Surface Cracking in Layers Under Biaxial, Residual Compressive Stress

Thin two-phase, Al₂O₃/ t -Zr(3Y)O₂ layers bounded by much thicker Zr(3Y)O₂ layers were fabricated by co-sintering powders. After cooling, cracks were observed along the center of the two-phase, Al₂O₃/ t -Zr(3Y)O₂ layers. Although the Al₂O₃/ t -Zr(3Y)O₂ layers are under residual, biaxial compression far from the surface, tensile stresses, normal to the center line, exist at and near the surface. These highly localized tensile stresses can cause cracks to extend parallel to the layer, to a depth proportional to the layer thickness. A tunneling/edge cracking energy release rate function is developed for these cracks. It shows that for a given residual stress, crack extension will take place only when the layer thickness is greater than a critical value. A value of the critical thickness is computed and compared with an available experimental datum point. In addition, the behavior of the energy release rate function due to elastic mismatch is calculated via the finite element method (FEM). It is also shown how this solution for crack extension can be applied to explain cracking associated with other phenomena, e.g., joining, reaction couples, etc.