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.

Using the theory of complex variable functions, analytical solutions for dynamic symmetrical mode III interface cracks of two unalike materials were investigated. The issues considered could be very easily translated into Riemann–Hilbert problems according to the methods of self-similar functions, and analytical solutions of the stresses, displacements and dynamic stress intensity factors for the edges of symmetrical mode III interface cracks subjected to moving enhancive loadings, Pt 6/x 6 and Px 7/t 6, were obtained. The solutions were obtained by application of the superposition principle. The solutions of discretionally intricate queries could be readily acquired.

By means of the theory of complex variable functions, dynamic extension queries solutions of symmetrical mode III interface cracks in bismuth-copper alloys were researched in this paper. The crack extension should also appear in the form of self-similarity because interface failure is ascertained by the maximum tensile stress. The formulation involves the development of a Riemann-Hilbert problem. The issues which were considered can be very easily transformed into Riemann-Hilbert problem according to the methods of self-similar functions, and the general representations of analytical solutions of the stresses, displacements and dynamic stress intensity factors for the edges of symmetrical mode III interface crack subjected to moving enhancive loadings Px 6/t 6 and Pt 7/x 6. In the light of correlative material properties, the changeable law of dynamic stress intensity factor was illustrated very well. The solutions were obtained by application of superposition principle in this paper, and the solutions of discretionally intricate queries could be readily acquired.