The manufacturer of a product that is subjected to repetitive cycles has specified that the product should be removed from service when any crack reaches 15% of the critical crack length required to cause fracture.

Consider a crack that is initially 0.02 mm long in a material with a fracture toughness of 55 MPa(m. The product is continuously cycled between compressive and tensile stresses of 300 MPa at a constant frequency. Assume external cracks for which f = 1.12. The materials constants for these units are n = 3.4 and C = 2 × 10-11.

(1). What is the critical crack length required to cause fracture?

(2). How many cycles will cause product failure?

(3). If the product is removed from service as specified by the manufacturer, how much of the useful life of the product remains? Discuss.