Irene J. Beyerlein

In this paper, we discuss the formulation, recent developments and findings obtained from a mesoscale mechanics technique called phase field dislocation dynamics (PFDD). We begin by presenting recent advancements made in modelling face-centred cubic materials, such as integration with atomic-scale simulations to account for partial dislocations. We discuss calculations that help in understanding grain size effects on transitions from full to partial dislocation-mediated slip behaviour and deformation twinning. Finally, we present recent extensions of the PFDD framework to alternative crystal structures, such as body-centred cubic metals, and two-phase materials, including free surfaces, voids and bi-metallic crystals. With several examples we demonstrate that the PFDD model is a powerful and versatile method that can bridge the length and time scales between atomistic and continuum-scale methods, providing a much needed understanding of deformation mechanisms in the mesoscale regime.

Significance: Many processing techniques, such as solid-state phase transformation, epitaxial growth, or solidification, can make nanocomposite materials with preferred crystallographic orientation relationships at internal interfaces. On the other hand, metal-working techniques can make composites in bulk quantities for structural applications but typically the resulting bimetal interfaces lack crystallographic order and are unstable with respect to heating. Using a metal-working roll-bonding technique, we find that at extreme plastic strains, the bimetal interfaces develop a remarkably ordered, preferred atomic structure. Using atomic-scale and crystal-plasticity simulations, we study the dynamical stability conditions responsible for this counterintuitive phenomenon. We show that the emergent interface corresponds to a unique stable state, which leads to exceptional mechanical, thermal, and irradiation stability of the nanocomposite.

Two-phase bimetal composites contain both grain boundaries and bi-phase interfaces between dissimilar crystals. In this work, we use a crystal plasticity finite element framework to explore the effects of grain boundary interactions on the plastic stability of bi-phase interfaces. We show that neighboring grain interactions do not significantly alter interface plastic stability during plane strain compression. The important implications are that stable orientations at bimetal interfaces can be different than those within the bulk layers. This finding provides insight into bi-phase microstructural development and suggests a pathway for tuning interface properties via severe plastic deformation.

Bimetal interfaces hold the extraordinary potential to promote or suppress deformation twinning in nanostructured composites. This article constructs a methodology for developing maps for identifying the twinnability of chemically sharp, bimetal interfaces based on their structure and properties. The map is shown capable of rationalizing the variation in experimental observations among several different bimetal interface structures.

In this work, we propose dislocation mechanisms for the formation of double twin structures in hexagonal close packed (HCP) crystals through the nucleation of secondary twins within primary twin domains. The model considers that secondary twins associated with the most commonly observed double twin variants (i.e. type 1 and type 2) nucleate and thicken by a sequence of three distinct dissociation reactions of mixed basal dislocations. Provided that the less frequently observed double twin variants (i.e. type 3 and type 4) also form by a dislocation-based mechanism, we show that their development must proceed by a separate set of dissociation reactions involving pyramidal 〈c+a〉 slip dislocations. Mechanistic, crystallographic and energetic considerations indicate that the type 1 variant should be the most prevalent. The mechanisms proposed here would also apply to the analysis of compound twins and HCP metals other than Mg that exhibit double twinning, such as titanium.

To extract quantitative and meaningful relationships between material microstructure and deformation twinning in magnesium, we conduct a statistical analysis on large data sets generated by electron backscattering diffraction (EBSD). The analyses show that not all grains of similar orientation and grain size form twins, and twinning does not occur exclusively in grains with high twin Schmid factors or in the relatively large grains of the sample. The number of twins per twinned grain increases with grain area, but twin thickness and the fraction of grains with at least one visible twin are independent of grain area. On the other hand, an analysis of twin pairs joined at a boundary indicates that grain boundary misorientation angle strongly influences twin nucleation and growth. These results question the use of deterministic rules for twin nucleation and Hall–Petch laws for size effects on twinning. Instead, they encourage an examination of the defect structures of grain boundaries and their role in twin nucleation and growth.

This article presents a basic probabilistic theory for the nucleation of deformation twins in hexagonal close packed (HCP) metals. Twin nucleation is assumed to rely on the dissociation of grain boundary defects (GBDs) under stress into the required number of twinning partials to create a twin nucleus. The number of successful conversion events is considered to follow a stochastic Poisson process where the rate is assumed to increase with local stress. From this concept, the probability distribution for the critical stress to form a twin nucleus is derived wherein the parameters of the distribution are related to properties of the GBDs. The theory is implemented into a multi-scale constitutive model for HCP metals in order to test its predictive capability against measurements made previously on pure zirconium deformed at 76 and 300 K.