SAMPE Journal - March/April 2016 - 15
Feature Article
Figure 12. Distributed strain along
circumferentially embedded sensor over a
range of pressures before (a) and after (b)
introduction of localized point damage.
The inset provides a zoomed-in view of
the damage profile at location 0.4155 m.
(c) Strain contours along circumferentially
embedded sensor following localized
point damage, unpressurized vessel. 1000
psi = 6.9 MPa.
distribution over the lifetime of the vessel as well
as the stress ratio in development testing, thereby
feeding accurate values of the stress ratio into stress
fracture reliability models. Here we show that the
portion of volumetric expansion resulting from hoop
strain can be calculated from the distributed strain
measurements. The vessel is broken down into slices
corresponding to the fiber sensor gage length L0, as
shown in Figure 13.
Upon expansion, the arc length of the slice increases
to L1 as the vessel undergoes expansion. Strain, e, is
then defined as:
[2]
Substituting into and rearranging Equation [2],
[3]
[4]
Calculating the fractional volume change upon
pressurizing,
[5]
Figure 13. Nomenclature for volumetric expansion
calculated from hoop strain over the cylindrical region of
the COPV.
Unpressurized, the volume of each slice V0, with a
thickness H, can be expressed as
Thus
[1]
where r0 is the initial vessel radius and q is the angle
about the center line of the vessel, created by the arc
length L0.
SAMPE Journal, Volume 52, No. 2, March/April 2016
[6]
Using the average strain values for the undamaged
COPV, a volumetric expansion of approximately 101
cc is calculated, compared with 137 cc from the
hydrostatic test. These results are reasonable as we
are only calculating the expansion resulting from the
component of strain 6° off-axis of the hoop direction
for the cylindrical region of the vessel. Contributions
from the longitudinal strain as well as the ends of
the vessel will further increase the total expansion
calculated. For pressure vessels designed to fail in the
central cylindrical region, measuring the hoop strain
in this area may be sufficient to detect manufacturing
15
Table of Contents for the Digital Edition of SAMPE Journal - March/April 2016
Contents
SAMPE Journal - March/April 2016 - Cover1
SAMPE Journal - March/April 2016 - Cover2
SAMPE Journal - March/April 2016 - Contents
SAMPE Journal - March/April 2016 - 2
SAMPE Journal - March/April 2016 - 3
SAMPE Journal - March/April 2016 - 4
SAMPE Journal - March/April 2016 - 5
SAMPE Journal - March/April 2016 - 6
SAMPE Journal - March/April 2016 - 7
SAMPE Journal - March/April 2016 - 8
SAMPE Journal - March/April 2016 - 9
SAMPE Journal - March/April 2016 - 10
SAMPE Journal - March/April 2016 - 11
SAMPE Journal - March/April 2016 - 12
SAMPE Journal - March/April 2016 - 13
SAMPE Journal - March/April 2016 - 14
SAMPE Journal - March/April 2016 - 15
SAMPE Journal - March/April 2016 - 16
SAMPE Journal - March/April 2016 - 17
SAMPE Journal - March/April 2016 - 18
SAMPE Journal - March/April 2016 - 19
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