Answer Happy

Many brittle materials (such as poly-crystalline ceramics) contain large number of microcracks of various (random) orientations (n’s are unit normals to them). When compressive (negative) stresses p (axial) and q (lateral) are applied, microcracks are closed, and normal on and shear in tractions are induced on them. Then p increases while q is kept constant (|Pl>\q|). If in on a crack overcomes frictional resistance ulon| (u=0.6 -friction coefficient), then frictional slip occurs. q n Find: (a) the critical value of p when frictional sliding starts, and (b) orientation n of the crack on which it starts