An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

Stage-I fatigue crack propagation is investigated using 3D discrete dislocation dynamics (DD) simulations. Slip-based propagation mechanisms and the role of the pre-existing slip band on the crack path are emphasized. Stage-I crack growth is found to be compatible with successive decohesion of the persistent slip band/matrix interface rather than a mere effect of plastic irreversibility. Corresponding crack tip slip displacement magnitude and the associated crack growth rate are evaluated quantitatively at various tip distances from the grain boundary. This shows that grain boundaries systematically amplify slip dispersion ahead of the crack tip and consequently, slow down the stage-I crack growth rate. The results help in developing an original crack propagation model, accounting for the boundary effects relevant to polycrystals. The crack growth trend is then evaluated from calculations of the energy changes due to crack length increments. It is shown that the crack necessarily propagates by increments smaller than 10 nm.     

Localization of plastic strain under shock-wave loading of titanium alloy with a crack

The effect of shock-wave loading with an amplitude of 4 GPa and a duration of 10 μs on the localization of plastic flow and the dynamic fracture of VT-1 cast titanium alloy containing a disk-shaped crack is considered. It is found that the crack size decreases in the direction of shock wave propagation, the dislocation density grows and adiabatic shear bands appear near the crack, and secondary cracks originate in the areas of localized flow near the crack edges. The strain, strain rate, dislocation density, rate of dislocation generation, and dislocation velocity near and away from the healing crack are estimated.     

Nucleation of misfit dislocations and plastic deformation in core/shell nanowires

During fabrication of metal nanowires, an oxide layer (shell) that surrounds the metal (core) may form. Such an oxide-covered nanowire can be viewed as a cylindrical core/shell nanostructure, possessing a crystal lattice mismatch between the core and shell. Experimental evidence has shown that, in response to this mismatch, mechanical stresses induce plastic deformation in the shell and misfit dislocations nucleate at the core/shell interface. As a result, the mechanical, electrical and optoelectronic properties of the nanowire are affected. It is therefore essential to be able to predict the critical conditions at which misfit dislocation nucleation at the nanowire interface takes place and the critical applied load at which the interface begins deforming plastically. Two approaches are explored in order to analyze the stress relaxation processes in these oxide-covered nanowires: (i) energy considerations are carried out within a classical elasticity framework to predict the critical radii (of the core and shell) at which dislocation nucleation takes place at the nanowire interface; (ii) a strain gradient plasticity approach is applied to estimate the flow stress at which the interface will begin deforming plastically (this stress is termed “interfacial-yield” stress). The interfacial-yield stress, predicted by gradient plasticity, depends, among other material parameters, on the radii of the core and shell. Both approaches demonstrate how the geometric parameters of nanowires can be calibrated so as to avoid undesirable plastic deformation; in particular, method (i) can give the radii values that prevent misfit dislocation formation, whereas method (ii) can provide, for particular radii values, the critical stress at which interface deformation initiates.     

Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.     

A discrete dislocation plasticity analysis of a single-crystal semi-infinite medium indented by a rigid surface exhibiting multi-scale roughness

Discrete dislocation plasticity was used to analyse plane-strain indentation of a single-crystal elastic–plastic semi-infinite medium by a rigid surface exhibiting multi-scale roughness, characterised by self-affine (fractal) behaviour. Constitutive rules of dislocation emission, glide and annihilation were used to model short-range dislocation interactions. Dislocation multiplication and the development of subsurface shear stresses due to asperity microcontacts forming between a single-crystal medium and a rough surface were examined in terms of surface roughness and topography (fractal) parameters, slip-plane direction and spacing, dislocation source density, and contact load (surface interference). The effect of multi-scale interactions between asperity microcontacts on plasticity is elucidated in light of results showing the evolution of dislocation structures. Numerical solutions yield insight into plastic flow of crystalline materials in normal contact with surfaces exhibiting multi-scale roughness.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

Fundamental differences in mechanical behavior between two types of crystals at the nanoscale

We present differences in the mechanical behavior of nanoscale gold and molybdenum single crystals. A significant strength increase is observed as the size is reduced to 100 nm. Both nanocrystals exhibit discrete strain bursts during plastic deformation. We postulate that they arise from significant differences in the dislocation behavior. Dislocation starvation is the predominant mechanism of plasticity in nanoscale fcc crystals, while junction formation and hardening characterize bcc plasticity. A statistical analysis of strain bursts is performed as a function of size and compared with stochastic models.     

