Elastic behaviour of an edge dislocation near a sharp crack emanating from a semi-elliptical blunt crack

The interaction between an edge dislocation and a crack emanating from a semi-elliptic hole is dealt with. Utilizing the complex variable method, closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the edge dislocation are also calculated. The influence of the morphology of the blunt crack and the position of the edge dislocation on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases acutely when the dislocation approaches the tip of the crack. The effect of the morphology of the blunt crack on the stress intensity factor of the crack and the image force is very significant.     

Elastic behaviour of a wedge sharp crack emanating from a disclination dipole near a semi-elliptical blunt crack

The interaction between a wedge disclination dipole and a crack emanating from a semi-elliptic hole is investigated. Utilising the complex variable method, the closed form solutions are derived for complex potentials and stress fields. The stress intensity factor at the tip of the crack and the image force acting on the disclination dipole center are also calculated. The influence of the morphology of the blunt crack and the position of the disclination dipole on the shielding effect to the crack and the image force is examined in detail. The results indicate that the shielding or anti-shielding effect to the stress intensity factor increases when the wedge disclination dipole approaches the tip of the crack. The effects of the morphology of the blunt crack on the stress intensity factor of the crack and the image force are very significant.     

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.     

Shielding effect of a nano-circular inclusion acting on semi-infinite wedge cracks

The model of a screw dislocation near a semi-infinite wedge crack tip inside a nano-circular inclusion is proposed to investigate the shielding effect of nano inclusions acting on cracks. Utilizing the complex function method, the closed-form solutions of the stress fields in the matrix and the inclusion region are derived. The stress intensity factor, the image force, as well as the critical loads for dislocation emission are discussed in detail. The results show that the nano inclusion not only enhances the shielding effect exerted by the dislocation, but also provides a shielding effect itself. Moreover, dislocations may be trapped in the nano inclusion even if the matrix is softer than the inclusion. This helps the dislocation shield crack, and reduces the dislocation density within the matrix.     

The solution of a wedge disclination dipole interacting with an annular inclusion and the force acting on the disclination dipole

The interaction between a wedge disclination dipole and an elastic annular inclusion is investigated. Utilizing the Muskhelishvili complex variable method, the explicit series form solutions of the complex potentials in the matrix and the inclusion region are derived. The image force acting on the disclination dipole centre is also calculated. The influence of the location of the disclination dipole and the thickness of the annular inclusion as well as the elastic dissimilarity of materials upon the equilibrium position of the disclination dipole is discussed in detail. The results show that a stable equilibrium point of the disclination dipole near the inclusion is found for certain combinations of material constant. Moreover, the force on the disclination dipole is strongly affected by the position of the disclination dipole and the thickness of annular inclusion. The repulsion force increases （or the attraction force reduces） with the increase of the thickness of the annular inclusion. An appropriate critical value of the thickness of the annular inclusion may be found to change the direction of the force on the disclination dipole. The present solutions include previous results as special eases.     

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.     

一维六方准晶中螺形位错与楔形裂纹的相互作用

采用保角映射方法和扰动技巧,研究了一维六方准晶中螺形位错和半无限楔形裂纹的相互作用. 讨论了位错的位置和楔形角对作用在位错上的力的影响,得到了应力强度因子和作用在 位错上的力的解析解.此外,还详细地讨论了位错对裂纹的影响.当楔形角参数λ=1/2时, 半无限楔形裂纹退化成半无限尖裂纹,相应的结果 可以作为特殊情况而直接得到.     

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.     

Effect of cooperative nanograin boundary sliding and migration on dislocation emission from a blunt nanocrack tip in nanocrystalline materials

Theoretical model is suggested that describes the effects of the cooperative nanograin boundary sliding and stress-driven nanograin boundary migration (CNGBSM) process on the lattice dislocation emission from an elliptically blunt nanocrack tip in deformed nanocrystalline materials. Within the model, CNGBSM deformation near the tip of growing nanocrack carries plastic flow, produces two dipoles of disclination defects and creates high local stresses in nanocrystalline materials. By using the complex variable method, the complex form expression of dislocation force is derived, and critical stress intensity factors for the first lattice dislocation emission are obtained under mode I and mode II loading conditions, respectively. The combined effects of the geometric features and strengths of CNGBSM deformation, nanocrack blunting and length on critical SIFs for dislocation emission depend upon nanograin size and material parameters in a typical situation where nanocrack blunting and growth processes are controlled by dislocation emission from nanocrack tips. It is theoretically shown that the cooperative CNGBSM deformation and nanocrack blunting have great influence on dislocation emission from blunt nanocrack tip.     

