Thermal stresses in the laser disc from a tetragonal c-cut crystal

Analytical expressions for thermal stresses and strains, as well as displacements, are obtained for the laser disc from a tetragonal crystal cut along the [0 0 1] axis under plane stress approximation, for the first time, to our knowledge. This study illustrates that, in polar coordinates, the normal stresses, σr and σθ, are angular independent, while the shear one τrθ is zero. The thermal strains, εr and εθ, and displacements, u and υ, depend on both radial and tangential coordinates; this dependence has the shape of a four-leaf rose. For considered crystal cutting with isotropic in-plane thermal expansion, the displacements are not pure radial (υ≠0). The values of stresses, strains and displacements are calculated for the disc from a c-cut yttrium vanadate laser crystal, Nd:YVO4. The thermal fracture issues are analyzed for this crystal.