The centrally cracked Brazilian disc: closed solutions for stresses and displacements for cracks under opening mode

Closed-form solutions for the stress and displacement fields in a centrally cracked Brazilian disc are obtained. The disc is subjected to uniformly distributed radial pressure along two finite symmetric arcs on its perimeter. The solution is based on the complex potentials method introduced by Kolosov and Muskhelisvili, and advantage is taken of a recently introduced closed-form solution for the intact Brazilian disc. Special attention is paid to the displacements of the crack lips, since they dictate whether the lips are in an opening or closing mode. The solutions obtained are valid for configurations for which the crack lips are in an opening loading mode, where there are no contact forces along the crack flanks. As well as stresses and displacements, the stress intensity factors are also determined in closed form and are found to be in good agreement with the respective values obtained from existing approximate solutions. Preliminary experimental data obtained using the digital image correlation technique support the analytically deduced conclusions for the deformation and rotation of the crack flanks.