Constitutive Equations for Orientation in Polyurethane Elastomers

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Abstract
A constitutive equation describing the orientation‐strain behavior of the hard segments of a polyurethane elastomer is developed. The orientation functions of the hard and soft chain segments of the polyurethane, as determined by infrared dichroism, are shown to be simply related to each other and the tensile strain by assuming that the hard and soft segments act in series under load. A model for the irreversible changes in orientation of the hard segments with strain is constructed based on a distribution of hard elements, all with the same orientation‐strain behavior, but with different yield strains at which orientation may begin. The strain history dependence of the orientation function is of the permanent memory type and is described by Lebesgue norms of the strain. The model is developed for both time‐independent and time‐dependent orientation and predicts the observed hysteresis and time dependence in stress relaxation of the hard‐segment orientation. The soft‐chain‐segment orientation may then be predicted using the series model.

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