Plane stress, plastics mechanical behavior

In Chapters 2 and 3, the restrictions in the use of linear elastic fracture mechanics (LEFM) were discussed in terms of the dimensions of the crack and the body (specimen, component, or structure) relative to the size of the crack-tip plastic zone. Simple estimates of the plastic zone sizes were given in Section 3.6. A more detailed examination of the role of constraint (plane strain versus plane stress) and the variations in plastic zone size from the surface to the interior of a body would help in understanding fracture behavior and the design of practical specimens for measurements of fracture toughness. Note that the plastic zone size in actual materials... 

Figure 10 is a stress-strain-temperature diagram for a Ni-Ti shape-memory alloy that summarizes its mechanical behavior. At the extreme rear the stress-strain curve shown in the a-t plane corresponds to the deformation of martensite below Mf. The induced strain, about 4%, recovers between A and Af after the applied stress has been removed and the specimen heated, as seen in the e-T plane. At a temperature above Mj (and Af) SIM is formed, leading to a superelastic loop with an upper and lower plateau, the middle o-e plane. At a still higher temperature and above M, the front a-e plane, no SIM is formed. Instead, the parent phase undergoes ordinary plastic deformation. 

To determine the mechanical behavior of plastics under compressive load, it is possible to carry out the compressive test described in DIN ISO 604 for the testing of plastics [9]. By contrast to tensile tests, cylindrical, solid-material specimens are compressed between two plane-parallel plates and the compressive stress/compression behavior is recorded. One problematical aspect of these tests is that the friction that occurs between the plane-parallel clamping surfaces and the specimen inhibit the lateral extension of the test specimen and hence leads to a convex barrel shape, which is the manifestation of a multiaxial stress state inside the specimen. 

The metal azides are, by common experience, brittle when subjected to mechanical stress, they shatter before appreciable plastic deformation takes place. This arises because, as with most inorganic materials, dislocation densities are low, grown-in dislocations are usually immobile, and slip can take place only on a limited number of planes. However, with the possible exception of diamond and certain borides and nitrides, few materials are ideally brittle, and some plastic deformation is possible, the amount depending upon the temperature and the rate of strain low temperatures and high rates of strain both favor brittle behavior. 

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