Von Mises effective stress

Consider a sharp, Mode I crack in an elastic-power-law creeping solid (Eqn. (2)). The isotropic multiaxial generalization of Eqn. (2) is in terms of the Von Mises effective stress [Pg.337]

Deformation Process. The function of the rubber in PA-rubber blends is to create stable cavities upon loading. Because of cavitation, the von Mises effective stress in the matrix strongly increases and plastic deformation is possible (I, 20). The von Mises stress in a cavitated system is a function of cavity concentration. The cavity size does not play a role in this mechanism. 

Distribution of von Mises (effective) stress through the thickness of a tibiai component. Note that the location of the maximum von Mises stress, which aiso corresponds to the iocation of maximum shear stress, is located at a depth of 1-2 mm from the articulating surface. The slice is taken perpendicular to the contact surface of a tibiai component at heel strike during normal gait, using the model shown in Figures 8.3A and 8.4. 

The stresses around the particles are determined to find the maximum von Mises equivalent stress. These calculation show that the mean value of the stress concentrations is a few percent greater than the exact value for a single void in an infinite matrix. The effect of mechanical interaction globally increases the... 

Stress analysis of failures in the form of cracks due to fatigue of cord-rubber composites was carried out using micromechanical 2D and 3D finite element analysis. The von Mises-Tresca stresses were computed from the results of finite element analysis and compared. Results show that crack type, loading and crack size have a strong effect on the values of the von Mises-Tresca stress. Use of the results of the von Mises-Tresca stress should help in estimating the severity of local failures in cord-rubber composites, it is proposed. 12 refs. 

It has been shown in Sect. 6.6.1 how a multiaxial stress state can modify the ductility of a material. To this purpose the triaxiality factor (TF) was introduced with Eq. (6.41) as the ratio of the hydrostatic stress to the von Mises equivalent stress. It is quite logical to think that the TF should have an effect on fatigue... 

Of all the theories dealing with the prediction of yielding in complex stress systems, the Distortion Energy Theory (also called the von Mises Failure Theory) agrees best with experimental results for ductile materials, for example mild steel and aluminium (Collins, 1993 Edwards and McKee, 1991 Norton, 1996 Shigley and Mischke, 1996). Its formulation is given in equation 4.57. The right-hand side of the equation is the effective stress, L, for the stress system. 

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

Frictional effects (shear and Von Mises stress effects)—Murthy [16] and Guo et al. [17]... 

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] ... 

From the results obtained, for SiC coatings several cases can be identified for which the Von Mises and shear stresses and their gradients with respect to the interface are low. For example, Ta, Mo, Ti, Nb, and TiN produce this effect, when interposed between the steel substrate and the SiC coating. 

Figure 14.8 shows stress-strain curves for polycarbonate at 77 K obtained in tension and in uniaxial compression (12), where it can be seen that the yield stress differs in these two tests. In general, for polymers the compressive yield stress is higher than the tensile yield stress, as Figure 14.8 shows for polycarbonate. Also, yield stress increases significantly with hydrostatic pressure on polymers, though the Tresca and von Mises criteria predict that the yield stress measured in uniaxial tension is the same as that measured in compression. The differences observed between the behavior of polymers in uniaxial compression and in uniaxial tension are due to the fact that these materials are mostly van der Waals solids. Therefore it is not surprising that their mechanical properties are subject to hydrostatic pressure effects. It is possible to modify the yield criteria described in the previous section to take into account the pressure dependence. Thus, Xy in Eq. (14.10) can be expressed as a function of hydrostatic pressure P as... 

T3) are available in most FEA software packages and stresses are usually averaged by the FEA software packages to provide more accurate stress values when mapped (contoured) on to the mesh. A good first cut to the understanding of analysis results is the use of the von Mises stress (effective or equivalent stress). Fig. 10 shows the von Mises stress contour mapped to the FEA mesh in pounds/square inch (PSI). 

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... 

First, since tension and compression differ fundamentally by the presence of a positive or negative mean normal stress <7m, the S-D effect has been attributed in one case to the effect of on the governing mechanism of nucleation of STs, as we have done in Section 7.6.6. If deformation does not localize into shear bands and remains homogeneous at a mesoscale, this results in unsymmetrical von Mises- or Tresca-type yield criteria such that the critical shear resistance Zg is pressure-dependent (Ward 1983) as discussed in Chapter 3. 

While mechanistic models of plastic flow consider simple shear or pure shear (extensional flow where mean normal stress is absent), in experiments fundamental shear information may need to be extracted from more complex 3D flow fields. This is done through the use of multi-axial flow formalisms that are based on the von Mises approach of relating the 3D response to an equivalent ID response described in Chapter 3. In this formalism the deviatoric shear response of the multi-axial field of stress and plastic strain is taken to represent shear flow in the mechanistic context where the effect of the accompanying mean normal stress is considered through its effect on the plastic resistance. There exists an experimental procedure for extracting deviatoric plastic-response information from a tensile-flow field that accomplishes this through the use of specially contoured bars with pre-machined neck regions where the concentrated extensional flow is monitored under conditions of imposed constant deviatoric strain rates (G Sell et al. 1992). 

The strength-differential effect is also reflected prominently in the multi-axial yield criteria which translate the multi-axial stress driving forces for yield into an equivalent uniaxial state of extension (tension) or simple shear <7se that is most relevant to the mechanisms governing plastic flow. In a more mechanistieally relevant statement for polymers, the multi-axial yield criterion of von Mises defines a uniaxial equivalent stress Oe (or a o-se) as... 

The magnitude and distributions of stress in the knee are different from the hip. In the hip, the spherical contacting surfaces are highly conforming, and the effective (von Mises) stress levels are below yield, and, thus, below the onset of irrecoverable plastic deformation. Consequently, for hip components, UHMWPE can reasonably be considered to behave as an elastic material at the... 

While it is well established that the rupture stress of both brittle and ductile materials is increased significantly by the presence of compressive stress (known as the Mohr effect), it is generally believed that a similar relationship for flow stress does not hold. However, an explanation for this paradox with considerable supporting experimental data is presented below. The fact that this discussion is limited to steady-state chip formation rules out the possibility of periodic gross cracks being involved. However, the role of microcracks is a possibility consistent with steady-state chip formation and the influence of compressive stress on the flow stress in shear. A discussion of the role microcracks can play in steady-state chip formation will follow in the next section. Hydrostatic stress plays no role in the plastic flow of metals if they have no porosity. Yielding then occurs when the von Mises criterion reaches a critical value. Merchant [7, pp. 267-275] has indicated that Barrett [10]... 

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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