Grain-size relationship

Fig. 5.63 Strength-grain size relationship (a) and subcritical growth of radial indentation cracks (b) of sintered batches selected from Fig. 5.62. Straight lines are least squares fits. Strength ranking numbers associate specimens in (b) to batches in graph (a), numbers 1-3 are consistent with Table 5.2 and Fig. 5.62 [20]. With kind permission of Elsevier...

F.J.P. Clarke, Residual strain and the fracture stress-grain size relationship in brittle solids, Acta Metall. 12 (1964) 139-143. 

J.C.M. Li, Y.T. Chou, Role of dislocations in flow stress grain size relationships. Metall. 

Adsorption for gas purification comes under the category of dynamic adsorption. Where a high separation efficiency is required, the adsorption would be stopped when the breakthrough point is reached. The relationship between adsorbate concentration in the gas stream and the solid may be determined experimentally and plotted in the form of isotherms. These are usually determined under static equilibrium conditions but dynamic adsorption conditions operating in gas purification bear little relationship to these results. Isotherms indicate the affinity of the adsorbent for the adsorbate but do not relate the contact time or the amount of adsorbent required to reduce the adsorbate from one concentration to another. Factors which influence the service time of an adsorbent bed include the grain size of the adsorbent depth of adsorbent bed gas velocity temperature of gas and adsorbent pressure of the gas stream concentration of the adsorbates concentration of other gas constituents which may be adsorbed at the same time moisture content of the gas and adsorbent concentration of substances which may polymerize or react with the adsorbent adsorptive capacity of the adsorbent for the adsorbate over the concentration range applicable over the filter or carbon bed efficiency of adsorbate removal required. 

Fig. I The relationship between optimum superplastie strain rate and grain size for superplastie aluminum alloys (data from Ref. [4]). Subseripts "w" and "p" stand for whisker and partieulate, respectively.

The mechanical properties of Watts deposits from normal, purified solutions depend upon the solution formulation, pH, current density and solution temperature. These parameters are deliberately varied in industrial practice in order to select at will particular values of deposit hardness, strength, ductility and internal stress. Solution pH has little effect on deposit properties over the range pH 1 0-5-0, but with further increase to pH 5 -5, hardness, strength and internal stress increase sharply and ductility falls. With the pH held at 3-0, the production of soft, ductile deposits with minimum internal stress is favoured by solution temperatures of 50-60°C and a current density of 3-8 A/dm in a solution with 25% of the nickel ions provided by nickel chloride. Such deposits have a coarse-grained structure, whereas the harder and stronger deposits produced under other conditions have a finer grain size. A comprehensive study of the relationships between plating variables and deposit properties was made by the American Electroplaters Society and the results for Watts and other solutions reported... 

It is worth elucidating mineral particle behavior in hydrothermal plumes in order to consider the formation mechanism of chimney and massive ores on the seafloor. Using the grain size data on sulfides and sulfates, the density of the fluids and of the minerals, the relationship between vertical settling rate and grain size of sulfides and sulfates can be derived based on the following Stokes equation ... 

Where D is in cm yr and Depth in m. Although these two relationships explain some of the variability in D, it is clear that other environmental factors are also important, including sediment grain-size (Wheatcroft 1992) and the organic carbon flux (Trauth et al. 1997). 

Some authors suggest that there is no clear relationship between grain size and DON levels (Lepschy, 1992). However, Perkowski (1998) reported that the fraction of smallest barley kernels contained more than 75% of the total DON. On the other hand, Chelkowsky and Perkowski (1992) determined... 

We examine grain-size normalization by means of multivariate log-ratio techniques. Specifically, published data are reanalyzed to explore the relationship between normalizing agents and grain-size composition, and to compare the log-ratio method with the traditional approach of heavy metal normalization. 

Since the grain boundaries essentially act as barriers to slip in adjacent crystals (see Figure 5.14), it makes sense that the yield strength should depend on grain size. This is indeed the case, and the Hall-Petch relationship shows an inverse square-root dependence of yield strength on grain size, d ... 

Based on the above mentioned, the programme of theoretical and experimental investigation of the main parameters of coal-methanol (or its water solution) mixture pipeline transport should be opened. As the first step of the programme the comparison of power consumption (dependency of hydraulic gradient I on slurry flow velocity V and solid concentration Cs) for the pipeline transport of coal-water mixture and coal-methanol solution mixture was realised. The special laboratory measurements were made to define unknown input data of semi-empirical relationships, i.e. the limit volumetric concentration Cm and the coefficient of mechanical friction of coal in the water or water-methanol solution ka. The resultant comparison of the hydraulic gradient I of the coal-water and coal-methanol solution mixture flow is presented in Figure 2, where density of coal was pc = 1480 kg/m3, diameter of the pipe was D = 0.103 mm, the maximal grain size of coal dmax was less than 0.25 mm, volumetric concentration - C = 20 %. 

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