IRJET - Analysis and Designing of Diaphragm Spring Washers
Design Mohammed Aldousari
1. A Test Apparatus For Obtaining
Triaxial Stress-Strain Behavior Of
Foam
By: Mohammed Aldousari
Advisor: Dr. Hoo Fatt
ME Senior Design Project I
4600 461
Department of Mechanical Engineering
The University of Akron
May 14, 2016
2. 1
Abstract:
The design and improvement of the Arcan fixture is the main object of this
project. In order to create a new Arcan from the original design, we must identify the
mechanical properties for the specimen; to do so we built an apparatus for triaxial-shear
stress testing of polymer foam. The modified Arcan fixture will allow for rotation of the
loading axis. This allows us to determine the performance of, and determine likelihood of
failure for the material under multidirectional stress. The modified Arcan fixture is
designed to be inside an air pressure vessel to observe the form behavior. The modified
Arcan fixture is connected to the actuator of the MTS 831 servo-hydraulic testing
machine. In this project it was necessary to design the Arcan fixture, and a pressure
vessel design would be part of a follow-on project. The overall design of the pressure
vessel will be discussed, but a detailed design is not included here. At the end, as a result
of many trials, we developed suitable designs for the modified Arcan fixture. A detailed
investigation of this modified Arcan fixture is discussed.
3. 2
Table of Contents Pg #
Abstract (or Executive summary) 1
Introduction 3
Problem description 3
MTS Machine/Actuator 4
Arcan Fixture and Modifications 5
Universal joint 7
Screw for the holders 8
Butterfly Specimen 9
Finite Element Analysis 13
Conclusion 15
References 16
Appendices 17
4. 3
Introduction:
Arcan test fixtures have been used with polymer foams and other lightweight
materials that compose the core of a sandwich structure, to obtain stress concentrations,
especially for combined normal and shear stress. Here we are interested in modifying the
Arcan fixture to allow for measurement of stress induced in a small cylindrical pressure
vessel as well as to accommodate cyclic stress fields.
The testing method used here involved an MTS machine (shown in Figure 1) that
delivers a linear force of up to 1334.45 N, oriented up and down, with a 25.4 mm range
of travel. A load cell mounted beneath the test sample registers the applied force. The test
section, where the Arcan fixture is pinned to the MTS, is to be placed inside a pressure
vessel, allowing for the sample to be exposed to both multi-axis stress and the applied
linear force from the MTS. Tests in this project should be on the foam Divinycell PCV
H100.
Problem Description:
The traditional fixture (shown in Figure 2) includes a series of holes, each of
which can be pinned to an actuator, allowing for a rotated load axis. With this basic
design, we can modify the orientation of the fixture, enabling testing of the sample at
different angles by pinning the fixture through different pairs of holes. This essentially
allows for different fixtures, each small enough to be encased in a pressure vessel that
will be connected to the MTS. Sealing the Arcan inside the pressure vessel and
connecting it with the actuator is a design challenge that has been considered. In addition,
5. 4
the Arcan fixture must be very small and lightweight to fit in the tank and rest on top of
the load cell and the cost of the whole test setup should be less than $10K.
MTS Machine/Actuator:
An MTS 831 servo-hydraulic testing machine (shown in Figure 1) provides linear
force for this test. The MTS 831 is pinned to the Arcan fixture at top and bottom, via
universal joints, to allow for an applied force to the sample. This applied force can reach
14679.13 N. The actuator has a 431.8 mm range of travel. The MTS actuator is
computer-controlled. A load cell mounted at the base of the MTS measures dynamic
load, and that load cell has a measurement limit of 14679.13 N.
Figure 1
6. 5
Arcan Fixture and Modifications:
The basic Arcan fixture includes a series of holes, each of which can be pinned to
an actuator, allowing for a rotated load axis. With this basic design, we can modify the
orientation of the fixture, enabling testing of the core sample at different angles by
pinning the fixture through different pairs of holes. This essentially allows for different
fixtures, each small enough to be encased in a pressure vessel that delivers fluid pressure.
The original Arcan fixture is too large to use in a small pressure vessel.
