Crack loading modes

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.

At this stage, it should be noted that Kj refers to a crack loaded in uniform tension, or Mode I. Other crack loading modes exists as shown in Figure 14.6, and Eq. (19) may be more completely defined as ... 

Figure 14.6 Crack loading modes. Mode I =tension Mode II =shear Mode III =torsion.

John, C.F. The effect of crack loading mode on stress corrosion cracking. Scr. Metall. 9, 141 (1974)... 

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. 

In more recent work embrittlement in water vapour-saturated air and in various aqueous solutions has been systematically examined together with the influence of strain rate, alloy composition and loading mode, all in conjunction with various metallographic techniques. The general conclusion is that stress-corrosion crack propagation in aluminium alloys under open circuit conditions is mainly caused by hydrogen embrittlement, but that there is a component of the fracture process that is caused by dissolution. The relative importance of these two processes may well vary between alloys of different composition or even between specimens of an alloy that have been heat treated differently. 

A crack at a notch tip in a solid sample can propagate according to three different loading modes. The propagation occurs in ... 

Some other factors, including the metallurgical condition of the material (such as composition and heat treatment) and the loading mode (such as uniaxial), affect corrosion fatigue crack propagation. (Glaeser and Wright)5... 

We present recent results on the analysis of the interaction between plasticity and crazing at the tip of a preexisting crack under mode I loading conditions. Illustrations of the competition between these mechanisms are obtained from a finite element model in which a cohesive surface is laid out in front of the crack. 

The first term is symmetric in 0, while the second is skew symmetric and they repre nt the opening Mode I and sliding Mode II of crack loading, respectively. Mode I is essentially that for loading normal to the crack, while Mode II is that for shear loading. Since Mode I is by far the most common, we shall confine our attention to the first term which is usually expressed as ... 

Brittle separation of an adhering system, under loading perpendicular to the interface, normally occurs in a crack-opening mode. 

This approach tends to be limited to high strength alloys since these often have mechanical properties that are closest to the ideal required and because of their engineering importance. The type of specimem employed takes into account the stress concentration arising from the presence of a crack in a specimen and employs a measured component K, the stress intensity factor, which is obtained from the applied stress a X c1/2, where c is the crack depth. It has units MN m 3/2. If such specimens are now tested as a function of time-to-failure, the results obtained are of the kind shown in Figure 2. Again, the question arises of a threshold which is such specimens is termed where the subscript I refers to the loading mode( 5). The whole term represents that value of K below... 

FIGURE 39.4 Modes of crack loading for the scenarios considered here, mode in is assumed to be zero due to the absence of deformation gradients parallel to the crack front. 

The geometry given in Fig. 8.3, a crack loaded in uniaxial tension (mode I), has been discussed several times in this chapter. It is also shown in Fig. 8.16(a), emphasizing the presence of infinite boundaries (small crack size). For this geometry... 

Superposition of K solutions is subjected to the same restrictions as those used for stresses and displacements. For example, the stress intensity factors must be associated with a single loading mode, often mode I, and the body geometry should be the same. An additional restriction is that the crack surfaces must be separated along their entire length in the final configuration. This can be a problem if one of the basic solutions involves compressive stresses that push the crack surfaces together. 

In these expressions P, Q and R are the point forces for the various loading modes, 2a is the crack size and b is the position of the point force. Allowing b to... 

Brittle failure appears to occur almost exclusively in mode I loading but it is clear that cracks that initiate fracture may be oriented such that other loading modes are present. For example, consider the crack shown in Fig. 8.49. The applied stress can be resolved into the normal and shear components using Eqs. (2.42) and (2.44) with 0=ir+a, thus... 

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