Micromechanical simulations of microstructure-sensitive Stage I fatigue crack growth

Simulations of dislocation dynamics at the tip of a Stage I crack are performed, taking into account the influence of the normal stress on the friction of the crack flanks and on the condition for dislocation emission at the crack tip. The interactions of the emitted dislocations with microstructural obstacles are analysed. The repeated decelerations and sometimes arrests that characterize Stage I crack growth are properly described by the model, and the differences in Stage I kinetics observed in reversed torsion and push–pull are analysed in terms of crack tip–grain boundary interactions.     

Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids

A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.     

A Griffith crack shielded by a dislocation pile-up

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.     

The Interaction between a Piezoelectric Screw Dislocation Dipole and an Elliptic Blunt Crack in Elliptical Inhomogeneity

The interaction problem of a piezoelectric screw dislocation dipole with a confocal elliptic blunt crack in elliptical inhomogeneity subjected to remote anti-plane stress field and in-plane electric field is investigated by using the complex method of elasticity. The exact closed-form solutions of a series of quantities, such as singularity stress field, image force and image torque acting on the center of screw dislocation dipole, stress intensity factor and electric displacement intensity factor of crack tip, energy release rate, and generalized strain energy density are obtained. Then the influence laws of remote load, the dip angle of dislocation dipole, the size of blunt crack, and the material constants on the quantities are analyzed. The numerical results show that the image force, image torque, stress intensity factor, and electric displacement intensity factor make periodic variation as the dip angle of dislocation dipole; the energy release rate of crack tip is negative when subjected to pure electric field, however, it can be positive or negative when subjected to the combined action of mechanical field and electric field; the sharp crack is not easy to expand in some combined action of mechanical field and electric field.     

Screw dislocation in the two-phase isotropic thin film of an interfacial crack

The screw dislocation in the two-phase isotropic thin film of an interfacial crack has been investigated. The stress field, stress intensity factors at the crack tip and for dislocation emission, crack extension force, strain energy and the image force on the dislocation are obtained and found to be related to the thickness and effective shear modulus. The effect of size on fracture is pronounced when the thickness is smaller than the distance between dislocation and crack tip by a factor of 1000. The effect of the second phase on fracture is pronounced when μ⁽²⁾/μ⁽¹⁾ is in the range from 0.01 to 100. Newton's third law is proved to be valid for any thickness and shear modulus ratio. This result can be reduced to three special cases.     

The Stress Intensity Factor of an Edge Dislocation Near an Elliptically Blunted Crack Tip

The stress field around the tip of an elliptically blunted crack induced by an edge dislocation has been obtained in closed form, from which the mode I and mode II stress intensity factors induced by the edge dislocation are obtained. The solutions apply to the edge dislocation either emitted from crack-tip surface or originated elsewhere, and for the dislocation located anywhere around the crack tip. The effects of the crack length, the crack-tip bluntness, the origination and position of the dislocation on the stress intensity factors are examined.     

A Zener–Stroh crack at the interface of a thin film bonded to a substrate

A Zener–Stroh crack can nucleate at the interface of a multi-layered structure when a dislocation pileup is stopped by the interface which works as an obstacle. During the entire fracture procedure of a crack, Zener–Stroh crack mechanism controls the initial stage, or the first phase of crack initiation and propagation. In our current research, stress investigation on a Zener–Stroh crack initiated at the interface of a thin film bonded to a half plane substrate has been carried out. With the application of dislocation-based fracture mechanics, the micro crack is simulated by the distributed dislocations along the crack line. To eliminate the contradictory oscillation phenomenon for the stress field near the interfacial crack tip, a contact zone behind the crack tip is introduced. The physical problem is thus formulated into a set of non-linear singular integral equations. Through careful examination of the crack singularities at the crack tips for different configurations, the formulated integral equations are solved with numerical methods developed in our research. The contact zone length, the stress fields near the crack tip and the stress intensity factors of the crack are evaluated accordingly. Numerical examples based on practical engineering structures are provided to discuss the influence of the key parameters, such as the thickness of the film, and the Dundurs constants, on the fracture behaviour of the crack.     

A thermodynamic approach to the interaction between dislocation and crack and its applications

By using a thermodynamic approach, the image force of the dislocation due to the semiinfinite crack in an infinite medium has been completed. If the influence of all the other force can be neglected, the screw dislocation subjected to the crack will approach the crack surface along the direction of the resultant force. The stress intensity factors at the crack tip due to the dislocation dipole are also included. This can be applied to the phase transformation toughening in zirconia.     

The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.     

