Radial Tensile Test Method for Thick Composite Rings
Ambuj Sharma (Graduate Research Assistant) and Charles E. Bakis (Professor)
Dept. of Engineering Science & Mechanics, 212 Earth-Engineering Science Building
The Pennsylvania State University, University Park, PA 16802
INTRODUCTION
Thick, polymer composite rings and cylinders with reinforcement fibers wound circumferentially are under widespread
consideration for use as rotors in high performance flywheels on account of their high specific energy storage capability [1].
The ideal test method for the characterization of the mechanical behavior of composite flywheel rotors uses specimens
fabricated with representative filament winding methods. Spin testing of flywheel rotors is an excellent method of evaluating
rotor strength, but the tests are expensive and potentially dangerous [2]. However, the biaxial, inertially-induced stress field in
composite rotors is difficult to economically reproduce in most laboratories. Therefore, most tests methods in current use
interrogate separate hoop and radial direction properties. To characterize the tensile hoop strength of composite rotors, thin
rings have been tested using a split-D fixture [3], and hydrostatic internal pressurization [4]. For evaluating the tensile radial
strength of flywheel rotors, one can use spin tests with thick rotors (in which radial failure is more likely than hoop failure) or
coupon type specimens machined out of actual rotors. The spin tests have the previously mentioned expense problem while
the coupon type tests suffer from high specimen machining expense as well as potential grip effects. Therefore, the objective
of this current investigation is to evaluate a thick, C-shaped ring for determining radial strength of flywheel rotors by using a
very simple and cost effective test setup. This paper summarizes the results of the analysis, describes the procedure for
testing a C-ring specimen, and evaluates the results from a series of three experiments.
Theory and Experimental Procedure
Theory of elasticity of an anisotropic body formulated by Lekhnitskii [5] was used for developing closed form solutions to
predict stresses in the C-ring. The equations for predicting stresses and strains in the C-ring as functions of applied load are
reported in [6]. The C-rings used in this investigation were made of T700 carbon fibers and epoxy resin. The fibers were
filament wound in a nearly-circumferential pattern on a cylindrical mandrel to produce a cylinder with a nominal inner and outer
diameter of 14 cm and 25 cm, respectively. Three rings of axial thickness 3.18 cm were then cut from the cylinder and labeled
835-1, 835-2 and 835-3. To effect a C-shape, a circumferential section was cut from the rings. The cut edges were made
parallel to each other and equally spaced about a diametric line as shown in Fig. 1. All machining was done with diamond
abrasive tools and water cooling. The rings were instrumented with electrical resistance strain gages at various r-θ locations.
The basic concept of the test method is to apply opposing forces at the straight ends of the C-ring such that it is opened in the
r-θ plane as shown in Fig 1. Such forces cause the maximum tensile radial stress to occur at a location near the mid-radius of
the ring, opposite to the region of load application (i.e. at θ=180 deg). The loading was done using a short hydraulic jack
(Enerpac model RSM-100) having a stroke length of 1.1 cm and a maximum load capacity of 98 kN. The load was applied
slowly to effect failure in 4-5 minutes.
Results
The failure of the ring is defined as the onset of the first circumferential crack. The load a t formation o f the first
circumferential crack for each ring is reported in Table 1. Formation o f the first crack a s shown in Fig. 2 suggests the onset of
failure by radial stress at θ=180 deg. Radial strength was set equal to the radial stress predicted by the theory of elasticity at
the observed position of cracking using virgin material properties and the measured failure load. The radial strength obtained
using the theory of elasticity for each ring is reported in Table 1. A comparison between the maximum stress value and the
stress evaluated at crack location is also made in Table 1. It can be seen for all the rings that, at the radial location of the first
crack, the hoop stress is of the same order of magnitude as the radial stress. However, the calculated hoop stresses at the
location of the crack are rather small in comparison to the considerable tensile hoop strength of the rings (~2600 MPa, by
estimation). Since the maximum value of radial stress was not the same as that calculated at the crack location, additional
analysis employing the maximum strain failure criterion was done. According to the maximum strain criterion, the location of
the circumferential crack should be where the maximum radial strain occurs. The location of predicted maximum strain was
also not found to agree with the location of the observed crack, but it was closer than that predicted by the maximum stress
criterion. A comparison of the failure locations determined using these approaches is made with the actual crack location in
Table 2. The comparison suggests that the maximum strain failure criterion best predicts the crack location.
Hydraulic
C-ring jack
r
Hydraulic
jack
Crack
θ
Load(P)
Figure 1. Assembly depicting usage of hydraulic jack for
loading the ring.
Ring
Number
Failure
load,
kN
835-1
835-2
835-3
22.6
20.0
21.9
Ring Number
835-1
835-2
835-3
Figure 2. Photograph of first circumferential crack (shown
after test for C-ring No. 835-2).
Table 1. Stresses and strains predicted by theory of elasticity at failure loads.
Exp. Crack
Max. Theo.
Theo. Radial Theo. Hoop Max. Theo.
Theo.
Location, cm
Radial
Stress at
Stress at
Radial
Radial
Stress, MPa
Crack, MPa
Crack, MPa
Strain at
Strain, µε
Crack, µε
9.59
37.5
36.0
9.27
4480
4370
9.58
33.7
32.0
-1.93
4030
3890
9.12
36.4
36.3
41.8
4340
4340
Average
34.8
4200
Table 2. Comparison of theoretical and experimental failure locations.
Theoretical Crack Location, cm
Experimental
Crack Location,
Max. Stress
Difference as % of
Max. Strain
cm
Criterion
Radial Thickness
Criterion
9.59
8.98
11
9.12
9.58
8.90
13
9.05
9.12
8.94
3.3
9.09
Theo.
Hoop
Strain at
Crack, µε
-9
-76
209
Difference as % of
Radial Thickness
8.5
10.2
0.6
Conclusion
The tested rings failed by partial circumferential cracks located at radii slightly greater than that predicted by either the
maximum stress or maximum strain failure criterion. According to the analytical solution, the average radial strength at the
crack site was 34.8 MPa and the average maximum strain was 4200 µε. The maximum strain criterion was superior to the
maximum stress criterion in its prediction of the radial location of cracking.
Acknowledgments
Financial support was provided by the Energy Storage Program of the U.S. Dept. of Energy via a subcontract through The
Boeing Company. The encouragement and guidance of Drs. A. C. Day and K. M. Nelson of Boeing is greatly appreciated.
References
1. Gabrys, C. W., and Bakis, C. E., “Design and Testing of Composite Flywheel Rotors,” Composite Materials: Testing and
Design, 13th Vol., STP 1242, S. J. Hooper, Ed., American Society for Testing and Materials, West Conshohocken, PA,
pp. 3-22, 1997.
2. Sonnichsen, H. E., “Ensuring Spin Test Safety,” Mechanical Engineering, 115:72-77, 1993.
3. D2290-00, “Standard Test Method for Apparent Hoop Tensile Strength of Plastic or Reinforced Plastic Pipe by Split Disk
Method,” Annual Book of Standards, American Society for Testing and Materials, West Conshohocken, PA, 2003.
4. Thompson, R. C., Pak, T. T., and Rech, B. M., “Hydroburst Test Methodology for Evaluation of Composite Structures,”
Composite Materials: Testing and Design, 14th Volume, ASTM STP 1436, C. E. Bakis, Ed., ASTM International, West
Conshohocken, PA (in press).
5. Lekhnitskii . S. G., Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow, 1981.
6. Sharma, A. and Bakis, C. E., “Plane Elastic Stress Solutions for Thick, Polar-Orthotropic, C-Shaped Rings,” (in
preparation).