Plasticity theory

From this calculation, the condition for the onset of necking is 

This equation shows that there is a relation between the maximum strain or maximum deformation of the specimen and the hardening. High-strength materials with a large yield strength, but smaller hardening exponent n than low-strength materials, are thus normally less ductile. Table 3.1 shows the material parameters of some metals. 

All approaches discussed in this section have been derived phenomenologically. They are based on the theory of continuum mechanics and thus do not explicitly include the microscopic mechanisms occurring in the different material classes. Furthermore, isotropic behaviour is assumed because most materials, especially metals, are polycrystalline, and their macroscopic properties are thus averaged over many grains. 

Yield criteria, the subject of sections 3.3.1 to 3.3.3, describe the transition between elastic and plastic behaviour for arbitrary stress states. Next, we will study flow rules that can be used to calculate how the material deforms. 

How the flow stress changes during plastic deformation can be described using 

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J. C. Pearson Hydrodynamic Elastic Plastic Theory and Plane Shock Waves in Metals. I. 

The elastic-plastic theory of Weiderhom and Lawn can also be applied here, which leads to the following expression for S that is similar to Eq. (8.19) ... 

Ahmed, M. (1979) In Coloring of plastics theory and practice. Van Nostrand Rhein-hold. New York, chap 6... 

Richardson, T.L, and E. Lokensgard Industrial Plastics Theory and Application, Delmar Learning, Albany, NY, 2003. 

N.A. Fleck et al Strain gradient plasticity Theory and experiment. Acta Mater. 42,475 187... 

T. A. Richardson, Industrial Plastics Theory and Application, South West Publishing Co., Cincinnati, Ohio, 1993. 

Frenning G. Analysis of pharmaceutical powder compaction using multiplicative hyperelasto-plastic theory. Powder Technol 2007 172 103-112. 

In order to respect volumetric strain, a non-associated plastic theory is used. As suggested by Cambou et al. (1989), the unit vector n is calculated in such a way that equation 13 is equivalent to the definition of plastic volume change of equation 15. One can combine the equations to obtain the expression of vector n ... 

G.W. Ehrenstein, G. Riedel and P. Trawiel, Thermal Analysis of Plastics Theory and Practice Hanser Gardner, Cincinnatti, 2004. 

Polymer Solutions and Gels Elastomers Laboratory Biomedical Polymers Rubber/Plastics Theory Fibers Theory Fibers Laboratory... 

The research demonstrates that the form of the slurry infused into the rock mass is irregular, which can be reduced to the approximate cyhndrical in Older to calculate the disturbance effect of expansion pressure. The form will be changed from the state of elastic deformation to plastic one with grouting pressure increasing around the injection holes, then it can be analyzed by the elastic-plastic theory. 

The ultimate bearing capacity of spread foundations on uniform soils can be estimated with sufficient accuracy based on plasticity theory, and the theoretical relationship can be represented by Equation 10.46 ... 

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... 

Let us continue this discussion using the simple example introduced at the beginning of Section 5.6. The ultimate load of a beam in a steel framed building was calculated using simple plastic theory, and assuming simple supports, so that... 

It is worth dwelling briefly on the system uncertainty thatis intended to cover. In other words what are the assumptions of simple plastic theory and how does the application of it, in the calculation, match the structure we are attempt-... 

The source which maintains that this is so, is our system model based in the case of our example, upon plastic theory. Referring back to Rcscher s argument, A becomes the hypothesis H, and (X maintains A) becomes (the system model, SM, maintains ff). Now we are aware that the system model is imperfect and we wish to know the dependability of H. If this is a probability of H theu... 

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