An Approximate Method for Fatigue‐life Prediction of Framed Structures

Abstract

The propagation of fatigue cracks in framed metal structures, usually described by Linear Elastic Fracture Mechanics, is analysed here and described by a numerical method based on classical beam theory. A procedure to be used in practice for the evaluation of stiffness degradation and energy release rate is presented. The procedure uses formulae which are explicitly given for statistically determinate beam structures that are being progressively damaged. If implemented into any beamoriented finite element code as shown here, the proposed approach allows one to deal also with redundant structures. NOMENCLATURE a = crack length A = sack surface ci = beam width under the stress diffusion lines b, h, 1 = beam depth, width and length C1. C,, ml, m, = coefficients in Pariplike laws d = deflection E' = effective elastic modulus E = Young's modulus g,f', g' = functions of crack length and cross section aspect ratios G = energy release rate per unit crack length = energy release rate per unit crack surface J = second moment of the area of beam cross-sections k = rotational stiffness of damaging spring K = stress intensity factor M = bending moment M , = bending moment at a critical section M, = bending moment at the beam end N = number of loadineunloading cycles r = stress diffusion distance U* = complementary energy O* = approximate complementary energy x, x = coordinates along the beam axis a = a/h = dimensionless crack length d = ci/h = dimensionless width under the stress diffusion lines q = d/d, = dimensionless deflection to, ilr p I dimensionless contributions to complementary energy K = KZJob/Mc -dimensionless function of stress intensity factor p = M,/Mc = ratio of the bending moments at the beam ends v = Poisson's ratio o=ratio of the actual to the initial value of the bending p = r/h = dimensionless stress-diffusion distance moment in a critical section t, 4 = x/h, ~/ h = dimensionless coordinates ( 0)0 = reference value of ( 0 ) in the undamaged configuration ( O h = maximum value of ( 0 ) (Oh = threshold value of ( 0 ) A( 0 ) = variation of ( 0 ) over one loading cycle (O), = critical value of ( 0 )