Tresca theory

Consider for example, the maximum shear stress (or Tresca) theory of failure with respect to yielding, which can be stated as follows A material subjected to any combination of loads will yield whenever the maximum shear stress at any point in the material exceeds the value of the maximum shear stress in a simple tensile test at yield. ... 

Equations 9.1, 9.2 provide the means of putting the Tresca theory of failure in equation form as follows ... 

The maximum shear stress theory is often called Tresca s, or Guest s, theory. 

Tresca and R. von Mises criteria are for isotropic materials. In 1948, Rodney Hill provided a quadratic yield criterion for anisotropic materials. A special case of this criterion is von Mises criterion. In 1979, Hill proposed a non-quadratic yield criterion. Later on several other criteria were proposed including Hill s 1993 criterion. Rodney HiU (1921-2011) was bom in Yorkshire, England and has tremendous contribution in the theory of plasticity. 

Coulomb and Tresca theorized, that the elastic limit was reached only when the shear stress reached it s maximum value. The basis of their theory was based on the actual failure mode of material. Material stretched... 

Compare this to the prediction of ay/2 from the Tresca criterion. The yield criteria for both the Tresca and Von Mises theories are shown graphically in Figure 6. For simplicity, the plots are shown for conditions of plane stress (ie 03 = 0). We can see that the Von Mises criterion describes an ellipse in stress space, with the Tresca criterion consisting of a series of straight lines bounded by the Von Mises limits. 

According to the maximum shear stress theory, the maximum shear equals the shear stress at the elastic limit as determined from the uniaxial tension test. Here the maximum shear stress is one half the difference between the largest (say principal stresses. This is also known as the Tresca criterion, which states that pelding takes place when... 

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. 

Maximum shear stress theory (Tresca) Failure occurs when the maximum shear stress at-an arbitrary point in a stressed body is equal to the maximum shear stress at failure (rupture or yield) in a uniaxial tensile test. 

Give a definition for the classical failure theories of Tresca and von Mises. 

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. 

This theory was first proposed by Tresca in 1865 and experimentally verified by Guest in 1900. It states that in a multiaxial stress state failure occurs when the maximum shear stress exceeds the maximum shear stress at failure in a monotonic tensile traction test. In a tensile test it is... 

The standard criteria for yielding developed in elasticity theory for metals, namely the Tresca, von Mises or Mohr-Coulomb, do not apply quantitatively to polymeric materials because these criteria ignore the effect of the hydrostatic component of the stress tensor. This is important in determining the yield behaviour of polymers, not neces-... 

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