A Review on Capturing Twin Nucleation in Crystal Plasticity for Hexagonal Metals

Abstract

Owing to its ability to incorporate Schmid’s law at each integration point, crystal plasticity has proven a powerful tool to simulate and predict the slip behavior at the grain level and the ensuing heterogeneous stress/strain localization and texture evolution at the macroscopic level. Unfortunately, notwithstanding substantial efforts during the last three decades, this remarkable capability has not been replicated for materials where twinning becomes a noticeable deformation mechanism, namely in the case of low-stacking fault energy cubic, orthorhombic, and hexagonal close-packed structures. The culprit lies in the widely adopted unphysical pseudo-slip approach for capturing twin formation. While the slip is diffuse, twinning is a localized event that occurs as a drastic burst of a confined number of partial twinning dislocations establishing an interface that pursues growth through a thread of perfect twinning dislocations in the sense of bicrystallography. Moreover, at earlier stages, twin nucleation may require atomic diffusion (Shuffling) and faceting, generally demanding higher stress levels not necessarily on the twin shear plane, while triaxiality at adequate sites might be needed or preferred such as lower grain boundary misorientations or other twin boundaries. Identifying a mathematical framework in the constitutive equations for capturing these twin formation sensitivities has been a daunting challenge for crystal plasticity modelers, which has stalled ameliorating the design of key hexagonal materials for futuristic climate change-related industries. This paper reviews existing approaches to incorporating twinning in crystal plasticity models, discusses their capabilities, addresses their limitations, and suggests prospective views to fill gaps. The incorporation of a new physics-based twin nucleation criterion in crystal plasticity models holds groundbreaking potential for substantial progress in the field of computational material science.

The Microstructures and Deformation Mechanism of Hetero-Structured Pure Ti under High Strain Rates

“…It uncovers that twinning is not completely absent within ultrafine grains, but rather occurs under extremely stringent conditions. Numerous studies have demonstrated that dislocations play a pivotal role in the initiation of twinning in pure Ti [37][38][39]. Furthermore, the Hall-Petch relationship, which is based on the principle of dislocation obstacle at grain boundaries, has effectively explained the origin of strength [15].…”

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

“…Elastic part includes the information about rotation and stretching, plastic part influences on plastic shearing on crystallographic slip systems and defines dislocations (Fig. 1) (Paudel et al, 2021). 2) The macroscopic velocity gradient 𝑳 is decomposed additively into elastic and plastic parts (Eq.…”

Experimental Observations versus First‐Principles Calculations for Ni–Mn–Ga Ferromagnetic Shape Memory Alloys: A Review

“…[ 203 ] This, nevertheless, cannot capture the nucleation of a twin as a geometric object in a mechanically loaded crystal. However, the general mechanism of twin nucleation has been extensively studied within the frameworks of crystallographic theory and crystal plasticity theory over the last few decades, [ 202,204–210 ] including twins in low‐symmetry systems. [ 211 ] Hence, crystallography‐based models could be related to experimental observations and ab initio approaches, with the aim of qualitatively explaining the difference between Type I and Type II nucleation.…”