Gunjin Yun, A.B.M. Abdullah, and Wieslaw Binienda

University of Akron, Akron, Ohio

David L. Krause

Glenn Research Center, Cleveland, Ohio

Sreeramesh Kalluri

Ohio Aerospace Institute, Brook Park, Ohio

Test Methodology Development for Experimental 

Structural Assessment of ASC Planar Spring

Material for Long-Term Durability

NASA/TM—2014-216630

February 2014
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Gunjin Yun, A.B.M. Abdullah, and Wieslaw Binienda

University of Akron, Akron, Ohio

David L. Krause

Glenn Research Center, Cleveland, Ohio

Sreeramesh Kalluri

Ohio Aerospace Institute, Brook Park, Ohio

Test Methodology Development for Experimental 

Structural Assessment of ASC Planar Spring

Material for Long-Term Durability

NASA/TM—2014-216630

February 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors appreciate the inspiring leadership and management at NASA Glenn Research Center provided by Dick Shaltens,

Wayne Wong, Jeff Schreiber, Lanny Thieme, Scott Wilson, and Geoff Bruder, as well as the full support and technical management of 

Drs. Ajay Misra and Steven Arnold. The authors thank Ralph Pawlik and Frank Bremenour for their expert experimental advice and 

technical collaboration. The authors truly appreciate the efforts and cooperation enjoyed from Sunpower, including the professional 

work of Kyle Wilson, Doug Mansfi eld, Courtney Lenart, and their consultant Barry Penswick. The authors also would like to thank 

Mr. Brett Bell, Mr. William Wenzel, and Mr. Dale Ertley (all from the College of Engineering, the University of Akron) for their 

strong support in manufacturing and machining of materials. The Science Mission Directorate at NASA Headquarters provided 

funding to complete the work described herein, and the authors truly are grateful for that enduring commitment.

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Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2014-216630 1 

Test Methodology Development for Experimental Structural 

Assessment of ASC Planar Spring Material for 

Long-Term Durability 

Gunjin Yun, A.B.M. Abdullah, and Wieslaw Binienda 

University of Akron 

Akron, Ohio 44325 

David L. Krause 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Sreeramesh Kalluri 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Abstract 

A vibration-based testing methodology has been developed that will assess fatigue behavior of the 

metallic material of construction for the Advanced Stirling Convertor displacer (planar) spring 

component. To minimize the testing duration, the test setup is designed for base-excitation of a multiplespecimen arrangement, driven in a high-frequency resonant mode; this allows completion of fatigue 

testing in an accelerated period. A high performance electro-dynamic exciter (shaker) is used to generate 

harmonic oscillation of cantilever beam specimens, which are clasped on the shaker armature with 

specially-designed clamp fixtures. The shaker operates in closed-loop control with dynamic specimen 

response feedback provided by a scanning laser vibrometer. A test coordinator function synchronizes the 

shaker controller and the laser vibrometer to complete the closed-loop scheme. The test coordinator also 

monitors structural health of the test specimens throughout the test period, recognizing any change in 

specimen dynamic behavior. As this may be due to fatigue crack initiation, the test coordinator terminates 

test progression and then acquires test data in an orderly manner. Design of the specimen and fixture 

geometry was completed by finite element analysis such that peak stress does not occur at the clamping 

fixture attachment points. Experimental stress evaluation was conducted to verify the specimen stress 

predictions. A successful application of the experimental methodology was demonstrated by validation 

tests with carbon steel specimens subjected to fully-reversed bending stress; high-cycle fatigue failures 

were induced in such specimens using higher-than-prototypical stresses. 

1.0 Introduction 

The National Aeronautics and Space Administration (NASA) Glenn Research Center (GRC), 

Cleveland, Ohio provides life and reliability verification and advanced technology development for the 

Advanced Stirling Convertor (ASC) project. Sunpower, Athens, Ohio is developing the ASC under a 

NASA Research Announcement award. The ASC is a mechanism that converts the heat of decay from a 

General Purpose Heat Source into electrical power. It is proposed for use in the high-efficiency Advanced 

Stirling Radioisotope Generator (ASRG) being developed by Lockheed Martin, Valley Forge, 

