Dislocation-crack interaction

In this paper, recent developments in the understanding of the dislocation-crack interaction and its relationship to the phenomena of crack tip deformation and fracture toughness are reviewed. An enhanced research activity in this area began with successful observations of the behavior of crack tip dislocations by various techniques, namely etch pits technique, X-ray topography and transmision electron microscopy. The advantages and limitations of these techniques are compared and the information obtained from these experiments are discussed. The results show that dislocations are emitted from a crack tip when the applied stress is sufficiently high. During crack propagation, dislocations are also generated from other bulk sources and the number of these dislocations relative to those from the crack tip may be an important parameter. The elastic theory of the interaction between dislocations and a crack is presented by considering the force on the dislocations. The theory is applied to derive a dislocation emission condition, which may be expressed in terms of a critical stress intensity factor. It is concluded that the dislocations emitted from a crack tip are repelled from the crack tip and this repulsive interaction is responsible for the formation of a dislocation-free zone. These dislocations shield the crack tip from the applied stress and hence contribute to an increase in the fracture toughness. The physical origin of the dislocation-free zone lies in the presence of a barrier to dislocation emission from the crack tip. One of the barriers to dislocation emission is the image stress. With the dislocation-free zone, the crack tip can maintain a finite stress intensity factor following crack tip deformation. The lattice theories of dislocation-crack interaction indicate that the results are consistent with those of the continuum theory.     

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.     

脆性断裂统计理论

本文试图用统计方法,将金属脆性断裂的微观过程与宏观过程结合起来,把断裂理论建立于微裂纹发展动力学的统计基础上。脆性断裂实质上是在小的范性变形过程中微裂纹成核长大的非平衡统计过程和单个主裂纹的传播过程。本文导出了描述这种非平衡统计过程的微分积分方程,并从位错机理出发研究了微裂纹动力学,从而解出了微裂纹的分布函数,求出了金属试样的断裂几率,进而导出了延伸率、断裂强度、范性功、裂纹扩展力、断裂韧性、临界裂纹长度、范性-脆性转变温度以及它们的统计偏差与其它有关物理量之间的函数关系。 关键词：     

Characterization of the fracture toughness of micro-sized tungsten single crystal notched specimens

Fracture experiments using micrometer-sized notched cantilevers were conducted to investigate the possibility of determining fracture mechanical parameters for the semi-brittle material tungsten. The experiments were also used to improve the understanding of semi-brittle fracture processes for which single crystalline tungsten serves as a model material. Due to the large plastic zone in relation to the micrometer sample size, linear elastic fracture mechanics is inapplicable and elastic-plastic fracture mechanics has to be applied. Conditional fracture toughness values J _Q were calculated from corrected force vs. displacement diagrams. Crack growth was accessible by direct observation of in-situ experiments as well as with the help of unloading compliances. As a further tool, fracture toughness can be determined via crack tip opening displacement. The micro samples behave more ductile and exhibit higher fracture toughness values compared to macro-sized single crystals and fail by stable crack propagation.     

Fracture of brittle metallic glasses: brittleness or plasticity

We report a brittle Mg-based bulk metallic glass which approaches the ideal brittle behavior. However, a dimple structure is observed at the fracture surface by high resolution scanning electron microscopy, indicating some type of "ductile" fracture mechanism in this very brittle glass. We also show, from the available data, a clear correlation between the fracture toughness and plastic process zone size for various glasses. The results indicate that the fracture in brittle metallic glassy materials might also proceed through the local softening mechanism but at different length scales.     

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.     

Nanoscale periodic morphologies on the fracture surface of brittle metallic glasses

Out-of-plane, nanoscale periodic corrugations are observed in the dynamic fracture surface of brittle bulk metallic glasses with fracture toughness approaching that of silica glasses. A model based on the meniscus instability and plastic zone theory is used to explain such dynamic crack instability. The results indicate that the local softening mechanism in the fracture is an essential ingredient for controlling the formation of the unique corrugations, and might provide a new insight into the origin of fracture surface roughening in brittle materials.     

Atomistic scale fracture behaviours in hierarchically nanotwinned metals

In the present study, a series of large-scale molecular dynamics simulations have been performed to investigate the atomistic scale fracture behaviours along the boundaries of primary twins in Cu with hierarchically nanotwinned structures (HTS), and compare their fracture behaviours with those in monolithic twins. The results indicate that crack propagation along [1?1?2] on the twin plane in monolithic nanotwins is brittle cleavage and fracture, resulting in low crack resistance and fracture toughness. However, the crack resistance along the boundaries of primary twins in HTS is much higher, and a smaller spacing of secondary twins (λ ₂) leads to even higher fracture toughness. With large λ ₂, the crack growth is achieved by void nucleation, growth and coalescence. However, considerable plastic deformation and enhanced fracture toughness in HTS could be achieved by the crack blunting and by the extensive dislocation accommodation ahead of the crack tip when λ ₂ is small.     

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.     

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.     

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.     

