Plastic strain, plastics mechanical behavior

As an example, for room-temperature applications most metals can be considered to be truly elastic. When stresses beyond the yield point are permitted in the design, permanent deformation is considered to be a function only of applied load and can be determined directly from the stress-strain diagram. The behavior of most plastics is much more dependent on the time of application of the load, the past history of loading, the current and past temperature cycles, and the environmental conditions. Ignorance of these conditions has resulted in the appearance on the market of plastic products that were improperly designed. Fortunately, product performance has been greatly improved as the amount of technical information on the mechanical properties of plastics has increased in the past half century. More importantly, designers have become more familiar with the behavior of plastics rather than... 

Object in this section is to review how rheological knowledge combined with laboratory data can be used to predict stresses developed in plastics undergoing strains at different rates and at different temperatures. The procedure of using laboratory experimental data for the prediction of mechanical behavior under a prescribed use condition involves two principles that are familiar to rheologists one is Boltzmann s superposition principle which enables one to utilize basic experimental data such as a stress relaxation modulus in predicting stresses under any strain history the other is the principle of reduced variables which by a temperature-log time shift allows the time scale of such a prediction to be extended substantially beyond the limits of the time scale of the original experiment. 

Mechanical properties of plastics are invariably time-dependent. Rheology of plastics involves plastics in all possible states from the molten state to the glassy or crystalline state (Chapter 6). The rheology of solid plastics within a range of small strains, within the range of linear viscoelasticity, has shown that mechanical behavior has often been successfully related to molecular structure. Studies in this area can have two objectives (1) mechanical characterization of... 

Time dependence Viscoelastic deformation is a transition type behavior that is characterized by the occurrence of both elastic strain and time-dependent flow. It is the time dependence of the mechanical properties of plastics that makes the behavior of these materials difficult to analyze by mathematical theory. 

Viscoelasticity A combination of viscous and elastic properties in a plastic with the relative contribution of each being dependent on time, temperature, stress, and strain rate. It relates to the mechanical behavior of plastics in which there is a time and temperature dependent relationship between stress and strain. A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid. 

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

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... 

Similar stress-strain curves have been obtained for polystyrene crazes. However, these results do not necessarily reveal the real mechanical behavior of the craze. The removal of the solvent from samples will cause shrinkage and have a significant plasticizing effect on the craze fibrils. This has to... 

Figure 11. Typical stress-strain curve showing the three theoretically identifiable regions of mechanical behavior. Key A, elastic region B, elastic (Bj-plastic (BJ region and C, plastic region.

The applied stress results in the shear strain of the cube, i.e. the top face becomes shifted with respect to the bottom one by distance y. This displacement is numerically equal to the tangent of a tilt angle of the side face, i.e. it is equal to the relative shear strain, y, and at small strains tany y. The relationship between shear stress, x, and shear strain, y, and the rates of change in these quantities with time, dx/dt=x, dy/dt=y, represent mechanical behavior, which is the main subject in rheology. One usually begins the description of mechanical behavior with three elementary models, namely elastic, viscous, and plastic behavior. 

The equivalence of K and (7, which strictly holds for elastic materials with linear load-deflection characteristics, is referred to as linear-elastic fracture mechanics (LEFM). Subsequently this basic concept has been modified to describe also the behavior of ductile materials. For instance. Wells [3] considered the plastic strain at the crack tip as the crack... 

A particular distinction between the mechanical behaviors of metals and plastics (URPs and RPs) is explained in order to avoid a possible confusion that could have arisen from the preliminary review. A typical stress-strain curve for a metal exhibits a linear elastic region followed by yield at the yield stress, plastic flow, and ultimately failures at the failure stress. Yield and failure occur at corresponding strains, and one could define yield and failure in terms of these critical strains. This is not common practice because it is simpler in many cases to restrict step (a) to a stress analysis alone. By comparison, it may appear strange that it was stated that plastics failure criteria are usually defined in terms of a critical strain (rather than stress) and, by comparison with the metals case, switching back from strain to stress may appear to be a minor operation. 

If this deformation field does not fulfill the geometrical compatibility, a strain tensor related to stress is generated. The constitutive equation, which represents the mechanical behavior of the material, relates this strain tensor and the stress tensor. Due to the memory effect of wood, this tensor has to be divided into two parts (1) an elastic strain, connected to the actual stress tensor and (2) a memory strain, which includes all the strain due to the history of that point (e can deal with plasticity, creep, mechanosorption, etc.). 

Another failure mode for a material under mechanical load is the plastic strain. The stress concentration at the tip of a crack increases the probability that dislocations will nucleate and move at the head of the crack tip. However, unlike in brittle fracture, plasticity dissipates a lot of energy, thus reducing the stress concentration by blunting the crack. This type of ductile behavior, typical in metals, leads to robust structural materials the initiation of failure does not necessarily extend catastrophically through the entire specimen, and a lot of energy is dissipated during the process of the material strain. 

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