Research On Nano-cracks And Laminated Strips With Interfacial Diffusion And Sliding

In this thesis,the related problems of nano-cracks with interfacial diffusion and sliding effects are studied,and the calculation method is also applied to the study of the interfacial diffusion and sliding effect of laminated elastic strips.The transient stress concentration,stress relaxation and so on,which have important influence on the strength and toughness,hardness and fatigue properties of the material,are caused by the interfacial diffusion and sliding.The surface elasticity is incorporated by using a version of the continuum-based surface/interface theory of Gurtin and Murdoch.The Green's function method is used to derive a complete and transient solution by reducing the boundary value problem to a Cauchy singular integro-differential equation which can be further changed into state-space equations by means of the collocation method.The state-space equations are solved by a rigorous analysis of the eigenmodes.The transient stress field and its evolution process on the crack surface and the elastic strip surface are obtained.First,a mode III rate-dependent bridged crack with surface elasticity is studied.In terms of the interfacal sliding,there is the viscosity on the crack surface,which causes the bridging force being proportional to the time-rate of the crack opening displacement.Detailed numerical results are presented for eigenvalues,eigenfunctions,and the evolution of the bridging force,crack opening displacement and the strength of the logarithmic singularity at the crack tips.Second,time-dependent grain-boundary sliding in a nano-film on a substrate is studied.The grain-boundary is allowed to slide by the diffusion-controlled mechanism.We demonstrate that such a sliding process leads to the formation of a crack-like grain-boundary wedge which causes the shear stress along the grain boundary to decay exponentially with time.Detailed numerical results are obtained for eigenvalues,eigenfunctions,the transient shear stress along the grain-boundary,the opening displacement of the wedge and the strength of the logarithmic singularity at the wedge tip.Third,Time-dependent deformations of bilayered elastic strips with interfacial diffusion and sliding in cylindrical bending are studied.A film-substrate system is also addressed by letting the thickness of one layer approach infinity.Detailed numerical results are presented to show the influence of the material,geometric and interface parameters on the relaxation times and on the evolving displacements and stresses in the strip or in the film-substrate system.Finally,the state-space method is proposed to determine the transient elastic field in simply-supported multilayered elastic strips with interfacial diffusion and sliding under thermomechanical loads.