A unified theory for brittle and ductile shear mode fracture

A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids, this criterion is equivalent to Griffith's theory. In other cases, it provides a theoretical basis for the Irwin-Orowan formula. For purely ductile solids, the theory makes direct contact with the Bilby-Cottrell-Swinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the Peach-Koehler force overcomes it. A dislocation-free zone separates the plastic zone from and the tip of the crack. The dislocation-free zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth, the length of the dislocation-free zone is constant and the shielding dislocations advance in concert. As in Griffith's theory, the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocation-free zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture.     

α-Fe裂纹的分子动力学研究

通过分子动力学方法，模拟了α-Fe裂纹的单轴拉伸实验中的形变过程.研究了不同晶体取向裂纹的形变特点和断裂机理，观察到各种形变现象，如位错形核和发射，位错运动，堆垛层错或孪晶的形成，纳米空洞的形成与连接等.计算结果表明，裂纹扩展是塑性过程和弹性过程相结合的过程，其中塑性过程表现为由裂尖发射的位错导致的原子切变行为，而弹性过程的发生则是由无位错区中的原子断键所导致.同时还研究了α-Fe裂纹的形变特点和断裂机理与温度场和应力场的依赖关系.     

裂纹顶端的异号位错和无位错区的象力理论

本文改进BCS型裂纹位错模型,并对裂纹顶端范性区的位错密度分布进行了计算。结果指出,在紧靠裂纹顶端的滑移面上出现和裂纹位错异号的位错。这些负号位错将移至裂纹顶端并使之钝化而留下一个无位错区或低位错密度区。本文对无位错区形成的象力理论进行了讨论。 关键词：     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.     

Brittle-Ductile Transition of Ferroelectric Ceramics Induced by Thermally Activated Dislocation Emission

Thermally activated dislocation emission in high-temperature ferroelectric ceramics is investigated through an assumption of thermal stability and a novel analytical method. The stress intensity factor (SIF) arising from domain switching is evaluated by using a Green's function method, and the critical applied electric field intensity factor (CAEFIF) for brittle fracture at room temperature is obtained. Besides, the lowest temperature for single dislocation emission before brittle fracture is also obtained by constructing an energy balance. The multi-scale analysis of facture toughness of the ferroelectric ceramics at high temperature is carried out. Through the analysis, the CAEFIF for crack extension is recalculated. The results show that the competition and interaction effects between dislocation emission and brittle fracture are very obvious. Besides, the higher critical activation temperature, the more columns of obstacles will be overcome. Additionally, the shielding effect arising from thermally activated dislocations is remarkable, thus, the brittle-ductile transition can promote the fracture toughness of high-temperature ferroelectric ceramics.     

Brittle-Ductile Transition of Ferroelectric Ceramics Induced by Thermally Activated Dislocation Emission

Thermally activated dislocation emission in high-temperature ferroelectric ceramics is investigated through an assumption of thermal stability and a novel analytical method. The stress intensity factor (SIF) arising from domain switching is evaluated by using a Green's function method, and the critical applied electric field intensity factor (CAEFIF) for brittle fracture at room temperature is obtained. Besides, the lowest temperature for single dislocation emission before brittle fracture is also obtained by constructing an energy balance. The multi-scale analysis of facture toughness of the ferroelectric ceramics at high temperature is carried out. Through the analysis, the CAEFIF for crack extension is recalculated. The results show that the competition and interaction effects between dislocation emission and brittle fracture are very obvious. Besides, the higher critical activation temperature, the more columns of obstacles will be overcome. Additionally, the shielding effect arising from thermally activated dislocations is remarkable, thus, the brittle-ductile transition can promote the fracture toughness of high-temperature ferroelectric ceramics.     

Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal

By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.     

Dislocation Plasticity Effects on Interfacial Fracture

Analyses are reviewed where plastic flow in the vicinity of an interfacial crack is represented in terms of the nucleation and glide of discrete dislocations. Attention is confined to cracks along a metal-ceramic interface, with the ceramic idealized as being rigid. Both monotonic and fatigue loading are considered. The main focus is on the stress and deformation fields near the crack tip predicted by discrete dislocation plasticity, in comparison with those obtained from conventional continuum plasticity theory. The role that discrete dislocation plasticity can play in interpreting interface fracture properties in the presence of plastic flow is discussed.     

