This chapter deals with the birth and growth of dislocations and cracks in nanoscale, when the atomistic structure of a material being taken into account. Invariant integral is used as a basic variable. The fatigue crack threshold is determined by one atomic spacing of the crack growth per cycle. Superplastic flow of superfine grains is studied using the modified Arrhenius equation, and the theory of superplasticity is advanced. As a result, the neck-free elongation to failure, the maximum possible elongation, the critical size of ultrafine grains necessary to stop the growth of microcracks, characteristic dimensionless number, and other values of superplasticity are calculated in terms of stress, strain rate, and temperature. The theory was compared with, and supported by, the test data for the superplastic Pb–62%Sn eutectic alloy and Zn–22%Al eutectoid alloy, obtained by famous Japanese scholars. This chapter is designed for those who are interested in materials science.
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