Pseudo-plastic strain

Failure Mechanisms. BPF polycarbonate develops crazes at ascending stresses and fractures in a pseudo-brittle manner similar to polystyrene or PMMA. At room temperature the block polymers develop few separate crazes. As the yield is approached, shear bands grow from the edges. Fracture initiates at an edge from a point where the two shear bands initiated. When a neck forms, the plastic strain in the neck is ca. 80% however fracture occurs shortly after the neck is formed so that the ultimate elongation of the specimen is only 10 or 12%. The shear bands and necks show some stress whitening (Figure 9). 

Since these assumptions are not always justifiable when applied to plastics, the classic equations cannot be used indiscriminately. Each case must be considered on its merits, with account being taken of such factors as the time under load, the mode of deformation, the service conditions, the fabrication method, the environment, and others. In particular, it should be noted that the traditional equations are derived using the relationship that stress equals modulus times strain, where the modulus is a constant. From the review in Chapter 2 it should be clear that the modulus of a plastic is generally not a constant. Several approaches have been used to allow for this condition. The drawback is that these methods can be quite complex, involving numerical techniques that are not attractive to designers. However, one method has been widely accepted, the so-called pseudo-elastic design method. 

When a specimen is stretched plastically a few percent and then unloaded, x-ray measurements show a line shift indicating residual compressive macrostress in the direction of prestrain. The effect is symmetrical after plastic compression, x-rays indicate residual tensile stress. It is not a surface effect, because x-ray measurements made after successive removal of surface layers show that the stress persists throughout the specimen. On the other hand, dissection measurements show that a true macrostress does not exist, and, in fact, none would be expected after uniform deformation. The stress indicated by x-rays is called pseudo-macrostress, pseudo because it is not a true macrostress causing strain on dissection and macro because it causes an x-ray line shift. Pseudo-macrostress is actually an unusual kind of microstress, in which the portions of the material that are in tension and in compression are unequal in volume. It has been discussed in various reviews [16.26-16.28]. 

The problems of exact design for a viscoelastic polymer with non-linear properties are severe. For example, in Figure 8.1 a) the stress-strain curve is linear only at the smallest strains (below 0.2%). Most plastic parts are designed to operate at strains well above 0.2%, and in this case exact stress analysis is impossible. In practice, a safe approximate procedure known as the pseudo-elastic design method is used. The salient features of the method, which is veiy straightforward to apply, are as follows ... 

Initially the pseudo-elastic material is in its austenitic phase at room temperature. Initially the material in the austenitic phase deforms like a conventional material linear elastic under load. With increasing loads a stress-induced transformation of the austenitic to the martensitic phase is initiated at the pseudo-yield stress Rpe- This transformation is accompanied with large reversible strains at nearly constant stresses, resulting in a stress plateau shown in Fig. 6.53. At the end of the stress plateau the sample is completely transformed into martensite. Additional loading passing the upper stress plateau causes a conventional elastic and subsequently plastic deformation of the martensitic material. If the load is decreased within the plateau and the stress reaches the lower stress level a reverse transformation from martensite to austenite occurs. Since the strains are fully reversible the material and the sample respectively is completely recovered to its underformed shape. These strains are often called pseudo-elastic because the reversible deformation is caused by a reversible phase transformation and is not only due to a translation of atoms out of their former equilibrium position [74]. 

---