A theoretical model for roughness induced crack closure

Abstract

A theoretical model for the effects of grain size on the magnitude of roughness induced crack closure (RICC) at fatigue crack growth threshold has been proposed. With the basic configuration of a crack propagating incrementally along planar slip bands and deflecting at grain boundaries, an idealized zig-zag crack path is considered. The effective slip band length is considered to be equal to grain size. It is assumed that the dislocations emitted from the crack tip upon loading to form the pile-up are completely irreversible to produce a combined mode I and mode II displacement at the crack tip. The assumption of continuously distributed dislocations in the pile-up facilitated the calculation of crack tip sliding displacement (CTSD) along the slip plane from which the mode I closure disregistry just behind the crack tip can be calculated. The closure stress intensity factor at threshold, Kcl,t h could then be expressed as a function of critical resolved shear stress, average macroscopic yield stress, angle subtended by the slip plane with the crack plane and the length of the slip band. Comparisons of the predicted trends with experimental data from various alloy systems indicate good agreement. NomenclaturePICC = Plasticity induced crack closure U = OICC = Oxide induced crack closure RICC = Roughness induced crack closure U~, U u = AK~h = Alternating stress intensity range at 0 = threshold hk/ Tcrss = Kcl,t h = Closure stress intensity level at threshold r 0 = K,~ax = Maximum stress intensity factor in a fatigue cycle ~l(x), q(x') = Dislocation distribution functions CTOD = z,, = Applied shear stress CTSD = b = Burger's vector E = G = Shear modulus a~. = v = Poisson's ratio 6,n~x = 1 = Length of the slip band or pile-up 6~ = N = Number of dislocations in the pile-up d =

Effect of mean stress (stress ratio) and aging on fatigue-crack growth in a metastable beta titanium alloy, Ti-10V-2Fe-3Al

“…This is because of the fact that the FCG test data from regular CT and side-grooved CT specimens agreed als. [11,12,30] In this study, the relatively high fracture-surface roughness observed in the -aged microstructure suggests well with each other. that the dislocation pileup lengths were on the order of the prior-␤ grain size, with the crack deflecting at the prior-␤ E. Fatigue Fracture Mechanisms in the Neargrain boundaries, during crack growth.…”

“…In any case, this FCG region, crack propagation is accomplished by dislocation movement by mode II shear at the crack tip. Generally, effect could not be attributed to the macroscopic crackplane deviations observed in the FCG tests of the -aged a single slip system is suggested to be active, [11,12,30] promoting a zigzagged crack path in polycrystalline materimicrostructure. This is because of the fact that the FCG test data from regular CT and side-grooved CT specimens agreed als.…”

Further results on ?A theoretical model for roughness induced crack closure?; Effect of yield strength and grain size

“…The predictions offered by the above expression are in good agreement[ 1] with the experimental results on titanium alloys, nickel base alloys and iron base klloys. In (1), K d is also a direct function of % apart from grain size While analyzing grain size effects on K d, the effect of d also has to be…”

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Recently a theoretical model for roughness induced crack closure during threshold fatigue crack growth in metallic systems has been developed [1]. The model closely predicts the functional dependence of crack closure stress intensity level, K d at threshold on grain size.

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“…The macroscopic yield stress cy can be assumed to be related to the shear yield stress ¢0 in the slip band as: Taking l=d, 0=70.5 degrees and ~=0.3 similar to previous study [1], this reduces to:…”