Theory of Superplasticity and Fatigue of Polycrystalline Materials Based on Nanomechanics of Fracturing and Failure
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Fracture nanomechanics is the study of the interconnected process of the growth and birth of cracks and dislocations in the nanoscale. In this paper, it is applied to superplasticity and fatigue of metals and other polycrystalline materials in order to derive the basic equations describing some main features of these phenomena, namely, the fatigue threshold and the enormous neck-free superplastic elongation. It is shown that in most metals and alloys the fatigue threshold is greater than one per cent of the value of fracture toughness. Using the concepts of fracture nanomechanics, we study the superplastic deformation and fracturing of polycrystalline materials under uniaxial extension and calculate the neck-free elongation to failure in terms of strain rate, stress and temperature. Then, we determine the optimum strain rate of the maximum superplastic elongation in terms of temperature, creep index and other material constants. Further, we estimate the critical size o f ultrafine grains necessary to stop the growth of microcracks and open way to the superplastic flow, and find the superplastic deformation of grains, their maximum-possible elongation and the activation energy of superplastic state. Also, we introduce the dimensionless A-number in order to characterize the capability of different materials in yielding the superplastic flow. A t a very high elongation the alloying boundary of grains proves to be broken by a periodical system o f dead fractures of some definite period. It is shown that experimental results of the testing of the Pb-62% Sn eutectic alloy and Zn-22% A l eutectoid alloy at T = 473 K have substantially supported the theory of superplasticity advanced herewith.
Keywordssuperplasticity fatigue fracturing failure nanomechanics crack dislocation ultrafine grain size threshold stress intensity factor elongation to failure optimum strain rate material characterization
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