INTRODUCTION
It is well known that thin-walled structures, whose
material deforms in consequence of creep, collapse if
applied loads of constant magnitude act upon them for a
sufficient time[l]. For uniformly loaded spherical shells,
it is found that the length of the collapse time depends on
the magnitude of applied pressure [2]. The collapse time,
as may also be called the creep buckling time or the
structure life, is referred to the passage of time between
load application and structure failure. The calculation of
collapse times along with creep deformations for
axisymmetric shallow spherical shells is of major interest
in this paper.
A key element involved in the creep buckling analysis
is the selection of constitutive equations to describe the
creep behavior of the material[3-6]; an appropriate
selection should provide a good approximation to the test
data. If the equations selected only represent the secondary
creep, a linear relationship between the creep strain
and the time function evolves and the solution procedure
to deal with this situation is very straightforward. On the
other hand, if the equations represent either the primary
or tertiary creep, a nonlinear relationship results. Two of
widely adopted approaches to handle this rather complicated
situation are time-hardening and strain-hardening
rules@71. In general, predictions based on these two
approaches are quite different, and a choice between
them should depend on the comparison of their predictions
with experimental data.

Another key element is initial imperfections which, on
many occasions, are directly resulted from the unavoidable
inaccuracy of manufacturing process. It has been
shown that initial imperfections have a great impact on
reducing buckling pressures of spherical shells in both
static and dynamic responses[8-IO]. As to their influence
in the creep buckling analysis, there has been an indication
that the collapse time of cylindrical shells is
very much affected by the imperfection
magnitude [ 11,121.
In an earlier creep buckling analysis of shallow
tThe research reported on here was supported by the Office of
Naval Research, Contract Number NAVY 00014-75-C-0946.
spherical shells[2], a huge discrepancy was found between
theoretical predictions and experimental results on
creep deformations and collapse times. The shell specimens
used in experiments involved small departures
from sphericity. But the theoretical study on the same
specimens was performed by assuming the shells had no
imperfections. Therefore, it may be quite reasonable to
assume that initial imperfsctions, among other factors,
are at least in part responsible for the aforementioned
discrepancy.
The objective of this paper is to utilize the large
deformation creep buckling procedure to obtain creep
deformations and creep buckling times for simply supported
shallow spherical shells subjected to uniform
external pressure. Solutions to be obtained include those
of spherical caps with and without initial imperfections.
A comparison of these solutions with experimental
data[2] is intended to show the degree of sensitivity of
the shell collapse time to initial imperfections. The comparison
is also aimed at a close examination on the
reliability of constitutive equations of creep adopted,
from which a suggestion may be made on a more suitable