Von Mises

The distance from the crack tip, along the X-axis, at which the von Mises equivalent stress falls below the yield stress, defines the size of the plastic zone, r. For the plane stress case of unconstrained yielding, which corresponds to the free surface of the specimen in Figure 4, this gives... 

The yield function is usually taken in the simple form due to von Mises... 

R von Mises. Mathematical Theory of Probability and Statistics. New York Academic Press, 1964. 

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. 

Using von Mises Theory from equation 4.58, the probabilistic requirement, P, to avoid yield in a ductile material, but under a biaxial stress system, is used to determine the reliability, R, as ... 

Assuming that all the variables follow a Normal distribution, a probabilistie model ean be ereated to determine the stress distribution for the first failure mode using the varianee equation and solving using the Finite Differenee Method (see Appendix XI). The funetion for the von Mises stress, L, on first assembly at the solenoid seetion is taken from equation 4.75 and is given by ... 

The mean value of the von Mises stress ean be approximated by substituting in the mean values of eaeh variable in equation 4.78 to give ... 

The von Mises stress, L, is then determined for various values of pre-load, E, using the above method. Equally, we eould have used Monte Carlo Simulation to determine an answer for the stress standard deviation. The answer using this approaeh is in faet o- 36 MPa over a number of trial runs. 

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 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... 

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. 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

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... 

Fig. 42. Von Mises stress distribution for a sample containing 138 voids subjected to a deformation of 1%...

A related issue has to do with the initial wafer-level uniformity (wafer thickness, wafer warp and bow, thicknesses of thin films across the wafer surface, uniformity of stress in such thin films across the wafer) and the subsequent impact on wafer-level polish performance. Some examination has been made of the impact of wafer warp and bow on the polish performance [68], where it was found that the initial warpage can have significant impact (with the implication that reclaimed wafers may not be appropriate monitors of wafer-level polish performance). Other work has considered inherent variation due to Von Mises stress concentrations at the edge of the wafer (conceptually, a downward pressure on the wafer causes lateral stress buildup near the edge of the wafer) [64]. 

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

Finite-additive invariant measures on non-compact groups were studied by Birkhoff (1936) (see also the book of Hewitt and Ross, 1963, Chapter 4). The frequency-based Mises approach to probability theory foundations (von Mises, 1964), as well as logical foundations of probability by Carnap (1950) do not need cr-additivity. Non-Kolmogorov probability theories are discussed now in the context of quantum physics (Khrennikov, 2002), nonstandard analysis (Loeb, 1975) and many other problems (and we do not pretend provide here is a full review of related works). 

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] ... 

I was pleased that, contrary to the feeling of others who have reviewed it, the literature is reasonably ample. Innovation and government regulation are popular things to talk about. Such was not the case in the 1920 s and 1930 s when Ludwig Von Mises and Joseph Schumpeter discussed bureaucracy, innovation and the failure of capitalism. 

The argument can also be carried out on a philosophical level. Libertarians point to a fundamental right of persons to decide what they want to do to or with their own body. The pioneer ffee-market economist Ludwig von Mises, for example, also argued that if the government can control drugs, it can control anything else that it decides is harmful ... 

Ludwig von Mises, Human Action, A Treatise on Economics. 4th Rev. Ed. Irvington-on-Hudson, N.Y Foundation Education, 1996, pp. 728-729. 

---