Micromechanical model of stage I to stage II crack growth transition for aluminium alloys

Stage I to Stage II crack growth transition is a kinetic process that is particularly studied in this work. Crack growth transition is modelled to occur when small fatigue crack growth is deterred by an effective barrier that reduces the crack growth rate to a minimum. Effective blockage of small crack growth due to barriers is characterised by pile-up of dislocations. Crack tip pile-up sliding displacement is formulated by adopting a continuous configuration of dislocation pile-up. Transition condition is quantitatively determined when a crack tip sliding displacement of Stage I cracks just meets a crack tip opening displacement of Stage II cracks. As a result, a dislocation-based micromechanical model is systematically developed that enables kinetic predictions of crack growth transition and growth rates of small fatigue cracks. Moreover, the concept of microstructurally-affected-zone is further interpreted in terms of local microstructure and load levels, leading to good explanations for scatters of small crack growth. All model-based growth rate predictions show a good coincidence with experimental results.     

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     

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.     

Molecular dynamics simulation of crack-tip processes in copper

The crack tip processes in copper under mode II loading have been simulated by a molecular dynamics method. The nucleation, emission, dislocation free zone (DFZ) and pile-up of the dislocations are analyzed by using a suitable atom lattice configuration and Finnis & Sinclair potential. The simulated results show that the dislocation emitted always exhibits a dissociated fashion. The stress intensity factor for dislocation nucleation, DFZ and dissociated width of partial dislocations are strongly dependent on the loading rate. The stress distributions are in agreement with the elasticity solution before the dislocation emission, but are not in agreement after the emission. The dislocation can move at subsonic wave speed (less than the shear wave speed) or at transonic speed (greater than the shear wave speed but less than the longitudinal wave speed), but at the longitudinal wave speed the atom lattice breaks down. The project supported by the National Natural Science Foundation of China     

纳米晶体铝在单轴拉伸下的位错堆积对微裂纹扩展的影响

摘要：针对纳米晶体材料,研究了单轴拉伸载荷作用下纳米晶体铝中的裂纹与裂纹尖端发射的位错所形成的滑移面之间的相互作用。通过分布位错法,将裂纹和滑移面等效为均匀分布的连续位错,获得了裂纹面上应力场。并引入裂纹尖端的无位错区,研究了裂纹尖端无位错区对微裂纹的萌生和主裂扩展之间的影响。结果表明,不考虑裂纹尖端无位错区时,裂纹长度较短,会先在晶界处形成微裂纹,主裂纹较长时,主裂纹会直接穿晶扩展。滑移面与裂纹尖端夹角较大时,会增加裂纹尖端发射的位错个数,从而抑制主裂纹的扩展。考虑裂纹尖端无位错区时,无位错区先于晶界处出现微裂纹,通过主裂纹与微裂纹之间位错的相互发射,导致裂纹与尖端处微裂纹汇合,有效加速了主裂纹的扩展。     

二维位错裂纹的稳定性分析

在已有的一维穿透位错裂纹模型及能量计算的基础上，将其推广为二维椭圆盘状裂纹模型，并计算了其能量．根据能量平衡原理，给出了位错裂纹模型的裂纹平衡尺寸、裂纹扩展临界应力．并与不考虑位错影响的宏观断裂力学中Ⅰ型穿透裂纹的Ｇｒｉｆｉｔｈ解及椭圆盘裂纹的Ｇｒｉｆｉｔｈ解加以比较．给出的位错裂纹模型解在位错数目ｎ＝０时与宏观断裂力学解一致     

Exact solutions for piezoelectric screw dislocations near two asymmetrical edge cracks emanating from an elliptical hole

The interaction between piezoelectric screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under combined mechanical and electric load at infinity is dealt with. The closed-form solutions are derived for complex potentials and generalized stress fields. In the limiting cases, some well-known results can be obtained from the present solutions. Moreover, some new exact solutions are shown. The stress intensity factor and the energy release rate at the right tip due to a screw dislocation near the right interfacial crack are also calculated. The results show that the shielding effect of dislocation on crack expanding decreases with the increase in dislocation azimuth angle and the distance between the dislocation and the crack tip, and the repulsion acting on the dislocation from the other half plane demotes crack propagation. The increasing of the length of the other crack promotes crack growth, but the increasing of the minor semi-axis demotes it.     

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.     

Interfacial de-bonding caused by a screw dislocation pile-up at a circular cylindrical rigid inclusion

An array of continuously-distributed screw dislocations piled up against a circular cylindrical rigid inclusion is analyzed by the complex-variable method. Both uniformly applied shearing load at infinity and internal friction stress opposing the movement of dislocations are taken into account. The pile-up tip is away from the matrix-inclusion interface, its distance from the interface being determined by the condition that the stresses should be finite everywhere in the solid. Stress distributions on the interface are determined, and de-bonding of the interface, namely the formation of initial voids or cracks, is discussed. Stress and displacement near the tip of these initial voids are then analyzed. This analysis is combined with the virtual work argument of A.A. Griffith (1920) to yield a criterion for the initial voids to grow along the interface. The critical void-growth load is expressed by the sum of two terms, one proportional to the friction stress and the other inversely proportional to the square-root of the inclusion radius.     