The original Arcan fixture design (shown in Figure 2) has been modified here, for
the purpose of examining the simultaneous effects of multidirectional stress (from air
pressure) and axial force (from the actuator). Others have made modifications on the
Arcan design for similar reasons [1].
For the modified Arcan design proposed here, the holes are placed in such a way
that consecutive pairs of holes will amount to a 15-degree orientation difference, moving
from 0 to 90 degrees. With each change in orientation, a new specimen is placed in the
fixture. This enables a change in the angle of actuator force. There are 7 solid modeling
views of the modified Arcan fixture are shown in Appendix 1.
The modified Arcan fixture will be created from 6061 Aluminum, which is
lightweight, inexpensive and easy to machine. This material is also much less subject to
deformation under stress than is the butterfly specimen. As material was removed from
the original Arcan, edges were smoothed and corners rounded to minimize the risk of
unwanted stress concentrations.
7. 6
Figure 2
The Arcan fixture has been updated by removing some of the original material so
as to minimize the space it occupies, knowing that it must fit in a pressure vessel of
limited size, the available space is anticipated to be 152.4 mm diameter. It must,
8. 7
however, be large enough to accommodate connection to a universal joint. Also, the
Arcan was made extra long in its central area to accommodate a bracket to hold the
specimen. In different orientations, different geometries of butterfly specimen will be
mounted with this bracket. Instead of fixing the specimen in place, it can be easily
removed and replaced with another specimen.
Universal joint of Arcan:
In each orientation, the Arcan is pinned at top and bottom to universal joints,
which are in turn connected to the MTS actuator and load cell. The universal joints can
accommodate stress in both tension and compression, and offer degrees of freedom of
motion, reducing risk of failure at the point where the Arcan is pinned. The universal
joint allows for the motion of the actuator inside the pressure vessel.
The universal joint to be used here is McMaster-Carr part number 60645K611, 1
30.16 mm in length and #6-32 thread, as shown in Figure 3.
9. 8
Figure 3: Universal joint
While the original Arcan design is suitable only for tension, this modified design
can be used both for tension and compression. It was necessary to add thickness to the
Arcan fixture to allow for a mating with universal joints. This adds a degree of freedom
in motion, and also enables a change in orientation while still accommodating the
universal joints. For each angle of orientation, excess material was removed to make the
fixture at each orientation as small and lightweight as possible. This strategy also makes
the individual fixtures cheaper to create.
Screw for the holders:
There is a steel screw connected to the bonded tab of the butterfly specimen. It
enables a strong grip between the modified Arcan fixture and the bracket holding the
specimen. The screw is chosen to be strong so that it can maintain its grip through its
threads even while the actuator loads the Arcan. It can also withstand simultaneous axial
10. 9
and shear loads. The holes in the Arcan that were made for the screws were placed in a
flat area so it is easier to install screws, as shown in Appendix 1. A screw's power
depends on how close together the threads are, and how wide the head is, and knowing
this we were able to select a screw for the Arcan.
The screw to be used here is McMaster-Carr part number 91259A162, #6-32
thread, as shown in Figure 4
Figure 4
Butterfly Specimen:
The specimens used are of Divinycell PVC H100, a semi-rigid foam that, when
paired with a high-strength skin, will result in strong, stiff, lightweight sandwich
11. 10
structures [2]. This foam is supplied in large, thick rectangular sheets, and specimens are
cut and shaped from the sheet. There are two specimen types, corresponding to in-plane
and out-of-plane properties. The shear stress acting on the foam was determined to be
720 N, and the normal stress 1575 N.
Figure 5: Butterfly foam specimens:
(a) In-plane specimen and (b) Out-of-plane specimen
The samples (shown in Figure 5) are referred to as a butterfly because of the strong
resemblance. The butterfly shape is ideal for shear and multi-directional loading
10 25
15
R2.54
15
8.07
45°
25
15
15
R2.54
35
45°
(a) 25mm*15mm Front view
Side view
(b) 35mm*25mm
Front view
Side view
12. 11
scenarios [1]. A portion of the foam substance used in testing is cut into such a shape.
During testing, it is possible to identify and measure stresses acting on the specimen, and
to determine failure risk. If the specimen should fail, the stress that causes the failure
(magnitude and direction) is recorded.
