A fractographic study was carried out on fatigue crack closure and crack growth rates in an Al-Cu alloy under conditions of monotonic and cyclic yield at the notch root. Comparative tests were also conducted on smooth specimens subject to elastic loading conditions. A notch root fatigue crack can see substantial difference between crack closure and opening stress. This difference is considered responsible for local mean stress effects observed in notch fatigue response to complex load sequences. The difference between closure and opening stresses diminishes to negligible proportions as stress excursions reduce to elastic interval and is therefore hardly observed in long cracks. To support validation effort on predictions, notch root crack growth rates were determined from optical fractography under a programmed load adaptation of the FALSTAFF load sequence. The results of these measurements suggest that scatter in short crack growth data is similar to that in long cracks at comparable growth rates. Life to initiation of (naturally initiating) multiple notch root cracks is dissimilar. The crack having been in existence longest appears to assume the role of the dominant crack and accelerates others (smaller) cracks.

A numerical investigation of the fatigue crack closure phenomenon has been performed by an elastic-plastic finite element analysis. Computer software was developed to consider many aspects affecting plasticity-induced crack closure. Linear and power-law hardening models are considered in the finite element analysis. The paper presents results from the study carried out on compact tension (CT) coupons at various crack lengths corresponding to different loading conditions. Finally the results of the analysis are compared with the experimental estimates of fatigue crack closure levels obtained from laser interferometry, scanning-electron and transmission-electron fractography presented in Part I of this paper on identical specimens. NOMENCLATURE a, ai = length of the crack, initial crack length E = modulus of elasticity 2h = height of the specimen P = applied load level R = stress ratio S,, = applied stress level at which crack starts closing S, = applied stress level at which crack starts opening S,, = ratio of closure and maximum applied stress level gOp = ratio of opening and maximum applied stress level { U } = nodal displacement vector [ K , ] , [Re] = elastic stiffness matrix and modified elastic stiffness matrix S,,,,,, Smin = maximum and minimum applied stress levels t = thickness of the specimen W = width of the specimen Aa = smallest element length along crack plane A& = total strain increment A&e,, Acp1 = elastic and plastic strain increment go = yield stress in tension, i.e. effective yield stress ox, oy, uz = normal stress components E* = distortional strain E, = volumetric strain 963 964 N. E. ASHBAUGH et al.

Aluminium alloy sheet coupons with a central hole were tested in fatigue under specially designed programmed load sequences. Electron microscopy of the fatigue fracture surfaces showed striation mode fatigue crack extension up to more than a millimeter before onset of rapid failure. Crack opening stress was determined from striation patterns. Under variable amplitude loading and conditions of notch root cyclic inelasticity, crack opening stress exhibits noticeable hysteresis. The hysteresis is attributed to a difference between crack closure and opening stresses. A linear model of this phenomenon appears to describe observed behaviour.

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