On the use of effective properties for the fracture analysis of microstructured materials

摘要: Abstract This paper addresses some fundamental theoretical and numerical issues concerning the application of effective properties for failure analysis microstructured materials, with a focus on functionally graded materials. An edge-cracked square region is considered which taken to be size representative volume element in larger structural system. The made by utilizing non-homogeneous probability density function (PDF) governing spatial distribution constituents. non-homogeneity PDF exists only direction crack plane. Based upon type microstructure region, an accurate homogenization method employed obtain properties. For functional forms PDF, energy release rates stress intensity factors (SIFs) are then calculated using both based pointwise realizations specific microstructures generated from PDF. all calculations, we employ eXtended finite method, alleviating need remesh domain between different microstructural realizations. Enrichment strategies capture singular fields near tip as well discontinuous strain at fiber–matrix interfaces, even relatively coarse meshes. SIFs form J-integral that does not exhibit any dependence. results show excellent agreement implicit mean explicit trials densities. also seem indicate predict SIF arbitrary initial geometry. Furthermore, good approximation tips may estimated re-interpreting according knowledge distinct crack-tip location microstructure. Quasi-static growth studies performed investigate finding within either composite phases.