Deformation-hardening rates

Some measured values of hardness are given in Table 8.1 which shows how the hardness varies with stoichiometry (Qian and Chou, 1989). The values in the table are averages of 30 measurements for each composition. The stoichiometric value is 16X the yield stress (albeit from different authors). Since hardness numbers for metals are determined by deformation-hardening rates, the latter is very large for Ni3Al causing the hardness numbers to be 16X the compressive yield stress instead of the 3X of pure metals. 

Another possibility is that the vibrational frequency difference increases the cross-gliding rate, and therefore the deformation-hardening rate. In this case, when the temperature becomes high enough, dislocation climb causes rapid enough recovery to cancel the deformation-hardening rate. 

In order to start the multiscale modeling, internal state variables were adopted to reflect void/crack nucleation, void growth, and void coalescence from the casting microstructural features (porosity and particles) under different temperatures, strain rates, and deformation paths [115, 116, 221, 283]. Furthermore, internal state variables were used to reflect the dislocation density evolution that affects the work hardening rate and, thus, stress state under different temperatures and strain rates [25, 283-285]. In order to determine the pertinent effects of the microstructural features to be admitted into the internal state variable theory, several different length scale analyses were performed. Once the pertinent microstructural features were determined and included in the macroscale internal state variable model, notch tests [216, 286] and control arm tests were performed to validate the model s precision. After the validation process, optimization studies were performed to reduce the weight of the control arm [287-289]. 

As developed in Section 10.3, the stability of extensional flow in visco-plastic solids is governed by intrinsic properties of the solid, such as its plastic resistance, its strain-hardening rate and its strain-rate-hardening rate, through the sensitivity of the plastic resistance to the strain rate. In many instances, however, the deforming bar or fiber contains imperfections that can affect or hasten localization in necks and subsequent rupture. Such perturbations of flow by imperfections and their effect on material stability in extensional flow have been of great interest. A well-defined scenario of this was conceived by Hutchinson and Obrecht (1977) and further developed by Hutchinson and Neale (1977). 

With an increase in strain-rate sensitivity of the flow stress a change in the condition of onset of necking can be expected, since a change in deformation rate results in a change of flow stress without much change in the strain-hardening rate. 

It was indicated in the above curves that strain hardening is related to an increase in the yield stress, which can be observed after unloading, followed by an increment of plastic deformation and upon reloading the specimen. The slope of the stress-strain curve, being a measure of the increase in the stress on a stress-strain curve, usually defines the strain hardening rate. The slope, at a constant stress rate, is expressed as ... 

This procedure may be used unless the rate-dependence, load history-dependence, or deformation-hardening characteristics of the isolation system necessitate explicit consideration of their nonlinear and/or velocity-dependent force-deflection properties. 

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. 

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