Pennsylvania, and is identified as a promising power source for future long duration scientific space 

missions. More information about the ASC and ASRG projects is available in References 1 to 3. The 

work presented herein supports the experimental structural assessment of ASC Displacer (planar) Spring 

material for long-term durability. The ASC planar spring provides translational stiffness and the 
NASA/TM—2014-216630 2 

corresponding spring rate for oscillation of the displacer component. This spring design uses geometry, 

materials, and fabrication processes in unique ways that require fatigue testing of the material of 

construction to accurately assess the part’s structural life. Accelerated component-level testing of the 

planar spring is being performed at Sunpower to help validate design life by the extrapolation of high 

stress, low cycle count test results to the low stress, high cycle count design conditions. The planar spring 

life assessment requires further testing in the giga-cycle fatigue (GCF) range to verify and properly 

evaluate the processed material’s durability for the long-term life requirement of tens of billions of low 

stress cycles without degradation. This testing must be performed at prototypical and near-prototypical 

stress levels, and at high frequencies to assure that test results are available within a reasonable time 

period. The objective of this work was to develop a GCF test procedure, geometric designs of test 

specimens and fixtures, test controls, and instrumentation, to assure that valid experimental data can be 

obtained from specimens fabricated from actual planar spring material and using planar spring processing 

techniques in future testing. This effort included validation that the test method permits stable operation 

of an electro-dynamic exciter in closed-loop control. 

In this effort, experimental development of a closed-loop GCF test configuration for multiple 

specimens was emphasized. This resonance fatigue test mechanism was synchronized by a GCF Test 

Coordinator. Substantial change in dynamic responses, such as resonant frequency or other damage 

sensitive indices, imply stiffness changes associated with fatigue crack initiation and propagation. With 

the closed-loop control technique, re-tuning the excitation frequency to the shifted resonant frequency of 

specimen was accomplished, and thus by tracking preset phase angle and frequency change monitored by 

the GCF Test Coordinator, satisfactory control of the test over the fatigue crack propagation period was 

attained. 

2.0 Equipment for Closed-Loop GCF Testing 

The GCF test configuration includes the following components. 

1. Polytec Scanning Vibrometer (PSV), Model PSV-400-M2-20, from Polytec, Inc. (Fig. 1) is a 

scanning laser vibrometer (SLV) system (Refs. 4 to 7) which includes the following modules: 

a. Junction Box, PSV-E-400: The junction box is an interface between the laser scanning head, the 

controller, and the data management system PC. It has four available ICP-compatible analog 

input channels: one channel is used for an accelerometer attached to the shaker armature; another 

is used for velocity data from the OFV-5000 controller. An auxiliary output of the digital I/O port 

sends high and low TTL signals to the Data Physics (DP) ABACUS chassis to activate 

programmed functions on the DP shaker system. 

b. Controller, OFV-5000: The vibrometer controller has standard BNC connectors to send velocity 

data in analog voltage signals to the control channel of the DP ABACUS chassis and the junction 

box. The controller can measure up to 10 m/sec (33 ft/sec) velocity. 

c. Data Management System PC, PSV-W-400: This is a desktop PC for accessing measured data 

using PSV vibrometer software. 

d. Scanning Head, PSV-I-400: The scanning head is a long-range laser scanning unit which is 

installed on a stable tripod. It is positioned at an optimum stand-off distance, approximately 

500 mm (20 in.) from the front face of the head to the specimen. 

 
NASA/TM—2014-216630 3 

Figure 1.—PSV-400-M2-20 system. Figure 2.—DP ABACUS chassis and relay box. 

2. SignalStar Vector Vibration/Shaker Controller System, from DP (Ref. 8), which includes the 

following components (Fig. 2): 

a. ABACUS Chassis: The chassis has four standard BNC input channels: one is connected to the 

OFV-5000 controller for acquiring velocity data from the specimens; another channel is 

connected to the accelerometer installed on the shaker armature. The accelerometer is also 

connected to the reference channel of the PSV junction box. 

b. Relay Box, ONTRAK ADU 208: The relay box physically interfaces system I/0 signals; it 

connects the OFV-5000 controller to the desktop PC through a USB cable, and it transmits digital 

TTL signals to coordinate dwell testing when multiple specimens are used. 

c. Desk Top PC and Monitor: A Windows XP desktop computer runs the DP SignalStar Vector 

software for vibration control, and it is connected to the DP ABACUS chassis through TCP/IP. 

3. SignalForce Electrodynamic Shaker System, from DP (Ref. 9), which includes the following 

components (Fig. 3): 

a. Shaker, V100/DSA1-1K: This air-cooled electro-dynamic exciter (shaker) has a maximum sine 

force capability of 1000 N (225 lbs) and maximum acceleration of 1225 m/s2

 (125 g). The 

moving armature mass is 0.8 kg (1.7 lbs). Its frequency range is from DC to 7000 Hz, with an 

armature resonant frequency at 6850 Hz. It is connected to the field supply unit. 

b. Power Amplifier, SS1000T: The amplifier is connected to the field supply unit for power 

acquisition and to the ABACUS chassis for shaker driving voltage. 

c. Field Supply Unit, FSU100: The field supply unit provides power to the amplifier and shaker. 

d. Cooling Blower Unit: A flux jet cooling blower unit is connected to the V100 shaker to lower the 

operating temperature during long-term use. 

