Research On The Dynamic Response To Moving Loadings Of Cracks In Multi-layered Mediums

With the progress of the society and development of the modern industry, single material can not satisfy the necessary of engineering practice, and multi-layered mediums play a more and more important role in production and life due to its flexible performance combination. As the interfaces of different materials are prone to defects such as cracks and fracture characteristics of the interface are much more complex compared to a single material's, therefore, the fracture damage issue of the interfaces in multi-layered media has been a key concern. This paper mainly studied the dynamic response to moving loadings of single interfacial crack, many interfacial cracks within multi-layered mediums and the crack vertical to the interface, and calculated the norm of complex stress intensity factor or dynamic stress intensity factor of three kinds of crack by integral transformation-singular integral equation and numerical inversion method of Laplace integral transformation. With examples, the change laws with time of all the norm of complex stress intensity factor or dynamic stress intensity factor were analyzed. The main contents of this paper are as follows:First of all, combining the adaptive integral method and the inversion formula of Laplace integral transformation, an improved numerical inversion method, adaptive inversion method, for Laplace integral transformation was proposed. This method can make an accurate inversion calculation in any interval pointed for common functions and their combinations.Secondly, in order to study the response to real dynamic loadings of multi-layered structure with cracks, three types of moving loading model, cosine moving loading, moving loading with uniform speed, expanding loading with constant speed, were presented in this paper. To some extent, these models can simulate the real dynamic loadings of automobiles to the road, airplane to the runway and effects of the friction and squeeze of crack surfaces each other under external loadings.Follow-up in the third section of Chapter, derive the singular integral equation of multi-layered medium with a single interface crack composed of isotropic mediums under moving loadings, and calculate the norm of the complex stress intensity factor of I, II types crack tips under moving loading and the dynamics stress intensity factor of III type crack. Using contour integration method and Gauss integral formula, the generalized integral of infinite domain arising in the course of the derivation were calculated and evaluated, and the singular integral equation(s) were solved numerically through the variable separation method and the Jacobi polynomial expansion method. In the meantime, a simple example calculated proved the validation of the progress, the method and the programs made by myself. Finally, the dynamic responses to all moving loadings of multi-layered medium with an interfacial crack were calculated and analyzed in detailed for a specific case.In Chapter IV, the dynamic response to moving loadings of multi-layered medium with several interface cracks was introduced with details. Using integral transformation method, the singular integral equatins in the transform domain were obtained, and the norms of complex stress intensity factor and dymamic stress intensity factors of crack tips were calculated after the equations were solved numerically. The stress distributions of crack tips and the effect of different cracks each other were researched in-depth through specific examples when the crack surfaces were acting with different loadings.Finally, the solved process and method of the dynamic response of I, II, III crack vertical to the interface of multi-layered medium under moving loading were discussed in detail, respectively. The solutions of the Lame potential functions and the solutions of the corresponding displacement and the stress in the Laplace transform domain of the composed medium with crack were given using superposition principle. Considering the border conditions of displacement and stress continuity in the adhesive interfaces and the outer boundary conditions, the solutions of all unknown coefficient functions were derived. Using the stress boundary conditions on the crack surfaces, the singular integral equation was obtained and was carried out numerically. Finally, the dymamic stress intensity factor of crack tips for a specific case was calculated.