Failure criteria maximum shear stress

In predicting limit (threshold) conditions, such as the elastic Kmit, yield, and failure conditions, classical failure criteria, such as the maximum normal stress criterion, maximum shear stress criterion and the distortion energy (von Mises) criterion can be employed. 

Fig. 3.5. Failure in multiaxial stress, o PMMA tubes (Broutman et al., 1231), a 6 PA tubes, A buckling (Ely, 1241), x PUR tubes (Lim, 1221), SBR membranes (Dickie et al., (251) ------maximum strain failure criterion, - - - octahedral shear stress failure criterion.

Criteria of Elastic Failure. Of the criteria of elastic failure which have been formulated, the two most important for ductile materials are the maximum shear stress criterion and the shear strain energy criterion. According to the former criterion, from equation 7... 

The maximum shear-stress theory has been found to be suitable for predicting the failure of ductile materials under complex loading and is the criterion normally used in the pressure-vessel design. 

If the maximum shear stress theory is taken as the criterion of failure (Section 13.3.2), then the maximum pressure that a monobloc vessel can be designed to withstand without failure is given by ... 

Manning (1947) has shown that the maximum shear strain energy theory of failure (due to Mises (1913)) gives a closer fit to experimentally determined failure pressures for monobloc cylinders than the maximum shear stress theory. This criterion of failure gives ... 

The maximum intensity of stress allowed will depend on the particular theory of failure adopted in the design method (see Section 13.3.2). The maximum shear-stress theory is normally used for pressure vessel design, and is the criterion used in BS 5500. 

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. 

Criteria 2, 5, and 6 are generally used for yielding, or the onset of plastic deformation, whereas criteria 1,3, and 4 are used for fracture. The maximum shearing stress (or Tresca [3]) criterion is generally not true for multiaxial loading, but is widely used because of its simplicity. The distortion energy and octahedral shearing stress criteria (or von Mises criterion [4]) have been found to be more accurate. None of the failure criteria works very well. Their inadequacy is attributed, in part, to the presence of cracks, and of their dominance, in the failure process. 

The maximum shear stress criterion, also called Tresca s criterion, would predict failure when the shear stress in the shaft equals the shear yield stress (determined by a tensile test). By stress resolution, the shear stress in a tensile test is equal to the normal stress divided by two. Hence the shear stress to produce yield for the material of interest here would be Oq/2, so that failure of the shaft is predicted when... 

Now that three separate values for the failure torque have been found for this shaft, the logical question Is which (If any) of the answers Is correct. The answer to this question depends very strongly on the nature of the material Investigated. For very brittle materials (e.g., cast unplastlclzed polystyrene), experiments have shown that the maximum principal stress criterion gives quite reasonable results. For ductile materials such as molded nylon, experimental evidence Indicates that either the maximum shear stress or octahedral shear stress criterion Is more appropriate. 

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-... 

Accordingly, and based on a maximum shear stress failure criterion (for justification see below), the following equation was appHed [17] ... 

The maximum-shear-stress criterion states that yield (or failure) occurs whenever the maximum shear stress, which is necessarily half the difference between the principal stresses, reaches a critical value. 

It has become evident that failure criteria such as maximum shear stress are inadequate since failure can also occur through other modes, such as tensile stresses in adhesive joints. Also, the uncertainty in the stress mode is magnified because properties of and stresses in adhesive joints are highly dependent on joint geometry. Therefore, complexities arise when deciding the proper criterion applicable to designing structural adhesive joints. 

Two basic theories of failure are used in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section I, Section IV, Section 111 Division 1 (Subsections NC, ND, and NE), and Section VIII Division 1 use the maximum principal stress theory. Section ni Division 1 (Subsection NB and the optional part of NC) and Section VIII Division 2 use the maximum shear stress theory or the Tresca criterion. The maximum principal stress theory (sometimes called Rankine theory) is appropriate for materials such as cast iron at room temperature, and for mild steels at temperatures below the nil ductility transition (NDT) temperature (discussed in Section 3.7). Although this theory is used in some design codes (as mentioned previously) the reason is that of simplicity, in that it reduces the amount of analysis, although often necessitating large factors of safety. 

