Dislocation Pattern Formation Research Articles

Stress effects on interaction modes and cross-slip annihilation distance of screw dislocation interactions

Phase field microelasticity model is used to study the cross-slip and annihilation of screw dislocations in face-centered cubic crystals, revealing the non-negligible effects of Escaig stress on dislocation interactions. We find that the Escaig stress (in the direction that expands the stacking fault width) promotes the partial dislocation interactions and the Fleischer cross-slip mechanism. In addition to three fundamental dislocation interaction modes, three new dislocation interaction modes emerge with the formation of parallel stacking fault bands. Furthermore, with the increasing of Escaig stress, the critical annihilation distance in dislocation interactions can be appropriately reduced. This research provides novel insights for manipulating strain hardening and understanding the formation of dislocation patterns.

More severe surface relief but stronger fatigue resistance at small scales: Vacancy-assisted fatigue damage mechanism

Surface relief in forms of extrusions and intrusions as the substantial feature of early fatigue damage is one of the most important phenomena studied in metal fatigue. The most common surface relief models in bulk metals are agreed to be correlated with the formation of typical dislocation patterns as persistent slip bands (PSBs), while little is known about the fundamental mechanisms at submicron and even nanometer scales where dislocation pattern formation is fully inhibited. Here, as exampled with thin Au films, the underlying fatigue damage mechanism at small scales is investigated through the quantitative characterization of fatigue damages. Continuous generation and migration of vacancies is found to be crucial for the shape of extrusion/intrusions and kinetics of their growth at submicron and even nanometer scales. Due to the degraded dislocation interaction and intensified vacancy diffusion, the delayed vacancy accumulation in the small-scale metal interior suppresses the extrusion and interface void formation in thinner films, which finally leads to the superior ability to support tremendous surface relief and strong fatigue resistance. The finding of the vacancy-dominated fatigue mechanism at small scales extends our understanding of the metal fatigue mechanisms down to the submicron and even nanometer scales and suggests a novel interface engineering strategy by vacancy behavior modulation for fatigue-tolerance material design.

Stress-dependent activation entropy in thermally activated cross-slip of dislocations

Cross-slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross-slip. However, due to its limited timescale, MD can only predict cross-slip rates in high-stress or high-temperature conditions. The transition state theory can predict the cross-slip rate over a broad range of stress and temperature conditions, but its predictions have been found to be several orders of magnitude too low in comparison to MD results. This discrepancy can be expressed as an anomalously large activation entropy whose physical origin remains unclear. Here, we resolve this discrepancy by showing that the large activation entropy results from anharmonic effects, including thermal softening, thermal expansion, and soft vibrational modes of the dislocation. We expect these anharmonic effects to be significant in a wide range of stress-driven thermally activated processes in solids.

Superior Strength and Ductility of 304 Austenitic Stainless Steel with Gradient Dislocations.

Materials with designed gradient nanograins exhibit unprecedented mechanical properties, such as superior strength and ductility. In this study, a heterostructured 304 stainless steel with solely gradient dislocation structure (GDS) in micron-sized grains produced by cyclic-torsion processing was demonstrated to exhibit a substantially improved yield strength with slightly reduced uniform elongation, compared with its coarse grained counterparts. Microstructural observations reveal that multiple deformation mechanisms, associated with the formation of dense dislocation patterns, deformation twins and martensitic phase, are activated upon straining and contribute to the delocalized plastic deformation and the superior mechanical performance of the GDS 304 stainless steel.

