Two-dimensional elastic-plastic analysis of cylindrical cavity expansion considering uniform shear stress around the hole

In order to solve the elasto-plastic unified solution of cylindrical cavity expansion under the combined action of two-dimensional unequal pressure stress field and shear stress, the stress function is expanded into trigonometric series and the stress and displacement in elastic zone are derived; Then, the stress and displacement in plastic zone are derived by using unified strength theory and related flow law; Finally, the elastic-plastic boundary is determined by conformal mapping function, and then the constant coefficients of stress and displacement in elastic zone are determined by least square method according to the stress continuity condition at the elastic-plastic boundary. The new elasto-plastic unified solution provides a new framework for solving the problem of cylindrical cavity expansion, which not only extends the solution under Tresca yield criterion, but also reflects the "non-circular effect" of cylindrical cavity expansion. The correctness of the solution is verified by comparing with the complex function method and experimental values, and the influence of each parameter on the elastic-plastic boundary, stress and displacement is analyzed.