Elastodynamic analysis of mode III multiple cracks in a functionally graded orthotropic half-plane

• The displacement discontinuous technique is used to model dynamic crack problems.
• FGM constants greatly influence the overshoot of DSIFs.
• Durbin method for oscillatory loadings was much more accurate than Stehfest method.
• Orthotropic materials with higher ratios may result in more favorable behaviors in terms of DSIFs.

This paper presents a set of dynamic analyses of multiple parallel or perpendicular cracks to the boundary in a functionally graded orthotropic half-plane subjected to anti-plane shear stresses. The material properties are assumed to vary based on an exponential law. Integral transformations (Laplace and Fourier) and Green’s function method are applied to elastodynamic equations. The displacement discontinuous distribution method is used to model the crack problems which are solved by using a set of appropriate boundary conditions. As a result, a set of stress equations with both hypersingular and logarithm singular terms is obtained. Using Chebyshev series expansion and collocation points in Laplace domain, the solution of hypersingular integral equation for multiple cracks is achieved. Finally, different algorithms of numerical Laplace inversion are presented and the dynamic stress intensity factors (DSIFs) are obtained. The presented results are compared with the available published data and a very good agreement is observed. Moreover, it is also demonstrated that the present theoretical study is capable of modeling multiple cracks with different arrangements and variety of FG Orthotropic material properties. Furthermore, influence of FGM constant and shear modulus ratio on the dynamic overshoot of stress intensity is investigated.