To the Strength First Problem Full Solution: Mechanics of a Necking

Abstract

Essentially new approach to analysis of internal forces, arising in cylindrical rod under action of an axial tension force, has allowed to detect the three-dimensional axisymmetric stress state. According to the new conceptual model the axial tension force causes the tangential - hoop and radial - stresses side by side with axial (normal) stress in the rod volume. A completion of Lame's solution of the problem on the stress state in the thickwalled cylinder has allowed to ascertain a mutual direct and reverse connection of the tangential and radial stresses with the axial stress also in the rod under action of an axial tension force. The new approach for the first time has allowed to give the full physically adequate and mathematically sufficiently strict description of a change of the initial cylindrical form of a mild steel rod under action of an axial tension force on all stages of its deforming, including the necking, the fracture process and a view of the fracture surface. The new approach has allowed on the united methodological base to elucidate also a number of the questions, bound with an axisymmetric form of the soap solution film between two rings, with the breaking up of a liquid free jet nto drops, with the causes of a buckling of the long tube under action of internal pressure, created in it by the rested and moved fluid in it and others.