Analytical estimation of dislocation distribution at the tip of arrested cracks

Computer simulation technique is used for studying the plastic flow at the tip of an arrested crack in lithium fluoride crystals. Two stages of the dislocation structure formation at the tip of a crack are analyzed: the formation of slip lines at the instant of crack arresting, and their evolution after sample unloading and partial healing of the crack. The size and the number of dislocations in a slip line are determined as functions of the loading force at the instant of crack arresting and on frictional stresses. It is shown that, during sample unloading and healing, some dislocations emerge at the plane of the crack under the action of mutual repulsion and image forces, so that the dislocation density attains its maximum value at a distance from the crack tip. A finite region free of dislocations exists in the immediate vicinity of the crack tip.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Plasticity localization ahead of a crack tip modeled by 2D discrete dislocation dynamics

The formation of a plastic zone in the presence of a crack, in a bicrystal, is modeled by two-dimensional discrete dislocation dynamics. The influence of a large number of parameters is studied: the misorientation, the emission from the crack tip and the obstacle density which modifies the internal stress (hardening) and degree of localization of mobile dislocations (slip bands). Emphasis is put on obtaining the best ductility, since the focus is on face centered cubic materials. Finally, a strong effect of the plastic model on the dynamics and on the secondary slip (intensity and localization), beyond the influence of the initial distribution of sources and obstacles, is reported.     

基于点缺陷扩散理论与离散位错动力学耦合的位错攀移模型研究

位错的攀移运动对高温下晶体材料的塑性行为有重要影响,为了能够有效揭示攀移的物理本质及其对塑性行为的作用,本文基于点缺陷扩散理论,通过将体扩散和管扩散机理的共同作用与三维离散位错动力学耦合,建立了适用条件更广的位错攀移模型. 利用此模型我们模拟了单个及多个棱柱型位错环的收缩变形过程,发现影响位错攀移速率的决定因素不是传统理论认为的机械攀移力,而是位错周围(体扩散)及位错段上(管扩散)的空位浓度梯度. 该模型也能够完全重现棱柱型位错环群的粗化过程中不同位错环半径及晶体内平均空位浓度随时间变化的三个阶段. 关键词： 位错攀移 点缺陷扩散理论 位错动力学 棱柱位错环     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

A model of crack based on dislocations in smectic A liquid crystals

A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to construct the solution of the crack in the phase. From the solution, we can determine the size of the plastic zone at the crack tip and the crack tip opening （tearing） displacement, which are the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics.     

Confinement scaling laws for the conventional reversed-field pinch

Mechanical behavior of the Si(111)/Si(3)N4(0001) interface is studied using million atom molecular dynamics simulations. At a critical value of applied strain parallel to the interface, a crack forms on the silicon nitride surface and moves toward the interface. The crack does not propagate into the silicon substrate; instead, dislocations are emitted when the crack reaches the interface. The dislocation loop propagates in the (1; 1;1) plane of the silicon substrate with a speed of 500 (+/-100) m/s. Time evolution of the dislocation emission and nature of defects is studied.     

A New View of Incipient Plastic Instability during Nanoindentation

Whether the dislocation nucleation or the sudden dislocation multiplication dominates the incipient plastic instability during the nanoindentation of initial defect-free single crystal still remains unclear. In this work, the dislocation mechanism corresponding to the incipient plastic instability is numerically investigated by coupling discrete dislocation dynamics with the finite element method. The coupling model naturally introduces the dislocation nucleation and accurately captures the heterogeneous stress field during nanoindentation. The simulation results show that the first dislocation nucleation induces the initial pop-in event when the indenter is small, while for larger indenters, the incipient plastic instability is ascribed to the cooperation between dislocation nucleation and multiplication. Interestingly, the local dislocation densities for both cases are almost the same when the sudden load drop occurs. Thus it is inferred that the adequate dislocations generated by either nucleation or multiplication, or both, are the requirement for the trigger of incipient plastic instability. A unified dislocation-based mechanism is proposed to interpret the precipitate incipient plastic instability.     