Pressure Vessel:
A pressure vessel including two windows is needed to deliver three-dimensional
fluid pressure to the butterfly specimen. This pressure vessel will be off-the-shelf to limit
cost. It should deliver pressure up to 20.68 bar. Since the vessel must be mounted in the
MTS machine, there is a space limitation: the pressure vessel must accommodate one
inch of actuator travel.
The pressure vessel must be chosen so as not to fail when used in conjunction
with the MTS actuator. The pressure vessel is subject to hoop stress (σ=pr/t) and axial
stress (σ=pr/2t). It is also subject to shear and compression stress, as well as air pressure.
An aluminum pressure vessel offers lighter weight and lower cost than steel. Off-
the-shelf pressure vessels will come with caps that can accommodate an observation
window; other openings will be needed to accommodate the MTS actuator rod and load
cell.
The pressure vessel has caps on either end to allow access to the specimen.
Windows in these caps permit light to enter and enable one to observe the specimen
during the test.
13. 12
Stress Analysis of Pressure Vessel:
The pressure vessel to be manufactured from 6061 Aluminum: inexpensive and
simple both to machine and to weld. The following characteristics are to be sought:
• Safety factor of 2.5
• Maximum travel inside of 25.4 mm
• Maximum pressure of 20.68 bar
• Maximum linear force of 14679.13 mm
• Tensile Yield Strength 2757.90 bar
!
!
(𝜎! − 𝜎!)! + (𝜎! − 𝜎!)! + (𝜎! − 𝜎!)!=
!!
!"
The wall thickness was determined from a Von Mises calculation of principal stress:
Where
𝜎!! 𝜎! =
𝑃𝑅
𝑡
𝜎! =
𝑃𝑅
2𝑡
𝜎! = −𝑃 = −20.68
This results in a quadratic equation in wall thickness,
𝑥 =
!!± !!!!!"
!!
and the possible wall thickness is 0.41 mm.
14. 13
Figure 6
Finite Element Analysis:
The finite element analysis here was performed for one orientation of the Arcan
fixture (0 degrees), just to be certain it would not fail under stress. Especially of interest
were holes to accommodate universal joints, and curves in the Arcan structure, because
curves and discontinuities are especially subject to stress concentrations.
Testing revealed that stress even at locations of stress concentration was very low,
far below yield strength even when a safety factor of 10 was considered.
15. 14
Figure 7
The von Mises stress distribution in the Arcan fixture for 10 times the maximum design
loads is shown in Figure 7. The maximum von Mises stress accrued at the hole created
for joint and it is 1.10316 bar. This is much lower than the yield strength at Al 6061,
which is 2757.90 bar.
16. 15
Conclusions:
We have a design for testing the butterfly specimen, under conditions that include
multi-axial stress due to pressure, and shear and compression/tension forces delivered by
a linear actuator. The Arcan fixture has been modified to suit these tests, and will be
pinned to the actuator and to a load cell via universal joints. The butterfly specimen will
be mounted in such a way as to be securely in place during testing, yet easy to remove.
The entire test section will fit inside a pressure vessel, which uses air as its active fluid.
The test setup involves some modification of the Arcan fixture, but the Arcan will
be made from inexpensive and machinable Aluminum, so multiple fixtures can be
generated. An individual fixture can be easily removed and replaced. Butterfly specimens
can be made in large numbers as well, for repeated testing, although stress on the Arcan
fixture will be small and failure would seem to be unlikely in nearly all test cases.
Individual tests call for mounting of butterfly specimens at various angles relative
to the linear actuator force being applied, so the Arcan has been created with a series of
holes separated by 15 degrees, from 0 degrees (aligned with the actuator force) to 90.
17. 16
References:
[1] Taher, S. T., O. T. Thomsen, and J. M. Dulieu-Barton. "Bidirectional Thermo-
Mechanical Properties of Foam Core Materials Using DIC." Thermomechanics and Infra-
Red Imaging, Volume 7 Conference Proceedings of the Society for Experimental
Mechanics Series (2011): 67-74. Web.
[2] Hoo Fatt, Michelle S., and Linling Chen. "Transversely isotropic mechanical
properties of PVC foam under cyclic loading.” Journal of Material Science (2013): Web.
15 May 2016.
