Emission of dislocations from nanovoids under combined loading

Among all directions available for dislocation emission from the surface of a cylindrical circular void, the direction of the most likely emission is determined. It is shown that this direction is different from the direction of the maximum shear stress at the surface of the void due to the applied loading. The critical stress and the direction of the dislocation emission are determined for circular nanovoids under remote uniaxial, pure shear, and arbitrary biaxial loading. The analysis includes effects of the loading orientation relative to the discrete slip plane orientation. It is shown that dislocations are emitted more readily from larger nanovoids and that wider dislocations are emitted under lower applied stress than narrow dislocations. Different mechanisms, under much lower stress, operate for growth of the micron-size voids.     

An analysis of dislocation nucleation near a free surface

Molecular dynamics analyses of defect-free aluminum single crystals subject to bending are carried out to investigate dislocation nucleation from free surfaces. A principal aim of the analyses is to provide background for the development of dislocation nucleation criteria for use in discrete dislocation plasticity calculations. The molecular dynamics simulations use an embedded atom potential for aluminum. Bending is imposed on a strip by specifying a linear variation of displacement rate on opposite edges. The overall bending response is determined and the character of the dislocations nucleated is identified. It is found that the stress magnitudes at the instant of dislocation nucleation are nearly an order of magnitude smaller than for homogeneous bulk dislocation nucleation. The characterization of dislocation nucleation in terms of various phenomenological nucleation criteria is explored, in particular: (i) a critical resolved shear stress; (ii) the onset of an elastic instability; and (iii) a critical stress-gradient criterion. It is found that dislocation nucleation is not well-represented by a critical value of the resolved shear stress but is reasonably well-represented by the critical stress-gradient criterion.     

Simulation of edge dislocation emission from a crack under in-plane shear

Considered is the tandem emission of dislocations and dislocation dipoles from a crack under in-plane shear in one slip system as well as multiple slip systems. Effective stress intensity factors are determined by considering zones of local distortion similar to that in macro-plasticity. The dislocation free zone (DFZ) is also obtained which is analogous to the core region in fracture mechanics. Studied are effects of dislocation emission or development of plastic zone in front of the crack tip on the potential crack propagation based on the strain energy density factor criterion.     

Dislocation nucleation from bicrystal interfaces with dissociated structure

Atomistic calculations are used to model the nucleation of partial dislocations during a tensile deformation from bicrystal interfaces with dissociated structure. Interfaces with this type of structure occur primarily in materials with low intrinsic stacking fault energies. In this work, the initial structure of each bicrystal interface is refined using energy minimization techniques. Molecular dynamics simulations are then used to study the deformation of each interface in uniaxial tension perpendicular to the boundary plane at a constant strain rate. Analysis focuses on the evolution of the dissociated interface structure prior to the dislocation nucleation event and the resulting structure of the boundary after the emission of partial dislocations from the interface. Dislocation nucleation occurs predominantly at the dissociated interface structural unit, while the spacing between interface features is identified as an important length scale that affects the failure mode. The evolution of the dissociated interface structure and the nucleation of partial dislocations are found to be similar to results obtained in a previous atomistic study of the stress dependence of a lock formation containing a stair-rod dislocation.     

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic ‘butterfly’ curves; and others.     

Dislocation behaviours ahead of crack tip

In this paper, a unified mechanics model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations within the plastic zone in the form of an inverse pile up are treated as discrete elastic edge dislocations. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear governing equations are obtained which take into account for the interaction between the emitted dislocations and cohesive zone and the nonlinear interaction between sliding displacement and the opening displacement. After discretization, the governing equations are transformed into a set nonlinear algebraic equations which are solved with Newton-Raphson Method. The results of calculation for pure shearing and combined tension and shear loading after dislocation emission are given in detail. Finally, the process of dislocation nucleation and emission on a pair of symmetric slip planes of angle α with respect to the crack plane under pure mode I load is analysed. The equilibrium positions and the number of emitted dislocation are determined. Several possible competition behaviors of dislocation emission vs cleavage are revealed.     

