Superplasticity stress exponent

The above equations are deduced assuming the existence of dislocation activity. Although dislocation activity has been shovm in YTZP [17, 63, 64], this is likely to be an artifact (for details, see Section 15.3.1). Recently, superplastically deformed nano-MgO with grain size of 37 nm has been reported to deform at temperatures between 700 and 800 °C, and the stress exponent results in a value of 2. Dislocation activation in this system with this grain size requires an applied compressive stress in excess of 3 GPa. Such calculated stresses are far higher than the yield stresses measured experimentally (i.e., 190 to 640 MPa) [79]. 

A typical jump test is shown in Fig. 9.44 of flow stress versus strain. The stress temperature is 1450 °C. The slopes of each line in Fig. 9.44b yield for m 0.5, meaning that the stress exponent of the strain rate is 2 this indicates the superplastic behavior of the zirconia-alumina-spinel composite under the test conditions of temperature and strain rate. In order to determine the activation energy, a plot of strain rate versus the inverse absolute temperature must be made (as in Fig. 9.44c). The average activation energy of PS-HEBM-SPS is 945 kJ/mol, which is much higher than that of the composite processed from nanopowder mixtures (622 kJ/mol). This should represent GBS, if the concept of superplasticity is the dominant mechanism of deformation. Table 9.1 summarizes the strain rates and various temperatures of two and/or three specimens. PS-SPS appears in the Table 9.1 as PS-SPS and is listed under column C. For the purpose of comparison, the flow-stress results for nanopowder mixtures are also listed in Table 9.1 and are smaller than those processed from PS powders with/without HEBM. 

This relation determines the activation energy. A is the material constant, tr is the steady-state flow stress, d is the grain size, n and p are the stress and grain exponents, respectively, and Q is the activation energy for superplastic flow. Thus, it may be seen from this equation that the parameters n, p and Q play a role in the deformation mechanism. Superplasticity is considered to be similar to diffusion creep . 

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