Question

Consider the metal specimen described in Problem 11 above (KIC =58 MPa-sqrt(m); edge crack measures 9.711 mm; Y = 1.1; Paris’ m = 3.1 and Paris’ A = 1.7E-12 meters / (cycle-MPa-sqrt(m)) ^3.1).    Use Excel and Goal Seek to estimate the cyclic tensile stress amplitude that results in fatigue life of 1.714E6 cycles.

Answer 1

"k_1c = 58 MP/m^2 Initial crack length Delta i = 9.711 mm m = 3.1 A = 1.7 times 10^-12 m/(cycle - MPa - m^1/2)^3.1 N = 1.714 times 10^6 cycles cyclic Tensile strength amplitude sigma _max = ? let min stress be zero Poris eqn, da/dN = A (Delta k)^m Delta k = k_max - k_min Delta k = sigma _max squareroot pi a \r\n da/dN = A (sigma _max squareroot pi a)^m Rearranging, da/a^m/2 = A (sigma _max squareroot pi)^m dN Integrating, integral _a_i^a_c da/a^m/s = integral _0^N A (sigma _max squareroot pi)^m dN integral _a_i^a_c da/a^1.55 = integral _0^N A (sigma _max squareroot pi)^m dN -1.818/a^0.55