4. External Hard Drive, 1TB Element, from Western Digital: The hard drive is connected to the PC to 

save GCF test data (specimen velocity data, Frequency Response Function (FRF) and the number of 

cycles for each scanning point, displacement, etc.). 
NASA/TM—2014-216630 4 

Figure 3.—DP shaker system.

 

Figure 4.—Facility upgrade for GCF testing. 

5. Accelerometer, 3030B, from Dytran Instruments, Inc. (Ref. 10): The accelerometer is installed on the 

shaker armature to provide reference acceleration data; the signal is sent to both the DP ABACUS 

chassis and the PSV system. 

6. Strain Gage, WK-06-062AP-350, from Vishay Micro-Measurements, Inc. (Ref. 11): The WK series 

strain gage is made of fully encapsulated K-alloy with high endurance leads. The maximum strain 

range is 1.5 percent. Resistance of strain gages is 3500.3 percent . 

7. Signal Conditioning Unit, NI-1520; Strain Gage Termination Block, NI-1314; chassis module, NI 

SCXI-1001; M Series DAQ Board, PXI-6259; chassis module, PXI 1042, all from National 

Instrument (NI) Inc.: The strain gage signal conditioning equipment is used during calibration testing 

for stress evaluation. 

8. Network Camera, BL-C1A, from Panasonic: A network camera is installed for remote surveillance of 

shaker operations. 

9. Function Generator, 33250A, from Agilent Technologies, Inc.: Shaker driving voltage signals are 

generated from an external waveform function generator. 

10. Other laboratory facilities: For a secure testing environment, a permanent wall was built as shown in 

Figure 4. In addition, laboratory electric power was upgraded to accommodate the larger power 

consumption of the shaker system. 
NASA/TM—2014-216630 5 

11. Software, GCF Test Coordinator: For closed-loop GCF testing, a unique automated testing 

coordinator was developed. Its features are explained in Section 5.0. 

12. Software, Data Physics SignalStar Vector: The main use of this software is a feature that enables 

feedback-controlled resonant fatigue testing. 

3.0 Shaker Evaluation 

Along with specimen design and system damping, the maximum attainable amplitudes of the DP 

V100 shaker armature are important values that determine the maximum stress level attainable in the 

specimen. One of the goals in shaker evaluation was to determine if it had sufficient power to reach the 

targeted stress levels in the specimen to achieve fatigue failures within the requisite time frame. 

The approximate weight of 10 specimens, each 64 mm (2.5 in.) long, combined with the fixture was 

3.8 N (0.85 lb). Before the specimens and fixture were made, a circular dummy mass with comparable 

weight was manufactured, and the armature amplitudes were evaluated. The shaker was operated at 

different frequencies, and the armature displacement amplitudes (i.e., one half of the peak-to-peak 

displacements) were measured using the Polytec laser vibrometer. Figure 5 shows the dummy mass 

attached to the shaker, and Figure 6 shows 10 specimens properly mounted in the fixture, which is 

attached to the shaker. 

An analytical equation was derived for the armature displacement amplitude based on energy 

conservation between electrical and mechanical kinetic energy. Small losses due to friction, generated 

heat, inherent damping in the mechanical system, and other losses, were neglected. 

2 2

0-pk max

0 4 Excitation Frequency

Armature Mass Mass of Specimen & Fixture

Armature Mass 80% of Max Accl

 





  

D pk (1) 

As indicated in Equation (1), the displacement amplitude is dependent on mass of the armature, specimen 

and fixture, and operating frequency. 

Analytically computed displacement amplitudes were compared with experimental values over the 

range of 200 to 2100 Hz as shown in Figure 7. It was observed that test results were in close agreement 

with the analytical estimation in this frequency range. However, as the operating frequency approached 

6850 Hz for the V100 (not shown), it was observed that the displacement amplitude rapidly increases, 

diverging from analytical predictions. This was expected since the analytical estimation equation does not 

take into account dynamics of the shaker armature, which the manufacturer states has a first resonance at 

6850 Hz. Utilization of the shaker resonance phenomenon was considered for the purpose of gaining 

higher specimen displacement amplitudes for the test specimens, but large displacement amplitudes at the 

shaker resonance frequency were inherently inconsistent. Thus, it was decided to not operate the shaker 

near its own resonant frequency. 

 

Figure 5.—Dummy mass attached to shaker 

armature. 

Figure 6.—Specimen and fixture for shaker 

evaluation. 
NASA/TM—2014-216630 6 

Figure 7.—Performance of shaker over an operating frequency range. 

As discussed in the next section, the experimentally evaluated shaker amplitudes were used in subsequent 

three-dimensional (3D) finite element (FE) analyses to optimize the design of the specimen geometry, as 

well as to perform an evaluation of system damping. 

