Stress-optical Law Research Articles

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.

Photoelastic Analysis of Anisotropic Fiber Reinforced Composites

A theoretical and experimental investigation was made of the integrated photoelastic effect in a transparent fiber glass reinforced epoxy resin. Vacuum impregnation techniques were developed to render the material transparent. The integrated effect of the isochro matics and isoclinics in the material when subjected to both uniaxial and biaxial stresses was observed and compared to the predicted data. Isochromatic data proved to be representable by a proposed orthotropic stress-optic law. Isoclinics were predictable, but at a given point in a stressed model the isoclinic angle depends on both the fiber orienta tion with respect to the principal stress directions and the ratio of principal stress magnitudes. Thus, the isoclinics do not directly give the principal stress directions. At this point, the anisotropic photo elasticity solution has not been determined.

Mechanical foundations of birefringence of elastic media and viscous media

The general fundamental equations of birefringent phenomena are deduced theoretically for isotropic elastic solids and jsotropic viscous fluids from the equation proposed by Toupin. Their index tensors are quasi-linear functions of modified deformation tensor or modified deformation-rate tensor or modified stress tensor, which are reduced to the usual tensors for small deformation state or small stress state. The directions of polarization of a plane wave whose wave-vector is specified are parallel to the secondary principal axes of the diametral conic sections, cut by a plane perpendicular to the wave-vector, of the modified quadrics. The birefringent effects are proportional to the difference of the secondary principal values of the modified tensors. The polynomial approximations are presented. In first-order approximation, the well-known “stress optical law” holds for elastic and viscous media. The simple extension and the pure homogeneous strain of an elastic medium are investigated and the results are identical with Kuhn and Grun, and Treloar. The Couette flow of viscous media is also analysed, and the extinction angle of this material is 45° for all shearing-rate range.

Photoelastic studies of the two-dimensional dynamic stress-optic law

Studies of the two-dimensional dynamic stress-optic law were made using Castolite circular disks under diametral impact load. The dynamic stress-fringe relationship of Castolite was found to be approximately linear. The dynamic fringe values were slightly lower than the static values. In four of the five specimens used the maximum difference was 8.2 percent. Previous work on the dynamic stress-optic calibration was limited to cases of one-dimensional stress.

On the Meaning of Isoclinic Parameters in the Plastic State in Cellulose Nitrate

In applying the shear-difference method to the determination of stress distributions in photo plasticity, a basic question arises whether, under plastic flow, the isoclinic parameters represent the directions of the secondary principal stresses. Special equipment, new techniques, and a series of experiments are described to study this problem. Tests were made with stress systems which varied in magnitude and direction at normal and oblique incidence, and at strains for which a one-to-one stress-optic relation exists as well as at strains for which it breaks down. Typical results are given. These findings together with the method of scattered light and an appropriate stress-optic law may provide a foundation for three-dimensional photoplasticity. The effects described are limited to loading. Cases of loading plus unloading are not considered in the present paper.

Societies and Academies

Societies and Academies