A thick plate of the high-strength steel of Table 8.1 ( , ) is cycled between zero and

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Fracture: stress concentration, cracks and toughness

Problem

A thick plate of the high-strength steel of Table 8.1 (KIc=50 MPa m1/2K_{Ic}=50\,\mathrm{MPa\,m^{1/2}}, σY=500 MPa\sigma_Y=500\,\mathrm{MPa}) is cycled between zero and 150 MPa150\,\mathrm{MPa}. Cracks start at a free edge (Y=1.12Y=1.12), and an inspection method reliably finds an edge crack once it is 5 mm5\,\mathrm{mm} deep. The fatigue constants are CP=10−11 m cycle−1 (MPa m1/2)−3C_P=10^{-11}\,\mathrm{m\,cycle^{-1}\,(MPa\,m^{1/2})^{-3}} and m=3m=3. ((a)) Find the critical crack depth at the peak stress. ((b)) Check that small-scale yielding still holds at that point, using the plane-stress zone at the surface. ((c)) Find the number of cycles for a crack to grow from the detectable 5 mm5\,\mathrm{mm} to the critical depth. ((d)) The operator wants two inspections within that growth, so that a crack missed once is caught the next time. What is the longest allowed interval between inspections, in cycles?

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