Discrete dislocation analysis on lattice rotation of optimized lath martensite

Investigation of twin-dislocation interactions using a novel discrete dislocation plasticity framework

Machine learning accelerating prediction dislocation interaction force in 3D discrete dislocation dynamics

Prismatic dislocation loop and helical dislocation generation from ellipsoidal inclusion in inhomogeneous materials: A comprehensive discrete dislocation dynamics simulation

Discrete Dislocation Dynamics (DDD) is an established mesoscopic numerical method for simulating dislocation motion to determine the plastic behaviour of metals. However, DDD’s reliance on analytical expressions for internal stress fields limits its application to infinite isotropic media. The Discrete-Continuous Model (DCM), which couples DDD with a finite element elastic solver, has been proposed to handle more complex boundary conditions by regularising plastic strain using the eigenstrain formalism. However, this model still relies on analytical solutions for short-range dislocation interactions, making it unsuitable for anisotropic media. In this work, we present an improved DCM framework that replaces the FE solver with a Fast Fourier transform (FFT) solver for improved computational efficiency and full numerical calculation of stress fields, eliminating the need for analytical corrections. The proposed FFT solver employs a discrete theory of Green’s operators and uses a sharp eigenstrain field to describe dislocations. The solver mesh is aligned with the face-centred cubic (fcc) lattice of the DDD, forming an octahedral cell to address symmetry artefacts around { 111 } slip planes. Our FFT-based approach successfully maintains numerical stability by representing fcc dislocations as sharp fields without generating oscillations. This coupling allows the study of plasticity in anisotropic materials and interactions between dislocations and diffuse inclusions, such as precipitates, without short-range stress corrections.

Large-scale simulation of discrete dislocation dynamics based on dynamic heterogeneous parallel fast multipole method

Direct comparisons of the demographic and clinical risk factors between patients with anterior and posterior glenohumeral instability are uncommon. To identify and compare demographic, clinical, and perioperative variables in patients receiving arthroscopic labral repair for anterior and posterior shoulder instability. Case series; Level of evidence, 4. A retrospective chart review was performed for patients who underwent primary arthroscopy for shoulder instability by 7 surgeons at a single institution between 2012 and 2020, excluding revision surgeries and multidirectional instability patients. Demographics, radiological findings, and intraoperative data were collected. Patients with anterior instability (AI) were compared to those with posterior instability (PI) by number of dislocation events (0, 1, 2, or >2), chief complaint (dislocation event and direction, subluxation, or pain), and concomitant intraoperative procedures. A subgroup analysis was performed of patients with documented dislocations. Statistical analysis included the Student t tests and Mann-Whitney U test for continuous variables and chi-square or Fisher exact tests for discrete variables with significance defined as a P value <.05. Bonferroni corrections were applied. A total of 482 shoulders met the inclusion criteria. Overall, 80% (384/482) of the patients were evaluated with AI and 20% (98/482) with PI. The PI group demonstrated a greater mean BMI compared with the AI group (28 ± 7 vs 26 ± 6; P = .003). There were no significant differences in age, sex, or contact/collision athlete status. Overall, 80% (308/384) of the patients with AI sustained a dislocation compared to 43% (42/98) of those with PI. A higher proportion of patients with PI (without instability) reported more pain than patients with AI (without instability) (42% vs 12 %; P < .001). Recurrent dislocations (>2) were more common in the AI group compared with the PI group (51% vs 21%; P < .001). Patients with AI underwent concomitant posterior labral repair (17% [67/384]) at a similar rate to patients with PI who underwent concomitant anterior labral repair (16% [16/98]). Subgroup analysis of patients with discrete dislocations demonstrated similar rates of those receiving concomitant posterior labral repair in the AI group when compared with those in the PI group receiving concomitant anterior labral repair (14% vs 17%). Patients arthroscopically treated for AI undergo concomitant posterior labral repair at rates similar to those with PI requiring concomitant anterior labral repair. This finding suggests that tear extension occurs at similar rates in patients with AI and those with PI. Additionally, patients with AI requiring labral repair are more likely to experience multiple dislocation events as opposed to patients with PI who present with pain and subluxation.

