Dynamic solutions of mode III crack in copper matrix composites

By utilising the methods of the theory of complex variable functions, dynamic propagation problems on symmetrical mode III crack in copper matrix composite materials were analysed. The crack extension should also appear in the form of self-similarity because failure is ascertained by the maximum tensile stress in actual engineering structions and everyday applications occurring in usually dynamic conditions. The formulation and the development of a Riemann–Hilbert problem were involved in this kind of issue. According to self-similar functions, the queries considered in this paper can be very easily translated into a Riemann–Hilbert problem. Analytical solutions of stresses, displacements and dynamic stress intensity factors K ₃(t) for the edges of symmetrical mode III crack, subjected to motive alterable loads, P x ⁵/t ⁵ and P t ⁶/x ⁵ were obtained. In view of the relative material properties, the changeable law of dynamic stress intensity factor was illustrated very well. After the solutions were applied by the use of the superposition principle, the solutions of discretionally complicated problems were easily acquired.