— David Wagner 2009/10/25 22:49

√ME 5463-001 Fracture Mechanics, Homework #14

6.5 A thin steel plate (sigma_ys = 40 ksi), that is 6 inches wide contains a central crack 2.0 inches in length.

(a) If the plane-stress fracture toughness of the steel is 55 ksi sqrt(in), what is the maximum stress that can be supported by the plate (including the effects of local yielding at the crack tips)?

(b) What is the longest crack the plate can support without failure at an applied stress of 20 ksi?

(a) r_y = {1/{2 pi}}(K/{sigma_0})^2 = 0.30090 in; ⇒ a_eff=1.30090 in.

K_c = sigma_0 sqrt{2 pi r_y}= = 55000 = sigma_c sqrt{pi a_{eff}} sqrt{sec{{pi a_{eff}}/W}}. ⇒

  • sigma_c =2.4×104 psi = 24 ksi.

(b) For sigma=20000, Solving K_c = sigma sqrt{pi a_{eff}} sqrt{sec{{pi a_{eff}}/W}} iteratively yields a_eff = 1.6 in ⇒ a = 1.3 in.

  • Longest crack: 2.6 in

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