Design maps for fracture resistant functionally graded materials

•Study the Fracture of FGM's as a function of material contrast and crack length.•Introduce the notion of a non-dimensional ‘Fracture Index’.•Construct design maps to help identify fracture resistant microstructures.

The objective of this research is to generate design maps to identify functionally graded microstructures with enhanced fracture toughness. Several Functionally Graded Materials (FGMs) with an edge crack and membrane loading are considered and the resulting J-integral values are computed numerically using Finite Element Analysis. In order to capture the resulting stress fields accurately, Barsoum elements are used in the vicinity of the crack tip and the simulations are carried out for several crack lengths (a) and material contrasts (κ). The averages of the J-integral values are used to determine the normalized Stress Intensity Factors which are then benchmarked with existing analytical solutions in special cases. Furthermore, in order to facilitate an objective comparison between FGMs and homogeneous materials, a constraint is imposed on each of the microstructure so that the volume averaged modulus remains the same although the spatial variation is very different. Subsequently, we demonstrate that a FGM could perform either better or worse than the reference homogeneous material depending upon the crack length, the type of functional gradation and the material contrast (thereby the local gradient of the modulus at the crack tip). Finally, the notion of ‘Fracture Index’ is introduced using which ‘design maps’ are created in the (a−κ) space that reveal microstructures with enhanced fracture resistance. These maps are universal since any Functionally Graded Material can be mapped as a point on this space.