Fine-grained solids and, especially, nanostmctures are currently being intensely studied owing to their unique mechanical properties, such as strength, hardness, and super-plasticity. The necessity of allowing for effects that occur at grain interfaces has repeatedly been emphasized in descriptions of the mechanical behavior of these solids [1-3]. For example, their unusually high strength is explained by the crack nucleation at the grain boundaries, very high stresses being required to form cracks of a rather small size. Various approaches, including molecular-dynamics methods, have been developed to simulate the nucleation, accumulation, and convergence of such defects. However, it was shown in [4, 5] that consideration from the standpoint of continuum mechanics remains valid provided that the layer thickness exceeds more than ten atoms. On this basis, a model of nanocrack accumulation in an elastic polycrystalline solid subjected to uniaxial tension is proposed under the condition that the critical stresses are inversely proportional to the square root of the grain-boundary length, similar to the problem of a unit opening crack [6].
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