The hoop stress at the outer surface of a pipe of internal diameter 2R₁ and external diameter 2R₂ under internal pressure P is given by:

When a/W < 0.05, Y = 1.12. A toughened rigid PVC water pipe has R₁ = 147.5 mm and R₂ = 167.5 mm. Tests show KIC = 3.1 MPa m^0.5 and σY = 40 MPa. The largest defects are equivalent to 100 um cracks in the outer surface. (A) Determine whether the pipe will fail by yield or fracture in a pressurization test, and find the pressure to cause failure. (B) Find the maximum value of yield stress σY (max) that will permit ductile failure in the pipe as strain rate increases, assuming that KIC remains constant. (C) Calculate σY (max) for poorly processed PVC pipe, for which KIC = 1.5 MPa m^0.5, assuming that a remains unchanged at 100 um.

2PR? (R - R) ||