4.0 Test Specimen Design and Fixtures 

4.1 Design of the Test Specimen 

Motivated by good response from 3D FE simulation using frequency analysis and direct solution 

steady-state dynamic analysis in ABAQUS (Dassault Systèmes) for different boundary conditions, the 

test specimen was designed as a cantilever. The geometric constraints included the specimen thickness, 

which was required to be approximately 1.8 mm (0.071 in.), and the gage area width at the location of 

maximum stress, which was required to be approximately 5 mm (0.2 in.). To avoid the possible 

occurrence of fretting fatigue or highly localized stress concentrations, it was desired to identify a 

specimen geometry that possessed a mode shape producing the maximum stress, greater than the 

endurance limit, away from the clamped edge. Another consideration was to minimize the testing period 

by designing the mode shape to be of reasonably high natural frequency but within the operating 

frequency range of shaker. 

The original test plan was to shake the specimen near its second bending mode’s natural frequency. 

However, it was found that the DP shaker could not produce the necessary armature displacements to 

achieve stresses larger than the endurance limit at the high second mode frequency for reasonably sized 

specimens. Therefore, the specimen’s lower first bending mode natural frequency was used, which 

allowed the larger armature amplitudes necessary to reach the required higher stresses in the specimens. 

A series of FE analyses were performed to optimize specimen geometry. The specimen base (the 

gripped zone area near the fixed end) was widened to reduce the stress level adjacent to the fixed 

boundary. Once optimized, a test matrix could be formed by varying the length of specimens, which 

results in different natural frequencies, shaking amplitudes, and consequently stress levels, and thus, 

distinct fatigue lives. 

To explore the specimen design space, analyses were completed with several specimen configurations, 

including: added lumped mass at the tip of specimen; hourglass-shape specimen in which the section is 

reduced near the peak stress region; hourglass-shape specimens with a wider tip area; specimens with 

propped-cantilever boundary conditions; specimens with fixed-fixed boundary conditions; and, specimens 

with sharp notches in which high stress occurs in a constricted area. But, all these alternative designs 

resulted in localized stress concentrations. 
NASA/TM—2014-216630 7 

Test specimen model Bending stress contour and max stress location

 

Specimen (63.5 mm) and strain gage 

Figure 8.—Specimen and results of 3D FE analysis. 

Finally, optimized specimen geometry was achieved as shown in Figure 8; the highest stress occurs at 

the end of the curvature between the base and the gage area, with a very slight stress concentration, 

similar to the ASC Displacer Spring design. 

Scatter is an inherent characteristic of mechanical properties of structures and materials. This 

especially applies to fatigue properties. The fatigue test lives of similar specimens or structures under the 

same loading can be significantly different. Hence, a fixture block was designed to accommodate 10 

specimens to facilitate testing multiple specimens simultaneously. Simultaneous testing of 10 specimens 

also reduces the total amount of testing time to obtain fatigue repeat data. One design constraint was to 

keep the fixture weight low, as more weight would demand more shaker power to excite the specimens. 

Figure 9 shows the designed geometric model as well as 10 manufactured specimens and the fixture. 

Detailed drawings for the specimen and fixtures are illustrated in Appendix A, Figures 27 to 30. 

4.2 Evaluation of Damping 

Damping had a significant influence on the attainable stress level. Damping was observed to be 

dependent on tip displacement amplitudes of the specimen, as tip displacements fell far short of initially 

expected values for the lower frequency, higher stress cases. 

In 3D FE analyses, damping was modeled as structural damping; analyses were performed with 

varying values of damping so that the resulting calculated strains at the maximum stress location 

correlated to the measured experimental strains. In this way, an estimate of damping was obtained for 

various stress levels; these results are preliminary, particularly at high strain values, where testing 

indicated that yielding of at least some of the specimens occurred. 
NASA/TM—2014-216630 8 

Upper block model 

Lower block model 

 

Manufactured parts 

Figure 9.—Fixture and specimens.

5.0 Closed-Loop GCF Testing System 

A closed-loop GCF testing system was developed by connecting two systems, the PSV Scanning 

Laser Vibrometer and the Data Physics Shaker Controller (Ref. 12). This method permits multiple test 

specimens in a single run, monitors the health of all specimens, and tracks resonances of the specimens, 

while keeping the stress level (i.e., displacement level) constant. If substantial change in the resonant 

frequency of any specimen is detected (indicated evolution of damage), the test is automatically stopped 

and all test data is saved. To accomplish this, synchronized coordination between the two systems was 

made possible by the developed GCF Test Coordinator, explained in the following paragraphs. Figure 10 

depicts a schematic configuration of the closed-loop GCF testing algorithm in which the two systems are 

connected and coordinated. As shown, one of the important features of the GCF Test Coordinator is 

synchronization between the two systems with flexible testing time tracked for each specimen. 

