Homogenized constitutive equations for linear viscoelastic unidirectional composites with growing transverse cracks

Three-dimensional, thermomechanical constitutive equations and an associated correspondence principle are developed for a linear viscoelastic, unidirectional composite with growing damage. The type of damage modeled is transverse cracking, which is commonly observed in laminates consisting of unidirectional fiber layers. The equations allow for aging. First, the constitutive equations without damage are summarized. They are then modified to allow for time-dependent damage by means of a correspondence principle. This principle relates elastic and viscoelastic solutions in the time-plane; the familiar correspondence principle based on the Laplace transform is not applicable because of the aging and crack growth. Some existing, simplified micromechanical models for elastic media are extended to viscoelasticity and then used to demonstrate that the requirements of the correspondence principle are quite-well satisfied for realistic material behavior. The correspondence principle is developed in the Appendix. It generalizes a previously-developed principle for plane stress in fiber-composites to three-dimensional conditions, and is not limited to the specific type of damage covered in the body of the paper.