Shear cracking

Stresses can can be concentrated by various mechanisms. Perhaps the most simple of these is the one used by Zener (1946) to explain the grain size dependence of the yield stresses of polycrystals. This is the case of the shear crack which was studied by Inglis (1913). Consider a penny-shaped plane region in an elastic material of diameter, D, on which slip occurs freely and which has a radius of curvature, p at its edge. Then the shear stress concentration factor at its edge will be = (D/p)1/2.The shear stress needed to cause plastic shear is given by a proportionality constant, a times the elastic shear modulus,... 

The occurrence of earthquakes is a highly studied phenomena by geologists. The role of solid surfaces in such phenomena is obvious. Especially, faults are known to contribute to many earthquakes. Faults are treated as shear cracks, the propagation of which may be understood through the application of fracture mechanics. The stability of any fault movement, which determines whether the faulting is seismic or aseismic, is determined by the frictional constitutive law of the fault surface. It is well established that, once a fault has been formed, its further motion is controlled by friction (between the solid surfaces), which arises from contact forces across the two solid surfaces. 

Fig. 35a. Mechanism of crack I ormalion at intersections of shear bands (i) sequence of shear band formation, jii) chain scission at the intersections (schematic) b Shear crack formation (arrow) in a shear band of type A, leading to a 50 pm wide displacement of type B — shear bands on both sides of the crack...

Further fracture surface features, especially distinct for the highly isotactic, coarse spherulitic PP, are polyhedron shaped regions at which the shear crack has left the shear fracture plane in order to stay in a spherulitic boundary region oriented at a flat angle to the sliding direction (Fig. 37d). These sites often constitute secondary crack nuclei in boundaries perpendicular to the shear fracture plane. 

The use of the generalized Griffith criterion not only allows cracks to extend under tensile loading, but also allows cracks to extend in shear, even under moderate normal compression. This means that closed shear cracks can extend under intense loading (as near an explosive charge), causing the material to be much weaker under subsequent tensile loading. The reduction in the elastic moduli is also important in that it leads to the correct directional response as the rock is fractured. Thus, phenomena such as spall are modeled in a realistic fashion. 

Figure 5.35 Schematic diagram of responses of an oxide which is loaded in compression. (a) Buckling of the oxide, (b) shear cracking of the oxide, and (c) plastic deformation of the oxide and alloy.

The buckling stress. Equation (5.40), increases as the square of the scale thickness such that, for thick scales, buckling may not be feasible. In this case, shear cracks can form in the oxide and, if Equation (5.39) is satisfied, lead to scale spallation by a wedging mechaiusm, which is shown schematically in Figure 5.35(b). 

With increase of the roadway depth, the left side and the right side of the roadway are subjected to tensile, shear, or combined stress state. Thus, tension crack, shear crack or mixed mode crack are existed in these locations. 

Debonding failure mode 2 Debonding at shear cracks or discontinuities (high shear forces or discontinuities result in high shear stresses between the strip and concrete)... 

In order to prevent debonding of the strips at shear cracks or discontinuities, the existing shear stresses, Tb, should be limited. By using ordinary cross-section analysis, the strain in the EBFR and the shear stress can be calculated using (see Fig. 4.16) ... 

State I Uncracked cross-section, i.e. no shear cracks exist, the concrete carries the whole load, virtually no stress in the shear reinforcement. 

State II Shear cracks exist, the internal shear reinforcement (ISR) is in the elastic region, the ISR and the EBSR carry the load in proportion to their stiffness. 

State III Shear cracks exist, the ISR yields and the EBSR carries the further increase in load. 

Several equations for the concrete contribution can be found in the relevant literature. However, this equation describes the design shear resistance of a RC member without shear reinforcement. It is important to note that this definition for the concrete contribution is different from the definition of State r given above in this section. To determine Erc, the load at the first shear crack should be calculated. Additionally, all the usual design verifications for RC (failure of the concrete struts, shift of moment line, etc.) have to be considered. For ductility reasons, the member should have a minimum internal shear reinforcement ratio, otherwise strengthening is not recommended. 

The most common forms of cracks due to structural loading are those transverse to the direetion of the main reinforcement, caused by direct or flexural tension, and diagonal shear cracking. 

Shear strength. The bulk shear strength of the hardened adhesive at 20 C should be at least 12 MN m -. A specimen 200 mm X 12 mm x 25 mm deep tested in a shear box, as shown in Fig. A.3, is recommended(4). The complete assembly is loaded in compression through a spherical bearing at a rate of 1 mm/min. The failure load is taken as that load at which shear cracking first... 

Fracture t es are of interest in fracture mechanics in nnderstanding and classifying the way a material fails. Different terms are nsed to describe the cracking behavior. In the following section the terms opening crack and mode F are S5mon5mous, as well as mode II and mode III for shear cracks, with forces parallel to the crack (in-plane shear) or forces perpendicular to the crack (out-of-plane shear). In seismology, shear dislocations are described by a double couple (DC) source because the DC force representation allows simplification of some mathematics - this is explained later in more detail (see chapter 5.6.3). 

Fig. 5.17. Radiation pattern of a vertically oriented shear crack showing variation of polarities and amplitudes with angle from the source.

The deviatoric component can be further decomposed into a variety of eigenvalue combinations that represent simple arrangements of equivalent body forces, adapted from fracture mechanics, like that of an opening crack (mode I) or of shear cracks (mode II or III) (Fig. 5.27),... 

Fig. 7.17. (a) Dislocation model for a shear crack, (b) the corresponding moment tensor and (c) double-couple model. 

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