Anti-plane impact of a composite wedge with radial cracks

• Published in: European journal of mechanics, A, Solids A, Solids, 2022-01, Vol.91, p.104422, Article 104422
• Main Authors: Vafa, J.P., Fariborz, S.J.
• Format: Article
• Language: English
• Subjects: Burgers vector; Crack tips; Cracks; Elastic anisotropy; Elastic wedge; Elastic wedges; Energy dissipation; Impact load; Impact loads; Integral equations; Integral transforms; Laplace transforms; Radial crack; Screw dislocation; Screw dislocations; Singularity (mathematics); Stiffness coefficients; Stress analysis; Stress distribution; Stress intensity factors; Stress singularity; Time dependence; Viscous damping
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2021.104422

The Laplace transform of stress field in a cylindrically anisotropic elastic wedge, fixed at an edge and traction-free at the other, containing a screw dislocation with time-dependent Burgers vector is obtained by means of integral transform method. Energy dissipation in the wedge is modeled by viscous damping. Furthermore, solution to an intact wedge subjected to the dynamic anti-plane point load is obtained. These solutions are utilized to construct integral equations for a wedge weakened by several radial cracks subject to anti-plane impact loads. The integral equations are of Cauchy singular type. The stress analysis around a crack tip in cylindrically anisotropic material reveals that power of stress singularity depends upon the ratio of material stiffness coefficients. Therefore, a general definition for crack Stress Intensity Factor (SIF) is rendered for any power of stress singularity at a crack tip. Moreover, the numerical procedure for the solution to Cauchy integral equations is extended to solve integral equations with general power of singularity of solution. The procedure is utilized to obtain Laplace transform of the cracks SIFs. In the case of a cracked wedge under impact loads the inverse Laplace transforms of SIFs are determined numerically. To verify the formulation the quasi-static case of all the examples is solved by means of a different procedure. The results of latter case are compared with the dynamic solutions as time tends to infinity. Interaction between cracks, effects of structural energy dissipation, and wedge geometry on cracks SIFs are studied. •Equation of motion is derived for anti-plane deformation for a cylindrically anisotropic wedge.•The integral transform method is used to derive the solutions to dynamic and static screw dislocation.•The solution to an intact wedge under anti-plane point load is obtained.•The numerical solution to integral equations is used to determine cracks stress intensity factors.•Interaction between two radial cracks and effect of wedge geometry are studied.