Analysis of an orthotropic circular bar weakened by multiple radial cracks under torsional transient loading

•The transient torsional of a cylinder with a screw dislocation has been analyzed.•The problem is governed by the Saint-Venant torsion theory.•We use the dislocation distribution technique for analysis of multiple cracks.•The solution has been rewritten in the term of new functions which converge very rapidly.•The dynamic torsional rigidity and the stress intensity factors has been calculated. In this research, the problem of a circular orthotropic bar with multiple cracks under torsional transient loading is investigated. The solution to the problem weakened by a Volterra-type screw dislocation is first obtained with the aid of the Laplace and finite Fourier sine transform. The bar is considered to be subjected to a torsional transient loading. The solution is obtained for stress fields and displacement in the domain under consideration. Then, the dislocation solution is used to derive a set of Cauchy singular integral equations for analysis of the circular bar containing several cracks. The solution to these equations is used to analyze the torsional rigidity of the bar and also the mode III stress intensity factors at the crack tips. Finally, several examples of a single and multiple cracks are presented.