Transient studies of screw and edge dislocation generation at crack edges

Exact transient analyses of the generation of screw and edge dislocations at the edges of stationary cracks subjected to the diffraction of, respectively, plane SH- and SV-waves, and their subsequent arrest are performed. The solutions are examined in light of a dislocation emission criterion which is based, simultaneously, on standard dislocation force concepts and quasi-static emission studies.This examination allows expressions for the times of emission and arrest, the distances traveled by the dislocations, and the dynamic stress intensity factors to be derived in terms of parameters such as dislocation speed and yield stress. These expressions exhibit distinctive dynamic effects and reveal several features of the generation process:In particular, the times and distances are, while on a micromechanical scale, not necessarily insignificant, and imply that purely brittle fracture may not easily occur. Then, edge dislocation emission would appear to occur at a preferred speed, while screw dislocation emission apparently prefers to take place quasi-statically.Examination of a general incident waveform class shows that a continuous wave could cause dislocation generation to occur before a step-stress wave can. Moreover, the emission process depends upon a weighted time history of the incident wave stress, not its instantaneous value. This, in turn, implies that dislocation emission does not necessarily shield the crack edge by lowering the dynamic stress intensity factor. Finally, unless the dislocations are allowed to decelerate to zero speed upon arrest, a repetitious process of start-stop motion can in principle take place.     

Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation

Mechanics of nano- and meso-scale contacts of rough surfaces is of fundamental importance in understanding deformation and failure mechanisms of a solid surface, and in engineering fabrication and reliability of small surface structures. We present a micro-mechanical dislocation model of contact-induced deformation of a surface step or ledge, as a unit process model to construct a meso-scale model of plastic deformations near and at a rough surface. This paper (Part I) considers onset of contact-induced surface yielding controlled by single-dislocation nucleation from a surface step. The Stroh formalism of anisotropic elasticity and conservation integrals are used to evaluate the driving force on the dislocation. The driving force together with a dislocation nucleation criterion is used to construct a contact-strength map of a surface step in terms of contact pressure, step height, surface adhesion and lattice resistance. Atomistic simulations of atomic surface-step indentation on a gold (1 0 0) surface have been also carried out with the embedded atom method. As predicted by the continuum dislocation model, the atomistic simulations also indicate that surface adhesion plays a significant role in dislocation nucleation processes. Instabilities due to adhesion and dislocation nucleation are evident. The atomistic simulation is used to calibrate the continuum dislocation nucleation criterion, while the continuum dislocation modeling captures the dislocation energetics in the inhomogeneous stress field of the surface-step under contact loading. Results show that dislocations in certain slip planes can be easily nucleated but will stay in equilibrium positions very close to the surface step, while dislocations in some other slip planes easily move away from the surface into the bulk. This phenomenon is called contact-induced near-surface dislocation segregation. As a consequence, we predict the existence of a thin tensile-stress sub-layer adjacent to the surface within the boundary layer of near-surface plastic deformation. In the companion paper (Part II), we analyze the surface hardening behavior caused by multiple dislocations.     

QUASICONTINUUM SIMULATION OF NANOINDENTATION OF NICKEL FILM

A large-scale atom simulation of nanoindentation into a thin nickel film using thequasicontinuum method was performed. The initial stages of the plasticity deformation of nickelwere studied. Several useful results were obtained as follows: (1)The response of the load versusindentation depth—on the load versus indentation depth curve, besides the straight parts cor-responding to the elastic property of nickel, the sudden drop of the load occurred several times;(2) The phenomena of dislocation nucleation—the dislocation nucleation took place when theload descended, which makes it clear that dislocation nucleation causes the drop of the load;(3)The mechanism of the dislocation emission—the Peierls-Nabarro dislocation model and a pow-erful criterion were used to analyze the dislocation emission. And the computational value was ingood agreement with the predict value; (4) The density of geometrically necessary dislocations.A simple model was used to obtain the density of geometrically necessary dislocations beneaththe indenter. Furthermore, the influence of the boundary conditions on the simulation results wasdiscussed.     

温度对金属材料钼位错发射的影响

应用关联参照模型、随位错位置变化的柔性位移边界条件和三维分子动力学方法研究了体心立方（ＢＣＣ）金属晶体钼在不同温度下裂尖发射位错的力学行为，随着温度的提高，不但发射位错的临界应力强度因子下降而且在同一应 度因子条件下，发射位错的数量出增加，位错速度和不全位错之间的扩展距离对温度不敏感，在位错发射过程中，发现了稳定的和不稳定的两个变形状态，在稳定的有状态，位错发射后，塞积在远离裂纹尖端处；必须增加外     

Plasticity size effects in voided crystals

The shear and equi-biaxial straining responses of periodic voided single crystals are analysed using discrete dislocation plasticity and a continuum strain gradient crystal plasticity theory. In the discrete dislocation formulation, the dislocations are all of edge character and are modelled as line singularities in an elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Over the range of length scales investigated, both the discrete dislocation and strain gradient plasticity formulations predict a negligible size effect under shear loading. By contrast, under equi-biaxial loading both plasticity formulations predict a strong size dependence with the flow strength approximately scaling inversely with the void spacing. Excellent agreement is obtained between predictions of the two formulations for all crystal types and void volume fractions considered when the material length scale in the non-local plasticity model is chosen to be (about 10 times the slip plane spacing in the discrete dislocation models).     

