Yield criteria von Mises

If the extruder is to be used to process polymer melts with a maximum melt viscosity of 500 Ns/m, calculate a suitable wall thickness for the extruder barrel based on the von Mises yield criterion. The tensile yield stress for the barrel metal is 925 MN/m and a factor of safety of 2.5 should be used. 

The yield criteria of polymers have been reviewed by Ward (7) and more recently by Raghava et al. (8). Except for the craze yield criteria of Sternstein and Ongchin (9) and Bowden and Oxborough (10), most of the yield data can be described by a pressure-modified, von Mises-yield criterion. The corresponding yield surface is everywhere convex. A typical yield locus on the [Pg.103]

The tensile yield stress variation as a function of W for a material which has a von Mises-type yield locus is illustrated schematically in Figure 5. This variation is caused by the fact that as the width of the specimen increases, the biaxiality also increases toward the asymptotic value at plane strain. If the material obeys the von Mises yield criterion exactly, the plane strain yield stress should be 15% higher than it would be for simple tension. On the other hand, if the material obeys the Tresca yield criterion, the plane strain yield stress should be identical... 

The shear component of the applied stress appears to be the major factor in causing yielding. The uniaxial tensile stress in a conventional stress-strain experiment can be resolved into a shear stress and a dilational (negative compressive) stress normal to the parallel sides of test specimens ofthe type shown in Fig. 11-20. Yielding occurs when the shear strain energy reaches a critical value that depends on the material, according to the von Mises yield criterion, which applies fairly well to polymers. 

Using the von Mises yield criterion, shear yielding occurs at a critical value of the octahedral stress ... 

Since the stresses are singular at the crack tip, then clearly the yield oiterion is exceeded in some zone in the crack tip region. If this zone is assumed to be small, then it will not greatly disturb the elastic stress field so that the extent of the plastic zone will be defined by the elastic stresses. If it is assumed that the Von Mises yield criterion is applicable (a reasonable first approximation for polymers), then the shape and e of the plastic zone may be derived from the stresses given in Eq. (15). As-sumii a state of plane strain so that the transverse stress is given by 1/(0 + oee)> then for a yield stress of Oy, the dastic zone radius becomes ... 

Equivalent stresses (a) and strains (e) were derived from surface shear stresses and strains by means of the Von Mises yield criterion ... 

Apply the modified von Mises yield criterion to convert these data into the simple shear mode, to estimate the yield stress Ty in simple shear, and thus to provide a common working framework to compare all of the data. 

This is the so-called von Mises yield criterion. It can also be written (see problem 8.1) in the form = VC/3, where Tgct is the so-called octahedral shear stress given by... 

Derive the von Mises yield criterion in the form tod = VC/3 from equation (8.6) and the definition of the octahedral shear stress Tod-... 

Gradually increasing stresses and aj = —ctj are applied to a material with the third principal stress <73 constant and equal to zero and the magnitudes of (Tj and ct2 are found to be a when the material yields. Assuming that the material obeys the von Mises yield criterion, calculate the magnitudes of and [Pg.246]

Von Mises stress is originally formulated to describe plastic response of ductile materials. It is also applicable for the analysis of plastic failure for coal undergoing high strain rate. The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant J2 reaches a critical value. In materials science and engineering the von Mises yield criterion can be also formulated in terms of the von Mises stress or equivalent tensile stress, a scalar stress value that can be computed from the stress tensor ... 

It should be emphasized that two fundamentally different types of craze tests were performed in this work. The test described initially, in which the craze stress below a notch was calculated from the slip line plasticity theory, without exposure to solvent, is a test in which the strain is changed as a function of time. The craze stress itself is calculated assuming that both slip line plasticity theory and the simple von Mises yield criterion are both applicable. The second test, used to determine the effect of solvent on crazing, is a surface crazing test under simple tension in which the strain... 

An alternative approach is the von Mises yield criterion, in which the role of all three principal stresses is introduced, i.e.. 

From the expression for the elastic energy of an isotropic solid in terms of the principal stresses and strains, show that the von Mises yield criterion is obtained when the dilatational part is removed, leaving the elastic shear strain energy. 

For the case of an isotropic metallic material, the well-known von Mises yield criterion is often sufficient to describe yielding. This is, however, not true for anisotropic materials, especially aluminium sheet metals. In order to take into account anisotropy, the classical yield criterion proposed by von Mises should be modified by introducing additional parameters. A simple approximation for the case of planar anisotropy is given by the quadratic criterion of (Hill 1948) ... 

This can be compared with the von Mises yield criterion, written in a rearranged form as... 

Consider von Mises yield criterion written as follows ... 

A three-dimensional formulation of the Bingham plastic was developed by Hohenemser and Prager [H19] in 1932 using the von Mises yield criterion (see Reiner [R4] and Prager [P15]). This employs a deviatoric stress tensor T and has the form... 

Von MiSOS Yiold Critorion. The Von Mises yield criterion (also known as the maximum distortional energy criterion or the octahedral stress theory) (25) states that yield will occur when the elastic shear-strain energy density reaches a critical value. There are a number of ways of expressing this in terms of the principal stresses, a common one being... 

The von Mises yield criterion [11] assumes that the yield behaviour is independent of hydrostatic pressure and that the yield stresses in simple tension and compression are equal. It is expressed most simply in terms of the principal components of stress so that... 

In rather more sophisticated terms the von Mises yield criterion assumes that the 3(ield criterion depends only on the components of the deviatoric stress tensor obtained by subtracting the hydrostatic components of stress from the total stress tensor. In terms of principal components of stress the deviatoric stress tensor is... 

The von Mises yield criterion is often written in terms of the so-called octahedral shear stress Toct, where... 

The yield point in compression a was measured for various values of applied tensile stress 02. The results, shown in Figure 11.16, give Oi = —110.0 + 13.65ct2s where both o and 02 are expressed as true stresses in units of MPa. The results therefore elearly do not fit the Tresca criterion, where 0 - 02 = constant at yield neither do they fit a von Mises yield criterion. They are, however, consistent with a Coulomb yield criterion with r = 47.4 — 1.58(/n. 

A very simple explanation of the effect of notching has been given by Orowan [95], For a deep, symmetrical tensile notch, the distribution of stress is identical to that for a flat frictionless punch indenting a plate under conditions of plane strain [102] (Figure 12.31). The compressive stress on the punch required to produce plastic deformation can be shown to be (2 + 7t)K, where K is the shear yield stress. For the Tresca yield criterion the value is l.Sloy and for the von Mises yield criterion the value is 2.82oy, where 0 is the tensile yield stress. Hence for an ideally deep and sharp notch in an infinite solid the plastic constraint raises the yield stress to a value of approximately 2>Oy which leads to the following classification for brittle-ductile behaviour first proposed by Orowan [95] ... 

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