twinning) to demonstrate its effect on the texture evolution.…”