Evaluation of crack tip fields and stress intensity factors in functionally graded elastic materials: Cracks parallel to elastic gradient

Particulate functionally graded materials (FGM) made of glass-filled epoxy with edge cracks parallel to the direction of the elastic gradient and subjected to pure bending have been studied. Crack tip measurements are used to examine continuum models for FGMs by treating the material as isotropic and nonhomogeneous at macroscales. Situations where cracks are located on the compliant and the stiff sides of the beams are separately examined by mapping crack tip deformations using optical interferometry. Comparative experiments on homogeneous compositions corresponding to identical elastic properties of the crack tip region in the FGM are also undertaken. A methodology for extracting fracture parameters in FGMs based on locally homogeneous material descriptions is advanced. Companion finite element models are used to aid the development of fringe analysis procedures and to provide a direct comparison to the optical measurements. Stress intensity factors in FGMs are compared to each other and to their homogeneous counterparts. Optical measurements near quasi-statically growing cracks in FGMs have been undertaken, and crack growth resistance behavior is explained using crack initiation toughness variation as a function of filler volume fraction in homogeneous sheets.