Fabrication of transparent homogeneous functionally graded materials and crack analysis by photoelasticity

To analyze the stress of functionally graded materials (FGMs) through an experiment, transparent homogeneous FGMs (THFGMs) with similar theoretical and physical properties need to be created. This study developed such THFGMs and proposed a method for determining their stress intensity factors (SIFs) and T-stresses via photoelastic experiments. The Young’s modulus and Poisson’s ratio of these THFGMs linearly change along the physical variation direction, and the shear modulus varies almost linearly. The SIFs and T-stresses were obtained for the central and edge cracks in finite rectangular FGM plates with linear variations in the shear modulus under constant density along the direction of the crack under mode I loading. The SIFs and T-stresses can be obtained using the exponential and linear variation in the stress fields, even if the physical properties of FGM plates show linear variation in the shear modulus. The characteristics of the experimental SIFs obtained in this study generally agree with those of theoretical SIFs reported in previous research. For center crack tips, the SIFs at the hard right crack tip were greater than those at the soft left crack tip. For edge crack tips, when a/W < 0.35, the SIFs were lower than the homogeneous materials. By contrast, when a/W > 0.35, the SIFs were greater than the homogeneous materials. The experimental T-stresses for the center crack agreed well with the numerical T-stresses reported in previous research. For the edge crack, when a/W ≤ 0.3, the experimental T-stresses agreed with the numerical T-stress, but when a/W ≥ 0.4, considerable differences were observed between the experimental and numerical T-stresses. Where a(a) denotes the crack length for edge cracks or half the crack length for center cracks, and W is the width of the specimen. Experimental results coincide well with those reported in the literature, except for the T-stresses for edge crack when a/W > 0.3. Therefore, the THFGMs, which are new FGMs developed in this study, can be effectively used in experimental fracture analysis.