Question

A relatively large sheet of PC is to be exposed to cyclic tensile and compressive stresses of magnitudes 30 MPa and 20 MPa, respectively. Prior to testing, it has been determined that the length of the largest surface crack is 1.0 mm. Estimate the fatigue life of this sheet if its plane strain fracture toughness is 2.5 MPa√m and the values of m and A (in Equation 9.26, Callister & Rethwisch) are 3.0 and 1×10-12 , respectively, for Δσ in MPa and a in m. Assume that the parameter Y is independent of crack length and has a value of 1.0.

Answer 1

Given , solution ao = Imm = 0.0olm. Initial coack length, plane strain fracture toughness, kic = 2.5 .5 MPa vm. Parameter m and A; values of m=3 A = 1x102 Pasameter Y=li Cyclic tensile stress = 30 MPa. (omax. Cyclic Compressive stress = 20 mpa, (5min. Since Compressive stress is minimum, so it is a taken as Only Emax. is considered. zego 2 Final coack length, ac kic ac = T 2 2.5 11 ㅈ 30X1 = 0.002 m. ac Number of fatigue life cycle, da Np = ym m. m/21 АЛ m a (A) ao - 3/2 a Blo da . 3 3 A x ²(A6) Y ao

ac, (1x2) ਨੇ 8 3 30 ( :) ਟੀ ( xox % 3 3 3. 7 ac - (x2)x 7 1 3 3 X 7 x 30 X॥ 0 · 0p | 0.002 - 123, 30 x (0 ਯੂc . (Answers Hence Fatigue life (N) = (23 . 30 X10 yc ਓ