Domain-integral methods for computation of fracture-mechanics parameters in three-dimensional functionally-graded solids

A natural or engineered multiphase composite with macro-scale spatial variation of material properties may be referred to as a functionally graded material, or FGM. FGMs can enhance structural performance by optimizing stiffness, improving heat, corrosion or impact resistance, or by reducing susceptibility to fracture. One promising application of FGMs is to thermal barrier coatings, in which a ceramic coating with high heat and corrosion resistance transitions smoothly to a tough metallic substrate. The absence of a discrete interface between the two materials reduces the occurrence of delamination and spallation caused by growth of interface and surface cracks. Fracture remains an important failure mechanism in FGMs, however, and the ability to predict critical flaw sizes is necessary for the engineering application of these materials.; This presentation describes the development of numerical methods used to compute fracture parameters necessary for the evaluation of flaws in elastic continua. The current investigation employs post-processing techniques in a finite-element framework to compute the J-integral, mixed-mode stress intensity factors and non-singular T-stresses along generally-curved, planar cracks in three-dimensional FGM structures. Domain and interaction integrals developed over the past thirty years to compute these fracture parameters have proved to be robust and accurate because they employ field quantities remote from the crack. The recent emergence of promising engineering applications of FGMs motivates the extension of these numerical methods to this new class of material.; This work first develops and applies a domain integral method to compute J-integral and stress intensity factor values along crack fronts in FGM configurations under mode-I thermo-mechanical loading. The proposed domain integral formulation accommodates both linear-elastic and deformation-plastic behavior in FGMs. Next discussed is the extension of interaction-integral procedures to compute directly mixed-mode stress intensity factors and T-stresses along planar, curved cracks in FGMs under linear-elastic loading. The investigation addresses effects upon interaction integral procedures imposed by crackfront curvature, applied crack-face tractions and material nonhomogeneity. Additional considerations for T-stress evaluation include the influence of mode mixity and computation of the anti-plane shear component of non-singular stress, T13.