Fafigue Fmcf. zyxwvutsrqponm Engng Mafer. Struct. Vol. 9, No. 4, pp. 291-304, 1986 8756-758X/86 zyx $3.00 zyx + 0.00 Printed in Great Britain. All rights reserved Copyright zyxwv 0 1986 Fatigue of Engineering Materials Ltd ANALYSIS OF FATIGUE CRACK PROPAGATION UNDER BIAXIAL LOADING USING AN INCLINED STRIP YIELD ZONE MODEL OF CRACK TIP PLASTICITY J. AHMAD,' B. N. LEIS' and M. F. KANNINEN' *Southwest Research Institute, San Antonio, Texas, U.S.A. 'Battelle Columbus Division, zyxwvut 505 King Avenue, Columbus, OH 43201-2693, U.S.A. (Received zyxwvut in final form 9 June 1986) Abstract-The work reported in this paper is based upon an inclined strip yield zone model of crack tip plasticity under biaxial remote loading. Equations are developed to predict fatigue crack growth rate under steady state conditions. A qualitative agreement between model predictions and experimental data is shown. NOMENCLATURE E = modulus of elasticity Y = tensile yield stress of material zyxwvut p = biaxiality ratio; minimum/maximum principal stress u = far field stress; u,,, maximum value in cycle a = crack length K = stress intensity factor; K,,,, corresponding to u, R = ratio of minimum to maximum stress zyxwvu u, = closure stress; zyxwvutsrq Kct, corresponding value of K AK = range of stress intensity factor Kop = value of K corresponding to crack opening u(x) = crack opening displacement at position x along crack line B, b = strengths of the residual and nascent dislocations L, I = distances from crack tip to dislocation along slip plane related to B and 6, respectively da/dN = crack growth rate per cycle b, = strength of most recently emitted dislocation b, = strength of j t h superdislocation a, = crack length at time j t h dislocation is emitted 0 = angle between crack-line and slip-plane T,, = shear stress on slip-plane occupied by n th superdislocation h,, g, = normalized known functions of the position of the superdislocation &, d, = known functions of position INTRODUCTION Direct consideration of the plastic deformation attending a crack tip is becoming essential in many different aspects of fatigue analysis. As examples, crack tip plasticity is undoubtedly a key element in fatigue crack growth retardation and in the short crack effect. Unfortunately, elastic-plastic computations generally require finite element or other numerical methods that are too cumbersome to be applied in routine fatigue crack growth analyses. An alternative that has found favor with many investigators is a quasi-plastic approach based on a strip yield zone representation. One such model is the inclined strip yield zone originally suggested by Bilby and Swinden [ 11. This approach has been extended 29 1