磁电弹性体中多条位错与Griffith裂纹

根据本征方程，研究磁电弹性体中若干平行螺型位错与Griffith裂纹的相互作用.结合Muskhelishvili方法和算子理论，得到磁电弹性体中由位错和裂纹所诱导的应力场、电场和磁场的解析解.数值算例表明：在裂纹的端点及位错点上仍然存在应力的奇异性，离位错点越远处广义力越小，结论与已有的结果相符，证明了结论的正确性.当位错点与裂纹端点距离越近时，裂纹与位错间的应力场越小，并逐渐趋近于零.     

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interfacial blunt crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the blunt crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increase of emission angle and curvature radius of blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.     

Atomistic simulations to study crack tip behaviour in single crystal of bcc niobium and hcp zirconium

In this article, molecular dynamics based simulations were carried out to study the fracture toughness of single crystals of niobium (Nb) and zirconium (Zr). Separate set of simulations were performed with different orientations of crack plane in Nb and Zr. In each case, efforts were made to align the crack front with principal planes of corresponding crystal structure, that was bcc for Nb and hcp for Zr. Deformation in single crystal of Nb and Zr was governed either by twinning or emergence of dislocations from the crack tip and surfaces. The deformation mechanism in single crystal of Nb and Zr also helps in governing the overall toughness of the material, while deforming via twinning leads to higher change in the crack length, whereas dislocations emerging from the crack tip blunts the opening and improves the toughness.     

Unstable Fracture Behavior of Rubber Toughened Poly(Styrene-co-Acrylonitrile)

A linear elastic fracture mechanics (LEFM) approach was used to study fracture characteristics of ABS materials. The effects of crack (ligament) length and rubber content on the microscopic deformations taking place at the front of crack tip and in the bulk of the specimens were investigated. The results of fractography studies showed that, in addition to rubber content, the microscopic deformations are influenced by crack length. For some materials this manifests itself as a change in macroscopic response. The ligament length dependent behavior was increased for the samples with higher rubber contents. The results also showed that, although the elastic behavior with unstable crack growth is the dominant micromechanism of deformation, stable crack propagation still occurred in some compositions. All the fracture parameters, including fracture toughness, fracture energy, plastic zone size, and crack tip opening, increased with rubber content. The changes in microscopic and, as a consequence, in the macroscopic deformation behavior of a given specimen with ligament length were attributed to changes in yield stress of the sample and maximum stress on the ligament.     

Screw dislocations interacting with two asymmetrical interfacial cracks emanating from an elliptical hole

The interaction between screw dislocations and two asymmetrical interfacial cracks emanating from an elliptic hole under loads at infinity is studied. The closed-form solution is derived for complex potentials. The stress intensity factor and the critical applied stress for the dislocation emission are also calculated. In the limiting cases, well-known results can be obtained from the present solutions. Moreover, new exact solutions for a screw dislocation interacting with some complicated cracks are derived. The results show that the shielding effect increases with the increase in the length of the other cracks and the minor semi axis, but decreases with the increase of dislocation azimuth. The repulsion acting on the dislocation from the other phase and the other crack extend in the horizontal direction, which makes the dislocation emission at the crack tip take place more easily, but the minor semi axis of the elliptical hole extending in the vertical direction makes it more difficult.     

体心立方金属钽Ⅱ型裂纹尖端缺陷萌生的多尺度分析

本文采用多尺度准连续介质法(quasi-continuum method, QC)模拟体心立方(body-centered-cubic, bcc)金属钽(Ta)Ⅱ型裂纹尖端位错的形核与发射过程,获得位错发射位置与应力强度因子关系曲线,分析裂纹尖端缺陷萌生过程,研究全位错分解以及扩展位错形成机理. 位错活动在不同阶段表现出不一致的特征,新位错的发射对于位错运动具有促进作用. 研究表明,裂纹扩展初始阶段首先萌生点缺陷,点缺陷随着加载强度增加会萌生新的点缺陷,点缺陷最终运动到边界,导致Ⅱ型断裂破坏. 在全位错发射之前有不全位错的形核与发射表明全位错的分解分步进行,从势能曲线上来看,也就是两个极小值点的形成机理不同. 关键词： 多尺度 准连续介质法 Ⅱ型裂纹 扩展位错     

