David Rodney

Phase field methods and dislocations

Abstract We present a general formalism for incorporating dislocations in Phase Field methods (PFM) based on the elastic equivalence between a dislocation loop and a platelet inclusion of specific stress-free strain. Dislocations may be elastically and dynamically coupled to any other field such as a concentration field. Special attention is paid to the treatment of dislocation cores after the discretization of real and reciprocal space required by the computer implementation of any PFM. In particular, we propose a method based on two length scales to account for dislocation cores much smaller than the grid spacing. The method is illustrated through the simulation of the motion of a dislocation loop in a microstructure representative of a late-stage γ/γ′ microstructure.

Modeling the mechanics of amorphous solids at different length scale and time scale

We review the recent literature on the simulation of the structure and deformation of amorphous solids, including oxide and metallic glasses. We consider simulations at different length scale and time scale. At the nanometer scale, we review studies based on atomistic simulations, with a particular emphasis on the role of the potential energy landscape and of the temperature. At the micrometer scale, we present the different mesoscopic models of amorphous plasticity and show the relation between shear banding and the type of disorder and correlations (e.g. elastic) included in the models. At the macroscopic range, we review the different constitutive laws used in finite-element simulations. We end with a critical discussion on the opportunities and challenges offered by multiscale modeling and information transfer between scales to study amorphous plasticity.

Quantum effect on thermally activated glide of dislocations

Crystal plasticity involves the motion of dislocations under stress. So far, atomistic simulations of this process have predicted Peierls stresses, the stress needed to overcome the crystal resistance in the absence of thermal fluctuations, of more than twice the experimental values, a discrepancy best-known in body-centred cubic crystals. Here we show that a large contribution arises from the crystal zero-point vibrations, which ease dislocation motion below typically half the Debye temperature. Using Wigners quantum transition state theory in atomistic models of crystals, we found a large decrease of the kink-pair formation enthalpy due to the quantization of the crystal vibrational modes. Consequently, the flow stress predicted by Orowans law is strongly reduced when compared with its classical approximation and in much closer agreement with experiments. This work advocates that quantum mechanics should be accounted for in simulations of materials and not only at very low temperatures or in light-atom systems.

Atomic-scale study of dislocation–stacking fault tetrahedron interactions. Part I: mechanisms

Stacking fault tetrahedra (SFTs) are formed under irradiation in fcc metals and alloys. The high number density of SFTs observed suggests that they should contribute to radiation-induced hardening and, therefore, be taken into account when estimating mechanical property changes of irradiated materials. The key issue in this is to describe the interaction between a moving dislocation and an individual SFT, which is distinguished by a small physical size of the order of ∼1–10 nm. We have performed atomistic simulations of edge and screw dislocations interacting with SFTs of different sizes at different temperatures and strain rates. Five possible interaction outcomes have been identified, involving either partial absorption, or shearing or restoration of SFTs. The mechanisms that give rise to these processes are described and their dependence on interaction parameters, such as SFT size, dislocation–SFT geometry, temperature and stress/strain rate are determined. Mechanisms that help to explain the formation of defect-free channels cleared by gliding dislocations, as observed experimentally, are also discussed. Hardening due to the various mechanisms and their dependence on loading conditions will be presented in a following paper (Part II).

Atomic-scale plasticity in the presence of Frank loops

The different reactions between edge or screw dislocations and interstitial Frank loops were studied by means of molecular dynamics simulations. The calculations were performed at 600 K using an embedded atom method (EAM) potential describing a model FCC material with a low stacking fault energy. An interaction matrix that provides the corresponding interaction strength was determined. In an attempt to investigate the role of pile-ups, simulations with either one or two dislocations in the cell were performed. We find that screw and edge dislocations behave very differently. Edge dislocations shear Frank loops in two out of three cases, while screw dislocations systematically unfault Frank loops by mechanisms that involve cross-slip. After unfaulting, they are strongly pinned by the formation of extended helical turns. The simulations show an original unpinning effect that leads to clear band broadening. This process involves the junction of two screw dislocations around a helical turn (arm-exchange) and the transfer of a dislocation from its initial glide plane to an upper glide plane (elevator effect).

Chapter 88 Dislocation–Obstacle Interactions at the Atomic Level

Abstract Dislocation–obstacle interactions that resist the glide of dislocations in metals, and hence increase the applied stress necessary for plastic deformation, are treated at the atomic scale. The chapter contains a summary of the techniques used for computer simulation and provides a comprehensive review of progress made over the past decade. Results are presented for the glide resistance of the crystal lattice itself, solute atoms, voids and precipitates. Obstacles with dislocation character, i.e. dislocations loops and stacking fault tetrahedra, are also considered and the varied and sometimes complex dislocation–dislocation reactions that occur are rationalised. Interpretation of results that can be obtained in some cases from the elasticity theory of dislocations is emphasised.

Reversible dilatancy in entangled single-wire materials

Designing structures that dilate rapidly in both tension and compression would benefit devices such as smart filters, actuators or fasteners. This property however requires an unusual Poisson ratio, or Poisson function at finite strains, which has to vary with applied strain and exceed the familiar bounds: less than 0 in tension and above 1/2 in compression. Here, by combining mechanical tests and discrete element simulations, we show that a simple three-dimensional architected material, made of a self-entangled single long coiled wire, behaves in between discrete and continuum media, with a large and reversible dilatancy in both tension and compression. This unusual behaviour arises from an interplay between the elongation of the coiled wire and rearrangements due to steric effects, which, unlike in traditional discrete media, are hysteretically reversible when the architecture is made of an elastic fibre.

Atomic-scale study of dislocation glide in a model solid solution

Based on atomic-scale simulation techniques, we study the dislocation pinning mechanism in a dilute Ni(Al) model solid solution. For a solute concentration between 1 and 10 at.% , we found that the pinning of the dislocation on obstacles made of Al pairs is an interaction that operates significantly. The statistics of the dislocation motion is then modified accordingly to the nature of the obstacles and follows modified Mott–Nabarro statistics. Finally, a method to address thermal activation is proposed and exemplified on a periodic row of solute pairs.

Plastic anisotropy and dislocation trajectory in BCC metals.

Plasticity in body-centred cubic (BCC) metals at low temperatures is atypical, marked in particular by an anisotropic elastic limit in clear violation of the famous Schmid law applicable to most other metals. This effect is known to originate from the behaviour of the screw dislocations; however, the underlying physics has so far remained insufficiently understood to predict plastic anisotropy without adjustable parameters. Here we show that deviations from the Schmid law can be quantified from the deviations of the screw dislocation trajectory away from a straight path between equilibrium configurations, a consequence of the asymmetrical and metal-dependent potential energy landscape of the dislocation. We propose a modified parameter-free Schmid law, based on a projection of the applied stress on the curved trajectory, which compares well with experimental variations and first-principles calculations of the dislocation Peierls stress as a function of crystal orientation.

First order pyramidal slip of 1/3 screw dislocations in zirconium

Atomistic simulations, based either on an empirical interatomic potential or on ab initio calculations, are used to study the pyramidal glide of a