Crack Tip Opening Angle as a Fracture Resistance Parameter to Describe Ductile Crack Extension and Arrest in Steel Pipes under Service Pressure

The angle between two element sides representing the crack tip is defined as the crack tip opening angle (CTOA). Its critical value is used as a criterion of fracture resistance for characterizing stable tearing in thin metallic materials. Various methods are used for determination of the CTOA. Optical microscopy is one of the most common methods as well as fitting of experimental load-displacement diagrams by the finite element method (DIC). Additionally, analytical analysis using the experimental load-displacement curve method (SSM) derived from the plastic hinge model of deflection in three-point bending of a ductile specimen is applied. This approach assumes a constant rotation centre distance. Values of CTOA for API 5L X65 pipe steel found by three methods—DIC, CNM, and SSM—are given. Values of CTOA given by these three methods are similar and close to 20°. A discussion on the different parameters used to characterize the fracture resistance of running cracks in a pipe under service pressure is presented. The energy of fracture at impact determined by Charpy or drop-weight tear test (DWTT) tests and the critical J energy parameter are considered as well as the yield locus after damage, cohesive zone energy, and CTOA is another approach. One notes that CTOA is assumed to be constant during stable crack extension and decreases linearly with crack length during the instable and primary phase. A numerical technique to describe a ductile running crack using the node release technique and using CTOA as the fracture resistance criterion is presented. This method is compared with three different two-curve methods (TCMs): the Battelle, high strength line pipe (HLP), and HLP-Sumitomo methods. The Batelle TCM, as the oldest method, based on Charpy energy, gives a strongly conservative prediction. Predictions by the CTOA method are close to those obtained by the HLP-Sumitomo one.     

A mathematical model of Panin’s prefracture zones and stability of subcritical cracks

Basic concept underlying Griffith’s theory of fracture of solids was that, similar to liquids, solids possess surface energy and, in order to propagate a crack by increasing its surface area, the corresponding surface energy must be compensated through the externally added or internally released energy. This assumption works well for brittle solids, but is not sufficient for quasi-brittle and ductile solids. Some new forms of energy components must be incorporated into the energy balance equation, from which the input of energy needed to propagate the crack and subsequently the stress at the onset of fracture can be determined. The additional energy that significantly dominates over the surface energy is the irreversible energy dissipated by the way of the plastic strains that precede the leading edge of a moving crack. For stationary cracks the additional terms within the energy balance equation were introduced by Irwin and Orowan. An extension of these concepts is found in the experimental work of V. Panin, who has shown that the irreversible deformation is primarily confined to the prefracture zones associated with a stationary or a slowly growing crack. The present study is based on the structured cohesive crack model equipped with the “unit step growth” or “fracture quantum”. This model is capable to encompass all the essential issues such as stability of subcritical cracks, quantization of the fracture process and fractal geometry of crack surfaces, and incorporate them into one consistent theoretical representation.     

How fast can cracks move? A research adventure in materials failure using millions of atoms and big computers

During the last decade, we have been simulating the dynamic failure of brittle and ductile solids at the atomic level using some of the world's fastest computers. Computer experiments encompassing crack dynamics in brittle fracture, crack blunting in ductile failure, and multi-dislocation entanglement in work-hardening are some examples and have given new and exciting insights into the failure processes of solids. Our presentation begins at an introduction level where basic concepts are presented before their application is needed for the understanding of specific phenomena. The story is primarily based on our past experiences, and our goal is to give the reader a fundamental appreciation for how materials fail.     

Glass breaks like metal,but at the nanometer scale

We report in situ atomic force microscopy experiments which reveal the presence of nanoscale damage cavities ahead of a stress-corrosion crack tip in glass. Their presence might explain the departure from linear elasticity observed in the vicinity of a crack tip in glass. Such a ductile fracture mechanism, widely observed in the case of metallic materials at the micrometer scale, might be also at the origin of the striking similarity of the morphologies of fracture surfaces of glass and metallic alloys at different length scales.     

Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group 10,10

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy. By developing the proposed generalized cohesive force model, the plastic deformation of crack in point group 10, 10 decagonal quasicrystals is analysed strictly and systematically. The crack tip opening displacement （CTOD） and the size of the plastic zone around the crack tip are determined exactly. The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material. In addition, the present work may provide a way for the plastic analysis of quasicrystals.     

On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate

Elastic–plastic stress analysis has been carried out for the plastic zone size and crack tip opening displacement of a sub-interface crack with small scale yielding. In our study, the shape of plastic zone is assumed as a long, slim strip at both crack tips. In the plastic zone, both normal stress and shear stress exist and are considered due to the bi-material interface. The values of the plastic zone size, normal stress and shear stress are determined by satisfying the conditions where both Modes I and II stress intensity factors vanish and Von Mises yield criterion is met. In the present paper, the sub-interface crack is simulated by continuously distributed dislocations which will result in singular integral equations. Those singular integral equations can be solved by reducing them to a set of linear equations. The values of the plastic zone size and crack tip opening displacement are obtained through an iterative procedure. Finally, the effect of normalized loading, normalized crack depth (distance to the interface) and Dundurs’ parameters on the normalized plastic zone size and the normalized crack tip opening displacement is discussed.     

金属穿晶脆性断裂统计理论

讨论了金属穿晶脆性断裂统计理论.根据穿晶裂纹和晶界作用的界面能模型及断裂非平衡统计理论框架,推导出了裂纹扩展速率、断裂强度、断裂韧性、脆性—韧性转变温度及其统计分布函数随晶粒尺度和界面能变化的公式. 关键词：