Tearing mode

Figure 5.39 The three modes of crack surface displacement (a) opening mode (b) sliding mode and (c) tearing mode.

Paris, P.C., Tada, H., Zahoor, A. and Ernst, H., (1979), The theory of instability of the tearing mode of elastic-plastic crack growth. In J.D. Landes, J.A. Begley and G.A. Clarke (Eds), Elastic-Plastic Fracture, ASTM STP 668. American Society for Testing Materials, Philadelphia, 5. 

For a very thin specimen i.e., with B (Kjc/ays) ), the influence of plastic deformation at the surfaces will relieve crack-tip constraint through the entire thickness of the specimen before Kj reaches Kjc. As such, the opening mode of fracture is suppressed in favor of local deformation and a tearing mode of fracture. The behavior is reflected in the load-displacement record by a gradual change in slope and final fracture, which could still be abrupt (see Fig. 4.7b), but the conditions of plane strain would not be achieved. 

Susceptibility to interlaminar failure is a major weakness of advanced laminated composite materials. It can occur by in-plane shearing (i.e., sliding) (mode II). and out-of-plane shearing (i.e.. tearing) (mode III) as well as by tensile (mode I) deformation. Mode II loading is of particular interest, as values have been shown to correlate with compression after impact data [142.143]. which is required for such purposes as civil aircraft certification. 

Figure8.il The three basic crack loading modes used in linear elastic fracture mechanics I, uniaxial tensile (opening) mode II in-plane shear mode III, out-of-plane shear (tearing) mode.

Mode III - the tearing mode - shear stress between the crack faces acting in a direction parallel to the crack front. 

Kic, K2c, Kic = critical stress intensity factor in the extension, shear, and tearing modes... 

Figure 1 shows a compact tension specimen in which a starter crack propagated at a controlled rate such that the test could be stopped prior to specimen failure. Whitened areas above and below the fracture surfaces are a result of particle cavitation. This particular material was a flexibilized vinyl ester containing a rubber particulate phase. The large volume of material involved in the fracture process resulted in high toughness and a ductile tearing mode of fracture as opposed to the brittle fracture mode of the base resin. 

Brittle solids fail in one of three possible modes, shown in Fig. 5.47. In mode I (the opening mode), both the crack plane and the direction of propagation are normal to the applied tension. In mode II (the sliding mode), a tensUe shear acts to slide the fracture planes over each other in the direction of stress. Mode IE (the tearing mode) is also a shear failure, except that the shear causes the fracture to propagate normal to the stress. Corresponding to these three modes, a material has three critical values of the stress intensity factor and... 

Cracks are usually subdivided into mode I, mode II, and mode III, based on the crack surface displacement. Mode I is the tensile mode and the most commonly encountered mode. The crack tip is subject to displacements perpendicular to the crack plane. In mode II or the sliding mode, the crack faces move relative to each other in the crack plane. Mode III is also referred to as the tearing mode, where the shear stress is acting parallel to the plane of the crack and parallel to the crack front (Figure 2.5). 

Some standard terminology will occasionally be used. If the stresses on the crack face are purely normal, the crack is said to be subject to opening mode or Mode I displacement, or it is simply referred to as a Mode I crack. If the stresses are purely shear, the crack is subject to sliding mode or Mode II displacement, while if the stresses are perpendicular to the plane, we have tearing mode or Mode III displacement [Irwin (1960), Sih and Liebowitz (1968), Sneddon and Lowengrub (1969) for example]. In this Chapter, we consider mainly Mode I displacement and, to a certain extent. Mode II. Tearing mode cracks, which are typically the simplest to analyze, are considered briefly in Chap. 7, in the context of inertial problems. 

Relationships analogous to (7.1.15) will also be given for the antiplane strain configuration, which prevails for Mode III or tearing mode crack problems (Sect. 4.1). In this case. 

I. Displacement-Traction Relationships. Displacement-traction relationships, in terms of Fourier transformed quantities, on the surface of a half-space, under plane strain conditions, are derived in Sect. 7.1 and given by (7.1.15) for steady-state uniform motion. A similar relationship between the Fourier transform of the displacement and tearing stress is given by (7.1.23) for tearing mode fracture, along the line of the crack. These have the same form as the equivalent elastic relations, with moduli replaced by complex moduli, as required by the Classical Correspondence Principle. 

III. Tearing Mode Crack Problem. This problem is solved, utilizing constraints imposed by Causality. The form of the tearing stress off the crack face on the line of fracture is given by (7.3.11) for the case where the velocity is in the range of speeds of sound of the medium [see (7.3.4)] and by (7.3.13a) for the subsonic case. The quantity is defined by (7.3.1 p) for a standard linear solid. The stress intensity factor for the two cases is given by (7.3.12) and (7.3.13b), respectively. 

A mode I type of fracture is an opening mode whereby there is a tensile stress normal to the plane of the crack, mode II type of fracture is a sliding mode, where a shear stress acts parallel to the plane of the crack and perpendicular to the crack front and a mode III fracture is a tearing mode where a shear stress acts parallel to the plane of the crack and parallel to the crack front. 

Mode III (Tearing mode). The shear component of stress is applied parallel to the leading edge of the crack (antiplane strain). This mode corresponds to mutual shearing parallel to the crack front. 

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