On the Strain Hardening Behavior of a Twinning Deficient Fe–26mn–1al–0.14c Steel

The uniaxial tensile strain hardening behavior of an Fe–26Mn–1Al–0.14C steel with a medium grain size of ~ 5 µm has been investigated using X-ray diffraction and transmission electron microscopy and compared to that in the same steel treated to give a grain size of ~ 35 µm. The steel with the medium grain size exhibited no significant deformation twinning, until failure at ~ 50% true strain, yet it showed a stable high strain hardening rate i.e . ~ 2 GPa, comparable to that of the steel with the coarser grain size. The twin deficiency is explained by dearth of dislocation pile-ups and stacking faults. Grain refinement and interacting dislocations in the medium grain size steel increased its effective stacking fault energy, as determined using X-ray diffraction: it was ~ 60 mJ/m 2 compared to ~ 21 mJ/m 2 in the coarse grained steel. The dominant deformation mechanisms under these twinning deficient conditions are the formation of Taylor lattices at small strains (~ 2%) and dislocation cross-slip. The observed flow stress of the steel beyond 2% strain was interpreted as being due to lattice friction, dislocation loops and newly created mobile dislocations obeying Taylor’s hardening model. The contribution of dislocation loops to flow stress was estimated to be only ~ 33 MPa and assumed to remain constant throughout the deformation strain range. The nearly stable work hardening observed until higher strains could be explained through the cessation of cross-slip at high strains and the newly created mobile dislocations breaking away from the pre-existing dislocation obstacle configurations. The implications of this novel strain hardening mechanism based on the cross-slip assisted formation of organized dislocation patterns proposed by Kubin and Devincre is discussed.

Characterisation of dislocation patterning behaviour with a continuum dislocation dynamics model on two parallel slip planes equipped with a deep neural network resolving local microstructures

The self-organisation behaviour of dislocation upon loading is still a mechanistically mysterious phenomenon. The present article aims to present a computationally tractable dislocation dynamics model, which can be used for helping analyse the mechanism behind dislocation pattern formation. With an integrated use of asymptotic analysis and machine learning tools, the discrete dislocation dynamics on two parallel slip planes is self-consistently reformulated at a coarse-grained level. For the present case, asymptotic analysis helps in 1) reformulating the original globally discrete problem by a continuum model underpinned by a database resolving the almost singular short-range elastic interaction of discrete dislocations; 2) identifying the proper input and output quantities for implementing machine learning tools; 3) digging out a hidden but explicit interrelation between mean-field quantities to reduce the dimensionality of the data space. Machine learning tools serve for 1) inferring the inherently implicit interrelationships between continuum quantities; 2) capturing a low-dimensional manifold in the data space corresponding to the local flow stress. The non-monotonically increasing profile of the flow stress - density relationship, as revealed by machine learning, is found to play a key role in the onset of dislocation patterning behaviour seen in the simulation results. A scaling law relating the applied stress to pattern wavelength is also derived, providing a rationale to the widely used empirical similitude relation. The experimentally observed swing in similitude coefficient value is attributed to the randomness in slip plane distributions. In a methodological viewpoint, the treatment of using asymptotic analysis to help design the curriculum for implementing machine learning tools, offers a paradigm for self-consistently upscaling more complicated multiscale systems.

Dislocation pattern formation in finite deformation crystal plasticity

Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptions related to cross-slip. Crystal orientation effects on the pattern formation and mechanical response are also demonstrated. The manifest irrelevance of the necessity of a multiplicative decomposition of the deformation gradient, a plastic distortion tensor, and the choice of a reference configuration in our model to describe the micromechanics of plasticity as it arises from the existence and motion of dislocations is demonstrated.

Instability of dislocation fluxes in a single slip: Deterministic and stochastic models of dislocation patterning

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a driven system which tries to minimize an internal energy functional while subject to dynamic constraints and state dependent friction. This leads us to a novel interpretation which resolves the old 'energetic vs. dynamic' controversy regarding the physical origin of dislocation patterns. We demonstrate the robustness of the developed patterning scenario by considering the simplest possible case (plane strain, single slip) yet implementing the dynamics of the dislocation density evolution in two very different manners, namely (i) a hydrodynamic formulation which considers transport equations that are continuous in space and time while assuming a linear stress dependency of dislocation motion, and (ii) a stochastic cellular automaton implementation which assumes spatially and temporally discrete transport of discrete 'packets' of dislocation density which move according to an extremal dynamics. Despite the huge differences between both kinds of models, we find that the emergent patterns are mutually consistent and in agreement with the prediction of a linear stability analysis of the continuum model. We also show how different types of initial conditions lead to different intermediate evolution scenarios which, however, do not affect the properties of the fully developed patterns.

