Papers - New Method for Determination of Stress Distribution in Thin-walled Tubing (T.P. 1384, with discussion)

Simple methods can be used for the determination of the residual stresses in thin walled tubing if the stresses consist of high tensile stresses at the one surface and high compressive stresses at the other surface. Such a stress distribution is approximated in sunk tubing and in deep-drawn shells. It is possible to cut sections from such articles in such a manner that a major part of the residual stress is relieved by a bending of the Part that is separated from the adjacent metal. The circumferential stress is evaluated from the change in diameter D, occurring on splitting a length of tubing (Fig. Ib) or from deflection resulting from the cutting out of a circumferential tongue (Fig. Ia) .6 The bending moment M released by such a flexure is. M - EI (I-I) = EI R1-R0 I - u2(R0-R1) I -V2 R0XR1 where E = modulus of elasticity, v = Poisson's ratio, I = moment of inertia of the section, R0 =. mean radius before splitting, R1 = mean radius after splitting. The release of this bending moment corresponds to the release of stresses, which, in a thin section, vary linearly from one surface to the other, and have the following value in a particular fiber a certain distance (x) from the surface: S = c d I - V2 x c x d 2 2 RI - R0____E (d ) R1 - R0 X R0 X R1 ~ i - u2 (2 x) Ro X R1 where C is the section modulus and d is the thickness of the section, the ratio M:C being d: 2 for a rectallgular section.* The maximum stress values at the surfaces are. Smax = +E X d X R1-R0 I — u2- 2 R0 X R1 For most purposes the simpler equations: EXd AD1 = ± I - u2 x dm2 and will be satisfactory, where D,, is the aver. age of the mean diameters of the tubing