Strain hardening and softening

Stress-strain relationships for the steel material including strain hardening and softening... 

Finally, the Cogswell [5] and Binding method [6] were used for determination of the extensional viscosity in the strain hardening and softening parts, respectively. Of course, effective entry length correction [8] has been applied to deal with all extensional viscosity data. 

Shear band formation and evolution, and the change of shear displacement from one location to another, can be analysed numerically. The small and finite displacement on each band, after which the shear displacement is transferred elsewhere, can be explained by a progressive reduction of one or more stress components (and lower mean stress), thus dissipating strain energy. It is not necessary to invoke strain hardening or softening, change of pore pressure or any other intrinsic material weakness in the band. 

Continuing deformation after the end of this propagation, the stress increases again. This is called strain hardening and it is due to direct loading of the material which has experienced neck formation. The latter has higher modulus than material softened after the plasticity threshold. 

Fig. 16. Normalized stress versus radial position for a strain hardening and a strain softening model. Redrawn from ref. [13].

If forces are applied to a semicrystalline pol3rmer in the way of a tension, a compression or a simple shear, deformations take place imder a constant volume. Hence, they are always composed of a reversible elastic shear and an irreversible shear 3delding. In this section, we discuss the properties of tensile deformations. As it is found, here deformation mechanisms change at three critical strains associated with a strain softening, a strain hardening and a loss of memory of the initial sample shape. The drawing stress is set up of contributions from the amorphous network, the skeleton of crystallites and viscous forces, and experiments enable a separation to be carried out. 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

At high stresses and strains, non-linearity is observed. Strain hardening (an increasing modulus with increasing strain up to fracture) is normally observed with polymeric networks. Strain softening is observed with some metals and colloids until yield is observed. 

Fig. 2 Typical stress-strain curves for amorphous polymers, a Elastic, anelastic, strain softening, and plastic flow regions can be seen, b Plastic flow occurs at the same stress level as required for yielding so strain softening does not exist, c Strain hardening occurs very close to yielding, suppressing both strain softening and plastic flow behaviour...

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