Particularly, this feature allows controlling the speed of scanning over multiple specimens. Operators 

have the discretion to preset the dwell test duration assigned to each specimen to assure that any abrupt 

fatigue failure is captured.

5.1 GCF Test Coordinator 

Typically, the Polytec SLV system measures each scan point during a single pass (pass meaning one 

complete scan of all specimens). After a pass, it saves all the data in a single file and stops measuring. 

However, to run the GCF test until fatigue failure and to continuously monitor the health of specimens, it 

was required to measure each point multiple times throughout the length of the test. Consequently, a new 

automation technique was developed that employed the Visual Basic macro engine (Test Automation 

Object Library) that comes with the PSV system. Using this, it was possible to control and modify the 

PSV applications programmatically via the built-in macro subsystem. Thus the macro program was 
NASA/TM—2014-216630 9 

developed to control the PSV system for multiple measurements. The user pre-sets the intended number 

of passes, and after completing one pass of all the scan points, the measurement system restarts 

automatically, and this process continues. To facilitate data analysis, a program was also developed to 

save the pass data separately for each scan point for every measurement cycle. 

Macro code was also developed to access the data acquisition settings from the program. Time and 

frequency domain acquisition parameters, such as sampling frequency or number of samples, were predefined within the macro subroutine. 

Figure 10.—Closed-loop GCF test control using PSV macros; resonance dwell control algorithm in 

SignalStar Vector. 

 
NASA/TM—2014-216630 10 

Macro programming was used to synchronize the Polytec PSV system with the DP SignalStar Vector 

Shaker Controller; these communicate by sending digital pulses (TTL) to the digital output port. A DP 

relay box is used as a communicating device between the two systems. Two different types of digital 

pulse are generated thru macro code: high level pulse, and low level pulse; these create start and stop 

signals. The required duration of the pulse was also set in the macro program. When a new measurement 

is about to start, a start-up pulse is sent to the DP system to generate and control the excitation, and a 

stopping pulse is sent at the end of measurement. Thus, the macro code repeats starting and stopping the 

DP resonance dwell test multiple times, with preset time intervals for each of the scanning points. 

In frequency measurement mode, the macro was programmed to search for the maximum amplitude 

in the frequency response function (FRF) spectrum. Subsequently, the corresponding frequency at the 

maximum spectral amplitude is deemed the resonant frequency, and it is used as a controlling criterion for 

the closed-loop system. When the frequency drops a preset percentage (for example, 2 to 10 percent) of 

the previous frequency, the macro code sends a stopping pulse to the DP system to terminate the test. 

5.2 DataPhysics SignalStar Vector Software 

For closed-loop GCF testing, DataPhysics SignalStar Vector (Data Physics Corporation) (referred as 

DP Vector software in the following) is used as the shaker controller. The resonance dwell test option in 

DP Vector software is designed to perform vibration-based fatigue testing by tracking the resonant 

frequency of a tested specimen. To track resonant frequencies, a sine sweep test needs to be undertaken 

prior to the dwell test in order to save the frequency response function and phase angle. 

Two signal channels are used: one for the control channel, which is fed continuously by velocity 

signals from PSV system (OFV-5000), and the other for a measurement channel, where acceleration 

signals are measured by the Dytran accelerometer installed on the shaker armature. 

The peak frequency and its corresponding phase angle are selected in the resonance dwell test 

window. In the dwell test, the phase angle is set to be continuously tracked. This allows a change in 

shaker driving frequency to the initial resonant frequency of the specimen. Another important feature in 

DP shaker system is its capability to control the vibration level. Operators can set a targeted displacement, 

velocity, or acceleration signal level, measured by PSV laser vibrometer. Then the DP software 

continuously adjusts shaker driving voltages to maintain the preset targeted level. 

5.3 Procedures for Closed-Loop GCF Testing 

Descriptive procedures for the developed testing methodology steps follow. 

Step 1. A pretest should be conducted prior to running any test with the DP shaker system. Its purpose is 

to check the signal-to-noise ratio and to verify closed-loop control with the control channel (laser 

vibrometer), the reference channel (accelerometer), and the transfer function. If this pretest is passed, it 

need not be run again. 

Step 2. Sweep sine tests are conducted for each of the 10 specimens installed prior to running closed-loop 

GCF testing. This evaluates the 10 specimens to assure that they have nearly identical natural frequencies 

and corresponding phase angles, so that one representative FRF and phase angle can be used for control. 

