Failure criteria octahedral shear stress

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.

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

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). 

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. 

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. 

If a limiting octahedral shearing stress, r, is postulated as a failure criterion the same mathematical expression as in Eq. (3.9) is obtained with... 

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. 

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