Maximum shear stress 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... 

If it is assumed that yield and subsequent plastic flow of the material occurs in accordance with the maximum shear stress criterion, then /2 may be substituted for in the above and subsequent equations. For the shear strain energy criterion it may be assumed, as a first approximation, that the corresponding value is G j fz. Errors in this assumption have been discussed (11). 

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 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... 

The octahedral shear stress criterion has some appeal for materials that deform by dislocation motion In which the slip planes are randomly oriented. Dislocation motion Is dependent on the resolved shear stress In the plane of the dislocation and In Its direction of motion ( ). The stress required to initiate this motion is called the critical resolved shear stress. The octahedral shear stress might be viewed as the "root mean square" shear stress and hence an "average" of the shear stresses on these randomly oriented planes. It seems reasonable, therefore, to assume that slip would initiate when this stress reaches a critical value at least for polycrystal1ine metals. The role of dislocations on plastic deformation in polymers (even semicrystalline ones) has not been established. Nevertheless, slip is known to occur during polymer yielding and suggests the use of either the maximum shear stress or the octahedral shear stress criterion. The predictions of these two criteria are very close and never differ by more than 15%. The maximum shear stress criterion is always the more conservative of the two. 

Both AS ME Code, Section 1I1, Division 2 and AS ME Code, Section III, utilize the maximum shear stress criterion. This theor) closely approximates experimental results and is also easy to use. This theory also applies to triaxial states of stress. In a triaxial stress state, this theory predicts that yielding will occur whenever one-half the algebraic difference betu een the maximum and minimum stress is equal to one-half the yield stress. Where 0 > a i> 0.3. the maximum shear stress is (oi —03)72. 

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

In the case of laminate design the stresses normal to the plane of the laminate are typically zero, or negligible, and hence the maximum-shear-stress criterion imposes a limit on the remaining two principal stresses. 

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. 

Both the pre-2007 ASME Section Vni, Division 2 and Part 4 of the new Section VIII, Division 2 utilize the maximum shear stress criterion for determining the primary thicknesses of a shell under internal pressure. 

This equation is applicable in the quadrants where cti and 02 have different signs. Where they have the same signs the maximum shear stress criterion requires that... 

It is possible to modify the Tresca maximum shear-stress criterion in several ways. The simplest way is to make the critical shear stress a function of the hydrostatic pressure p and so oi can be expressed by an equation of form... 

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. 

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 ... 

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. 

---