Tresca shear stress

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

The simplest yield criterion is that of Tresca. This criterion states that yielding will occur when the maximum shear stress on any plane in the tested sohd reaches its critical value [20] ... 

In order to estimate the onset yield stress of the material, three common criteria are introduced. The Tresca criterion is based on maximum shear stress and is given as... 

It can be proved from Eq. (2.156) that, for materials with Poisson s ratio of 0.3 (which is true for most solids), the maximum shear stress oz — or occurs at z/rc = 0.48. Consequently, according to Tresca s criterion, the yield stress Y in a simple compression is 0.62 p0. Therefore, when the hardness or the yield stress Y of the particle material is less than 0.62 times the maximum contact pressure, the sphere will, most likely, undergo plastic deformation. From the elastic collision of two solid spheres, the maximum contact pressure is given by Eq. (2.134). Thus, the relation between the critical normal collision velocity, Ui2Y. and the yield stress is given by... 

Two comments should be made first, the yield criteria involved e.g. von Mises, Tresca are based on yielding in response to shear stresses secondly the above solution — although established on physical grounds — is mathematically not exact. 

The yield criterion first suggested for metals was Tresca s criterion, which proposes that in isotropic materials yield occurs when the maximum shear stress X reaches a critical value (10). ... 

Our geometric model of the crystal is most appropriate for polycrystals since we have hypothesized that any and all planes and slip directions are available for slip (i.e. the discrete crystalline slip systems are smeared out) and hence that slip will commence once the maximum shear stresses have reached a critical value on any such plane. This provides a scheme for explicitly describing the yield surface that is known as the Tresca yield condition. In particular, we conclude that yield occurs when... 

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... 

Transition to plastic deformation will occur when the maximum shear stress satisfies both the Tresca and the Huber-Mises criteria. For the... 

The Mohr circle representation (Fig. 9.6c) is a graphical method of relating stress components in different sets of axes. When the axes in the material rotate by an angle B, the diameter of the circle rotates by an angle 2 B. If the material yields, the circle has radius k, the constant in the Tresca yield criterion. The axes of the Mohr diagram are the tensile and shear stress components. Thus, in the left-hand circle, representing the stresses at A in Fig. 9.6b, the ends of the horizontal diameter are the principal stresses. The principal axes are parallel and perpendicular to the notch-free surface. There is a tensile principal stress Ik parallel to the surface, and a zero stress perpendicular to the surface. The points at the ends of the vertical diameter represent the stress components in the a)3 axes, rotated by 45° from the principal axes. In the a/3 axes, the shear stresses have a maximum value k, and there are equal biaxial tensile stresses of magnitude = k (the coordinate of the centre of the circle). 

In the second form the von Mises criterion expresses directly the fact that the yield depends equally on the three shear stresses (cTj — oy)/2. A somewhat simpler criterion, the Tresca yield criterion, makes the slightly different assumption that yield takes place when the largest of these three shear stresses reaches a critical value. The surface in cr-space that represents the criterion is therefore defined by the six equations... 

One simple criterion for yielding under multiaxial stresses is known as the Tresca yield criterion. This approach recognizes that the maximum shear stress is one-half the difference between the maximum and minimum principal stresses. In terms of the uniaxial yield stress [Pg.187]

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... 

The 3rielding of soUds imder multiaxial stresses gives rise to question about the yield criteria. One of the simplest yield criteria was proposed by Tresca already in 1864. It states that srielding occurs when the maximum shear stress exceeds a critical value. In terms of principal stresses we have (23) ... 

Tresca Yield Criterion. The earliest proposal for a yield criterion in metals is due to Tresca (24), and it stated that yield occurs when the maximum shear stress reaches a critical value. With <7i > <72 > <73 the criterion can be written as... 

ModifiGd Von MiSGS Criterion, in the same manner as the modification to the Tresca jdeld criterion one can modify the Von Mises criterion by introducing a linear dependence of the critical shear stress on the hydrostatic pressure ... 

As shown earlier, a simple criterion for yield is that the maximum shear stress reaches a critical value given by t = Oy/2, where Oy is the tensile yield stress (ie the Tresca yield criterion). Substituting and rearranging equation 29 gives... 

The Tresca yield criterion assumes that the critical shear stress is independent of the normal pressure on the plane on which yield is occurring. Although this assumption is valid for metals, it is more appropriate in polymers to consider the possible applicability of the Coulomb yield criterion [10], which states that the critical shear stress r for yielding to occur in any plane varies linerarly with the stress normal to this plane, i.e. 

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. 

The in-plane normal stresses in a flat plate are 10 MPa and 60 MPa and the shear stress is 30 MPa. Find 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 150 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. 

The Tresca yield criterion or maocimum shear stress criterion is not directly based on the considerations of the previous sections, but it fulfils them nevertheless. It states that the maximum shear stress in the material point determines yielding. This maximum shear stress can be determined graphically using Mohr s circle, see figure 2.3 on page 34. The maximum principal stress is denoted as a, the intermediate value as au, and the smallest as crni- The maximum shear stress is... 

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. 

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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