Papers by Keyword: Moving Crack

Abstract: In this paper the anti-plane moving crack in a functionally-graded material is studied by the analytical method. First the governing equations for a functionally-graded material are obtained using a Fourier cosine integral transform. Then the dual integral equations for moving crack are established according to the mixed boundary value conditions. It is shown that the dual integral equations can be reduced to the Fredholm integral equation of the second kind. Numerical results shown in the present paper indicate that the non-homogeneity of material has an important influence on the dynamic stress intensity factor.

Abstract: The moving crack problem in an infinite plate of orthotropic anisotropy functionally graded materials (FGMs) subjected to an anti-plane shear loading is studied by making use of non- local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form. Fourier transform is employed to solve the partial differential equation. The mixed boundary value problem is reduced to a pair dual integral equations which is solved by using Schmidt’s method. The semi-analytic solution of crack-tip stress is obtained, contrary to the classical elasticity solution, the crack-tip stress fields does not retains the stress singularity. The influences of the characteristic length, graded parameter, orthotropic coefficient and crack velocity on the crack-tip stress are analyzed. The numerical results show that the stress at the crack tip decrease as the characteristic length, crack velocity, graded parameter are increased and increase as the orthotropic coefficient is increased.

Abstract: A moving crack in a laminated structure with free boundary subjected to anti-plane shear loading is investigated in this paper. Using the bonding conditions of the interface between different media, all the quantities in our question have been represented with a single unknown function, and the problem is transformed into a dual integrated equation with the method of Fourier transform. The equation is solved using Schmidt method. Finally the numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of different laminated material, shear moduli of different laminated material.

Abstract: A moving crack in an infinite strip of orthotropic anisotropy functionally graded material (FGM) with free boundary subjected to anti-plane shear loading is considered. The shear moduli in two directions of FGM are assumed to be of exponential form. The dynamic stress intensity factor is obtained by utilizing integral transforms and dual-integral equations. The numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of the strip, gradient parameters and nonhomogeneous coefficients.

Abstract: This paper investigates a moving crack in a nonhomogeneous piezoelectric material (NPM) plate. The mechanical and electrical properties of the plate are considered for a class of functional forms for which closed-form expressions for the moving crack tip electromechanical fields are obtained. Effect of material non-homogeneity and crack moving velocity on the crack tip fields are discussed. The crack moving velocity can increase or decrease the stress intensity factor. The cleavage stress, τθz, however, is always an increasing function of crack moving velocity.