Crack extension modes

Irwin [6-14] extended Griffith s theory to elastic-plastic materials and pointed out the three kinematically admissible crack-extension modes shown in Figure 6-10. These modes, opening, fonward-shear, and parallel-shear, can be summed to obtain any crack. 

The symmetric stress-intensity factor k, is associated ith the opening mode of crack extension in Figure 6-10. The skew/-symmetric stress-intensity factor l<2 is associated ith the fonward-shear mode. These plane-stress-intensity factors must be supplemented by another stress-intensity factor to describe the parallel-shear mode. The stress-intensity factors depend on the applied loads, body geometry, and crack geometry. For plane loads, the stress distribution around the crack tip can always be separated into symmetric and skew-symmetric distributions. 

Fig. 8.6. Mode I potential energy release rate, GJ, plotted as a function of crack extension, Aa, for carbon fiber composites containing different matrices E (pure epoxy) ER (rubber-modified epoxy) ERF (short fiber-modified epoxy) ERP (rubber-and particle-modified epoxy). After Kim et al. (1992).

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

Available theoretical solutions in dynamic fracture are few, and limited to finite or semi-infinite cracks in an infinite solid for Mode I, self-similar crack extension. Despite the above limitations, short of conducting detailed numerical analysis of the crack tip state of stress, these solutions must be used to deduce the characteristics of the crack tip state of stress, as well as to extract the dynamic stress intensity factor for elastodynamic fracture mechanics. In the following sections, a brief description of available theoretical solutions is presented. 

A test may typically involve the extraction of force P and energy associated with the initiation of crack extension from an instrumented impact load-deflection trace (see Fig. 7) for a test conducted in three-point bending mode (Charpy arrangement). The associated fracture stress can be calculated from... 

If one compares Eqs. (8.31) and (8.34), one notes that G increases with crack length for constant load but decreases for constant displacement. Thus, crack extension in the DCB geometry can be stable or unstable, depending on the mode of loading. A third variant of the DCB test is to load the cantilever arms using a constant moment arrangement, as depicted in Fig. 8.18. For this case, it has been shown that... 

When cracks extend in mode I loading in LEFM they release elastic strain energy in the surrounding stress field. The rate of release of such energy with crack extension can be considered as a generalized crack-driving force and is alternatively a direct representation of the work of fracture when a critical condition Gic for crack extension is reached. 

K characterizes the stress distribution field near the crack tip the subscript Roman one, I, refers to the opening or tensile mode of crack extension a is a geometric factor appropriate to a particular crack and component shape the remainmg symbols are the same as in Eq. (24.15). Unfortunately, Kt and K have similar symbols, similar names, and are expressed in terms of the same quantities. However, oin effort to change this situation would largely be wasted. 

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