Generalized Plane Strain Study of Rotational Autofrettage of Thick-Walled Cylinders—Part I: Theoretical Analysis

In recent years, a few new methods of achieving autofrettage in thick-walled hollow cylinders have been developed. Rotational autofrettage is one of the new methods proposed recently for prestressing thick-walled cylinders. The principle of rotational autofrettage is based on inducing plastic deformation in the cylinder at the inner side and at its neighborhood by rotating the cylinder about its own axis at a certain angular velocity and subsequently bringing down it to zero angular velocity. However, the analysis of the process is still in its nascent stage. In order to establish the rotational autofrettage as a potential design procedure for prestressing thick-walled cylinders, accurate modeling of the process is necessary. In this paper, the rotational autofrettage for thick-walled cylinders is analyzed theoretically based on the generalized plane strain assumption. The closed form analytical solutions of the elasto-plastic stresses and strains and the residual stresses after unloading during the rotational autofrettage of a thick-walled cylinder are obtained. In Part II of the paper, the numerical evaluation of the theoretical model will be presented in order to assess its feasibility.

Comparison of Analytical Model to Experimental and Numerical Simulations Results for Tailor Welded Blank Forming

Tailor welded blanks (TWBs) offer several notable benefits including decreased part weight, reduced manufacturing costs, and improved dimensional consistency. However the reduced formability and other characteristics of the forming process associated with TWBs has hindered the industrial utilization of this blank type for all possible applications. One concern with TWB forming is that weld line movement occurs, which alters the final location of the various materials in the TWB combination. In this technical brief, an analytical model to predict the initial weld line placement necessary to satisfy the desired, final weld line location and strain at the weld line is used. Results from this model are compared to an experimental, symmetric steel TWB case and a 3D numerical simulation, nonsymmetric aluminum TWB case. This analytical model is an extension of one previously presented, but eliminates a plane strain assumption that is unrealistic for most sheet metal forming applications. Good agreement between the analytical model, experimental, and numerical simulation results with respect to initial weld line location was obtained for both cases. Results for the model with a plane strain assumption are also provided, demonstrating the importance of eliminating this assumption.

Vibrations of a Thick-Walled Pipe or a Ring of Arbitrary Shape in Its Plane

This paper is concerned with a method for solving in-plane vibration problems of thick-walled pipes and rings of arbitrary shape. The solution to the equation of motion based on the theory of elasticity under the plane-strain assumption is obtained exactly by using polar coordinates. The boundary conditions along both the outer and the inner surfaces of the ring of arbitrary shape are satisfied directly by means of the Fourier expansion collocation method which has been developed in the author’s previous reports concerning vibration, dynamic response, and wave propagation problems of plates and rods with various shapes. Numerical calculations have been carried out for a thick elliptical ring, a rectangular ring with rounded corners, and a rectangular ring with a circular inner boundary. To discuss the accuracy of the present analysis, the results of a thick circular ring have also been calculated, and the present results are compared with the previously published ones.