Dislocation nucleation in Σ3 asymmetric tilt grain boundaries

Atomistic simulations were used to investigate dislocation nucleation from Σ3 asymmetric (inclined) tilt grain boundaries under uniaxial tension applied perpendicular to the boundary. Molecular dynamics was employed based on embedded atom method potentials for Cu and Al at 10 K and 300 K. Results include the grain boundary structure and energy, along with mechanical properties and mechanisms associated with dislocation nucleation from these Σ3 boundaries. The stress and work required for dislocation nucleation were calculated along with elastic stiffness of the bicrystal configurations, exploring the change in response as a function of inclination angle. Analyses of dislocation nucleation mechanisms for asymmetric Σ3 boundaries in Cu show that dislocation nucleation is preceded by dislocation dissociation from the boundary. Then, dislocations preferentially nucleate in only one crystal on the maximum Schmid factor slip plane(s) for that crystal. However, this crystal is not simply predicted based on either the Schmid or non-Schmid factors. The synthesis of these results provides a better understanding of the dislocation nucleation process in these faceted, dissociated grain boundaries.     

镍单晶薄膜纳米压痕的准连续介质模拟

用准连续介质方法模拟了大规模原子的镍薄膜在纳米压痕下发生初始塑性变形的行为.主要得到了:(1)载荷-位移响应.在载荷位移曲线上除了反应晶体弹性性质的直线外还有数次的载荷突然下降过程.(2)位错形核现象.与载荷-位移曲线上的载荷突然下降相对应的在受压的晶体上发现了位错形核现象,说明载荷的下降是因为位错形核引起的.(3)位错的发射机制.用Peierls-Nabarro位错模型以及能量法分析了位错的发射机制,理论值与计算值吻合较好.(4)几何必需位错密度.用一个简单的模型计算了几何必须位错密度.此外还考虑了边界条件对模拟结果的影响.     

Elastic precursor decay and radiation from nonuniformly moving dislocations

Precursor decay in plate impact experiments on single crystals is re-examined from the viewpoint of the elastodynamics of moving dislocations. Superposition of solutions for many dislocations set in motion by an incident plane wave is used to relate the decay of the wave amplitude at the front of the plane wave to the density and velocity of dislocations at the wavefront. The resulting precursor decay relation is the same as the one derived from an elastic/visco-plastic model of the material, except for a small correction due to differences between the effects of forward and backward propagating dislocations. Motivated by this added support for the validity of the precursor decay equation, the values used for the quantities in this equation are re-examined. Recent experimental results and the elastodynamics analysis are interpreted as indicating that the commonly-used values of dislocation velocity are probably satisfactory, but that the values used for dislocation density are several orders of magnitude too small near the lapped surfaces of the crystal. These large dislocation densities are identified as the probable dominant cause of the lower-than-predicted precursor amplitudes that are recorded in experiments. More accurate experimental data and inclusion of the non-linear elasticity effects are essential in determining whether or not the observed precursor decay in the bulk of the specimen can be explained by the motion of dislocations present initially. Calculations of energy radiated from screw and edge dislocations that start from rest and move thereafter at constant velocity confirm that dislocation drag forces due to continuum elasticity effects are small for dislocation velocities less than, say, 80% of the elastic shear wave speed. At supersonic speeds the continuum drag effects become so large that sustained supersonic motion of dislocations appears unlikely.     

BCC晶体中韧位错运动特性的分子动力学模拟

采用镶嵌原子法 (EAM) ,采用沿 <111>方向插入两层 (2 11)半原子面的方法形成位错 ,模拟金属Mo中韧位错的运动特性 .模拟大于Peierls Nabarro应力时不同剪切力下的韧位错运动速度及相同剪切力下不同温度时韧位错运动速度 ,结果表明 :剪切力越大 ,韧位错运动速度越大 ;温度对韧位错运动有明显的阻碍作用 ,在相同剪切力下 ,随着温度的升高 ,韧位错运动速度减小 ,即拖动系数B(T)随温度升高而增大 .随剪应力增大 ,B(T)变化趋势减缓 .     

Effect of temperature on dislocation emission from crack tip for BCC metal Mo

The effect of thermally activated energy on the dislocation emission from a crack tip in BCC metal Mo is simulated in this paper. Based on the correlative reference model on which the flexible displacement boundary scheme is introduced naturally, the simulation shows that as temperature increases the critical stress intensity factor for the first dislocation emission will decrease and the total number of emitted dislocations increase for the same external load. The dislocation velocity and extensive distance among partial dislocations are not sensitive to temperature. After a dislocation emission, two different deformation states are observed, the stable and unstable deformation states. In the stable deformation state, the nucleated dislocation will emit from the crack tip and piles up at a distance far away from the crack tip, after that the new dislocation can not be nucleated unless the external loading increases. In the unstable deformation state, a number of dislocations can be emitted from the crack tip continuously under the same external load. The project is supported by the National Natural Science Foundation of China.     

