Fracture in functionally gradient materials: Static and dynamic analyses.

摘要

A theoretical and numerical treatment of a finite crack in a medium with spatially varying material properties is provided in this work. The variation of material properties is in a direction perpendicular to the crack surfaces. At first, response of an interfacial layer which is made of functionally gradient materials subjected to an anti-plane shear impact load is considered. Laplace and Fourier transforms are applied to reduce this mixed boundary value problem to a system of dual integral equations which in turn will be reduced to a standard Fredholm integral equation of the second kind. The Fredholm integral equation is solved in the Laplace transform plane numerically. The time inversion is accomplished by a numerical scheme. The dynamic stress intensity factor is found to either increase or decrease with the crack length to layer thickness depending on the relative magnitudes of the material properties of the adjoining layer.; Next, a numerical treatment of an interfacial crack subjected to an in-plane mechanical loading is provided. The current investigation studies cracks in an essentially compressive environment in which the crack faces are in contact and frictional effects play an important role. A simple and efficient, iterative finite element technique for solving frictional contact problems under small deformations is described. Stress intensity factors and energy release rates are calculated by using numerical crack flank displacement and two term parameter techniques. Numerical examples are provided to verify the technique and to show the effect of the thickness of the interfacial layer, the coefficient of friction, and the material properties upon the stress intensity factors and energy release rates of the crack.; Frictional contact problem of cracks in functionally gradient materials under combined mechanical and thermal loadings is studied. Both steady-state and transient thermal stresses are considered. Due to the nonuniform temperature distribution in the transient thermal field, the possibility of heat transfer across the crack surfaces in the contact region exists. The heat transfer across the crack surfaces results in a two-way coupling between the thermal and mechanical fields. Stress intensity factors are calculated. The effect of the coefficient of friction, crack length, and material properties of the interfacial layer on the stress intensity factors in the mixed mode is studied. From the results it is revealed that the stress intensity factors are reduced considerably when functionally gradient material is used as an interfacial layer instead of homogeneous materials.; Finally, a nonlinear theory on the statics of multilayered shells, including transverse effects and delamination of general shapes, is studied. Delaminations are included by introducing new vectors which we name as conjugate directors. (Abstract shortened by UMI.)