Screening of the elastic field of disclinations by a dislocation ensemble

A self-consistent dynamics of a dislocation ensemble in the disclination field is analyzed within the kinetic approach. The effective Airy stress functions for the wedge disclination and the disclination dipole with due regard for the screening effect of the system of distributed dislocation charges are determined. The coordinate dependences of the stress tensor components and dislocation charge density for the screened disclination systems are found. The elastic energies of the screened disclination systems are calculated.     

Effect of plastic deformation at the crack tip in a crystal on the direction of the tip growth under a mixed load

Evolution of plastic deformation at the tip of a wedge-shaped crack in a crystal under planar strain (modes I and II) was calculated for different cleavage planes, easy-slip systems, angles at the wedge tip, and ratios of the external extension and shear loads. Time distributions are obtained for the plastic deformation, the effective shear stress, the stress intensity factor, and the crack growth direction under monotonic load of the crystal up to a specified limit and further relaxation to establishment of equilibrium distributions under a constant external load. Numerical calculations were performed for an α-Fe crystal.     

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.     

Effect of electric current on the migration of hydrogen interstitial atoms in the region of a crack tip in a crystal

The effect of a constant electric current on the migration of interstitial atoms dissolved in a crystal in the region of a tensile crack tip is estimated. The calculation takes into account plastic deformation that is produced in the vicinity of the crack tip in the loaded sample by dislocation motion in active slip planes of the crystal under the action of mechanically and electrically induced shear stresses, Joule heat release, the Thomson effect, and ponderomotive forces and allows for the effect of gas exchange near the crack edges on the evolution of the distribution of interstitial impurity atoms. The time dependence of the stress intensity factor is found for both the cases of the presence and absence of a constant electric current near the crack tip. Numerical calculations are performed for an α-Fe crystal.     

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.     

The interaction of two collinear cracks in a rectangular superconductor slab under an electromagnetic force

The interaction of two collinear cracks is obtained for a type-II superconducting under electromagnetic force. Fracture analysis is performed by means of finite element method and the magnetic behavior of superconductor is described by the critical-state Bean model. The stress intensity factors at the crack tips can be obtained and discussed for decreasing field after zero-field cooling. It is revealed that the stress intensity factor decreases as applied field increases. The crack-tip stress intensity factors decrease when the distance between the two collinear cracks increases and the superconductors with smaller crack has more remarkable shielding effect than those with larger cracks.     

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.     

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：     

A model of a belt chamber cracking based on crack profiles calculations

Abstract

The problem of a Belt chamber matrix cracking is presented. The influence of crack surface quality on the effective values of near crack tip stress is discussed. It is shown that under working conditions of the vessel, the existing shear friction between upper and lower crack surfaces caused by crack surface roughness can prevent the crack surface sliding displacement. Therefore, the control variable for matrix cracking is the value of stress intensity factor K_I corresponding to normal node of loading only. The calculations are performed by finite element method within the range of linear elastic fracture mechanics.     

Dynamic optical visualization on the interaction between propagating crack and stationary crack

Dynamic interactions between the propagating crack and the static crack in PMMA material are studied by combining high-speed Schardin camera with optical caustic method. A series of dynamic optical bifocal patterns (the specimen-focused image and the off-focused image) around the propagating crack tip and the static crack tip are recorded for PMMA thin strip which contains two collinear-edge-cracks subjected to tensile loading, the variations of the caustic diameter and the distortion of the caustic shape are revealed due to the influence of local stress singularity at the crack tip. Interactions between the moving crack and the static crack are analyzed by means of the evolution of dynamic fracture parameters. The influence of crack interaction on fracture parameters is discussed based on both a K-dominance assumption and a higher order transient crack-tip expansion. These results will be useful to the evaluation of dynamic properties and the design of structures in the cracked polymer material.     

Simulated caustic patterns for dynamic crack growth in a plate based on a three-dimensional numerical analysis

The rapid growth of a through-the-thickness crack in a nominally elastic plate under Mode I conditions is considered, with emphasis on the three-dimensional aspects of the elastodynamic crack growth process. For points near the crack edge, the assumptions on stress state consistent with plane stress analysis are not valid, and the possibility of an inertial effect associated with rapid lateral contraction must be considered. The steady crack growth process is analyzed here by means of the finite element method, and the degree to which the local fields are described by plane stress analysis is established. In addition, synthetic shadow spot patterns are generated from the numerical three-dimensional solutions. The inferred values of stress intensity factor are compared with the values of the corresponding plane stress dynamic stress intensity factor.