A closed-form criterion for dislocation emission in nano-porous materials under arbitrary thermomechanical loading

Our traditional view of void nucleation is associated with interface debonding at second-phase particles. However, under extreme dynamic loading conditions second-phase particles may not necessarily be the dominant source of void nucleation sites. A few key experimental observations of laser spall surfaces support this assertion. Here, we describe an alternative mechanism to the traditional view, namely shock-induced vacancy generation and clustering followed by nanovoid growth mediated by dislocation emission. This mechanism only becomes active at very large stresses. It is therefore desirable to establish a closed-form criterion for the macroscopic stress required to activate dislocation emission in porous materials. Following an approach similar to Lubarda and co-workers, we derive the desired criterion by making use of stability arguments applied to the analytic solutions for the elastic interactions of dislocations and voids. Our analysis significantly extends that of Lubarda and co-workers by accounting for a more general stress state, finite porosity, surface tension, as well as temperature and pressure dependence. The resulting simple stress-based criterion is validated against a number of molecular dynamics simulations with favorable agreement.     

Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading

Atomistic simulations are used to investigate how the stress required for homogeneous nucleation of partial dislocations in single crystal copper under uniaxial loading changes as a function of crystallographic orientation. Molecular dynamics is employed based on an embedded-atom method potential for Cu at 10 and 300 K. Results indicate that non-Schmid parameters are important for describing the calculated dislocation nucleation behavior for single crystal orientations under tension and compression. A continuum relationship is presented that incorporates Schmid and non-Schmid terms to correlate the nucleation stress over all tensile axis orientations within the stereographic triangle. Simulations investigating the temperature dependence of homogeneous dislocation nucleation yield activation volumes of ≈0.5- and activation energies of . For uniaxial compression, full dislocation loop nucleation is observed, in contrast to uniaxial tension. One of the main differences between uniaxial tension and compression is how the applied stress is resolved normal to the slip plane on which dislocations nucleate—in tension, this normal stress is tensile, and in compression, it is compressive. Last, the tension-compression asymmetry is examined as a function of loading axis orientation. Orientations with a high resolved stress normal to the slip plane on which dislocations nucleate have a larger tension-compression asymmetry with respect to dislocation nucleation than those orientations with a low resolved normal stress. The significance of this research is that the resolved stress normal to the slip plane on which dislocations nucleate plays an important role in partial (and full) dislocation loop nucleation in FCC Cu single crystals.     

A stress-gradient based criterion for dislocation nucleation in crystals

Dislocations are the main lattice defects responsible for the strength and ductility of crystalline solids. The generation of new dislocations is an essential aspect of crystal defect physics, but a fundamental understanding of the mechanical conditions which lead to dislocation nucleation has remained elusive. Here, we present a nucleation criterion motivated from continuum thermomechanical considerations of a crystalline solid undergoing deformation, and demonstrate the criterion's ability to correctly predict dislocation nucleation via direct atomistic simulations. We further demonstrate that the commonly held notion of a nucleation criterion based on the magnitude of local stress components is incorrect.     

Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening

The study of micro-plastic behavior of rough surface contacts is the critical link towards a fundamental understanding of contact, friction, adhesion, and surface failures at small length scales. In the companion paper (Yu, H.H., Shrotriya, P., Gao, Y.F., Kim, K.-S., 2007. Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation. J. Mech. Phys. Solids 55, 489–516), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micro-mechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice–Thomson criterion is used to model dislocation nucleation. Dislocations nucleated from the surface step are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pileup will exert a strong back stress to prevent further dislocation nucleation and thus lead to the contact hardening behavior, the degree of which depends on the slip-plane orientation. Particularly, we find that dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named “latent softening”. A mechanistic explanation shows that the latent softening is closely related to the stress-concentration mode mixity at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes, which influences the subsequent dislocation nucleation. Our calculations show that the dislocation pileup on one slip plane can even cause the spontaneous dislocation nucleation on the other slip plane without further increase of the contact load. Furthermore, it is found that rough surface contacts at small length scale can lead to the dislocation segregation and the formation of a surface tensile sub-layer. The discrete-dislocation model presented here and in the companion paper provides novel insights in bridging the atomistic simulations and continuum plastic flow analysis of surface asperity contact.