Plastic regions

The increase in stress needed to produce further strain in the plastic region. Each strain increment strengthens or hardens the material so that a larger stress is needed for further strain. 

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. 

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. 

Elasto-Plastic Region - The deformation range from formation of the first plastic hinge up to formation of the final plastic hinge (i.e. ultimate capacity). 

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... 

Plastic Region - The deformation range from ultimate capacity up to failure of the element. 

Fig. l-(a). Stress-Strain curve of iron (Fe) containing 0.15 wt. % carbon (C) at room temperature 1-(b). Representing material without conduction band no plastic region, and is brittle. 

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...

For material with small amount of free electron and subsequently a narrow conduction band, the plastic region will be very small, i.e., the material will be brittle and weak in impact strength or toughness. This type of material includes intermetallic compounds or n-type semiconductors. 

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. 

Metal targets under shaped-charge jet attack behave like fluids because, at the impact velocities of the jet, both Jet and target at the interface are at several megabars pressure, well into the plastic region for almost all materials. This erosion process continues until the entire jet has been used up or until the target has been perforated. 

We looked briefly and qualitatively at what shaped charges are and how they work. Now let us consider a simple model that will help quantify some of these observations. The model assumes that both the jet and the target are ideal liquids (that is, they do not exhibit any viscosity). This is not a bad assumption because at the impact pressure at the interface of jet and target (several hundred kilobars), most metals are far into the plastic region and do indeed behave like liquids. 

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.

From a plot of true stress-true strain behavior on logarithmic coordinates K and n can be found where K is determined by extrapolating the curve to unit strain value while the /(is defined by the slope of the plastic region. 

Compared to the DMTA spectra of the slow cure of the homo-polymers two differences are striking 1) Compared to PMDA-ODA (Figure l.b) pronounced plasticization is observed due to the presence of the flexible BTDA based polymer. This leads to an increase in the imidization rate of PM DA compared to the slow cured homo-PMDA-ODA. 2) Compared to homo-BTDA-ODA/MPDA a much narrower plasticization region is found the spectrum resembles fast cured PMDA-ODA. This is explained again as indication of the catalytic effect of the PMDA based amic acid on the imidization rate of the BTDA based system. Thus, both polyamic acids have an accelerating effect on the cycloimidization of each other in a slow cure. 

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... 

Figure 5 Two views of an overlay of structurally plastic regions of microsomal cytochrome P450 2B4 in complex with CPI (orange) and with bifonazole (yellow). The heme is shown in red, CPI in green, and bifonazole in cyan. Note that the ligands are bound in strikingly different orientations. Five plasticity regions labeled PR1-PR5 show significantly different conformations in the two complexes. Reproduced with permission from Y. Zhao M. A. White B. K. Muralidhara L. Sun J. R. Halpert C. D. Stout, J. Biol. Chem. 2006, 281, 5973-5981.

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