Hardening perfectly plastic

Metallic glasses are almost elastic-perfectly plastic, so indentations in them are limited by the critical shear stress, not by strain-hardening as in crystalline... 

FIGURE 17 (A) Stress-strain diagram of elastic perfectly plastic material and (B) stress-strain diagram of elastic material power law with strain hardening. Source. Adapted from Ref. 98. 

For elastic perfectly plastic models there is no elastic deformation in the post-yielding phase however, with the power law strain hardening there is continued elastic and plastic deformation combined. The extent of elastic and plastic deformation post-yielding can be determined by looking at. some arbitrary stress a as shown on Figure 17B. For this stress the elastic and plastic deformations are... 

Fig. 5.10 Stress-strain curves recorded by compression of rectangular NC-MgO bars at constant cross-head speed and different temperatures. The curves exhibit elastic and perfectly plastic behavior with no strain hardening. Specimen (A) was annealed to grow the grain size to 1 pm and thus exhibited brittle behavior by compression at 800 °C arrowed solid line) compared with the ductile behavior of its nanocrystalline counterpart specimen dashed curve) at 800 °C [26]...

The above equation is then represented by a straight line in a log-log plot, and the linear slope yields the strain hardening exponent while its ordinate gives the strength coefficient. The strain hardening exponent may exhibit values from n = 0 for perfectly plastic solids (e.g., waxes) to n = I for elastic solids (e.g., diamond). For most metals the strain hardening exponent usually ranges between 0.10 and 0.50. 

According to ASME PCC-2 (2006), the main purpose of FRP wrap repair is to strengthen an undamaged section of the pipe to carry the additional loads caused by the damaged or weakened section. Assuming that the repair is applied at zero internal pressure and the pipe material behaves elastic-perfectly plastic (i.e. no strain hardening), the minimum composite repair thickuess. 

The material is assumed as rigid-perfectly plastic, i.e. no strain-hardening effects are taken into consideration. 

It is impossible to create a stress state that is outside of the yield surface only the cases / < 0 and / = 0 can occur in reality. This can be explained using the example of a perfectly plastic material with a stress-strain diagram as in figure 3.19(a). It is easy to see that it is not possible to increase the stress beyond i p. But what happens in a material that hardens In such materials, stresses larger than Rp are indeed possible (see figure 3.19(b)). This, however, does not imply that the stress state leaves the yield surface. Instead, the yield... 

A perfectly plastic material does not harden so that its yield surface, equation (3.23), remains unchanged during deformation. Thus, the yield criterion is... 

B) Two idealized types of plastic behavior perfectly plastic with a yield stress of Oy and linear hardening. When the stress is removed, the plastic strain does not recover. If the... 

Particulate materials, such as clay or particulate gels of the type discussed in Chapter 4, may be plasticy rather than viscoelastic. Two simple types of plastic behavior are illustrated in Fig. 18b a perfectly plastic material is elastic up to t)xt yield stress, Oy > but it deforms without limit if a higher stress is applied in a linearly hardening material there is a finite slope after the yield stress. In real plastic materials, the stress-strain relations are likely to be curved, rather than linear. If the stress is raised above Oy and then released, the elastic strain is recovered but the plastic strain is not. This differs from viscous behavior in its time-dependence if the stress on a linearly hardening plastic material is raised to Oh and held constant, the strain remains at a viscoelastic material would continue to deform at a rate proportional to Ou/ri-... 

In structures that do not exhibit considerable strain hardening in the nonlinear range, the elastic-perfectly plastic idealization is accurate. When the strain hardening is considerable, e.g., in some types of bridges, bilinear idealization is more appropriate (see section Application of the Inelastic Static Methods to the Analysis of Bridges for more details). 

In engineering practice, the nonlinear material behavior is commonly described in a simplified maimer. Two common such idealizations are the bilinear ones, either elastic-perfectly plastic or elastic-plastic with linear hardening, shown in Fig. 3. The stress corresponding to the end of the linear region is called yield stress of the material and is denoted by fy, while the maximum stress, also called ultimate stress, is denoted by fu. The corresponding strains are Sy and and the difference between them is a measure of the material s ductility. In the elastic-plastic idealization, the higher value of f compared to fy is conservatively ignored. 

Simple hysteretic models that can be used in the practice are presented in Fig. 1. Model (a) represents an elastic-perfectly plastic behavior, while model (b) is a variant allowing for strain hardening. Model (c) (Masing 1926) takes into account the stiffness deterioration, using smooth curves, and model (d) is the degrading stiffness model due to Takeda. 

Fig. 1 (a) Elastic-perfectly plastic model (b) bilinear strain hardening model (c) Masing-type model (d) degrading stiffness model due to Takeda... 

The flow curves received by upsetting tests are shown in Figures 7 and 8. The curves prove that the tested materials became more plastic under hydrostatic pressure, as well as their plastic state was similar to the perfect plasticity (there is no more hardening). 

Recent studies indicate that back pressure can affect the plastic deformation zone of the quasi-perfect plastic and strain hardening materials, resulting in beneficial effects such as reduced plastic deformation zone and corner gap and more uniform strain distribution. However, an increase in the back pressure may also lead to the broadening of plastic deformation zone and a decrease in strain homogeneity [49]. 

The strengthening effect of a monobloc cylinder due to autoffettage practically is achieved by two effects First the introduction of the compressive (tangential) residual stresses which extend the elastically admissible internal pressure and second the increased available material strength by strain hardening. The maximum admissible pressure for optimum autoffettaged cylinders based on perfectly elastic-plastic materials, completely elastic stress (plus/minus) conditions at the inner bore diameter and the assumption of the GE-hypothesis can be calculated as [11]. 

Imagine a glue that does not shrink at all as it hardens it fills gaps perfectly so that pieces don t need to be fitted closely. It holds forever in water, is at least as strong as wood and plastic, and sticks to anything wood, metal, plastic, etc. It lasts forever on the shelf without hardening, yet hardens quickly once the pieces are in place. It can be made runny so it fills tiny voids, or thick and pasty so it stays in place while it hardens. 

Examples of load-deflection curves in Figure 10.30 show the possible deficiencies of this type. Curve a describes a small strain hardening while curve a represents a rapid decrease of load after cracking and both are characterized by the same toughness index I5. Similarly, for curves b and b index I o is the same and only index I5 shows small difference, while the material s behaviour is completely different. Also, for curves c and c only I5 and I o are different while the values of I20 are the same. These examples prove that the determination of the toughness index is only a useful method of comparison for the effective material s behaviour with that of an idealized linear elastic-plastic material. However, it cannot be considered as a perfect material characteristic. 

The embedding of catalyst particles in quick hardening plastic Technovit 4071 (Kolzer) causes no problems, provided the pellets have a constant cross sectional area across the sample height L. With irregular shaped particles the determination of the densities needed in Equation 5 and gas bubbles included in the sample lead to uncertain results. Additionally, with a large sample diameter (method Ila) it is difficult to obtain a perfectly plane contact surface. 

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