Quenching stresses in transparent isotropic media and the photoelastic method

Introduction. It is well known that when a transparent non-crystalline solid, such as glass, is heated to a uniform temperature Tx and then rapidly quenched in a bath at temperature T0(T1 > T„) there results a non-uniform stress distribution. Depending on T, , one can divide these stresses into two distinct classes. If is sufficiently lower than the softening temperature of the material, then the stresses are transient, but if T1 is sufficiently high (say 550° C for lime glass) then the quenching stresses are not transient but, on the contrary, remain permanently set into the glass. The latter are referred to in the literature as quenching or residual stresses. As is well known, the existence of such residual stresses is made manifest when the object is examined in polarized light, and by violent explosive characteristics of quenched objects when cut.f Each distribution of such stresses is characterized by a definite double refraction pattern. In 1841, F. E. Neumann1 developed a general mathematical theory of the double refraction of light in non-uniformly heated isotropic solids. In turn the problem was studied theoretically by such men as Maxwell,2 and Lord Rayleigh.3 The purpose of this paper is three-fold: (1) To develop a mathematical theory of residual stresses based on a simple model