Investigation of crack tip evolution in functionally graded materials using optical caustics

The local singularity and fracture characterization of a functionally graded material (FGM) specimen with a crack oriented along the direction of the elastic gradient were studied combining optical caustics technology with the finite element method. First, the governing equations related to the caustics measurements and the elastic solutions at mode I crack in FGMs were obtained in terms of the stress intensity factor, material constants, graded index and the characteristic size. Then, caustics experiments using three-point-bending of FGM beams with crack location on both the stiff and the compliant sides were performed. The influences of material gradient variation on crack initiation, singularity field and stress intensity factor at the crack tip were analyzed. The stress intensity factors from caustics measurements were obtained with the aid of a numerical iterative method, which were in good agreement with those predicted by a finite element analysis under K-dominance assumption. These results are useful for better design and reliable evaluation of FGMs.