Plastic-elastic behavior

A customary name for substances showing the plastic-elastic behavior, characteristic for vulcanized rubberlike synthetic or natural polymers, viz., mbbers and weakly cross-linked polyether and polyester urethanes. 

Elastic Behavior. Elastic deformation is defined as the reversible deformation that occurs when a load is appHed. Most ceramics deform in a linear elastic fashion, ie, the amount of reversible deformation is a linear function of the appHed stress up to a certain stress level. If the appHed stress is increased any further the ceramic fractures catastrophically. This is in contrast to most metals which initially deform elastically and then begin to deform plastically. Plastic deformation allows stresses to be dissipated rather than building to the point where bonds break irreversibly. 

Elastic Behavior The assumption that displacement strains will produce proportional stress over a sufficiently wide range to justify an elastic-stress analysis often is not valid for nonmetals. In brittle nonmetallic piping, strains initially will produce relatively large elastic stresses. The total displacement strain must be kept small, however, since overstrain results in failure rather than plastic deformation. In plastic and resin nonmetallic piping strains generally will produce stresses of the overstrained (plasfic) type even at relatively low values of total displacement strain. 

It is usual in the classical theory to assume that the stress rate is independent of the hardening parameters, since the elastic behavior is expected to be unaffected by plastic deformation. Consequently, the stress rate relation (5.23) reduces to... 

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.

The properties of the lamina constituents, the fibers and the matrix, have been only briefly discussed so far. Their stress-strain behavior is typified as one of the four classes depicted in Figure 1-8. Fibers generally exhibit linear elastic behavior, although reinforcing steel bars in concrete are more nearly elastic-pertectly plastic. Aluminum, as well as... 

The simplified failure envelopes differ little from the concept of yield surfaces in the theory of plasticity. Both the failure envelopes (or surfaces) and the yield surfaces (or envelopes) represent the end of linear elastic behavior under a multiaxial stress state. The limits of linear elastic... 

Fig. 2-17 Elastic and plastic flexural behavior of unreinforced and reinforced plastics.

Elastic-plastic transition It is the changes from recoverable elastic behavior to non-recoverable plastic strain which occurs on stressing a material beyond its yield point. 

Elastomers are often blended with plastics either to improve the impact resistance or to develop new materials having both plastic and elastic behavior. When the elastomer in the blend is dynamically vulcanized, the product is called a thermoplastics vulcanizate (TPV). Blends with unvulcanized mbber phase are usually known as thermoplastic elastomers. TPVs are discussed in another section of this book. This section will deal with recent developments in rubber-plastic blends. 

Ceramic-matrix fiber composites, 26 775 Ceramics mechanical properties, 5 613-638 cyclic fatigue, 5 633-634 elastic behavior, 5 613-615 fracture analysis, 5 634-635 fracture toughness, 5 619-623 hardness, 5 626-628 impact and erosion, 5 630 plasticity, 5 623-626 strength, 5 615-619 subcritical crack growth, 5 628—630 thermal stress and thermal shock, 5 632-633... 

The characteristic property of elastomers is their rubber-elastic behavior. Their softening temperature lies below room temperature. In the unvulcanized state, i.e. without crosslinking of the molecular chains, elastomers are plastic and thermo-formable, but in the vulcanized state—within a certain temperature range — they deform elastically. Vulcanization converts natural rubber into the elastic state. A large number of synthetic rubber types and elastomers are known and available on the market. They have a number of specially improved properties over crude rubber, some of them having substantially improved elasticity, heat, low-temperature, weathering and oxidation resistance, wear resistance, resistance to different chemicals, oils etc. 

Rgure 4.9. Schematic mechanical behavior of the interface (a) elastic behavior the 2-D stress is proportional to the relative surface extension, (b) ideal plastic behavior after a narrow elastic regime the stress becomes constant and equal to standard plastic behavior in the plastic regime the stress slowly increases with the relative surface extension. (Adapted from [31].)... 

