Mechanical strain hardening

A hardness indentation causes both elastic and plastic deformations which activate certain strengthening mechanisms in metals. Dislocations created by the deformation result in strain hardening of metals. Thus the indentation hardness test, which is a measure of resistance to deformation, is affected by the rate of strain hardening. 

Casey, J. and Naghdi, P.M., Strain Hardening Response of Elastic Plastic Materials, in Mechanics of Engineering Materials (edited by C.S. Desai and R.H. Gallagher), Wiley, New York, 1984, Chap. 4, pp. 61-89. 

Strain hardened. Material subjected to the application of cold work after annealing (or hot forming) or to a combination of cold work and partial annealing/stabilising in order to secure the specified mechanical properties. The designations 1-8 are in ascending order of tensile strength... 

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. 

J. J. Gilman, Debris Mechanism of Strain-Hardening, Jour. Appl. Phys., 33, 2703 (1962). 

Other strengthening mechanisms include solid solution formation and strain hardening. Solid solution strengthening involves replacing a small number of atoms in the lattice with substitutional impurities of a slightly different size. This creates strain in the crystal. 

Wahl [33] describes the production of highly wear resistant sieves in soft annealed plates of chromium steel by punching, plasma cutting or mechanical working followed by heating and strain hardening. 

These two examples illustrate two particular situations where strain rate effects are similar to temperature effects, the spurious hysteretic heating having been isolated. In most cases, strain rate effects (strain hardening, increase of the mechanical properties with speed) are mixed with heating effects due to mechanical energy absorption (softening, decrease of the material properties with temperature). 

As could be expected, the mechanical properties of a crazed polymer differ from those of the bulk polymer. A craze containing even 50% microcavities can still withstand loads because fibrils, which are oriented in the direction of the load, can bear stress. Some experiments with crazed polymers such as polycarbonate were carried out to get the stress-strain curves of the craze matter. To achieve this aim, the polymer samples were previously exposed to ethanol. The results are shown in Figure 14.24 where the cyclic stress-strain behavior of bulk polycarbonate is also illustrated (32). It can be seen that the modulus of the crazed polymer is similar to that of the bulk polymer, but yielding of the craze occurs at a relatively low stress and is followed by strain hardening. From the loading and unloading curves, larger hysteresis loops are obtained for the crazed polymer than for the bulk polymer. 

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