Transient dislocation emission from a crack tip under dynamic mode III loading

Summary  Transient dislocation emission from a crack tip under dynamic mode III loading is analyzed. By taking into account the dynamic interaction between the crack and dislocation, the governing equation for the dislocation motion is derived under the quasi-steady assumption. The behavior of dislocation emission is explored in detail by solving this equation numerically. A critical initial speed can be determined, which must be exceeded by dislocations to escape from the crack tip. The dislocation emission process is found to be completed in such a short time period that the applied load may be approximately treated as constant during dislocation emission. Based on this fact, an asymptotic criterion for transient dislocation emission is developed, from which the critical initial speed can be evaluated. In the case that the dislocation is emitted from rest, we recover the quasi-static criterion of dislocation emission. Received 22 November 2000; accepted for publication 20 March 2001     

Cracking characteristics of mixed mode dislocations near a lip-like mode crack

This work is concerned with the cracking characteristics of mixed mode dislocations near a lip-like mode crack, stress intensity and strain energy density factor are obtained by using conformal mapping, singularity analysis and Cauchy integrals. Shielding effect generated by screw dislocation near a lip-like mode crack decreases with the increment of the distance between screw dislocation and crack tip. Larger distance between two faces of the crack leads to the shielding effect waning. The strain energy density factor of mode III decreases with the increment of the distance between dislocation and crack tip. Larger distance between two faces of lip-like mode crack also leads to the strain energy density factor waning and encourages crack initiation; the shielding effects generated by edge dislocation near the crack decrease with the increment of the distance between edge dislocation and crack tip.     

分子动力学方法在研究材料力学行为中的应用进展

报道近年来分子动力学方法应用于研究位错、裂纹、晶界及其相互作用方面的进展．主要包括:裂纹尖端的位错发射,位错发射的不稳定堆垛能,晶体与裂纹’几何关系对位错发射的影响,温度对位错发射的影响以及由裂纹尖端发射的位错列与不对称倾侧晶界的相互作用．报道主要以我们的工作为主,重点讨论裂纹尖端位错发射的研究结果      

位错、裂纹与断裂

本文评述近些年来在位错、裂纹与断裂方面的研究进展.内容主要包括:①以屈服强度温度依赖性为例,讨论力学性能的结构敏感性,使其对位错芯结构与塑性之间的关系有一定的认识;②纯弹性断裂总是极少的,因之在加载应力作用下,裂纹顶端总是存在着或大或小的塑性区,存在着裂纹与位错的交互作用.这里以我们自己的工作为主,重点讨论裂端位错过程的研究结果.      

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.     

EFFECTS OF DISLOCATION CONFIGURATION, CRACK BLUNTING AND FREE SURFACES ON THE TRIGGERING LOAD OF DISLOCATION SOURCES

The effects of dislocation configuration,crack blunting and free surfaces on the triggering load of dislocation sources in the vicinity of a crack or a wedge tip subjected to a tensile load in the far field are investigated.An appropriate triggering criterion for dislocation sources is proposed by considering the configurational forces acting on each dislocation.The triggering behaviors of dislocation sources near the tips of a crack and a wedge are compared.It is also found that the blunting of crack tip and the presence of free surfaces near the crack or the wedge have considerable influences on the triggering load of dislocation sources.This study might be of significance to gaining a deeper understanding of the brittle-to-ductile transition of materials.     

Atomistic/continuum simulation of interfacial fracture part I: Atomistic simulation

The phenomenon of interfacial fracture, as manifested by atomistic cleavage, debonding and dislocation emission provides a challenge for combined atomistic-continuum analysis. As a precursor for fully coupled atomistic-continuum simulation^[1] of interfacial fracture, we focus here on the atomistic behavior within a nanoscopic core surrounding the crack tip. The inter-atomic potential under Embedded Atom Method is recapitulated to form an essential framework of atomistic simulation. The calculations are performed for a side-cracked disc configuration under a remoteK field loading. It is revealed that a critical loading rate defines the brittle-to-ductile transition of homogeneous materials. We further observe that the near tip mode mixity dictates the nanoscopic profile near an interfacial crack tip. A zigzag interface structure is simulated which plays a significant role in the dislocation emission from an interfacial crack tip, as will be explored in the second part of this investigation. The project supported by the National Natural Science Foundation of China     

压电双材料界面钝裂纹附近螺型位错的屏蔽效应与发射条件

研究了压电双材料界面钝裂纹附近螺型位错的屏蔽效应与发射条件.应用保角变换技术,得到了复势函数与应力场的封闭形式解,讨论了位错方位、双材料电弹常数及裂纹钝化程度对位错屏蔽效应和发射条件的影响.结果表明,Burgers矢量为正的螺型位错可以降低界面钝裂纹尖端的应力强度因子(屏蔽效应),屏蔽效应随位错方位角及位错与裂纹尖端距...     

Nonlocal elasticity and dislocation image force due to cracks

Summary   Fundamental field equations of nonlocal elasticity are presented. With these equations, the image force on a screw dislocation due to a crack is analyzed using the conformal mapping technique. Two cases are considered: one is for a finite-length crack, the other is for an infinite one. All classical singularities of the dislocation image force are eliminated when the dislocation tends to the crack tip. The maximum of the force is obtained at the crack tip. Received 10 June 1999; accepted for publication 8 February 2000     

Atomistic/continuum simulation of interfacial fracture Part II: Atomistic/dislocation/continuum simulation

Coupled atomistic/dislocation/continuum simulation of interfacial fracture is performed in this paper. The model consists of a nanoscopic core made by atomistic assembly and a surrounding elastic continuum with discrete dislocations. Atomistic dislocations nucleate from the crack tip and move to the continuum layer where they glide according to the dislocation dynamics curve. An atoms/continuum averlapping belt is devised to facilitate the transition between the two scales. The continuum constraint on the atomic assembly is imposed through the mechanics atmosphere along the overlapping belt. Transmissions of mechanics parameters such as displacements, stresses, masses and momenta across the belt are realized. The present model allows us to explore interfacial fracture processes under different mode mixity. The effect of atomistic zigzag interface on the fracture process is revealed: it hinders dislocation emission from the crack tip, especially under high mode mixity. The project supported by the National Natural Science Foundation of China     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE Ⅲ INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode Ⅲ interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. zThe image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.