Experimental observations and computational modeling of fracturing in an anisotropic brittle crystal (Sapphire)

摘要

The commonly used fracture cirteria-maximum KI,zero KII, maximum hoop-stress, and maximum energy-releaserate-predict similar fracture paths in isotropic materials, but notin anisotropic materials. In the general anisotropic case, thefracture path depends on the material-symmetry properties, thenature of the applied loads, and the overall geometry of thespecimen. In addition, anisotropy in the material's resistance tofracturing play a key role in defining crack initiation and itspropagation path. Experiments are performed on notchedspecimens made from sapphire, a microscopically homogeneousand brittle single-crystal solid. The force required for fractureinitiation is measured. The experimentalmeasurements/observations are compared with the numericalresults of the FEM simulations. A stress-based fracture parameter,A=√2πR0 σN/√γN E N is shown to be a good measureof the fracture criterion, where σN EN, respectively, arethe tensile stress and Young's modulus in the direction normal tothe cleavage plane, with surface energyγN, and R0 is acharacteristic length, e.g., the notch radius. Thisparameter takes into account the effects of thesurface energy of the corresponding cleavage plane,as well as the strength of the atomic bonds in thedirection normal to the cleavage plane. More than twoplane, as well as the strength of the atomic bondsin the direction normal to the cleavage plane whereA is maximum. The measurements of the applied forcemade it possible to quantitatively obtain a criticalvalue for parameter A. Finally, experiments show thatfor the notched sapphire specimens the weakest familyof cleavage planes, {1012} and {1010}, are thefracture planes, although a few specimens fractured along non-cleavage planes.