To attain the narrowest frequency range between specimens, a precise torque wrench is used to tighten 

fixture bolts, and specimen lengths are trimmed also as needed. In the near future, it is expected that DP 

Vector software will be able to accommodate multiple FRFs assigned to multiple resonance dwell tests in 

the closed-loop GCF testing; DP plans to revise the Vector software to accommodate these special needs 

for GCF testing. 

Step 3. The sweep sine test results, i.e., the FRF and phase angle chart, are assigned to the resonance 

dwell test. 
NASA/TM—2014-216630 11 

Step 4. The closed-loop resonance dwell GCF testing is triggered by a start TTL signal from GCF Test 

Coordinator to the DP system. 

Step 5. The PSV scans the first specimen for 32 sec (the scanning interval can be user-modified). In the 

DP system, a resonance dwell test runs for 24 sec. For smooth restarting, the resonance dwell test should 

end before the PSV system completes scanning the first specimen. The time difference is set to 8 sec. This 

time is used for initializing and ending the DP software and for transferring stop and start TTL signals, etc. 

During the resonance dwell test, frequency or amplitude abort criteria can be turned on to stop the test 

should these limits be exceeded. 

Step 6. The GCF Test Coordinator stores the maximum magnitude of the FRF and its corresponding 

frequency, which is close to the excitation frequency that is determined by the DP system, and computes 

the accumulated number of cycles. Test data for each specimen are saved in files on an external hard disk. 

Step 7. If the frequency drop for a specimen is found to exceed the preset criterion (for example, 10 Hz), 

the GCF Test Coordinator sends a stopping pulse to the DP system, and the test is terminated. It is 

presumed that the stiffness loss is due to fatigue cracking, and this is verified later by optical examination. 

Step 8. If the frequency change for the specimen is less than the preset limit, the laser beam moves to next 

specimen and the GCF Test Coordinator sends a start TTL signal to the DP system. Steps 3 to 8 are 

repeated until the preset frequency drop criterion is exceeded. 

6.0 Experimental Testing and Results 

6.1 Stress Evaluation 

First, a series of simple tension tests on the specimen material were conducted to determine the yield 

stress level. Stress-strain curves for two samples are shown in Figure 11. 

To ensure that the stress level was high enough to induce fatigue cracking in specimens for the given 

shaker power, specimens with lengths ranging from 139 to 42.5 mm (5.475 to 1.675 in.) were 

manufactured. Figure 12 shows five of the tested specimen lengths. For the various length specimens, the 

maximum attainable specimen strains, specimen tip displacements, and shaker armature displacement 

amplitudes were measured, using the shaker at maximum power. Vishay strain gages (WK-06-062AP350), the scanning laser vibrometer, and Dytran accelerometer (3030B) were used to measure specimen 

strains, specimen tip displacements, and armature displacements, respectively. For this test, all 10 

specimens were installed in the 10-specimen fixture, which was mounted on the shaker armature as is 

planned for actual ASC GCF testing. The strain gage lead wires were connected to four hair-like copper 

wires (two of them were for backup) to minimize any mechanical effects on specimen vibration; they 

were soldered together using adapters, and then insulated with an enamel coating. A distance away from 

the specimen, the shielded sensor cables were connected to the NI-DAQ system. The strain gages were 

installed at the location of maximum stress as predicted by the 3D FE analysis. After successful testing, 

this location was verified from actual crack locations in failed specimens. 

Before running the GCF test, the first bending mode natural frequencies of the test specimens were 

identified from sine sweep testing using the DP Vector software. As shown in Figure 13, natural 

frequency of the first mode increased as the length of specimen decreased. (The specimen length was 

measured from clamped edge to free end excluding the gripped zone.) Natural frequencies ranged from 

82 to 1100 Hz. After identifying the natural frequencies, the DP shaker system was operated at its 

maximum power level and with the excitation frequency tuned to the identified natural frequencies. 

Shaker driving voltage signals were generated from an external function generator (Agilent Function 

Generator 33250A). In the test, specimens longer than 100 mm (4 in.) failed within 1 min since the stress 

levels were very high (over 645 MPa). Because of the short test duration, the tip displacement and 

armature displacement amplitude could not be measured. Fatigue crack locations for these two cases are 

shown in Figure 14. As previously mentioned in Section 4.2 (Evaluation of Damping), damping 
NASA/TM—2014-216630 12 

significantly influences the stress level in 3D FE analyses. It was observed that damping gradually 

increased as the specimen tip deflection amplitude increased. The source of damping could be a 

combination of effects from the clamped edge, inherent material damping, hysteretic damping during 

plastic deformation, air damping, or other damping losses. Due to such uncertainties in predicting 

damping, the value of damping used for the 3D FE model was based on the experimentally measured 

strains and corresponding stresses and was modeled as structural damping. Likewise, measured amplitude 

data for the shaker armature (previously discussed in Section 3.0) at maximum operating power were used 

in 3D FE analyses. 