螺型位错偶极子与圆形夹杂界面裂纹的弹性干涉

该文研究了螺型位错偶极子和圆形夹杂界面裂纹的弹性干涉作用。利用复变函数方法,得到了该问题的复势函数以及应力场的封闭形式解答。求出了裂纹尖端的应力强度因子以及作用在螺型位错偶极子中心的像力和像力偶矩,并分析了位错偶极子对应力强度因子的影响及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。研究结果表明:位错偶极子对应力强度因子具有很强的屏蔽或反屏蔽效应;硬夹杂排斥位错偶极子,而裂纹吸引位错偶极子,在一定条件下,位错偶极子在裂纹附近出现一个平衡位置;当裂纹的长度和材料剪切模量比达到临界值时,可以改变偶极子和界面之间的干涉机理。同时,裂纹长度对位错偶极子中心像力偶矩也有很大的影响。     

Distribution of dislocations at a mode I crack tip and their shielding effect

Distribution of dislocations at a finite mode I crack tip is formulated. Closed form solutions for the dislocation distribution function, the dislocation-free zone (DFZ), the local stress intensity factor and the crack tip stress field are obtained. The dislocation distribution has similar features to a mode III crack model. Under a given applied stress, there may exist different configurations of plastic zone and DFZ. Crack tip shielding by dislocations depends on both applied stresses and the configuration.     

Shielding and amplification of a penny-shape crack due to the presence of dislocations

The interaction between a penny-shape crack and a dislocation in crystalline materials is investigated within the framework of dislocation dynamics. The long-range and singular stress field resulting from the crack is determined by modeling the crack as continuous distribution of dislocation loops. This distribution is determined by satisfying the traction boundary condition at the crack face, resulting into a singular integral equation of the first kind that is solved numerically. This crack model is integrated with the dislocation dynamics simulation technique to yield the stress field of the combine system of crack and different types of dislocations situated at different positions in a three dimensional space. The integrated system is then used to investigate the dislocation behavior and its influence on the crack opening displacement and the characteristic of the stress field near the crack tip. It is shown that, depending on the relative position of the dislocation and its character, the dislocation may result in reduction in the stress amplitude at the crack tip and in some cases in closure of the crack tip. These analyses yield shielding and amplification zones near the crack providing an insight of the dislocation influence on the crack. The full dislocation dynamic analysis reveals the nature of the crack dislocation interaction and the manner in which the dislocation morphology changes as it is attracted to the crack surfaces, as well as the changes it causes to the crack profile.     

Transient dislocation emission from a crack tip in an anisotropic elastic material

The emission of a dislocation with a general Burgers vector from the tip of a stationary semi-infinite crack in an anisotropic elastic material is examined. The dislocation is assumed to leave the crack tip along the crack extension plane at constant speed. Explicit expressions for the transient shielding stress intensity factors at the crack tip and the drag forces on the dislocations are derived. Numerical results for a class of cubic materials and two hexagonal crystals, zinc and cobalt, are given. Dislocation emission under plane stress wave loading is discussed.     

In-situ Observation of Initiation and Propagation of Cleavage Microcrack in TiAl

Nucleating and propagating of nancrack formed in dislocation free zone (DFZ) for the brittle TiAl alloy has been studied through in-situ tensile test in TEM and analyzed using microfracture mechanics. The resufts show that a lot of dislocations can be emitted from a crack tip when the applied stress intensity Kla i5 larger than the stress intensity for dislocatin emission Kle=1.4 M Pa·m1/2 and a dislocation free zone, which smetimes is a close zone, can form after reaching equilibrium. The DFZ is a elastic zone with large strain and then the stress in the DFZmight equal to the cohesive strength σth because the crack tip is still sharp. When Kla is larger than the stress intensity for nanocrack nucleation Kli =2.4 M Pa·m1/2, the stress within a certain range in the DFZ would equal to σth and then a nanocrack initiates in the DFZ or sometimes at the notch tip. The nanocrack formed in the DFZ is stable and can propagate a small distance in cleavage mode through multiplication and movement of dislocation in the plastic zone, during keeping constant displacement. Increasing Kla can make the crack stably propagate continuously or discontinuously and it means that the stre5s intensity for crack propagation, Klp, is larger than Kli. Therefre, Kle 相似文献   

The penny crack beneath the surface of a half-space: with application to the blister test

The crack tip stress intensities are found for a penny shaped crack lying beneath the free surface of a half-space, and parallel with it. This is done by employing a novel distributed dislocation approach using axi-symmetric Somigliana dislocations as the kernel of an integral equation, and provides a precise solution at the expense of little computing cost. A comparison is made with the crack tip stress intensity factors for a simple plane crack, and predictions are made for the preferred crack extension direction.     