Analytical and numerical bifurcation analysis of dislocation pattern formation of the Walgraef–Aifantis model

We analyze the pattern formation due to dislocations under cyclic loading resulting from the Walgraef–Aifantis model. The model consists of a set of partial differential equations of the reaction–diffusion type in the one dimensional finite space with two different diffusion-like coefficients, for the mobile (free to move when the applied resolved shear stress in the slip plane exceeds a certain threshold) and for the immobile (of slow movement or trapped) dislocations. We derive analytically the Turing spatial and Andronov–Hopf temporal instabilities emanating from the homogeneous solutions and construct the complete bifurcation diagram of the far-from-equilibrium spatio-temporal patterns, with respect to the applied stress and the size of the domain. Finally, we analyze the symmetric properties of all branches of both steady and oscillating far-from-equilibrium regimes.

Abnormal grain coarsening in cyclically deformed gradient nanograined Cu

Microstructural evolution of gradient nanograined (GNG) Cu was investigated under strain-controlled cyclic deformation. Mechanically driven abnormal grain coarsening initiated from the ultrafine grained subsurface layer and eventually extended to the nanograined top surface with increasing cycles. Abnormal grain coarsening and the formation of dislocation patterns sustain the cyclic plastic strain and postpone the formation of extrusions/intrusions at the top surface, contributing to the enhancement of overall cyclic properties of GNG Cu.

A Mesoscale Model of Plasticity: Dislocation Dynamics and Patterning (One-Dimensional)

In this study, we developed a physically based mesoscale model for dislocation dynamics systems to predict the deformation and spontaneous formation of spatio-temporal dislocation patterns over microscopic space and time. Dislocations and dislocation patterns are emblematic of plastic deformation, a nonlinear, dissipative process involving the dynamics of underlying dislocations as carriers of plastic deformation. The mesoscale model includes a set of nonlinear partial differential equations of reaction–diffusion type. Here, we consider the equations within a one-dimensional framework and analyze the stability of steady-state solutions for these equations to elucidate the associated patterns with their intrinsic length scale. The numerical solution to the model yields the spatial distribution of dislocation patterns over time and provides respective stress–strain curves. Finally, we compare the stress–strain curves associated with the dislocation patterns with the experimental results noted in the literature.

繰り返し変形における圧縮変形が転位組織の発達に及ぼす影響

Slip deformation in tricrystal models subjected to cyclic deformation is investigated by a finite element crystal plasticity analysis code. Accumulation of geometrically necessary dislocations (GNDs) are studied in detail. Results of the analysis shown that non-uniform deformation and the high density of GNDs accumulated in the form of band around the grain boundary triple junction, this dislocation pattern formation shown that develop during increase of number of cyclic deformation and extend of development of dislocation pattern depend on the strain amplitude. Mechanism of dislocation pattern formation and extend of development of dislocation pattern are discussed from the viewpoint of influence of compressive deformation and strain amplitude on dislocation interaction of primary and secondary slip systems.

Basic criterion for the formation of self-organized dislocation patterns in fatigued FCC pure metals

Based on a large number of experimental results available, it is found that not all the fatigued face-centered-cubic (FCC) pure metals can form the classical persistent slip band (PSB)-ladder structure. The formation of the regular dislocation patterns, especially the PSB ladders, follows one unified principle on the dislocation aggregation and evolution. According to the principle, a simple criterion based on stacking fault energy is proposed to judge whether or not the regular PSB ladders in different FCC pure metals can form.

Screw dislocation cross slip at cross-slip plane jogs and screw dipole annihilation in FCC Cu and Ni investigated via atomistic simulations

Using atomistic simulations, the effect of jogs on the cross-slip of screw character dislocations and screw-dipole annihilation was examined for both FCC Cu and Ni. The stress-free activation energy for cross-slip at jogs is close to 0.4eV in Cu, determined using a nudged elastic band method. This value is a factor of 4-to-5 lower than the activation energy for cross-slip of screw dislocations in the absence of a jog. Similar results were obtained for Ni. Molecular dynamics simulations were used to study the annihilation of a jog-containing screw dipole. The critical Escaig stress on the glide plane for dipole annihilation drops quickly from the 0K value of ∼400MPa and, dipole annihilation is nearly athermal at room temperature. At 5K, Escaig stresses on the cross-slip plane are a factor of 1.5 less effective than Escaig stresses on the glide plane and, glide stresses on the cross-slip plane are a factor of 3 less effective for dipole annihilation by cross-slip. The activation volume for cross-slip of screw dislocations at jogs with respect to these three stress components range from 6 to 20b3. These results have been found to be useful in physics-based modeling of bulk cross-slip in higher length scale 3D dislocation dynamics simulations investigating dislocation pattern formation and fatigue structures in FCC crystals.

