Mode II cracking

When the interlaminar cracks form by tunneling, the solutions have a direct analogy within the transverse cracking results described above.98 In shear loading, the tunnel cracks evolve and orient such that a Mode II crack develops, as sketched on Fig. 1.36. There is a critical shear stress, r , at which interlaminar shear failure occurs, given by... 

Figure 3.493 displays the mode II crack top zone for CF/Epoxy composite. At very higher magnification it is observed that crack formation is similar to that observed in CF/PEEK composite. A significantly smaller damage zone is observed in the more brittle CF/... 

Figure 3.491. Higher magnifications of the damage zone ahead of a mode II crack in CF/PEEK fa) 0.25 mm ahead tbt 0.12 mm ahead (c) 0.06 mm ahead [1317].

Figure 3.493. In situ mode II crack in CF/epoxy (a) very high magnification of the region ahead of the crack tip (b) crack with shear cusps as the edges (arrow) and a bridging fibre in the interior of the crack [1317],...

The tests of concrete specimens subjected to Mode II fracture were aimed at a further investigation of relations between fractal dimension and roughness of the fracture surface after Mode II crack propagation and are presented below based on paper by Brandt and Prokopski (1993). 

Finite element modelling on a microstructural scale indicates that internal yield has the appearance of a Mode II crack phenomenon (the shear strength of the microstructure depends on the inverse of the square root of the platelet diameter and is independent of the magnitude of the normal stress on the grain). There is a correlation between the macroscopic yield stress Y used in (2) above with the inverse square root of the grain size. 

The relevance to the present work is that the scale of contacts in the mica platelets studied here is in the order of 1 to 10 pm. This is the intermediate zone referred to by Johnson in which the frictional stress depends upon the inverse square root of the grain size in the manner of a Mode II crack. It has been previously shown that estimations of yield stress for a range of platelet sizes based on an inverse square root law yielded predictions of macroscopic behavior that agreed well with experimentally observed behavior and that the macroscopic yield stress was determined to be in the order of 1 GPa. A yield stress in the order of 1 GPa gives a value of So in the order of 500 MPa, precisely within the intermediate zone described above. The nature of the observed Mode II behaviour on the microstructural scale is thus explained. 

A crack in a body may grow as a result of loads appHed in any of the three coordinate directions, lea ding to different possible modes of failure. The most common is an in-plane opening mode (Mode I). The other two are shear loading in the crack plane (Mode II) and antiplane shear (Mode III), as defined in Figure I. Only Mode I loading is considered herein. 

The above discussion has assumed that the crack is loaded in mode 1 (the crack opening mode, with a tensile stress normal to the plane of the crack). Hydrogen has relatively little effect in modes II or III, as these generate shear stresses at the crack tip, rather than tensile stresses, and the shear behaviour of steels is relatively little affected by hydrogen, presumably because dilation of the lattice at the crack tip (which does not occur in modes II and III) is required for hydrogen accumulation. 

Composite structures in service are often subjected to complex 3-D load paths. In general, a delamination will be subjected to a crack driving force with a mode I opening, a mode II forward shear and a mode III anti-plane shear, as illustrated in Fig 3.29. Because delamination is constrained to grow between individual plies, both interlaminar tension and shear stresses are commonly present at the... 

Fig. 3.29. Modes of interlaminar crack propagation (a) Mode I opening mode (b) Mode II sliding shear...

Benzeggagh, M.L., Prel, Y.J. and de Charentenay, F.X. (1985). Instrumentation of mode I and mode II tests for crack tip strain profile study under static and cyclic loading. In Proc. ECCM-l, p. 291. 

Vu-khanh, T. (1987). Crack arrest study in mode II delamination in composites. Polym. Composites i, 331. 

Three modes are clearly defined for crack propagation from a very thin (radius of the order of 10 gm) notch-machined in the specimen (Fig. 12.3). This notch induces a stress concentration effect, higher than those produced by all the other defects already present in the specimen, which governs the fracture initiation. For isotropic materials, mode I (the most severe) is generally used and gives the lowest value of toughness. In the case of adhesives and laminates, modes II and III are also performed. 

During a fracture-mechanical test performed in mode I, the crack propagates in this mode from a macroscopic point of view. But the crack can be deflected locally by the rubbery particles and can also propagate in mode II. As for isotropic materials, GIIc is generally higher than GIc an artificial increase of the macroscopic GIc value will be then evidenced. 

CMCs with 2-D fiber architecture are susceptible to interlaminar cracking in various component configurations (Fig. 1.38). In such cases, as the crack extends through the component, conditions range from Mode I to Mode II. Tests and analyses are needed that relate to these issues. Most experience has been gained from polymer matrix composites (PMCs).99 The major issue is the manner whereby the interlaminar (transverse) cracks interact with the fibers. In principle, it is possible to conduct tests in which the cracks do not interact. In practice, such interactions always occur in CMCs, as the crack front meanders and crosses over inclined fibers.100,101 These interactions dominate... 

Fig. 18 Calculated values of the mode I (Ki) and mode II (Kn) stress intensity factors within a cracked epoxy at various stages of a cyclic contact loading. Two cracks 350 nm in length and oriented at 10° with respect to the normal to the epoxy surface have been considered. For symmetry reasons, only the results corresponding to one crack (denoted A) have been represented. The tangential cyclic loading has been divided into eight successive steps...

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