Advanced modeling of the ductile–brittle transition in neutron-irradiated steel: A discrete dislocation dynamics approach

Calculation of geometrically necessary dislocation density within planar discrete dislocation plasticity: Application to cyclic loading

Anisotropic concurrent coupled atomistic and discrete dislocation for partial dislocations in FCC materials

Investigating the formation of a geometrically necessary boundary using discrete dislocation dynamics

The Discrete Dislocation Dynamics of Multiple Dislocation Loops

Van der Waals (vdW) heterostructures subjected to interlayer twists or heterostrains demonstrate structural superlubricity, leading to their potential use as superlubricants in micro- and nanoelectromechanical devices. However, quantifying superlubricity across the vast four-dimensional heterodeformation space using experiments or atomic scale simulations is a challenging task. In this work, we develop two multiscale models to predict the interface friction drag coefficient of an arbitrarily heterodeformed bilayer graphene (BG) system─an atomistically informed dynamic Frenkel-Kontorova (DFK) model and a discrete dislocation (DD) model. The DFK and DD models are motivated by molecular dynamics simulations of friction in heterodeformed BG. In particular, we note that interface dislocations formed during structural relaxation translate in unison when a heterodeformed BG is subjected to shear traction, leading us to the hypothesis that the kinetic properties of interface dislocations determine the friction drag coefficient of the interface. The constitutive law of the DFK model comprises the generalized stacking fault energy of the AB stacking, a scalar displacement drag coefficient, and the elastic properties of graphene, which are all obtained from atomistic simulations. Simulations of the DFK model confirm our hypothesis, since a single choice of the displacement drag coefficient, fitted to the kinetic property of an individual dislocation in an atomistic simulation, predicts interface friction in any heterodeformed BG. In addition, we develop a DD model to derive an analytical expression for the friction coefficient of heterodeformed BG. While the DD model is analytically tractable and numerically more efficient, the drag at dislocation junctions must be explicitly incorporated into the model. By bridging the gap between dislocation kinetics at the microscale and interface friction at the macroscale, the DFK and DD models enable a high-throughput investigation of strain-engineered vdW heterostructures.

Abstract Composition inhomogeneities arise in multicomponent alloys during processing, e.g. spinodal alloys, during rapid solidification, e.g. in additive manufactured alloys, and/or when the alloys are subjected to extreme conditions, such as irradiation. These inhomogeneities have a strong impact on the mechanical response and strength of the alloys. In this paper, a framework for studying single crystal plasticity in inhomogeneous alloys using discrete dislocation dynamics (DDD) is presented. Virtual realizations of a single Fourier mode sinusoidal and stochastic composition fields are generated for testing the impact of composition inhomogeneity within a three-dimensional DDD framework. The composition fields are also utilized to determine internal coherency stress arising due to lattice parameter dependence on composition by solving an eigenstrain boundary value problem. Composition-aware dislocation velocities, determined from molecular dynamics simulations are utilized to model the composition dependent local lattice mobility of dislocations. The composition reconstruction scheme, internal coherency stress, and the composition-dependent dislocation velocities are coupled to DDD, and the effects of the composition fluctuations are studied on the stress–strain response and evolution of the dislocation densities in a model BCC FeCrAl alloy. The effects of the composition fluctuations on crystal plasticity are studied from the perspective of single dislocation and their collective dynamics. The influence of the inhomogeneous composition fields on the collective dynamics of dislocations is revealed through the statistics of cross-slip and the driving forces on the dislocations coming from the stress associated with composition fields, applied load, and dislocation–dislocation interactions.

Dark-field X-ray microscopy (DFXM) has recently been introduced for 3D mapping of dislocations and their strain fields in bulk samples and with high angular resolution (10-4°). In this work, we investigate the minimum information needed to identify the type of an isolated dislocation, parameterized by its Burgers vector, line direction and slip plane. Forward projections of DFXM weak-beam images are generated for a face-centred cubic symmetry using geometrical optics simulations with realistic noise levels. Cross correlating one DFXM image with similar images representing all possible combinations of dislocation types, we find that the cross-correlation values for all non-identical images are below 0.7, clearly demonstrating the feasibility of this method of identification. Experimental DFXM images of isolated dislocations are compared with forward-modelled ones. Complete identification is demonstrated, with the exception of the sign of the Burgers vector. The performance improvement obtained by acquiring data from a 3D volume is explored. This work verifies the use of geometrical optics to simulate DFXM weak-beam images and supports the interfacing of DFXM data with discrete dislocation dynamics simulations.

