Mises criterion

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... 

The von Mises criterion simply states that yielding (failure) will occur if... 

Lower values of the yield stress measured in tension compared to those measured in compression suggest that the effect of pressure, which is important for polymers, is not accounted for in this criterion. Hence, appropriate correction has to be made in order to account for the effect from external pressure. The most frequent version of pressure-dependent yield criterion is the modified von Mises criterion [20] ... 

Therefore, both modified criteria (hexagon and ellipse) appear now shifted to the low values of oq, but are still symmetrical between oq and Mises criterion gives a better fit with experimental results than the Tresca criterion. 

AGS may be expressed as proportional to compressive yield stress), yt (fracture strain), the plastic zone size, and the square of the concentration factor, K. The influence of hydrostatic pressure was taken into account with a modified von Mises criterion (Chapter 12). 

Eq. (8.24), and the modified Mohr-Coulomb yield (or failure) criterion, Eq. (8.27). It should be noted that other yield criteria, such as the von Mises criterion, are used to model the flow of bulk solids in hoppers, and more conditions may need to be imposed, such as the Levy flow rule, in order to close the system of equations [Cleaver and Nedderman, 1993],... 

Well-known yield criteria are the Tresca criterion and the Von Mises criterion. Discussion of this subject falls beyond the scope of this book, but a clear description is presented in, e.g. the monograph of Ward and Hadley (1993). If stresses increase above a certain value yield will occur. For metals this critical value is almost independent of pressure, whereas for polymers it is strongly dependent on pressure. An example is shown in Fig. 13.72 for PMMA in Sect. 13.5.4. 

Fig. 11 Calculated surface profiles of the octahedral shear stress at yield assuming a modified Von Mises criterion (a), and of the octahedral shear stress for a glass/epoxy contact under gross sliding condition (b). The grey area delimits the region at the leading edge of the contact where the octahedral shear stress is exceeding the limit octahedral shear stress at yield (a is the radius of the contact area) (from [97])...

Of the 12 slip systems possessed by the CCP stmcture, five are independent, which satisfies the von Mises criterion. For this reason, and because of the multitude of active slip systems in polycrystalline CCP metals, they are the most ductile. Hexagonal close-packed metals contain just one close-packed layer, the (0 0 0 1) basal plane, and three distinct close-packed directions in this plane [I I 2 0], [2 I I 0], [I 2 I 0] as shown in Figure lO.Vh. Thus, there are only three easy glide primary slip systems in HCP metals, and only two of these are independent. Hence, HCP metals tend to have low... 

Body-centered cubic metals contain no close-packed planes, but do contain four close-packed directions, the four [111] body diagonals of the cube. The most nearly close-packed planes are those of the 1 10 set. In BCC crystals, slip has been observed in the [1 I 1] directions on the [1 10], [1 12], and 12 3 planes, but that, attributed to the latter two planes, may be considered the resultant of slip on several different (1 1 0) type planes (Weertman and Weertman, 1992). The von Mises criterion is satisfied, but higher shearing stresses than those of CCP metals are normally requited to cause slip in BCC metals. As a result, most BCC metals are classified as semibrittle. 

In spite of the relative simplicity of the Tresca criterion, conditions for shear yielding in isotropic polymers are best summarized by the von Mises criterion (11),... 

Experimental data show that neither the Tresca nor the von Mises criterion adequately describes the shear yielding behavior in polymers. 

For macroscopically isotropic polymers, the Tresca and von Mises yield criteria take very simple analytical forms when expressed in terms of the principal stresses cji, form surfaces in the principal stress space. The shear yield surface for the pressure-dependent von Mises criterion [Eqs (14.10) and (14.12)] is a tapering cylinder centered on the applied pressure increases. The shear yield surface of the pressure-dependent Tresca criterion [Eqs (14.8) and (14.12)] is a hexagonal pyramid. To determine which of the two criteria is the most appropriate for a particular polymer it is necessary to determine the yield behavior of the polymer under different states of stress. This is done by working in plane stress (ct3 = 0) and obtaining yield stresses for simple uniaxial tension and compression, pure shear (di = —CT2), and biaxial tension (cti, 0-2 > 0). Figure 14.9 shows the experimental results for glassy polystyrene (13), where the... 

Figure 14.9 Section of the yield surface in the plane 03 = 0 choosing the Tresca criterion (hexagonal envelope) and von Mises criterion (elliptical envelope) for polystyrene. The points correspond to experiments performed under pure shear (gi = -CJ2), biaxial tension (oj, 03 > 0), and uniaxial tension and compression. (From Ref. 13.)...

A sample of polypropylene tested at 30°C and 10 s shows a yield stress of 35 MPa in uniaxial tension and 38 MPa under uniaxial compression. Calculate the hydrostatic pressure that must be superimposed in order to reach yield stress of 80 MPa. Assume that the material obeys the pressure-dependent von Mises criterion. 

Equations (14.10) and (14.12) give the pressure-dependent von Mises criterion. Also, for any state of stresses, P is an invariant given by the expression P = (l/3)(ai-I-Q2-1-cy3). On the basis of this expression, in a uniaxial tension test 02 = a3 = 0)... 

A first stage in the analysis consisted in determining the elastic or plastic nature of the contact loading using the known yield properties of the bulk DGEBA/IPD system. The latter were established experimentally assuming that they obey a modified Von Mises criterion taking into account the effect of the hydrostatic pressure. This criterion may be written as ... 

A standard yield criterion, such as the modified von Mises criterion or the modified Tresca criterion, can be used to predict the yield stress in other modes of testing (such as uniaxial compression, plane strain compression and simple shear), from the value of ay(T) in uniaxial... 

Apply modified von Mises criterion to convert predictions of Ty to ay in other testing modes. 

A polymer is more likely to fail by brittle fracture under uniaxial tension than under uniaxial compression. Lesser and Kody [164] showed that the yielding of epoxy-amine networks subjected to multiaxial stress states can be described with the modified van Mises criterion. It was found to be possible to measure a compressive yield stress (Gcy) for all of their networks, while the networks with the smallest Mc values failed by brittle fracture and did not provide measured values for the tensile yield stress (Gty) [23,164-166]. Crawford and Lesser [165] showed that Gcy and Gty at a given temperature and strain rate were related by Equation 11.43. 

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. 

Figure 4.1. Estimated plastic zone sizes based on von Mises criterion for yielding (u = 0.3 for the plane strain case).

Figure 4.2. Schematic representation of the throngh-thick-ness variation in plastic zone size based on the von Mises criterion for yielding [1].

For unoriented particle systems, the von Mises criterion for plastic flow of solids should be obeyed. The yield stress in elongation and compression should be equal to each other, and larger by the factor of Vs than the yield stress in shear, o. However, for highly concentrated suspensions of anisometric particles, von Mises criterion should not be used. 

In qualitative agreement with the von Mises criterion = E3 - 2.0 was reported... 

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