Structural states and specific features of the deformation behavior of metals and alloys with mixed nano-and micrograin structure

A classification of the structural states of materials with a mixed nano-and microcrystalline structure is proposed. Theoretical analysis of the structural mechanisms and peculiarities of plastic flow of singlephase and two-phase nanostructured metals and alloys with a bimodal size distribution of grains and phases is performed. The effect of grain-boundary and dislocation mechanisms of plastic flow on the specific features of the deformation behavior and plasticity of nanocrystalline materials is analyzed. A microstructural model of strain hardening of a material with two-scale nano-and micrograin structure is proposed and the condition for the loss of plastic flow stability of such a material is investigated. The dependence of the yield strength and uniform strain of nanocrystalline materials with a two-scale structure on the grain size and the ratio of the volume fractions of the nano-and microstructural components is calculated.     

Two hardening mechanisms in single crystal thin films studied by discrete dislocation plasticity

Two-dimensional discrete dislocation plasticity simulations of the evolution of thermal stress in single crystal thin films on a rigid substrate are used to study size effects. The relation between the residual stress and the dislocation structure in the films after cooling is analyzed using dislocation dynamics. A boundary layer characterized by a high stress gradient and a high dislocation density is found close to the impenetrable film-substrate interface. There is a material-dependent threshold film thickness above which the dislocation density together with the boundary layer thickness and stress state are independent of film thickness. In such films the stress outside the boundary layer is on average very low, so that the film-thickness-independent boundary layer is responsible for the size effect. A larger size effect is found for films thinner than the threshold thickness. The origin of this size effect stems from nucleation activity being hindered by the geometrical constraint of the small film thickness, so that by decreasing film thickness, the dislocation density decreases while the stress in the film increases. The size dependence is only described by a Hall–Petch type relation for films thicker than the threshold value.     

Localization of twinning plastic strain in doped γ-Fe single crystals

The patterns of plastic flow localization in high-manganese γ-Fe fcc single crystals oriented for twinning upon stretching are obtained. Basic space-time features of strain localization at the stages of yield plateau, easy glide, and linear hardening are established. The velocity of strain localization sites during stretching is determined. Conditions under which plasticity autowaves appear in the strained medium are discussed. It is demonstrated that the local strain distributions in the case of twinning are similar to those due to dislocation glide.     

Fracture and cavitation in a constrained thin metal layer under a scale effect in layered materials

Dislocation activities are confined within a thin metal layer. Therefore instead of continuum plasticity theory, individual dislocation activities are considered in order to analyse their effects on fracture, especially interface fracture. Three failure modes may occur in the thin ductile layer: interface fracture, metal fracture and metal cavitation. These failure modes are studied and the competition between them is examined. It seems that interface fracture occurs prior to metal fracture provided that the cohesive strengths of the interface and the metal are similar. In general, the fracture toughness of the thin layer will increase with increasing layer thickness. However, at a layer thickness of about 10 mm, the layer is more likely to fail by interface debonding, prior to any failure by ductile cavitation. Finally, using material and geometric parameters, a relation is given which determines the competition between crack fracture and cavity instability.     

裂纹尖端塑性区非线性超声混频定位表征

基于非共线体波混频的方法,本文对金属材料中裂纹尖端的塑性变形区开展定位表征研究.基于二阶微扰理论和矢量分析方法,理论研究非共线体波混频的共振条件及其定位塑性变形区的机理.有限元仿真表明,两横波混频产生的纵波可用于定位塑性变形区.以Al7075-T6材料为检测对象,通过实验证明两列横波混频定位裂纹尖端塑性区的可行性.实验...