Analysis of the limiting states of cylindrical elastic-plastic shells under tension and combined loading by internal pressure and tension

Abstract

The elastic-plastic deformation, limiting states and supercritical behavior of cylindrical shells under tension and combined loading by internal pressure and tension to failure are studied theoretically and experimentally. This problem is characterized by the occurrence of large strains, shape changes and, as a result, an inhomogeneous stress-strain state. In the numerical solution of such problems, the problem arises of constructing true stress-strain curves of materials. In this regard, to study the deformation and strength properties of materials, it is important to use an experimental-computational approach, which makes it possible to take into account the non-uniaxiality and inhomogeneous of the stress-strain state without accepting simplifying hypotheses. The paper presents a new efficient algorithm for constructing a true stress-strain curve, which is based on the procedure of nonlinear extrapolation of the curve. Such an algorithm, in the process of direct numerical solution of the problem, consistently constructs a stress-strain curve without using repeated direct calculations, which significantly (at times) increases its efficiency. Based on the experimental-computational approach, the true stress-strain curves for solid rods and shells made of 10KhSND and 10G2FBYu steels were determined under tension and combined loading by internal pressure and tension to failure. The failure of shells under tension occurs at lower (at times) values of true strain than solid rods. Significant differences in true stresses and strains at the moment of failure are due to different localization of deformation of solid rods and shells after the loss of stability of plastic deformation in tension. It is shown numerically and experimentally that after loss of stability of plastic deformation according to Considerer in tension, the cylindrical shell contains two forms of loss of stability until the moment of failure. The first form of loss of stability, as in solid rods, is characterized by localization of deformations along the diameter of the sample in the form of a neck, and the second form is characterized by localization of deformations along the thickness of the sample, which determines the final stage of failure. Under the action of internal pressure on the shell, the first form of loss of stability of plastic deformation degenerates with the formation of a neck inside the shell, and only the form of loss of stability is observed, caused by the localization of deformations along the thickness of the shell.