Triple-line disclinations representations, continuity and reactions

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Abstract
In a polycrystalline material it is usual for three grains, and therefore three grain boundaries, to meet on a line, the ‘triple line’. Since grain boundaries can be interpreted as dislocation networks, a question arises about the dislocation balance at the triple line. It is shown that, if the dislocation balance is not satisfied, the triple line acquires the character of a disclination, an oriented line with a tensor of rank 2 attributed to it. The paper deals with the mathematical representation of these ‘triple-line disclinations’, their balance in a triple-line node and their reactions.