Precipitation hardening theory

The creep stress-rupture strength of Ni-base superalloys increases with increasing y volume fraction,/y< (Jackson et al., 1977). This is in accordance with precipitation-hardening theory in the under-aged state, which shows (Ardell, 1985) that ... 

The loops around the precipitates act as stress concentrators. They exert shearing stresses in addition to the applied stress on the particles. When enough of them have accumulated, the precipitates will be plastically sheared as the loops disappear one by one. This is the basis of a theory of precipitation hardening in an aluminum-copper alloy by Fisher, Hart, and Pry (1953). The precipitate in this case is CuA12, and the precipitates cause an increment of hardening added to the hardness of the solid-solution (Al-Cu) matrix. Quantitative agreement with experimental measurements is fair. 

Mott played a major part, with his collaborator Frank Nabarro (b. 1917) and in consultation with Orowan, in working out the dynamics of dislocations in stressed crystals. A particularly important early paper was by Mott and Nabarro (1941), on the flow stress of a crystal hardened by solid solution or a coherent precipitate, followed by other key papers by Koehler (1941) and by Seitz and Read (1941). Nabarro has published a lively sequential account of their collaboration in the early days (Nabarro 1980). Nabarro originated many of the important concepts in dislocation theory, such as the idea that the contribution of grain boundaries to the flow stress is inversely proportional to the square root of the grain diameter, which was later experimentally confirmed by Norman Fetch and Eric Hall. 

Twenty milliliters of petroleum ether is added to precipitate the nitramide. The suspension is stirred with a small porcelain or platinum spatula. The precipitate is filtered on a smooth, hardened filtered paper or fritted glass plate using slight suction. The solid is returned to the bottle by means of the spatula, washed by decantation with 10 ml. of petroleum ether, and filtered. This washing-by-decantation procedure is repeated once more. The funnel is covered with filter paper, and a slow stream of air is drawn through until the product is dry. The nitramide should be in the form of pure white, shiny leaflets. If the product is slightly yellow, it should be dissolved in a minimum amount of anhydrous ethyl ether and reprecipitated with petroleum ether as above. Theoretical yield 3.1 g. actual yields 2.3 to 2.6 g. (75 to 85 per cent of theory). 

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