Figure 11.—Simple tension test of specimen material. Figure 12.—Five specimens tested for stress evaluation. 

 

Figure 13.—Specimen lengths and natural frequencies. Figure 14.—Fatigue failure and location of crack. 
NASA/TM—2014-216630 13 

Figures 15 and 16 show correlations between natural frequencies, strains, and stress levels. Note that 

calculated stresses (749 and 646 MPa, corresponding to failed specimens) at the lower frequencies were 

overestimated by the employed assumption of linear behavior (Young’s modulus = 205,000 MPa) which 

was not valid for the observed plastic deformation cases. 

As shown in Figure 17, the measured tip displacement amplitude gradually decreased as the natural 

frequency increased. However, at low natural frequencies, the tip amplitudes were overestimated since the 

natural frequencies were not re-tuned to account for material yielding. 

Figure 18 indicates variation of structural damping calculated from the 3D FE analyses. As expected, 

the damping significantly increased as the natural frequency decreased. As previously mentioned, this 

may be due to air damping at large tip amplitudes, hysteretic damping due to material yielding, or some 

other effect. 

For a validation test of the closed-loop GCF test method, preliminary stress levels and the resulting 

specimen lengths were determined from fatigue curves (Stress vs. Number of cycles, or simply, S-N 

curves) for the AISI 1095 steel specimen material, using data from References 13 and 14 for bending 

mode fatigue. Yield stress of 350 to 450 MPa was known based on tensile tests previously discussed and 

shown in Figure 11. With this information, 10 specimens with an initial overall length of 107 mm (4.2 in.) 

were prepared for the validation test. To demonstrate that the shaker system could precipitate fatigue 

damage, one test was performed until a specimen failed by high cycle fatigue. A detailed description of 

the testing is included in the following paragraphs. 

Figure 15.—Max. bending strain vs. natural frequency. Figure 16.—Max. bending stress vs. natural frequency. 

Figure 17.—Tip displacement vs. natural frequency. Figure 18.—Damping vs. natural frequency. 
NASA/TM—2014-216630 14 

6.2 Validation Tests for Closed-Loop GCF Testing 

Two validation tests were performed. For the first validation test, a 106-cycle experimental fatigue 

test was conducted. The purpose of this test was to assure that the closed-loop GCF testing could run 

successfully with the programmed fatigue testing scheme for a 10-specimen configuration (Fig. 19) in 

coordination with the DP Vector software. At the beginning, sine sweep tests were performed for the now 

shortened 63.5 mm (2.5 in.) long specimens to obtain FRFs. The first bending mode’s natural frequencies 

and the corresponding phase angles are shown in Figure 20. Reflective film was used at the specimen tips 

for higher quality velocity signals from the laser. 

As seen in the chart, the natural frequencies among the 10 specimens were quite similar. The FRF for 

Specimen ID 5 was chosen arbitrarily as the reference FRF, which was used for the entire test duration of 

the resonance dwell test. The maximum tip displacement was set as 0.45 mm (0.018 in.) from zero to 

peak (0-pk), and this was maintained by the DP shaker controller throughout the test. The stress level at 

this level of tip amplitude was calculated to be between 250 and 300 MPa. It was found that fatigue 

failure was not induced in the specimens at this stress level within the desired cycle range. However, the 

test did demonstrate validity of the developed GCF test methodology. At the 9th pass, it was decided to 

alter the test by attaching a weight to Specimen ID 10 (only), simulating crack growth by lower its natural 

frequency below the threshold level. 

Figure 19.—Ten specimens mounted on armature. 

Figure 20.—Frequencies and phase angles of 10 specimens.

 
NASA/TM—2014-216630 15 

 

Figure 21.—Pop-up showing detection of fatigue failure. Figure 22.—Ten long specimens on armature. 

In the GCF Test Coordinator, the number of passes was set to an arbitrarily large number to enable a 

long test duration. A frequency drop of 10 Hz below the previous measurement was set as the test abort 

criterion. Smooth running of the closed-loop method was observed during the experiment. The GCF Test 

Coordinator sent a starting pulse before the commencement of each measurement and a stopping pulse at 

the end. After measurement of all the specimens, it went back to the first specimen and started the next 

pass. Finally, at the end of that 9th pass and after completing over 106

 fully reversed bending cycles, the 

GCF Test Coordinator successfully stopped the shaker test after measuring the frequency drop triggered 

by the weight-simulated fatigue crack initiation. Figure 21 shows the pop-up message which names the 

specimen ID and total number of accumulated cycles. 