The interaction between a screw dislocation and a nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface

The interaction between a screw dislocation and a circular nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface is investigated. By using Riemann-Schwartz’s symmetry principle integrated with the analysis of singularity of complex functions and the conformal mapping technique, the analytical expressions of the stress field in both the circular nano-inhomogeneity and the infinite matrix, the image force acting on the screw dislocation and the stress intensity factor at the crack tip are obtained. The influence of elastic mismatch of materials, inhomogeneity size, interface stress, wedge crack opening angle and the relative location of dislocation on the image force and on the equilibrium position of the screw dislocation and the shielding effect of the screw dislocation are discussed in detail. The results show that interface stress has a significant impact on the movement of dislocations near the interface, and the effect of interface stress enhances when the inhomogeneity radius decreases. With the decrease in the wedge crack opening angle, the influence of interface stress on the movement of the screw dislocation and on the SIF enhances. With the increment of the relative shear modulus, the influence of interface stress weakens with the screw dislocation locating in the inhomogeneity and strengthens with the screw dislocation locating in the matrix. When the screw dislocation is located in the inhomogeneity, the positive (negative) interface stress increases (decreases) the shielding effect, while this phenomenon is opposite when the screw dislocation locates in the matrix.     

Elastic interaction between screw dislocations and the internal crack near a free surface

The elastic interaction between screw dislocation and the internal crack near a free surface has been investigated. The stress intensity factor at the crack tip, crack extension force, the image force on the dislocation are affected by the free surface. The number and nature of dislocations, m, inside the crack also play an important role in fracture. In order to understand the plastic zone, the zero-force points of dislocation along the x-axis are involved. The dislocation emitted from the right-hand crack tip is enhanced by positive m and reduced by negative m. On the other hand, if the internal crack is closer to the free surface, a dislocation generated from the right-hand crack tip is easier for negative m and more difficult for positive m. However, the role of m on the dislocation emission for the left-hand crack tip is opposite to that for the right-hand crack tip. Finally, three special cases can be obtained from our results. (1) The interaction between a dislocation and a surface crack; (2) the interaction between a dislocation and an internal crack; (3) the interaction between two dislocations.     

Electro-elastic stress analysis for a wedge-shaped crack interacting with a screw dislocation in piezoelectric solid

The electro-elastic stress investigation on the interaction problem of a screw dislocation near the tip of a semi-infinite wedge-shaped crack in piezoelectric material has been carried out. Explicit closed-form analytical solutions are obtained for the stress intensity factor (SIF) and the electric displacement intensity factor (EDIF) of the crack, as well as the force on dislocation. The derivation is based on the conformal mapping method and the perturbation technique. The dislocation has Burger's vector normal to the isotropic basal plane, with a line force and a line charge being applied at the core of the dislocation. The influence of the location and the wedge angle of the crack on the image force of the dislocation has been discussed in detail. At the same time the effect of the dislocation on the crack behavior has been also examined under different configurations. Two types of PZT materials are used to numerically illustrate the influences of the wedge angle and the location of the dislocation on the image force and the crack intensities. Results obtained in the current study can be fully reduced to various special cases available in the literatures.     

Comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane

A comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane was made. Four cases of single crystalline material, sliding grain boundary, perfectly bonded interface, and sliding interface were considered. The stress intensity factors arising from edge and screw dislocations and their image forces for the above four cases were compared. The stress intensity factor at a crack tip along the perfectly bonded interface arising from screw dislocation can be obtained from that in a single crystalline material if the shear modulus in the single crystalline material is replaced by the harmonic mean of both shear moduli in the bimaterial. The stress intensity factor at a crack tip along the sliding interface arising from edge dislocation in the bimaterial can be obtained from that along the sliding grain boundary in the single material if the μ/(1−ν) in the single material is substituted by the harmonic mean of μ/(1− ν) in the bimaterial where μ and ν are the shear modulus and Poisson's ratio, respectively. The solutions of screw dislocation near a crack along the sliding grain boundary and sliding interface are the same as that of screw dislocation and its mirror image. Generally, the effect of edge dislocation for perfectly bonded interface on the crack propagation is more pronounced than that for the sliding interface. The effect of edge dislocation on the crack propagation is mixed mode for the cases of perfectly bonded interface and single crystalline material, but mode I fracture for the cases of sliding interface and sliding grain boundary. All curves of Fx versus distance r from the dislocation at interface to the right-hand crack tip are similar to one another regardless of dislocation source for both sliding interface and perfectly bonded interface. The level of Fx for m=0 is larger than that for m=−1. This revised version was published online in August 2006 with corrections to the Cover Date.     

Micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in piezoelectric solids

A dislocation emission mechanism for micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in a piezoelectric solid is proposed in the present paper. For a rigid line inhomogeneity embedded in a piezoelectric matrix, dislocations of one sign are driven away from the tip due to high stress level, while the stationary dislocations of the opposite sign are left behind near the tip of the inhomogeneity. As a result, a micro-Zener–Stroh crack is initiated ahead of the line inhomogeneity. In the current study, a dislocation pileup mechanism for micro-crack initiation at the inhomogeneity tip is proposed. An interesting result is that the critical stress intensity factors for a line inhomogeneity perpendicular to the poling direction can be related to the fracture toughness of a conventional crack in the same material. Analytical solutions show that the critical plane shear stress intensity factor depends on the plane shear mechanical and displacement loadings, and the critical opening stress and electric displacement intensity factors depend on not only the mechanical and displacement loadings, but the electric field and displacement loadings as well.