The specific material properties of most import to the compaction operation are elastic deformation behavior, plastic deformation behavior, and viscoelastic properties. These are also referred to as mechanisms of deformation. As mentioned earlier, they are equally important during compression and decompression i.e., the application of the compressional load to form the tablet, and the removal of the compressional load to allow tablet ejection. Elastic recovery during this decompression stage can result in tablet capping and lamination. 

This is also true for the calculation of the internal pressure pei at which the elastic behavior ends and the plastic deformation (overstrain) begins, based on the GE (v. Mises) hypothesis a (proof stress in N/mm2, pei = internal pressure in N/mm2, u diameter ratio)... 

A new ASME code for calculating high pressure vessels (Sect VIII Div. 3) is based on the formulae to determine the internal pressure pcompi-pi for complete plastic yielding through the full wall with some assumptions, e.g. perfectly elastic-plastic material behavior and the GE-hypothesis [2]. 

The residual stresses can be calculated either by approximation on analytical base with the assumption of ideal elastic-plastic material behavior or numerically by FEM for arbitrary material properties. 

The simplest model assumes ideal elastic behavior (Figure 7.12A). At a stress below the yield stress (Fy), the sample behaves perfectly elastically. In this region, a modulus of elasticity can be determined. At the yield stress, the sample flows. It continues to flow until the stress is lowered again to below the yield stress value. Therefore, both the elastic modulus and yield stress describe the behavior of a plastic material. They can be determined easily by compression testing. The continuous network of fat crystals in a fat bears the stress below the yield stress and therefore contributes solid or elastic properties to the material (Narine and Marangoni, 1999a). 

This property of viscoelasticity is possessed by all plastics to some degree, and dictates that while plastics have solid-like characteristics, they also have liquid-like characteristics (Figure 1.2). This mechanical behavior is important to understand. It is basically the mechanical behavior in which the relationships between stress and strain are time dependent for plastic, as opposed to the classical elastic behavior of steel in which deformation and recovery both occur instantaneously on application and removal of stress.1... 

Fig. 14 Stress distribution in a cracked film. The dotted lines correspond to the elastic behavior of the film/substrate system, the solid lines to the presence of plasticity in the substrate at the crack/interface intersection (a) crack opening in a film deposited on a substrate which is uniaxially stretched, (b) longitudinal strain distribution In the film, (c) normal stress distribution in the film, and (d) shear stress distribution In the film at the Interface.

Tablet capping and lamination typically create the most difficult problems, due to a variety of causes. Identification of the cause often leads to the solution. The basic concepts to alleviate these problems center on minimizing elastic behavior while promoting plastic deformation. Depending on the exact nature of the problem, this can be achieved from a formulation perspective by modifying the formula to incorporate a plastically deforming matrix, by adding components to enhance bonding, or by increasing the moisture level. Alternatively, from a machine perspective the following guidelines should be followed ...

Nevertheless, machines with concave die rings do have advantages. In particular, if materials with a certain elastic behavior must be pelleted, compaction force in the relatively long and slender nip increases more slowly, which allows for a more complete conversion of temporary elastic into permanent plastic deformation. 

The mechanical behavior of Zr02-Ni system strongly depends on constitutional variation. The Ni-rich materials exhibit typical behavior of elasto-plastic deformation and ductile fracture similar to metallic material. The materials containing PSZ from 40-80 vol% mainly presents typically linear elastic behavior and macroscopic brittle fracture. However, the material with 60 vol% PSZ behaves as non-linear elastic behavior after the linear stage. 

The dependence of mechanical behavior on constitution in Zr02-Ni system results from the variation of microstructure and its distribution. In the regions rich in Ni or PSZ, the mechanical performance is controlled by continuous matrix component and displays elasto-plastic or linear elastic characteristics, respectively. The non-linear elastic behavior at 60 vol% PSZ is related to the connectivity transition of matrix component. 

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