Stress perfectly plastic

Anzellotti G., Giaquinta M. (1982) On the existence of the fields of stresses and displacements for an elasto-perfectly plastic body in static equilibrium. J. Math. Pure Appl. 61, 219-244. 

Perfectly Plastic. When A = Q then / = 0. The elastie limit surfaee in stress space is stationary, and the material is said to be perfectly inelastic. 

In the numerical calculations, an elastic-perfectly-plastic ductile rod stretching at a uniform strain rate of e = lO s was treated. A flow stress of 100 MPa and a density of 2700 kg/m were assumed. A one-millimeter square cross section and a fracture energy of = 0.02 J were used. These properties are consistent with the measured behavior of soft aluminim in experimental expanding ring studies of Grady and Benson (1983). Incipient fractures were introduced into the rod randomly in both position and time. Fractures grow... 

The second physical quantity of interest is, r t = 90 pm, the critical crack tip stress field dimension. Irwin s analysis of the crack tip process zone dimension for an elastic-perfectly plastic material began with the perfectly elastic crack tip stress field solution of Eq. 1 and allowed for stress redistribution to account for the fact that the near crack tip field would be limited to Oj . The net result of this analysis is that the crack tip inelastic zone was nearly twice that predicted by Eq. 3, such that... 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

Fig. 2.8. Idealized elastic/perfectly plastic solid behavior results in a stress tensor in which there is a constant offset between the hydrostatic (isotropic) loading and shock compression. Such behavior is only an approximation which may not be appropriate in many cases.

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... 

A plastic material is defined as one that does not undergo a permanent deformation until a certain yield stress has been exceeded. A perfectly plastic body showing no elasticity would have the stress-strain behavior depicted in Figure 8-15. Under influence of a small stress, no deformation occurs when the stress is increased, the material will suddenly start to flow at applied stress a(t (the yield stress). The material will then continue to flow at the same stress until this is removed the material retains its total deformation. In reality, few bodies are perfectly plastic rather, they are plasto-elastic or plasto-viscoelastic. The mechanical model used to represent a plastic body, also called a St. Venant body, is a friction element. The... 

For k 1, isothermal conditions prevail, while /< -c 1 when the situation is adiabatic. The characteristic timescale to for the present study is defined as the time to attain the material toughness A[r for a given loading rate, i.e., to = Kf1/K. The characteristic length Lq is taken as the size of the plastic zone of a perfectly plastic material with yield stress s0 so that L0 = (fQ/so)2 [57]. For k 1, heat conduction needs to be accounted for and this condition results in the estimation of... 

In this context it has to be pointed out that in the original Dugdale model the material behavior is assumed to be linearly elastic and perfectly plastic the latter assumption leads to a uniform stress distribution in the plastic zone. This may be a simplified situation for many materials to model, however, the material behavior in the crack tip region where high inhomogeneous stresses and strains are acting is a rather complex task if nonlinear, rate-dependent effects in the continuum... 

One idealized material is the elastic perfectly plastic material a typically stress strain curve is shown in Figure I7A, For this curve we can substitute Equation (32) into Equation (43) to yield ... 

For perfectly plastic materials, post>yieldtng the strain rate is a constant function of the stress and the stress is constant and never exceeds ay (Fig. ISA). The extent of pla.stic deformation p depends upon the proportionality between plastic strain rate and the stress and the how long the. stress is applied as shown in Figure 17A. The elastic perfectly plastic material is highly idealized and not many materials exhibit this type of behavior. 

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... 

Each block is modeled as linear, isotropic, homogeneous and elastic medium and subdivided with a mesh of constant-strain triangle finite-difference elements. Key factors affecting the hydraulic behaviour of fractures such as opening, closure, sliding and dilation of fractures are modeled by an elasto-perfectly plastic constitutive model of a fracture. A step-wise non-linear normal stress-normal closure relationship is adopted with a linear Mohr-Coulomb failure for shear (Figure 3). 

This model is based on the mean features of the Mohr-Coulomb model and is expressed with stress invariants [Maleki (1999)] instead of principal stresses. Until plasticity is reached, a linear elastic behaviour is assumed. It is fully described by the drained elastic bulk and shear moduli. The yield surface of the perfectly plastic model is given by equation 7. Function 7i(0) is chosen so that the shape of the criterion in the principal stress space is close to the Lade criterion. 

Under the situation that the disturbance factor is independent of the stress state in the plastic zone, i.e. a fixed D-value, the presented analytical model can be degenerated to an elastic perfectly-plastic or elastic-brittle-plastic model. The corresponding analytical solutions of the elastic perfectly-plastic or elastic-brittle-plastic model can be easily derived. We only give the analytical results of the elastic perfectly-plastic and elastic-brittle-plastic models for comparison with the present analytical model. 

Elastic recovery n. That fraction of a given deformation that behaves elastically. A perfectly elastic material has a recovery of 100% while a perfectly plastic material has no elastic recovery. Elastic recovery is an important property in films used for stretch packaging because it relates directly to the ability of a film to hold a load together. Retention of the elastic-recovery stress over a period of time is also important. Shah V (1998) Handbook of plastics testing technology. John Wiley and Sons, New York. 

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]...

Fig. 25.3 Constitutive modelling for soil (a) Stress-strain in deviatoric mode, (b) Multi-phase yield modelling, (c) Division of envelope into n broken straight parts, (d) Decomposition into some elasto-perfectly plastic surface with different yield strength and stiffness...

A nonlinear path-dependent constitutive model for the soil mainly depends on the shear stress-shear strain relationship, which is extended to three-dimensional generic conditions and assumed to follow Masing s rule for the soil hysteresis. The soil is idealized as an assembly of a finite number of elasto-perfectly plastic elements connected in parallel as shown in Fig. 25.3 (Okhovat et al. 2009, Mohammed and Maekawa 2012 Mohammed et al. 2012a). The nonlinear behavior of the soil system in liquefaction is assumed as in undrained state, since its drainage takes much longer than the duration of an earthquake (Towhata 2008). The soil undrained behavior is shown in Fig. 25.4. 

Although the relative values of the principal stresses acting on the shell element may vary with process parameters related to the thickness t of the sheet and to the radius of the single-point forming tool, the term 5" = 6 - 6 should always be kept equal to the flow stress of the polymer under perfectly plastic material assumptions. If the... 

According to Equation 8.17, the meridional stress <7 decreases along the inclined wall of the sheet, being higher at the transition point C and smaller at point D. Because the meridional stress at point C must be kept below the yield stress in tension (for a perfectly plastic material), it follows that the inclined wall surface of the sheet adjacent to the forming tool is elastic. This result, together with the stress field in the small localised plastic zone that is summarised in Table 8.2, results in the schematic distribution of the principal stresses that is depicted in Figure 8.4. 

The primary stress intensity in the ASME Boiler and Pressure Vessel Code is intended to prevent uncontrolled plastic deformation and to provide a nominal factor of safety on the ductile burst pressure. These limits are based on the principles of limit design. The material is assumed to be elastic-perfectly plastic. For a straight bar in tension, a load producing yield stress, Sy, results in a collapse. If it is loaded in bending, collapse does not occur until the yield moment has been increased by the shape factor of the section. 

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