Appendix B, Figure 31 shows the data saved by the GCF Test Coordinator, which for each specimen 

includes: specimen ID, number of measurement passes, measured natural frequency, FRF magnitude, and 

accumulated number of completed cycles. 

The resonance dwell test was repeated to validate the test abort operation upon fatigue failure 

detection for a revised test procedure. For this case, the DP Vector software was set to abort the test upon 

breach of the frequency upper and lower bounds set at 10 percent of the resonance frequency. (This 

abort option in DP Vector was turned off during the first validation test, as the criterion was set in macro 

code.) 

For this test, specimens were 93.3 mm (3.675 in.) long (Fig. 22); including the clamped region, the 

end-to-end length was 107 mm (4.2 in.). Stress analysis indicated a maximum stress of 550 MPa for a tip 

displacement amplitude of 5.2 mm (0.205 in.) 0-pk using maximum shaker power. The specimen’s first 

bending mode was calculated as 190 Hz; Figure 23 shows the measured natural frequencies and phase 

angles for the 10 specimens. 

The test was initiated using the planned 550 MPa stress level, but being over the yield point caused 

rapid specimen failure. To reach longer fatigue lives, the tip displacement amplitude was reduced to less 

than 5.0 mm. Figure 24 shows the resulting velocity amplitude and excitation frequency as measured by 

the laser vibrometer. As evident, the velocity amplitudes displayed high signal noise after 100 sec, which 

indicated the formation and propagation of fatigue cracking in the specimen. The frequency dropped at a 

higher rate after 140 sec. This result was coincident with velocity amplitude, which also dropped 

synchronously. On the contrary, tracking of phase angle proved to be less discriminatory, as shown in 

Figure 25; the resonance dwell test tracked the phase angle (173) that was assigned prior to the testing, 

but changed little, even during crack initiation and growth. After automated termination of the test, the 

specimen was visually inspected, and the fatigue crack seen in Figure 26 was discovered. 
NASA/TM—2014-216630 16 

Figure 23.—Natural frequencies and phase angles. 

(a) (b) 

Figure 24.—(a) Velocity and (b) frequency measured by laser vibrometer; changes due to fatigue cracking. 

Figure 25.—Phase angle tracking. Figure 26.—Fatigue crack in specimen after test. 

fatigue crack 

natural frequency shift 
NASA/TM—2014-216630 17 

7.0 Summary 

A test procedure and necessary instrumentation to acquire valid experimental data was developed and 

verified for giga-cycle fatigue testing. Required control over test operation and automated abort was 

attained with the described GCF Test Coordinator, which managed the equipment involved. At various 

stages of the effort, the shaker was evaluated to check adequacy of power to reach the targeted stress 

levels in test specimens at various excitation frequencies. Several specimen and fixture geometries were 

tested to obtain a design that optimized the excitation frequency, test time, and attainable stress levels in 

the test specimens. Damping evaluation was carried out by measuring the experimental response from 

specimens of various lengths to known excitation inputs, and then iterating the value of structural 

damping in finite element analyses to produce the equivalent calculated response. Experimental strain 

measurements as well as calibration testing were conducted to obtain relationships between the specimen 

peak tip displacements and maximum stresses. 

The multi-specimen closed-loop testing methodology was verified by preliminary experiments that 

confirmed the feasibility and applicability of the technique. It was shown that this vibration-based 

automated method was able to detect the presence of fatigue cracking in test specimens while the crack 

was still in the early stages of propagation, through observed changes in the specimen’s resonant 

frequency; thus, testing can be terminated to prevent further damage if desired. The development of this 

technique was an important step in obtaining very high cycle count bending fatigue data. The next step 

will be to use this novel testing methodology to study and control fatigue crack propagation in specimens 

fabricated from the Advanced Stirling Convertor’s Displacer Spring material. 

 

NASA/TM—2014-216630 19 

Appendix A.—Detailed Drawings for Giga-Cycle Fatigue Specimen 

and 10-Specimen Fixture 

Figure 27.—Drawing of 64 mm (2.5 in.) long specimen 

(all dimensions shown in inches). 

Figure 28.—Drawing of upper block for 

10-specimen fixture (all dimensions 

shown in inches). 
NASA/TM—2014-216630 20 

Figure 29.—Drawing of lower block for 10-specimen fixture (all dimensions shown in inches). 
NASA/TM—2014-216630 21 

Figure 30.—Ten-specimen fixture arrangement on shaker armature (all dimensions shown in inches).

 
NASA/TM—2014-216630 22 

Appendix B.—Data Saved by the GCF Test Coordinator 

Figure 31.—Data saved by the GCF test coordinator.

 
NASA/TM—2014-216630 23 

Figure 31.—Continued.

 
NASA/TM—2014-216630 24 

Figure 31.—Concluded. 
NASA/TM—2014-216630 25 

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