M. Ayatollahi

Multiple moving interfacial cracks between two dissimilar piezoelectric layers under electromechanical loading

The dynamic problem of several moving cracks at the interface between two dissimilar piezoelectric materials is analyzed. The combined out-of-plane mechanical and in-plane electrical loads are applied to the layers. Fourier transforms are used to reduce the problem to a system of singular integral equations with simple Cauchy kernel. The integral equations are solved numerically by converting to a system of linear algebraic equations and by using a collocation technique. The results presented consist of the stress intensity factors and the electric displacement intensity factors. It is found that generally the field intensity factors increase with increasing crack propagation speed.

Stress analysis of a functionally graded magneto-electro-elastic strip with multiple moving cracks

This paper investigates the linear steady state problem of several moving cracks in a functionally graded magneto-electro-elastic strip subjected to anti-plane mechanical and in-plane electric and magnetic loading. For simplicity, it is assumed that the properties of the strip vary continuously according to exponential functions along the thickness of the functionally graded piezoelectric piezomagnetic (FGPP) layer. By combining the dislocation method and integral transform technique, an exact solution in closed form to this problem is obtained. Electro-magneto-mechanical loads are applied on the crack surfaces, which are assumed to be magneto-electrically impermeable. Numerical examples are presented to show the interesting mechanical and electromagnetic coupling phenomena induced by multi-crack interactions. Finally, the effects of crack velocity, material constants, and geometric parameters upon the field intensity factors are studied. The results are useful for the design of the magneto-electro-elastic structures.

Dynamic Behavior of Several Cracks in Functionally Graded Strip Subjected to Anti-Plane Time-Harmonic Concentrated Loads

This paper contains a theoretical formulations and solutions of multiple cracks subjected to an anti-plane time-harmonic point load in a functionally graded strip. The distributed dislocation technique is used to construct integral equations for a functionally graded material strip weakened by several cracks under anti-plane time-harmonic load. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to evaluate the stress intensity factor and strain energy density factors (SEDFs) for multiple cracks with different configurations. Numerical calculations are presented to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded strip with multiple curved cracks.

Analytic solutions of multiple moving cracks in an orthotropic layer bonded to an orthotropic FGM coating

In this paper, the dynamic behavior of an orthotropic substrate weakened by moving cracks and reinforced by a non-homogenous coating is studied. First, the solution to the screw dislocation in an orthotropic strip with imperfect orthotropic functionally graded coating is obtained. Then, for the anti-plane analysis of cracks, the screw dislocations are distributed along the crack lines and the dislocation solution is used to derive integral equations for dislocation density functions on the surface of cracks. The effects of non-homogeneity parameters, geometrical parameters and bonding coefficient on the stress intensity factors are investigated.

Transient Analysis of Multiple Interface Cracks in Two Bonded Elastic and Piezoelectric Layers

In this paper, the dynamic behavior of multiple interface cracks between piezoelectric and elastic layers subjected to impact loading is investigated. The Fourier and Laplace transforms are used to reduce the problem to singular integral equations in which the unknown variables is the jump of displacement across the crack surface. The resulting integral equations together with the corresponding single-valued conditions are solved numerically for the density of screw dislocations on a crack surface. It is shown that in general the crack interaction and stress intensity factors strongly depend on material dissimilarity, crack geometry.

Analysis of multiple edge cracks in a non-homogeneous piezoelectric layer

This study is concerned with the treatment of the several edge cracks in a functionally graded piezoelectric (FGP) layer under anti-plane mechanical and in-plane electrical loading. The edge crack is assumed to be either electrically impermeable or permeable. The problem is formulated by using distributed dislocation technique. The integral equations are constructed for the analysis of a FGP layer, in which the unknown variables are dislocation densities. By use of the dislocation densities, the field intensity factors are calculated. Numerical examples are provided to show the effect of the location and orientations of edge crack upon the stress intensity factors.

Response of an orthotropic half-plane subjected to transient anti-plane loading with multiple edge cracks

This study deals with the problem of multiple edge cracks in an elastic orthotropic half-plane under transient loading. The dislocation solution is utilized to derive integral equations for multiple interacting edge cracks in an orthotropic half-plane. These equations are solved numerically thereby obtaining the dislocation density function on the crack faces and stress intensity factors at crack tips. Numerical results are obtained to illustrate the variation of the dynamic stress intensity factors as a function of crack length and material properties.

Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane

This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velocity has great effect on the field intensity factors.

Cracking in orthotropic half-plane with a functionally graded coating under anti-plane loading

This investigation evaluates, by the dislocation method, the dynamic stress intensity factors of cracked orthotropic half-plane and functionally graded material coating of a coating–substrate material due to the action of anti-plane traction on the crack surfaces. First, by using the complex Fourier transform, the dislocation problem can be solved and the stress fields are obtained with Cauchy singularity at the location of dislocation. The dislocation solution is utilized to derive integral equations for multiple interacting cracks in the orthotropic half-plane with functionally graded orthotropic coating. Several examples are solved and dynamic stress intensity factors are obtained.

Elastodynamic Analysis of a Functionally Graded Half-Plane with Multiple Sub-Surface Cracks

The stress fields are obtained for a functionally graded half-plane containing a Volterra screw dislocation. The elastic shear modulus of the medium is considered to vary exponentially. The dislocation solution is utilized to formulate integral equations for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically. Several examples are solved and the stress intensity factors are obtained.