Pattern formation in a minimal model of continuum dislocation plasticity

The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect communities, there is no general consensus regarding the physical mechanism which leads to the formation of dislocation patterns. In order to establish the fundamental mechanism, we formulate an extremely simplified, minimal model to investigate the formation of patterns based on the continuum theory of fluxes of curved dislocations. We demonstrate that strain hardening as embodied in a Taylor-type dislocation density dependence of the flow stress, in conjunction with the structure of the kinematic equations that govern dislocation motion under the action of external stresses, is already sufficient for the formation of dislocation patterns that are consistent with the principle of similitude.

G0301402 繰り返し変形における振幅が主すべり系と二次すべり系の転位相互作用に及ぼす影響

Slip deformation in tri-crystal models subjected to cyclic deformation is investigated by a finite element crystal plasticity analysis code. Accumulation of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) are studied in detail. Results of the analysis shown that non-uniform deformation and the high density of GNDs and SSDs accumulated in the form of band around the grain boundary triple junction, these dislocation pattern formation shown that develop during increase of number of cyclic deformation and extend of development of dislocation pattern depend on the strain amplitude. Mechanism of dislocation pattern formation and extend of development of dislocation pattern are discussed from the viewpoint of influence of strain amplitude on dislocation interaction of primary and secondary slip systems.

Microstructurally based cross-slip mechanisms and their effects on dislocation microstructure evolution in fcc crystals

Three newly identified cross-slip mechanisms from atomistic simulations of fcc crystals, namely surface, bulk and intersection cross-slip types, were hierarchically informed into discrete dislocation dynamics simulations. The influence of each cross-slip type on the evolution of the dislocation microstructure in face-centered cubic microcrystals having different crystal sizes and initial dislocation densities was investigated. Dislocation pattern formation, surface slip localization and initial strain hardening were observed, in agreement with experimental observations, and possible explanations are given in the light of these simulations.

G0310101 繰り返し変形における振幅が転位パターン形成に及ぼす影響(材料力学部門一般セッション:変形・ひずみ(1))

Slip deformation in tri-crystal models subjected to cyclic deformation is investigated by a finite element crystal plasticity analysis code. Accumulation of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) are studied in detail. Results of the analysis shown that non-uniform deformation and the high density of GNDs accumulated in the form of band around the grain boundary triple junction, SSDs accumulated in the form of band during cyclic deformation. Mechanism of dislocation pattern formation is discussed from the viewpoint of influence of strain and stress amplitude.

Thermodynamics of Dislocation Pattern Formation at the Mesoscale

We introduce a mesoscopic framework that is capable of simulating the evolution of dislocation networks and, at the same time, spatial variations of the stress, strain and displacement fields throughout the body. Within this model, dislocations are viewed as sources of incompatibility of strains. The free energy of a deformed solid is represented by the elastic strain energy that can be augmented by gradient terms to reproduce dispersive nature of acoustic phonons and thus set the length scale of the problem. The elastic strain field that is due to a known dislocation network is obtained by minimizing the strain energy subject to the corresponding field of incompatibility constraints. These stresses impose Peach-Koehler forces on all dislocations and thus drive the evolution of the dislocation network.

G031051 三重結晶の繰り返し変形に伴うSS転位パターン形成([G031-05]材料力学部門,一般セッション : 破壊力学,転位)

Slip deformation in tri-crystal models subjected to cyclic deformation is investigated by a finite element crystal plasticity analysis code. Accumulation of geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) are studied in detail. Results of the analysis showed that the high density of GNDs and SSDs accumulated in the form of band around the grain boundary triple junction, and dislocation pattern are developed during cyclic deformation. Mechanism of dislocation pattern formation is discussed from the viewpoint of dislocation interaction between primary and secondary slip systems.