Edge dislocation interacting with a nonuniformly coated circular inclusion

This paper investigated the interaction between an edge dislocation and a nonuniformly coated circular inclusion. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with alternating technique, the solutions to plane elasticity problems for three dissimilar media are derived explicitly in a series form. For a limiting case when the thickness of the interphase layer is uniform, the derived analytical solutions of this paper are reduced to exactly the same results available in the literature. The image force acting on the dislocation is then determined by using the Peach–Koehler formula. It is found that the combination of material constants and nonuniformity of the interphase thickness will exert a significant influence on the dislocation force.     

A magnetoelectric screw dislocation interacting with a circular layered inclusion

Within the framework of the linear theory of magnetoelectroelasticity, the problem of a circular layered inclusion interacting with a generalized screw dislocation under remote anti-plane shear stress and in-plane magnetoelectric loads is investigated in this paper. The generalized dislocation can be located either in the matrix or in the circular layered inclusion. The layers are coaxial cylinders of annular cross-sections with arbitrary radii and different material properties. Using complex variable theory and the alternating technique, the solution of the present problem is expressed in terms of the solution of the corresponding homogeneous medium problem subjected to the same loading. Some numerical results are provided to investigate the influence of material combinations on the shear stress, electric field, magnetic and image force. These solutions can be used as Green's functions for the analysis of the corresponding magnetoelectric crack problem.     

Piezoelectric screw dislocations interacting with a circular inclusion with imperfect interface

The electroelastic coupling interaction between multiple screw dislocations and a circular inclusion with an imperfect interface in a piezoelectric solid is investigated. The appointed screw dislocation may be located either outside or inside the inclusion and is subjected to a line charge and a line force at the core. The analytic solutions of electroelastic fields are obtained by means of the complex-variable method. With the aid of the generalized Peach–Koehler formula, the explicit expressions of image forces exerted on the piezoelectric screw dislocations are derived. The motion and the equilibrium position of the appointed screw dislocation near the circular interface are discussed for variable parameters (interface imperfection, material electroelastic mismatch, and dislocation position), and the influence of the nearby parallel screw dislocations is also considered. It is found that the piezoelectric screw dislocation is always attracted by the electromechanical imperfect interface. When the interface imperfection is strong, the impact of material electroelastic mismatch on the image force and the equilibrium position of the dislocation becomes weak. Additionally, the effect of the nearby dislocations on the mobility of the appointed dislocation is very important.     

Edge dislocation interacting with an interfacial crack along a circular inhomogeneity

The elastic interaction of an edge dislocation, which is located either outside or inside a circular inhomogeneity, with an interfacial crack is dealt with. Using Riemann–Schwarz’s symmetry principle integrated with the analysis of singularity of the complex potentials, the closed form solutions for the elastic fields in the matrix and inhomogeneity regions are derived explicitly. The image force on the dislocation is then determined by using the Peach–Keohler formula. The influence of the crack geometry and material mismatch on the dislocation force is evaluated and discussed when the dislocation is located in the matrix. It is shown that the interfacial crack has significant effect on the equilibrium position of the edge dislocation near a circular interface. The results also reveal a strong dependency of the dislocation force on the mismatch of the shear moduli and Poisson’s ratios between the matrix and inhomogeneity.     

Antiplane shear crack in an infinite plate with a circular inclusion

Summary The effect of an elastic circular inclusion of a different material on the stress state of a single-cracked infinite sheet subjected to anti-plane shear is investigated. The proposed method makes use of complex variables in conjunction with Muskhelishvili's technique and has given interesting results for the stress field in the cracked plate. Numerical results, derived from this technique, investigate the influence of the regional inhomogeneity, produced by the inclusion in the structure, on the variation of stress-intensity factors at the crack tips.

---

Nichtebener Schubspannungsriß in einer unendlichen Platte mit einem kreisförmigen Einschluß

Übersicht Es wird der Einfluß untersucht, den ein elastischer, kreisförmiger Einschluß aus verschiedenem Material in einer unendlichen Platte mit einem Riß, welche einer longitudinalen Schubspannung unterworfen ist, auf den Spannungszustand der Platte ausübt. Die vorgeschlagene Methode benutzt komplexe Variablen in Zusammenhang mit der Muskhelishvilischen Technik und gibt für den Spannungszustand in der Platte interessante Resultate. Numerische Ergebnisse wurden gefunden, um den Einfluß der Inhomogenität auf die Spannungsintensitätsfaktoren des Risses zu bestimmen.

     

Plastic extension of a shear crack at a circular inclusion

The plastic relaxation of a shear crack situated normal to the interface of a second phase particle of circular cross-section is quantitatively analyzed. The ratio of applied stress to yield stress and the relative displacement of the crack faces at the tips of the crack in the matrix and the interface in the second phase are related to the crack parameters namely the length of the crack, the width of the plastic zone in the matrix and the second phase. The effect of the shear modulus and size of the second phase particle on the behaviour of the plastic zones is determined. A critical value of the relative displacement of the crack faces at the tip of the crack is used as the criterion to determine the tendency to brittle crack extension into the matrix and the second phase.     

Stable growth of a central crack

The elastic fracture behavior of a plate subjected to uniform stress surrounding two equal cracks inclined at an angle is investigated. The orientation of the crack plane with applied stress can be varied. Among the cases are: (1) two cracks inclined symmetrically with respect to the vertical and horizontal applied stress, and (2) one crack is horizontal while the other is inclined to the vertical applied stress. The strain energy density criterion is used for determining the combined crack and load arrangement that correspond to the lowest critical load at global instability. The direction of crack initiation is also determined. Quantitative results pertaining to the fracture characteristics are given in graphical forms.     

