Crack, semi-infinite

The crack, semi-infinite in length, is assumed to propagate along the interface of two linearly elastic half spaces with a steady state velocity of a under small-scale yielding conditions, which implies that the region of pullout is small compared with typical specimen dimension. The interfaces are reinforced by chains which obey the pullout laws stated above. The steady state condition implies that all quantities are independent of time with respect to an observer moving with the crack tip. 

He and Hutchinson (1989) considered a crack approaching an interface as a continuous distribution of dislocations along a semi-infinite half space. The effect of mismatch in elastic properties on the ratio of the strain energy release rates, Gi/Gj, is related to two non-dimensional parameters, the elastic parameters of Dundurs, a and /f (Dundurs, 1968) ... 

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. 

The dynamic stress intensity factor, KId, of a stationary semi-infinite crack, which is impacted by a square plane tension wave, or0, of duration t, in... 

Figure 4. Crack extension curves for API 5L X42 tubular structure with a semi-infinite crack along the length of the structure 300 nun inside diameter, 10 MPa maximum gas pressure. The X denotes the critical crack depth for fracture under constant load.

For very thick films, the behavior is well described by results that assume the film behaves as a semi-infinite half-space. In this limit, the geometry corresponds to that of a pressurized crack, such that the inner surface of the film displaces according to the well-known analytical result (e.g., [33])... 

However, if a free surface is introduced, i.e. for an edge crack of length a in a semi-infinite sheet that is under a distant tensile stress, computer methods are needed to show that... 

To this point, it has been assumed that the external boundaries are infinite or semi-infinite. For the geometry shown in Fig. 8.16(d), this is not the case and the crack front can now sense the boundaries of the body. The crack tip stress field must be carried by a smaller amount of material and, thus, the stress intensity factor is enhanced. The external surfaces can be considered to attract the crack and the geometric factor can be written as... 

An alternative stress analysis approach, is based on the local stress field near a crack tip. Fig. 5. The solution of the boundary value problem for a semi-infinite, linear-elastic cracked body was found by Williams [48], and yields the Williams expansion of the stress field in a cracked body. The first term determines the local stress field in the vicinity of the crack tip ... 

A semi-infinite crack (as shown in Fig. 8.3) in a single Al crystal with H atoms at the crack tip has been studied by using the QCDFT method [85]. Ab initio studies have showed that the Al-Al bond can be attacked by H with a significant charge transfer from the Al atoms... 

Fig. 5.15. Simple expressions for stress intensity factor Kj can be obtained for a crack of width la in a plate of infinite dimension and for a notch of depth n in a plate of semi-infinite dimension...

Different formulations of fracture mechanics provide different fracture parameters. Linear elastic fracture mechanics (LEFM)(D defines a stress field parameter K which reflects the overall intensity of the stress field around the crack. Failure occurs when K achieves its critical value K. The formula for K depends on the test specimen configuration, but for a central crack of half-length c in a semi-infinite sheet, for example, it is given by... 

As it turns out, this relation holds not only for the considered configuration with a crack in the center of an infinite plate, but also for finite plates and even for other locations of the crack, for example, for a semi-infinite plate with a notch at the edge. The critical value of the stress intensity factor Kic follows from a combination of Eqs. (8.55) and (8.50), as... 

It has been shown [55,99] that, regardless of whether cracking occurs in the substrate, coating, or interface, the energy release rate driving crack propagation for a thin film on a semi-infinite substrate with a residual stress, cr, can be expressed in the following form ... 

In their analyses for the sandwich geometry shown in Fig. 4, the adherends were assumed to be semi-infinite, the adhesive was assumed to be linear elastic, and a semi-infinite straight crack was present within the adhesive layer. The... 

For an edge crack in a semi-infinite specimen, the integration is to be corrected with Y = replaced by. Vl fn (Table 7.2) ... 

Figure 8.9 Schematic representations of (a) an interior crack in a plate of infinite width and (b) an edge crack in a plate of semi-infinite width.

Concerning the original presence of cracks, it has to be said that their generation mechanisms are not all well understood. Generally they occur in welds. Concerning their shape, obviously the field of the various possibilities is infinite and therefore, for quantitative evaluations, it is necessary to apply simple conservative assumptions. Usually it is assumed that the cracks are semi-elliptical and superficial, with a depth a. The length 2c of the crack is assumed as a fixed multiplier of its depth (typically ajlc = 1/6). 

These figures have been obtained for a surface semi-elliptical crack with ajlc = 1 /6 if, with the same distribution of depth, all the cracks had been considered infinitely long, the final probabilities would have been 10 times higher. 

Figure 2. Schematic cross section illustrating the crack driving forces acting during indentation crack extension the localized loading of the residual stress intensity factor, K, and the uniform loading of the applied stress intensity factor, K. The semi elliptical surface crack is modeled as a circular crack in an infinite body.

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