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. 

Of the many theories developed to predict elastic failure, the three most commonly used are the maximum principal stress theory, the maximum shear stress theory, and the distortion energy theory. The maximum (principal) stress theory considers failure to occur when any one of the three principal stresses has reached a stress equal to the elastic limit as determined from a uniaxial tension or compression test. The maximum shear stress theory (also called the Tresca criterion) considers failure to occur when the maximum shear stress equals the shear stress at the elastic limit as determined from a pure shear test. The maximum shear stress is defined as one-half the algebraic difference between the largest and smallest of the three principal stresses. The distortion energy theory (also called the maximum strain energy theory, the octahedral shear theory, and the von Mises criterion) considers failure to have occurred when the distortion energy accumulated in the part under stress reaches the elastic limit as determined by the distortion energy in a uniaxial tension or compression test. 

Since the SSSC value is symmetric with respect to vectors n and s, it is invariant of the choice of the fault plane from the two nodal planes. The condition of the maximum shear stress Eq. 30 is not fully correct and physically means that faults should obey the so-called Tresca failure criterion where faults are assumed to have zero friction. Only faults with zero friction can achieve maximum shear stress and satisfy Eq. 30 for faults with friction, the SSSC value is always reduced (see Fig. 11). 

It is usually desirable to run a simple bulk tensile test program and subsequently predict (calculate) shear properties from their tensile counterparts. This approach requires a clearly defined relationship between shear and tensile elastic limit and yield variables and material properties. The elastic limit and yield stress values can be related between tensile and shear conditions by using an appropriate failure criterion, such as maximum normal stress, maximum shear stress, and distortion energy criteria. A material parameter that needs to be converted in addition to the usual elastic properties is the viscosity coefficient. This can be done by using Tobolsky s (1960) assumption of equivalent relaxation times in shear and tension. Application of this assumption results in the relation ... 

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. 

Cohesion c and angle of internal friction p are combined as failure criterion in Coulomb s law, which describes the maximum shear stress t at a given normal stress (T (Eq. 7.13) ... 

The von Mises criterion defines an ellipse in the 2D principal stress plane as shown in Figure 2.4. The maximum shear stress theory is also shown in Figure 2.4. However, for metals, while the maximum shear stress criterion is conservative, not only can the von Mises criterion be derived, but it also fits the experimental data better than the maximum shear criterion, and thus is the best estimation of the failure envelope. 

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 ... 

This failure criterion is given in terms of the octahedral shearing stress, ft is identical to the maximum distortion energy criterion, except that it is expressed in stress versus energy units. The criterion, expressed in terms of the principal stresses, is given in Eqn. (2.9). 

One advantage of the maximum stress failure criterion is that it gives an indication of the type of failure mode. By checking which of Eqn (6.33) is satisfied, one can determine whether the fibers or the matrix failed and whether it is a tension, compression, or shear failure. Of course, this is a macroscopic assessment as the failure criterion in this form does not allow a more detailed determination of failure initiation. For example, a shear failure determined by the last of Eqn (6.33) cannot be traced down to a matrix failure due to local tension or compression nor can it be determined whether the matrix crack was parallel or perpendicular to the fibers. 

Tsai—Hill The maximum stress and maximum strain failure criteria consider each stress component individually. This is a simplification. Test results show that if more than one stress is present in a ply, they can combine to give failure earlier (or later) than the maximum stress or maximum strain failure criterion would predict. One example that shows this effect is the case of a unidirectional ply under shear on which a tensile or a compressive stress is applied parallel to the fibers. The situation is shown in Eigure 6.7. 

For over three decades, there has been a continuous effort to develop a more universal failure criterion for unidirectional fiber composites and their laminates. A recent FAA publication lists 21 of these theories. The simplest choices for failure criteria are maximum stress or maximum strain. With the maximum stress theory, the ply stresses, in-plane tensile, out-of-plane tensile, and shear are calculated for each individual ply using lamination theory and compared with the allowables. When one of these stresses equals the allowable stress, the ply is considered to have failed. Other theories use more complicated (e.g., quadratic) parameters, which allow for interaction of these stresses in the failure process. 

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