Mode-3 Asymptotic Analysis Around A Crack Embedded In A Ductile Functionally Graded Material

Abstract

Functionally graded materials (FGMs) are composites with continuous material property variations. The distinct interfaces between the reinforcement and the matrix in classical composites are potential damage initiation sites. The concept of FGM aims at avoiding the material mismatch at the interfaces. Functionally graded materials originated from the need for a material that has high-toughness at very high operating temperatures that occur in rocket nozzles and aeroplane engines. One of the early applications of graded materials can be thus found in thermal barrier coatings of gas turbine blades. Recent applications of FGMs include optoelectronics, ballistic impact resistance structures, wear resistant coatings and others. Although the manufacturing and applications of FGMs are well developed the basic mechanics of failure is not well understood, which is important in developing engineering design methodologies. Modern day design practice uses the concepts of fracture mechanics and the fracture properties of graded materials is not well understood. Most studies in the literature have assumed that the material response of the bulk functionally graded material to be elastic even though the constituents are nominally ductile. Some asymptotic analysis available in the literature have described the effect of ductility on the fracture parameters. However, these analysis are not complete in the sense that they have some undetermined constants. The present thesis aims at performing whole-field finite element (FE) simulations of a crack embedded in a ductile functionally graded material subjected to an anti-plane shear (mode-3) loading. A J2-deformation theory based power-law hardening nonlinear material response is assumed. The material property variation is assumed to be in the radial-direction (r-FGM), tangential to the crack (x-FGM), normal to the crack plane (y-FGM) and also at an arbitrary angle to the crack-plane (xy-FGM). Yet another power law described the material property variation. The competition between the indices of the hardening and material property variation is understood by performing a parametric analysis by varying both systematically. Our results indicate that the first most singular term of the asymptotic series remains unaffected. For some values of the material property variation index, the second asymptotic term is affected. The semi-closed form solutions available in the literature were unable to decipher the relative range of dominance of the first and second terms. From the present whole-field FEM analysis were able to extract this relative range of dominance. Our results indicate the range of dominance of the first term is least for FGMs when the material property variation is in the direction to the crack (x-FGM), and it is more for y-FGM.