Large strains, plastic behaviour

Because large strains can occur during plastic deformation, we will start the chapter by discussing the notion of strain if strains become large. The plastic behaviour of materials is usually measured during a tensile test, discussed in detail in section 3.2. Next, we will consider the methods of continuum mechanics to describe the limit between elastic and plastic behaviour, plastic deformation, and hardening effects observed in plasticity (section 3.3). Another important material parameter, hardness, will be discussed in section 3.4. Finally, we will discuss different failure mechanisms leading to catastrophic rupture of materials. 

Wear in conventional UHMWPE has been measured at 30 mm per million cycles. Some of the macromolecules combine with each other to produce crosslinks. The amorphous region is snsceptible to large-strain plastic deformation while the crystalline region imparts strength and toughness to the material. The arrangement of macromolecules and crystallites that explains wear and mechanical behaviour is shown in Figure 3.26. 

It was considered initially that because there is no net tensile stress in a hydrostatic extrusion process it might be possible to impose very large plastic deformations without incurring fracture. It was indeed shown that Rj, of 30 can be imposed in polyethylene comparable to the draw ratios of 30 adiieved in a tensile drawing process, and that both processes are limited by the strain hardening behaviour of the material, which is determined solely by the total plastic strain imposed. This led to an important... 

Ductile fracture is accompanied by large deformation. In metals, there are deformations along slip planes and in specimens under test, which are subjected to tensile load, and can be observed as necking and horizontal sections of the stress-strain curves. It is also called plastic behaviour. ... 

It will be convenient to discuss these various aspects separately as follows (1) behaviour at large strains in Chapters 3 and 4 (finite elasticity and rubber-like behaviour, respectively) (2) time-dependent behaviour in Chapters 5-7 and 10 (viscoelastic behaviour) (3) the behaviour of oriented polymers in Chapters 8 and 9 (mechanical anisotropy) (4) non-linearity in Chapter 11 (non-linear viscoelastic behaviour) (5) the non-recoverable behaviour in Chapter 12 (plasticity and yield) and (6) fracture in Chapter 13 (breaking phenomena). However, it should be recognised that we cannot hold to an exact separation and that there are many places where these aspects overlap and can be brought together by the physical mechanisms, which underlie the phenomenological description. 

Contrary to metals and ceramics, the elastic strains in elastomers can become very large and attain values of several hundred percent. The reason is that the molecules are straightened during deformation, but the cross-links prevent the molecules from shding past each other and thus inhibit plastic deformation. Upon unloading, entropy-elasticity completely restores the initial arrangement of the molecules. This behaviour is called hyperelasticity. 

The incorporation of rubber particles into a brittle polymer has a profound effect upon the mechanical properties as shown from the stress-strain curves in Fig. 5.66. This can be seen in Fig. 5.66(a) for high-impact polystyrene (HIPS) which is a blend of polystyrene and polybutadiene. The stress-strain curve for polystyrene shows brittle behaviour, whereas the inclusion of the rubbery phase causes the material to undergo yield and the sample to deform plastically to about 40% strain before eventually fracturing. The plastic deformation is accompanied by stress-whitening whereby the necked region becomes white in appearance during deformation. As will be explained later, this is due to the formation of a large number of crazes around the rubber particles in the material. 

Unified equations that couple rate-independent plasticity and creep [114] are not readily available for SOFC materials. The data in the hterature allows a simple description that arbitrarily separates the two contributions. In the case of isotropic hardening FEM tools for structural analysis conveniently accept data in the form of tabular data that describes the plastic strain-stress relation for uniaxial loading. This approach suffers limitations, in terms of maximum allowed strain, typically 10 %, predictions in the behaviour during cycling and validity for stress states characterised by large rotations of the principal axes. 

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