Abstract Mechanism based discrete dislocation dynamics framework for modelling plasticity in metallic materials with the morphology of the underlying grains resembling an actual microstructure is extended to incorporate a second-phase. The formulation includes mechanisms that account for dislocation self-interactions and interactions with grain boundaries vis-a-vis grain boundary slip transmission. Dislocation interactions within the constituent grains result in the entangling of dislocations, forming locks essential for controlling various hardening phenomena by obstructing dislocation motion or nucleating fresh dislocations. The presence of the second-phase particle on the emergent mechanical response is studied under various conditions. Results depict an increase in strain hardening rate with increasing second-phase volume fraction until a point where the dimensions of the second-phase approach the grain size. Further, the dislocation-grain boundary interactions in the presence of dislocation self-interactions on the strain hardening are also analyzed. Towards the end, the scaling of yield stress with grain size in the presence of the second-phase is also investigated. The analysis is aided by providing spatial distribution of relevant components of stress and geometrically necessary dislocation density, contributing to the essential hardening mechanisms that lead to the observed effects of second-phase on polycrystalline materials.

In this note, we define material-uniform hyperelastic bodies (in the sense of Noll) containing discrete disclinations and dislocations and study their properties. We show in a rigorous way that the size of a disclination is limited by the symmetries of the constitutive relation; in particular, if the symmetry group of the body is discrete, it cannot admit arbitrarily small, yet non-zero, disclinations. We then discuss the application of these observations to the derivations of models of bodies with continuously distributed defects.

A discrete dislocation plasticity assessment of the effective temperature in thermodynamic dislocation theory

Crack-tip dislocation emission is often considered to be the key mechanism that controls the so-called “intrinsically ductile” fracture behaviour. Yet, high fracture toughness and ductility in metals are determined by extensive plastic deformation that dissipates much more energy than solely due to the crack-tip emission process. Thus, there is a gap between intrinsically ductile behaviour and large toughness. Here, we implement the dislocation emission process within a 2D discrete dislocation plasticity (DDP) framework. The framework, which includes anisotropic elasticity and a cohesive-zone model to simulate crack propagation, enables to investigate the interplay between dislocation emission and near-crack-tip plasticity associated with activation of dislocation sources. Guided by dimensional analysis and a sensitivity study, we identify the main variables controlling the fracture process, including dislocation source and obstacle density, dislocation emission strength and the associated dwelling time-scales. DDP simulations are conducted with a range of parameters under mode-I loading. The initiation fracture toughness and the crack-growth resistance curve (R-curve) are calculated accounting for the statistics of dislocation and obstacle distributions. Comparison is performed with cases where no dislocation emission is enabled. Our findings show that dislocation emission can slow down crack growth considerably, resulting in a significant increase in slope of the R-curve. This phenomenon is due to crack-tip shielding caused by the emitted dislocations. Thus, intrinsic ductility can enhance crack-growth resistance and fracture toughness. However, we find that the extent of shielding can also be negligible for some emission planes, making the connection between intrinsic ductility and fracture toughness not straightforward.

Dark-field X-ray microscopy (DFXM) is a novel diffraction-based imaging technique that non-destructively maps the local deformation from crystalline defects in bulk materials. While studies have demonstrated that DFXM can spatially map 3D defect geometries, it is still challenging to interpret DFXM images of the high-dislocation-density systems relevant to macroscopic crystal plasticity. This work develops a scalable forward model to calculate virtual DFXM images for complex discrete dislocation structure(s) (DDS) obtained from atomistic simulations. Our new DDS-DFXM model integrates a non-singular formulation for calculating the local strain from the DDS and an efficient geometrical optics algorithm for computing the DFXM image from the strain field. We apply the model to complex DDS obtained from a large-scale molecular dynamics simulation of compressive loading on single-crystal silicon. Simulated DFXM images exhibit prominent contrast for dislocation features between the multiple slip systems, demonstrating the potential of DFXM to resolve features from dislocation multiplication. The integrated DDS-DFXM model provides a toolbox for DFXM experimental design and image interpretation in the context of bulk crystal plasticity for a range of measurements across shock plasticity and the broader materials science community.