Mode Ii Stable Crack Growth

Abstract

Mode I1 stable crack extension has been examined for an aircraft grade aluminium alloy D16AT. Both theoretical and experimental results are presented. The experimental observations include load displacement diagrams, plastic wake, crack front tunnelling and scanning electron micrographs of the fracture surfaces. The crack shows a tendency for in-plane extension, and the fracture surface is very flat, smooth and free of any dimples. The crack front advances with neghgible tunnelling at all stages of extension. The span of mode II stable crack growth (SCG) is longer than in the case of mode I SCG reported earlier for the same material and there is also more extensive plastic deformation. In the presence of a slight mode I load, the crack grows out-of-plane and the fractured surface facets resemble that of a mode I or mixed-mode dimpled fracture. The theoretical study is based on a finite element analysis using small deformation theory and incremental plasticity. Some of the experimental results have been theoretically predicted using the COA criterion as the governing criterion. The theoretical results include loaddisplacement diagrams, crack edge displacement curves, plastic zones and the J resistance curves. There is good agreement between the load-displacement diagrams. The initiation and maximum loads differ by less than 15%. The J resistance curve has a constant slope over the whole span of stable crack growth. Keywords: Mode I1 crack growth, crack opening criterion, plastic zones, D16AT (2024-T3) aluminium alloy. NOMENCLATURE a,, a = initial, and instantaneous crack length COA, COD = crack opening angle and displacement Aa = crack extension d = element size around crack tip f = notch size E, ET = Young's modulus and tangent modulus Jc(I), Jc(l,) = plane stress fracture toughness in mode I and mode I1 Kc,), qe, = plane stress fracture toughness in mode I and mode I1 P, Pi, P, , = load, initiation load, and maximum load Ji, = initiation value of J r, r, = radius, and plastic zone size SCG = stable crack growth SIF = stress intensity factor t =thickness of specimen v = Poisson's ratio 6, = critical crack opening displacement A = crack opening displacement & = critical crack opening angle zy = yield stress in shear ou, oy = ultimate and yield stresses 'Permanent address:

Experimental investigation on ductile stable crack growth emanating from wire-cut notch in AISI 4340 steel

“…It may also be noted here that, the tunnelling is linked to a non-uniform distribution of SIF along the crack front. It is maximum at the centre and minimum at the surface (Mourad and Maiti, 1996). As a consequence, crack growth will initiate early at the centre.…”

“…The tunnelling effect can be as large as 8 mm (Ahmad et al, 1983) in mode I and mixed mode. There is no tunnelling effect in pure mode II (Mourad and Maiti, 1996). The crack sometimes grows through the centre of the specimen stably up to 6 mm (Shan et al, 1994).…”

“…In the second stage predictions based on the trial criterion are verified by experiment. Some of the candidate criteria, that are considered, are the contour integral J (Narasimhan et al, 1992), crack opening displacement COD (Ma et al, 1999(Ma et al, , 2001, crack opening angle COA and crack tip opening angle CTOA (Newman, 1984;Mourad, 1995a, 1995b;Mourad and Maiti, 1996), stretch zone width (Otsuka et al, 1974(Otsuka et al, , 1976(Otsuka et al, , 1977Ebrahimi and Seo, 1996) and local energy criterion (Tvergaard and Hutchinson, 1992). In the micromechanics approach the ductile fracture mechanism is studied through void/damage nucleation and growth model.…”

“…There is also a considerable similarity in the facets for pure mode I and mixed modes (I and II). The facets for pure mode II are different (Mourad and Maiti, 1996). Rice and Thomson (1974) were among the first to investigate the problem of the competition between ductile and brittle behaviour of a material.…”

“…The characterization of mixed mode loading is therefore important. Many investigators have addressed the problem at the micro-(e.g., Aoki et al, 1987;Otsuka et al, 1987;Knott, 1991, 1992;Tvergaard and Hutchinson, Nomenclature a 0 initial crack length a 0 /W crack length to specimen width ratio CMOA crack mouth opening angle COA, COD crack opening angle and displacement CTOA, CTOD crack tip opening angle and displacement E Young's modulus J the contour integral L-LLD load-load line displacement MTPS maximum tangential principal stress MTS maximum tangential stress P, P i , P max load, initiation load, and maximum load SCG stable crack growth t specimen thickness σ y yield stress in tension φ load line-crack orientation angle ( • ) θ crack initiation direction ( • ) 1992; Narasimhan et al, 1992) and macro-levels (e.g., Aoki et al, 1990;Newman, 1984;Ma et al, 1999Ma et al, , 2001Sutton et al, 2000;Mourad, 1995a, 1995b;Mourad and Maiti, 1996;Otsuka et al, 1974Otsuka et al, , 1976Otsuka et al, , 1977Otsuka et al, , 1987. Majority of the investigators focus on the combination of modes I and II.…”