ORNL-1771 - Oak Ridge National Laboratory

In order to determine the error involved in using
the formulas for thin-walled vessels, ratios of the
stresses computed by the exact and the approximate
theories are given below.
s, i
T. t
24.-
T .
Equations 9 through 11 are plotted in Fig. 7.1.
T .
The so-called "exact" formulas (often called the
Lam; formulas) are valid only while the stresses
are elastic. The approximate formulas are based
on equilibrium considerations and the assumption
that the stresses are distributed uniformly across
the wall. Under inelastic (including creep) con-
ditions, it is believed that the tangential (hoop)
stress distribution lies somewhere between those
assumed in the Lam; and in the approximate elastic
theories. With increasing stress, increasing temper-
ature, and increasing time, the actual stress dis-
tribution will depart from the Lame' assumption and
approach the thin-wall theory assumption. Thus
the two theories give the upper and lower bounds
for the actual stress distribution.
For the longitudinal (axial) stresses, the Lam:
and the thin-wall theories both use the assumption
that the stresses are uniformly distributed over the
cross section. Since the Lam; theory uses the
correct value for the cross-sectional area, while
the thin-wall theory uses an approximate area, the
Lam; theory is believed to be more correct in both
the elastic and the inelastic ranges of stress. The
majority of the tube-burst tests made to date have
been of 0.010- and 0.020-in.-woll tubing, and thus
the approximate formula applies. Specimens are
now being tesfed which have 0.060-in. walls. Since
it is predicted that under the test conditions the
1.28
I 24
1.20
It6
1.12
108
U
i?
1.04
4 .oo
0.36
0 32
0.M
o a4
PERIOD ENDING SEPTEMBER IO, 7954
UNCLASSIFIED
ORNL-LR-DWG 2848
s STRESS COMPIJTED BY THIN-WALL THEORY
A 1 l--_l_.._
- f
'i
Fig. 7.1. Comparison of Elastic Stress in
Cylinders as Computed by Lam6 Theory and by
Thin-Walled Pressure Vessel Theory.
stress will be uniform across the wall thickness
the approximote formula will be used for calculating
the stresses, ond the slight error thus introduced
wi II be neglected.
It is well known that in the case of o thin-walled
closed-cylinder pressure vessel the ratio of the
tangential (hoop) stress to the longitudinal (axial)
stress is 2:l. Some investigators have shown that
this stress distribution results in the minimum
ductility for a given material. Therefore, in order
to better understand the criteria for predicting
failure of tubular specimens and in order to study
the effects of anisotropy of the tubular material, it
would be desirable to be able to test a series of
specimens with varying stress ratios. Jordan has
devised the apparotus described below with which
it is possible to stress a tubular specimen purely
tangentially, purely axially, or in ony desired ratio
of these stresses.
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