不同对称性下晶界结构演化及微观机理的晶体相场法研究

采用晶体相场法研究了单轴拉伸下三角相双晶变形过程及机理, 并重点分析了小角对称与非对称晶界和大角对称与非对称晶界在变形过程中的演化及微观机理, 变形过程中应力方向与初始晶界方向平行. 结果表明, 小角对称晶界由柏氏矢量夹角呈60°的两种刃型位错组成, 变形过程中不同类型的位错运动方向相反, 并各自与另一晶界上同一类型位错相互吸引以致部分位错发生湮没; 小角非对称晶界上的位错类型单一, 在应力作用下先沿水平方向攀移, 后各自分解成柏氏矢量约呈120°的两位错, 并通过位错运动和湮没最终形成理想单晶; 大角晶界在应力的作用下先保持水平状态而后锯齿化并发射位错, 伴随着位错运动和湮没, 最终大角非对称晶界发生分解, 而大角对称晶界则重新平直化, 表明大角对称晶界比大角非对称晶界更稳定, 这与实验和分子动力学模拟结果一致. 关键词： 晶体相场 双晶 晶界 对称性     

Evolution of the concentration of point defects at the tip of a crack

The evolution of the distribution of interstitial impurity atoms in the plastic zone around the tip of a tension crack is analyzed. The transport of point defects is determined by: 1) the hydrostatic component of the elastic stress at the crack tip, created by the superposition of the elastic fields of the crack and dislocations; 2) the elastic field of moving dislocations (“sweeping out” of interstitial impurity atoms); 3) the dislocation-driven transport of point defects present in the dislocation cores. The contributions of each mechanism of transport of point defects to the crack tip are calculated over the entire time from the start of loading of a sample containing a crack until an equilibrium distribution of plastic deformation is established after the cessation of loading. Numerical calculations are carried out for interstitial hydrogen atoms dissolved in an α-Fe crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1580–1585 (September 1997)     

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks

The interaction between a screw dislocation and an interfacial cruciform crack and collinear linear cracks under loads at infinity was investigated. General solutions of complex potentials to this problem were derived by using complex potential theory. As illustrative examples, the closed form solution for a screw dislocation interacting with an interfacial cruciform crack and a linear crack is obtained. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The results show that the shielding effect increases with the increase of the shear modulus and the distance between the two cracks, but it decreases with the increase of dislocation azimuth and the distance between the dislocation and the cruciform crack tip. The critical loads at infinity for dislocation emission increase with the increment of the emission angle, the distance the two cracks and the vertical length of the cruciform crack.     

The use of Electronic Speckle Pattern Interferometry (ESPI) in the crack propagation analysis of epoxy resins

The ESPI (electronic speckle pattern interferometry) technique at high magnification levels is demonstrated to be of considerable value in interpreting the fracture behaviour of epoxy resins. The fracture toughness of powder coating system at different thicknesses has been measured using a TDCB (tapered double cantilever beam) technique and the deformation zone at the tip of the moving crack monitored. Initial indications are that a mechanistic changeover occurs at a critical bond (coating) thickness and that this is synonymous with the occurence of a fracture toughness maximum, which in turn is associated with a deformation zone of specific diameter.     

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.     

Crack tip plasticity in dynamic fracture

The mechanics of crack tip plasticity in dynamic crack growth is considered as it influences two modes of dynamic fracture—cleavage and micro-void nucleation, growth and coalescence. The subject is approached using both the continuum theory of visco-plasticity and dislocation dynamics. The viewpoint underlying each approach is that the crack is traveling through material with a relatively high density of pre-existing mobile dislocations. Analysis is directed at discovering the role played by the associated rate-dependent plasticity in establishing conditions for dynamic crack propagation. The theory is far from complete, but the contents of the paper should serve to aid understanding of basic material fracture phenomena, such as cleavability and the ductile-brittle transition, as well as provide a background for the engineering theory of dynamic fracture.