Interaction between a circular inclusion and a symmetrically branched crack

The interaction problem between a circular inclusion and a symmetrically branched crack embedded in an infinite elastic medium is solved. The branched crack is modeled as three straight cracks which intersect at a common point and each crack is treated as a continuous contribution of edge dislocations. Green's functions are used to reduce the problem into a system of singular equations consisting of the distributions of Burger's dislocation vectors as unknown functions through the superposition technique. The resulting integral equations are solved numerically by the method of Gauss-Chebychev quadrature. The proposed integral equation approach is first verified for two limiting cases against the literature. More effort is paid on the effect of inclusion on both the Mode I and Mode lI stress intensity factors at the branch tips. The effect of inclusion on the branching path is also investigated.     

含圆形嵌体弹性平面中径向裂纹问题的超奇异积分方程方法

根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究.根据有限部积分原理,建立了问题的数值算法.计算结果表明,嵌体半径、裂纹位置及材料剪切弹性模量等都对裂纹应力强度因子具有较为明显的影响.     

Stable crack growth in viscoelastic media

Conclusions It follows from the last two examples, that for unsteady creep, with the creep effect diminishing in time, the crack grows at a diminishing rate, and after a certain time crack growth comes almost completely to a stop. For steady creep, however, crack growth does not diminish, but proceeds at a constant rate. These conclusions are in good agreement with results obtained earlier by L. M. Kachanov [3, 4] and G. P. Cherepanov [12].Prikladnaya Mekhanika, Vol. 4, No. 6, pp. 74–79, 1968     

A conducting arc crack between a circular piezoelectric inclusion and an unbounded matrix

The present paper investigates the problem of a conducting arc crack between a circular piezoelectric inclusion and an unbounded piezoelectric matrix. The original boundary value problem is reduced to a standard Riemann–Hilbert problem of vector form by means of analytical continuation. Explicit solutions for the stress singularities δ=−(1/2)±iε are obtained, closed form solutions for the field potentials are then derived through adopting a decoupling procedure. In addition, explicit expressions for the field component distributions in the whole field and along the circular interface are also obtained. Different from the interface insulating crack, stresses, strains, electric displacements and electric fields at the crack tips all exhibit oscillatory singularities. We also define a complex electro-elastic field concentration vector to characterize the singular fields near the crack tips and derive a simple expression for the energy release rate, which is always positive, in terms of the field concentration vector. The condition for the disappearance of the index ε is also discussed. When the index ε is zero, we obtain conventionally defined electro-elastic intensity factors. The examples demonstrate the physical behavior and the correctness of the obtained solution.     

A crack along the interface of a circular inclusion embedded in an infinite solid

The two-dimensional problem of an arc shaped crack lying along the interface of a circular elastic inclusion embedded in an infinite matrix with different elastic constants is considered. Based on the complex variable method of Muskhelishvili, closed-form solutions for the stresses and the displacements around the crack are obtained when general biaxial loads are applied at infinity. These solutions are then combined with A.A. Griffith's virtual work argument to give a criterion of crack extension, namely the de-bonding of the interface. The critical applied loads are expressed explicitly in terms of a function of the inclusion radius and the central angle subtended by the crack arc. In the case of simple tension the critical load is inversely proportional to the square-root of the inclusion radius. By analyzing the variation of the cleavage stress near the crack tip, the deviation of the crack into the matrix is discussed. The case of uniaxial tension is worked out in detail.     

Stable crack growth in aluminum tensile specimens

Post's white-light moiré interferometry was used to obtain sequential records of the transientU _y -displacement fields associated with stable crack growth in 7075-T6 and 2024-0, single-edge-notched (SEN) specimens with fatigued cracks. TheU _y -displacement fields are used to evaluate the crack-tip opening displacement (CTOD), far- and near-fieldJ-integral values, Dugdale-strip-yield model, William's polynomial function and the HRR field. Paper was presented at 1985 SEM Spring Converence on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface

An analytical method is developed for scattering of SH-waves and dynamic stress concentration by an interacting interface crack and a circular cavity near bimaterial interface. A suitable Green‘s function is contructed, which is the fundamental solution of the displacement field for an elastic half space with a circular cavity impacted by an out-plane harmonic line source loading at the horizontal surface. First, the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and the other is a complete half space. Then the problem is solved according to the procedure of combination and by the Green‘s function method. The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, or with some forces to recover cracks by means of crack-division technique. A series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions as expressed in terms of the Green‘s function. Moreover, some expressions are given in this paper, such as dynamic stress intensity factor (DSIF) at the tip of the interface crack and dynamic stress concentration factor (DSCF) around the circular cavity edge. Numerical examples are provided to show the influences of the wave numbers, the geometrical location of the interface crack and the circular cavity, and parameter combinations of different media upon DSIF and DSCF.     

Elastic-plastic analysis of a flat plate with a circular rigid inclusion

Summary An elastic-plastic solution is presented for a circular rigid inclusion in a unidirectionally stressed flat plate of linearly strain hardening material. The results are compared to the results obtained for the free hole. It is postulated that for intermediate constraints the plastic flow would be less pronounced than in these limiting cases.     

Stress analysis of a wedge disclination dipole interacting with a circular nanoinhomogeneity

This paper investigates the interaction between a wedge disclination dipole and a circular nanoinhomogeneity embedded in an infinite matrix. The Gurtin–Murdoch surface/interface elasticity model is applied to account for the interface stress effect of the nanoinhomogeneity. A closed form solution for the stress fields inside the inhomogeneity and matrix is derived with the complex variable method of Muskhelishvili. The influences of the interfacial and bulk material properties as well as the geometric parameters on the material force of the wedge disclination dipole are systematically discussed. It is found that the interface stress effect may influence the material force of the wedge disclination dipole significantly.