Yield criteria tensile

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 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... 

First, the role of rubber modification in high rate impact is to suppress spallation by inducing the material to yield in the presence of dynamic tensile stresses arising from impact. Second, this yield-spall transition occurs at different strain rates for different rubber contents and may be predictable using quasistatic, low temperature tests of this type. These tests can also provide information concerning the basic nature of the yield process in these materials through the activation parameters which are obtained. Third, the Bauwens-Crowet equation seems to be a good model for the rate and temperature sensitive behavior of the American Cyanamid materials and is therefore a likely candidate for a yield criterion to use in the analytical code work on these materials which we hope to perform as a continuation of this work. 

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. 

These stresses are related by a yield criterion. According to Tresca s yield criterion, the most tensile principal stress ci is related to the most compressive principal stress (Ti by... 

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). 

If yielding is to occur by sliding parallel to any plane, it seems reasonable to suppose that there must be a critical shear stress r parallel to that plane. It is also physically reasonable to assume that this critical stress x will be increased if the compressive stress —mean normal stress, as just defined, not nominal stress. Remember also that the usual convention for stress makes - -a the tensile stress.) The simplest assumption is that x depends linearly on Coulomb yield criterion ... 

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 ... 

A yield criterion defines the limit of elasticity (or onset of plastic flow) under any combination of stresses. Figure 1 shows a stress-strain curve that might be derived from a simple uniaxial tensile test. 

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 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] ... 

The yield criterion Ueq pM = Rp is used for compressive and tensile loads. 

In order to determine which is the most appropriate yield criterion for a particular material it is necessary to follow the yield behaviour by using a variety of different combinations of multiaxial stress. However, with polymers rather unusual features are revealed when the yield stress of the same polymer is measured just in simple uniaxial tension and compression. Both the Tresca and von Mises criteria predict that the yield stress should be the same in both cases and this is what is found for metals. But for polymers the compressive yield stress is usually higher than the tensile one. This difference between the compressive and tensile yield stress can be taken as an indication that the hydrostatic component of the applied stress... 

In order to determine which is the most appropriate yield criterion for a particular polymer it is necessary to follow the yield behaviour under a variety of states of stress. This is most conveniently done by working in plane stress = 0) and making measurements in pure shear (o- = -0-2) and biaxial tension (o-i, 02 > 0) as well as in the simple uniaxial cases. The results of such experiments on glassy polystyrene are shown in Fig. 5.28. The modified von Mises and Tresca envelopes are also plotted. In both cases they have been fitted to the measured uniaxial tensile and compressive yield stresses, oy, and oy. It can be seen that the von Mises... 

Bulk tensile testing has shown that adhesives generally exhibit plasticity and, hence, nonlinear material properties are required to model their behavior over the fiill load range. Nonlinear properties may also be required for adherends. Thus, a combination of elasto-plastic material models may be used to predict the behavior of adhesive joints under load. The definition of the yield surface is important when using elasto-plastic material models. Von Mises yield surface is commonly used for the analysis of metals, which assumes that the yield behavior is independent of hydrostatic stress. As a result, the yield surface is identical in tension and compression. However, the yield behavior of polymers has been shown to exhibit hydrostatic stress dependence (Ward and Sweeney 2004) as the yielding starts earlier in tension than in compression. Thus, a yield criterion which includes hydrostatic stress effects should be used to determine the yield surface. Various yield criteria with hydrostatic stress dependence such as Drucker-Prager, Mohr-Columb, and modified Drucker-Prager/cap plasticity model have been implemented in commercially available finite element software. 

Although a torsion test is simple to carry out, it is not commonly accepted as an integral part of a material specification furthermore, few torsion data exist in handbooks. If, as is usually the case, the design needs to be based on tensile data, then a criterion of elastic failure has to be invoked, and this introduces some uncertainty in the calculated yield pressure (8). 

The von Mises criterion relates the tensile yield stress of a material to a state of multi-axial stress in a component made from the material. In a cylinder (the... 

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