If a ply yarn formed by twisting together
i pieces of single yarns is loaded at
P=iP, an external force
P is applied onto each single yarn twisted in a ply yarn. When an external force is applied on a ply yarn, single yarns forming a ply yarn contact more tightly together. This article aims to calculate an internal stress applied on a single yarn by the Kirchhoff's equation, assuming that (1) an internal shearing stress can be ignored, (2) the effects of the constraint torsional moment are little, (3) the relation between internal stress and strain is subjected to the Hooke's law, and (4) the Hertz's contact theory are applicable to the portions applied by the contact pressure. After discussing an internal stress applied on a single yarn forming a ply yarn by using an elastic dynamics, equations have theoretically been derived to calculate a Young's modulus of a ply yarn.
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