Exact deformation analysis of a solid rotating elastic–perfectly plastic disk

• Rigorous continuous stress–strain semi-analytical solution is obtained.
• Solution also provides plastic portions of strain tensor during centrifugal loading.
• Plastic front starts from the disk׳s center and propagates towards its outer edge.
• Mises criterion with its flow rule has never been used before for this type of problems.
• Tresca criterion is inadequate to treat rotating solid disks within perfect plasticity model.

Taking into account paradoxes of elastic–perfectly plastic material model, the problem of solid rotating disk is considered from the perspective of delivering continuous stress–strain analytical solution for engineering applications. The novelty of the solution is based on the semi-analytical treatment of non-linear von Mises yield criterion with its associated flow rule applied to the solid disk geometry containing singularity at the plastic center. By the procedure proposed, both continuous stress and strain fields are obtained at the elastic–plastic interface as opposite to the more common application of the Tresca yield criterion which leads to discontinuity either in stress or in displacement fields. The results obtained are especially important in numerical codes where singularities are not admitted.