Maximum shear strength criterion

In the shear strength criterion, the debond crack propagates when the maximum IFSS at the debond crack tip z = L - tj reaches the shear bond strength, tb, i.e. 

Based on the shear strength criterion for the interface debonding, the condition for the fully bonded interface requires that the maximum IFSS be obtained at the... 

The maximum shearing stress criterion for failure simply states that failure (by yielding) would occur when the maximum shearing stress reaches a critical value (i.e., the material s yield strength in shear). Taking the maximum and minimum principal stresses to be and 03, respectively, then the failure criterion is given by Eqn. (2.3), where the yield strength in shear is taken to be one-half that for uniaxial tension. 

The Hart Smith criterion proposes that the strength of laminates be characterised by generalizing the maximum-shear-stress criterion for ductile isotropic metals. 

If adhesives are ductile, strength criteria based on shear stress components are often used with analogies to metals. For example, the maximum shear stress criterion called the Tresca s criterion (Tresca 1869) or the maximum shear-strain energy criterion called the Mises criterion (von Mises 1913) are well known, and they can be shown as follows ... 

As With the shear strength, the maximum shear strain is unaffected by the sign of the shear stress. The strains in principal material coordinates, 1- yi2 be found from the strains in body coordinates by transformation before the criterion can be applied. 

In many situations, the yield strength is used to identify the allowable stress to which a material can be subjected. For components that have to withstand high pressures, such as those used in pressurized water reactors (PWRs), this criterion is not adequate. To cover these situations, the maximum shear stress theory of failure has been incorporated into the ASME (The American Society of Mechanical Engineers) Boiler and Pressure Vessel Code, Section m. Rules for Construction of Nuclear Pressure Vessels. The maximum shear stress theory of failure was originally proposed for use in the U S. Naval Reactor Program for PWRs. It will not be discussed in this text. 

During the process of stress wave propagation, tensile stresses or shear stresses do occur and cause rock material to fail in tension or in shear. Therefore, a modified principal stress failure criterion is applied to determining material status, which is suitable for describing material tensile failure or shear failure. The modified principal stress failure criterion dictates that when the major principal stress or the maximum shear stress in an element exceeds material tensile or shear strength, the element fails. After an element has failed, it will not be able to sustain any tensile and shear loadings, but it is still able to sustain compressive loading. The normal compressive stresses, and cr, of a failed ele-... 

Kinloch(4) observed that the selection of appropriate failure criteria for the prediction of joint strength by conventional analysis is fraught with difficulty. The problem is in understanding the mechanisms of failure of bonded joints, and in assigning the relevant adhesive mechanical properties. Current practice is to use the maximum shear-strain or maximum shear-strain energy as the appropriate failure criterion. However, the failure of practical joints occurs by modes including, or other than, shear failure of the adhesive. This difficulty has led to the application of fracture mechanics to joint failure. 

The in-plane stresses in a flat plate are -50 MPa and -150 MPa on two perpendicular planes and a shear stress of 40 MPa on those planes. Compute the maximum shear stress, the stress intensity and the von Mises equivalent stress. What is the factor of safety corresponding to (a) Tresca criterion, and (b) von Mises criterion if the material yield strength is 200 MPa ... 

Within the context of pressure vessel design codes, the comparison of the allowable strength of the material is always done with respect to the stress intensities. This puts the comparison in terms of the appropriate failure theory either the maximum shear stress theory (Tresca criterion) or the maximum distortion energy theory (von Mises criterion). These failure theories have been discussed in some detail in Chapter 3. 

Fig. 21 shows interfacial shear stresses for a carbon fiber-epoxy system. The low modulus of the epoxy matrix produces a similar effect on the stress distribution, as in the case of isotropic fibers. Calculations of interfacial shear strength assume either a maximum interfacial shear stress criterion or a maximum radial tensile stress criterion, ignoring other stress components and residual stresses in both cases. The interfacial shear strength (T ) is calculated from ... 

Roberts [8] introduced a failure criterion concerning the vibrational powder flow so that the bulk density pb in the shear zone correlates strongly with the maximum vibration velocity Vpeak- From this point of view, the applied vibrations lead to a decrease of the bulk density in the shear zone and hence the shear strength does decline. For given powder and preconsolidation conditions we can write ... 

For joints with ductile adhesives, the failure load is given by the load that causes adhesive global yielding along the overlap. This criterion works reasonably well provided the failure shear strain of the adhesive is more than 20%. However, for brittle adhesives, this methodology is not applicable (da Silva et al. 2008). For joints with a brittle adhesive, the Volkersen s model can be used (da Silva et al. 2009b) and the failure occurs when the maximum shear stress at the ends of the overlap exceeds the shear strength of the adhesive. Alternatively, the finite element method can be used. 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

So far we have employed in this discussion a critical shear stress as a criterion for fibre fracture. In Sect. 4 it will be shown that a critical shear strain or a maximum rotation of the chain axis is a more appropriate criterion when the time dependence of the strength is considered. 

The strength of a fibre is not only a function of the test length, but also of the testing time and the temperature. It is shown that the introduction of a fracture criterion, which states that the total shear deformation in a creep experiment is bounded to a maximum value, explains the well-known Coleman relation as well as the relation between creep fracture stress and creep fracture strain. Moreover, it explains why highly oriented fibres have a longer lifetime than less oriented fibres of the same polymer, assuming that all other parameters stay the same. 

The other approach for the shear resistance of masonry shear walls is based on the Tumsek and Sheppard (1980) criterion, which is based on the assumption that diagonal cracking occurs when the maximum principal stress at the center of the wall reaches the tensile strength of the masonry. 

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