Plastic Limit Loading Analyses Of Thick-Walled Tube Based On Twin Shear Unified Strength Theory

In this paper calculating formula of plastic limit stress are derived with twin shear unified strength and concerned with the different and same nature of material in tention and compression ,by the limit analysis of thick-walled tube under the actions of both axial force and inner pressure. It is known that there are the relation of power functions in radial and perpheral stresses to the relative radius. The relative formulations between limit loads (both axial force and internal pressure ) acting on it are derived while the whole thick-walled tube is led to the yielded state. After transformed limit loads into non-dimension amount,relative formulations of limit loads become non-dimension forms.On the plane coordinate system of right angle indicating the amount of the horizontal axis with the relative axial force and that of the vertical axis with the relative inner pressure, the figure of the relative formulations containing relative limit loads can be plotted,and it is the curve of limit loads under the the yielded state of the whole thick-walled tube . When the coefficient a of tention and compression is chosen as different value,there are changes in the figure.Its law of changes is that the area surrounded by curvilinear figure will be enlarged when the coefficient α of tention and compression changed from large to small,and the direction of increase is mainly along the negative direction of horizontal axis and the positive direction of vertical axis.It may be indicated that the capability of thick-walled tube loaded by compression is enhanced.When the wall thick of thick-walled tube is chosen as different value, its curvilinear figure of limit loading takes place changes.Its changing law is that the area surrounded by curvilinear figure will be enlarged with wall thick β changing from small to largeand its direction of increase is mainly along the positive direction of vertical axis.It may be indicated that the capability of thick-walled tube loaded by compression is enhanced.It is proved that caculating formulae deduced in this paper is correct by comparing the caculating result in twin shear unified strength theory with that in Tresca criterion and Mises criterion,and contrasting the result caculated in twin shear unified strength theory with that of experiment.The superiority of formulae ,used for caculating limit loading, deduced in twin shear unified strength theory, is that they can apply for the material fitting different yield criterion and can flexibly consider the different and the same in the limit stress of tension and comprssion.Caculating formula and the figure of limit loads provide the reliable theory base and important referential value for the design of engineering struture,strength analysis and plastic forming technology.