Energy plastic work

When metals are rolled or forged, or drawn to wire, or when polymers are injection-moulded or pressed or drawn, energy is absorbed. The work done on a material to change its shape permanently is called the plastic work- its value, per unit volume, is the area of the cross-hatched region shown in Fig. 8.9 it may easily be found (if the stress-strain curve is known) for any amount of permanent plastic deformation, e. Plastic work is important in metal- and polymer-forming operations because it determines the forces that the rolls, or press, or moulding machine must exert on the material. 

Energy required to cause p/asfic deformation up to point of final fracture (plastic work at fracture)... 

Surface energy change -I- Plastic work done =... 

Since the surface energy term will usually be negligible by comparison with the plastic work term in the stress corrosion of ductile materials, it may be neglected. The remaining terms may be derived from fracture mechanics and conventional electrochemical conditions and, for the various boundary conditions indicated by West result in... 

In retrospect, it should not be surprising that a time independent theory modeled after elasticity theory does not apply to a plastic flow process. Elastic deformation is conservative with the work done on the material stored as elastic strain energy. Plastic deformation is non-conservative with the work done on the material dissipated as heat, or converted into internal defects... 

A second major difficulty with the Peierls model is that it is elastic and therefore conservative (of energy). However, dislocation motion is nonconservative. As dislocations move they dissipate energy. It has been known for centuries that plastic deformation dissipates plastic work, and more recently observations of individual dislocations has shown that they move in a viscous (dissipative) fashion. 

Griffith s law was derived for the surface energy for a perfectly brittle, elastic material undergoing no plastic work. However, for many materials, plastic work is not negligible and when included, 2es = G, where G can include both plastic and surface work. 

At this point, however, we need to be careful. The reason is that for solids we have to distinguish between surface tension and surface energy. The work required to form a new surface depends on how this surface is formed plastically (as for a liquid) or elastically. In an experiment, usually both effects contribute. Therefore we should consider the surface energy obtained from adhesion experiments as an effective surface energy. Inserting Eq. (6.70) into Eq. (6.69) leads to... 

This technique were used because of its simplicity and its ability to qualitatively decompose the energy at rupture into its two intrinsic components energy for creating new surfaces (essential work of fracture. We) and "plastic" work, or more seemingly dissipated energy due to the deformation of the bulk. 

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