Interferometry for the evaluation of the dynamical optical and mechanical properties of transparent materials

Abstract

A theory is developed which leads to an interferometric method for determining the dynamic ratio, Poisson's ratio to the modulus of elasticity, and the dynamic stress-optical coefficients of transparent plates, both during the same set of tests and without attaching mechanical or electrical sensors on the surface of the specimen. The method requires a monochromatic light source, that is, a parallel beam is directed perpendicularly to the vicinity of a crack tip which exists in the plate specimen under investigation. The rays impinging on the crack tip are transmitted through the plate and reflected by the two parallel surfaces of the plate. At the same time, because of the variation of the optical path (index of refraction and thickness of the plate) in the said area, the rays are refracted in such a way as to form two caustic surfaces, one by the transmitted and one by the reflected rays. These two caustic surfaces, when intercepted with two opaque screens, provide two strongly illuminated curves of a general epicycloid shape called caustics. The size of the caustics is directly related to the applied load, the material properties and the distance specimen-screen. Their ratio, however, as it is taken at equally distant screens, depends only on the optical and mechanical properties of the material in question. In addition, an interferogram consisting of fringes, as formed from rays reflected by the two surfaces of the plate, is obtained. The fringe number depends on the wavelength of the light source and the optical path. When the plate specimen is loaded, the optical path changes. This results in a change of the fringe number and consequently to a displacement of fringes with respect to a reference point as they are observed on an opaque screen. The ratio of the two caustics, taken during a static test, and the number of displaced fringes per applied load, taken during a dynamic test, provide enough information for the determination of the aformentioned mechanical and optical parameters. Experiments conducted according to the method developed on acrylic plates and for a tensile impulse of total time duration of 600 μsec produced a reduced by 23.5% ratio of Poisson's ratio to modulus of elasticity from the static value and a reduced by 21% stress-optical coefficient from the static value.