Anti-plane elastodynamic analysis of orthotropic planes weakened by several cracks

Stress analysis is carried out in an orthotropic plane containing a Volterra-type dislocation, the distributed dislocation technique is employed to obtain integral equations for an orthotropic plane weakened by cracks under time-harmonic anti-plane traction. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically. Several examples are solved and the stress intensity factors for multiple cracks with different configuration are obtained.     

Surface versus bulk nucleation of dislocations during contact

The indentation of single crystals by a periodic array of flat rigid contacts is analyzed using discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modeled as line singularities in a linear elastic solid. The limiting cases of frictionless and perfectly sticking contacts are considered. The effects of contact size, dislocation source density, and dislocation obstacle density and strength on the evolution of the mean indentation pressure are explored, but the main focus is on contrasting the response of crystals having dislocation sources on the surface with that of crystals having dislocation sources in the bulk. When there are only bulk sources, the mean contact pressure for sufficiently large contacts is independent of the friction condition, whereas for sufficiently small contact sizes, there is a significant dependence on the friction condition. When there are only surface dislocation sources the mean contact pressure increases much more rapidly with indentation depth than when bulk sources are present and the mean contact pressure is very sensitive to the strength of the obstacles to dislocation glide. Also, on unloading a layer of tensile residual stress develops when surface dislocation sources dominate.     

Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.The project supported by the National Natural Science Foundation of China(10272009 and 10472030) and the Natural Science Foundation of Hunan Province(02JJY2014)     

A SCREW DISLOCATION IN A THREE-PHASE COMPOSITE CYLINDER MODEL WITH INTERFACIAL RIGID LINES

The problem of the elastic interaction between a screw dislocation and a three-phase circular inclusion with interracial rigid lines （anti-cracks） is investigated. An efficient and concise method for the complex multiply connected region is developed, with which explicit series form solutions of the complex potentials in the matrix, and the interphase layer and inclusion regions are derived. Based on the complex potentials, the image force on the screw dislocation is then calculated by using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, interphase layer thicknesses and material property combinations. The main results show that the interracial rigid lines exert a significant perturbation effect on the motion of the screw dislocation near the circular inclusion surrounded by an interphase layer.     

晶体位错尺寸效应的多尺度分析

本文采用准连续介质多尺度方法,分析了面心立方（fcc）晶体铝阶梯孪晶界在不同尺寸情况下（试件尺寸长高比从1：1到8：1）受剪切作用的晶界变形。了解在不同尺寸下,晶界结构位错的成核过程,得到了大试件比值与小试件比值下作用力与应变的关系曲线及不同试件尺寸下应变能的变化曲线。其中随着试件比值的增加,作用力在应变比较小的时候变化情况相似,但当应变达到3％以后,呈现出明显的不同;应变能随试件长高比的增大而减小,各个试件在各自不同的加载阶段,应变能变化趋势同作用力变化趋势相一致。本计算揭示了不同尺寸下阶梯孪晶界在剪切作用下的微观机理,证实其尺寸效应性质。     

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.     

动态载荷下剪切变形局部化、微结构演化与剪切断裂研究进展

总结和评述了近年来金属与合金变形局部化的形成、微结构演化与剪切断裂方面作者和相关的研究工作成果. 材料包括低碳钢, SS304不锈钢, Fe-15%Ni-15%Cr单晶, Al-Li合金,α-Ti和Ti-6Al-4V, Al/SiCp复合材料等.综述内容主要包括:采用改进的Hopkinson扭杆装置,对剪切变形局部化形成、发展和演化过程进行了实验观察与数值模拟;采用"侧剖"与"对接"等定点方法制备电子显微镜薄膜试样,对剪切带内相变与再结晶、非晶转变、旋涡结构等动态变形现象,以及与宏观动态力学行为对应的位错胞的形成、发展和坍塌等微结构特征进行了观测;提出了应变和应变率同时作为剪切带形成的两个必要条件的直接实验证据;在剪切带内发现了α'$-马氏体相变现象,以及相变产物与母体之间的晶体学关系;通过位错单滑移或交滑移等微观剪切最后发展成为宏观剪切的机制;对剪切带内再结晶结构的观测和对再结晶动力学本构关系的定量描述;对剪切带特别是``白色'腐蚀带(或相变带)的形成机制的分析和新的解释,指出 ``白色'是带内亚结构取向趋于一致,其在光学或扫描显微镜下很难辨认这些亚结构的取向差所致,并非表明剪切带内一定发生了相变;通过截断实验和实时跟踪观测发现,剪切带内微裂纹的萌生与聚合是材料承载能力骤然下降并导致最后断裂的主控因素.此外,本文对近年来在准静态和循环加载下材料的局部化形变与剪切断裂的实验结果予以简要评述,指出其微观机制与动态载荷下的截然不同, 是由位错的平面滑移所控制的,与热效应无关的等温变形.      

位错偶极子和Ⅲ型界面裂纹的干涉效应

研究了多晶体材料中螺型位错偶极子和界面裂纹的弹性干涉作用.利用复变函数方法,得到了该问题复势函数的封闭形式解答.求出了由位错偶极子诱导的应力场和裂纹尖端应力强度应子,分析了偶极子的方向,偶臂和位置以及材料失配对应力强度因子的影响.推导了作用在螺型位错偶极子中心的像力和力偶矩,并讨论了界面裂纹几何条件和不同材料特征组合对位错偶极子平衡位置的影响规律.结果表明,裂纹尖端的螺型位错偶极子对应力强度因子会产生强烈的屏蔽或反屏蔽效应.同时,界面裂纹对螺型位错偶极子在材料中运动有很强的扰动作用.     

Analysis for a screw dislocation accelerating through the shear-wave speed barrier

An analysis is performed for an accelerating screw dislocation through the shear-wave speed barrier. At this instant, the function that determines the interval of the path of the dislocation motion that contributes to the wave front has roots that change from a pair of complex conjugate to a double real, which subsequently splits into two real ones. The analysis is performed at this transition to supersonic that occurs at the double root maximum of the function that defines the interval of the dislocation path that contributes to the field points. It is found that the stress has a log|ξ-ξ^*|/|ξ-ξ^*|^1/2 singularity in the coefficient of the delta function of the forming Mach front, implying that for this phenomenon the Volterra dislocation model has too strong a discontinuity (step-function) in the displacement to be meaningful. A ramp-core displacement dislocation model analysis, which removes the singularity in the stress, is presented. These results can be useful in a multiscale dislocation dynamics modeling with inertia effects.     

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar.anisotropic. materials. Integrating Riemann-Schwarz＇s symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors, at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.