Photo-orthotropic-elasticity

A method of producing transparent model materials for photo-orthotropic-elastic studies is presented. This material fabricated from glass fibers and a modified polyester matrix exhibits continuous relatively smooth fringe patterns which are linearly related to the state of stress. As such, the heterogenous material can be treated as a homogenous medium with orthotropic properties. Three photoelastic constantsf _L ,f _T andf _LT are necessary to describe the photoelastic response of the orthotropic materials to a general state of stress. Methods are established for predicting these photoelastic constants from the properties of the constituents. These methods are based on stress proportioning between the fibers and the matrix and upon the linear summation of the retardation from each constituent. The relations derived forf _L ,f _T andf _LT were verified experimentally and found to be in close agreement with measured values. A stress-optic law is derived on the basis of stress partitioning between the two constituents in a unidirectionally fiber-reinforced laminate. The adequacy of this stress-optic relation is confirmed by experimental verification. Comparison of this stress-optic relation with the expression advanced by Pih and Knight shows the validity of their initial concepts but the inadequacy of their partitioning functions. Detailed comparison of the stress-optic law with the analog relation proposed by Sampson shows excellent agreement. Indeed, the use of Sampson's stress-optic law is recommended and the law based on stress partitioning is to be considered as a fundamental theoretical proof of the Sampson relation. Finally, the applicability of Sampson's stress-optic law to bidirectionally reinforced materials was confirmed with a thorough experimental verification.