Elastic-plastic region

Wave profiles in the elastic-plastic region are often idealized as two distinct shock fronts separated by a region of constant elastic strain. Such an idealized behavior is seldom, if ever, observed. Near the leading elastic wave, relaxations are typical and the profile in front of the inelastic wave typically shows significant changes in stress with time. 

Visualization of the above processes and the mechanisms of two-speed behavior in the elastic-plastic region and the process of shock front decay at lower pressures. 

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

Concret does not have well defined elastic and plastic regions due to its brittle nature. A maximum compressive stress value is reached at relatively low strains and is maintained for small deformations until crushing occurs. The stress-strain relationship for concrete is a nonlinear curve. Thus, the elastic modulus varies continuously with strain. The secant modulus at service load is normally used to define a single value for the modulus of elasticity. This procedure is given in most concrete texts. Masonry lias a stress-strain diagram similar to concrete but is typically of lower compressive strength and modulus of elasticity. 

Variation in internal resistance can be related to the strain because stress in a member is a function of the strain experienced at a given point. Deformation of a key point on the member can also be related to the strain producing a relationship between resistance and deflection as shown by the curve in Figure 5.1, Elastic resistance is the level at which the material reaches yield at the location of maximum moment in the member, Beyond the point of first yield of a member, plastic regions are formed in the section and an clastic-plastic condition occurs. Internal resistance... 

Fig. 3. Two-dimensional representation of Covalent bond potential energy curve. Subdivided into three regions Elastic region where the curve is symmetric with respect to Ro, Plastic region where the curve is asymmetric and affect only on the side of R greater than the yield stress. Beyond plastic limit the atoms physically breaks away...

Restoration Methods Based on Alternate Approaches. Other property changes occurring in the plastically or elastically deformed regions may be considered for utilization in serial number restoration their identification and exploitation for field use is a genuine challenge to the materials scientist. 

A tensile test on the peel arm is used to obtain the parameters of elastic modulus, plastic modulus and yield strain. In this test, it has been necessary to use an extensometer for measuring strain at small magnitudes (i.e. up to about 2%) in order to obtain sufficient accuracy in the determination of Ei. It is also important to continue the tensile test to fracture, in order to define enough of the plastic region for an accurate... 

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 general shape of the stress-strain curve is the same for all the blends with Q-series and Kraton compatibilizers. This shape is described by two tangent lines drawn from the initial elastic region and the plastic region, respectively. The intersection of the lines is defined as the yield point and is described by a yield stress (ay) and an apparent yield strain (ey). The stress (a) and strain (e) in the plastic region are related by... 

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