WO2024173527A2 - Resonance-based pneumatically centered axial fatigue tester and system for damage detection - Google Patents

Abstract

An axial fatigue test system (40) and method of conducting an axial fatigue test is disclosed. The axial fatigue test system (40) includes a vibration source (44) that includes a fixture (48) configured to receive a first end (50) of a test specimen (34, 36) and a control mass (54) attached to a second end (56) of the test specimen (34, 36). The vibration source (44) is configured to impart movement to the test specimen (34, 36) and the control mass (54) in a direction along a movement axis (A1). The axial fatigue test system (40) also includes an air bearing (58) configured to receive the control mass (54) in a contactless engagement to maintain alignment of the control mass (58) over the vibration source (44). The axial fatigue test system (40) includes one or more dynamic instrumentation (20, 28, 32, 100) for monitoring characteristics of the test specimen.

Description

RESONANCE-BASED PNEUMATICALLY CENTERED AXIAL FATIGUE TESTER AND SYSTEM FOR DAMAGE DETECTION

Cross-Reference to Related Application

[0001] The present application claims the filing benefit of U.S. Provisional Application Serial No. 63/484,775, filed February 14, 2023, the disclosure of which is incorporated herein by reference in its entirety.

Technical Field

[0002] The invention relates generally to systems and methods for fatigue testing, more particularly, to resonance-based axial fatigue testing systems.

Background

[0003] This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present invention, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

[0004] Metal fatigue is caused by the creation and growth of microscopic cracks due to repeated loading of a mechanical part. These cracks can propagate and eventually cause catastrophic and brittle-like failure even in ductile materials. It is estimated that roughly 90% of metallic failures are influenced by fatigue. Fatigue failure occurs across the range of several loading cycles to millions of loading cycles. Failure that occurs after a low number of loading cycles is called low cycle fatigue. Conversely, fatigue failure after a high number of cycles is called high-cycle fatigue. The cycle count that distinguishes low cycle fatigue from high-cycle fatigue is typically in the range of 103-104 cycles. Failure modes differ between low and high- cycle fatigue, and the magnitude of loading that causes high-cycle fatigue is often below the proportional limit for common engineering metals. This makes fatigue hard to predict because stresses under the proportional limit are thought to not cause permanent damage or deformation. Failure theories such as the von Mises failure criterion can predict static material performance based on fundamental equations, but this is not the case for fatigue failure. This has made the failure theories surrounding fatigue failure a highly statistical and empirical area of study. [0005] Conventional fatigue testing traditionally uses servo hydraulic, or shaft driven systems that can test specimens at frequencies from one to hundreds of cycles per second. Recent developments in electrodynamic vibrational systems have produced the ability to test specimens at speeds up to several thousand Hertz (Hz). Further, current ultrasonic testing systems are capable of testing at frequencies near 20 kHz. A 5 Hz servo hydraulic fatigue test would take 11 .57 days to reach the fatigue limit range of 5,000,000 cycles. A 100 Hz shaft driven fatigue test would take roughly 14 hours to reach this lifetime. High frequency testing, such as a 1000 Hz electrodynamic and a 20 kHz ultrasonic test would take 1 .4 hours and 4.2 minutes, respectively. However, the applicability of each test depends on the loading conditions of the part the test is being performed for. The testing performed to design a component should match the service conditions as closely as possible with regards to speed and loading condition.

[0006] Fatigue testing methods are constantly being developed to reduce the testing time and cost of a fatigue test. Traditional fatigue tests run at speeds typically below several hundred Hz, as described above. Resonance-based fatigue tests involve stressing a specimen using vibrational systems operating near the resonant frequency to increase the stress output of the test. Resonance-based systems are often modeled as simple mass-spring-damper(M-C-K) systems that are governed by second order differential equations. The differential equation for a mass-springdamper system is given in the equation (1 ) set forth below.

[0007] In equation (1 ), m is the vibrating mass, c is the damping coefficient, k is the spring constant, x is the displacement, and F(t) is the input forcing function. If system damping is ignored, an estimate of the fundamental natural frequency, f_n, is f_n = the square root of k/m. Therefore, to increase the natural frequency of oscillation, the designer can increase the spring constant of the vibrational system and/or decrease the mass. If the forcing function, F(t), is sinusoidal and operating near the natural frequency of the system, the system will experience a large increase in output motion relative to the input motion of the forcing function. This is called resonance. The frequency of the forcing function that maximizes the output motion is then called the resonant frequency. The large increase in output motion reduces the amount of input motion required from the forcing function. This reduces the energy requirements to reach a desired output displacement. Researchers have used this principle to design fatigue testing systems that decrease both testing time and energy requirements compared to traditional methods.

[0008] Conventional resonance-based fatigue tests often face challenges stemming from friction between two sliding components within the vibrational system. This friction generates random vibration characteristics, ultimately leading to unstable control. Consequently, the resultant fatigue test data often fails to accurately portray the material's fatigue performance. Moreover, attempts to expedite testing by increasing vibration frequency exacerbate this issue. The present invention aims to mitigate such challenges by eliminating the friction between the two sliding components, thereby addressing the root cause of instability.

[0009] Therefore, a need exists for an electrodynamic axial fatigue test setup that allows for axial fatigue tests to be done with reduced time, material cost, and energy requirements when compared to conventional methods. Additionally, there is a need for an electrodynamic axial fatigue test setup that operates below ultrasonic frequencies allowed for strain rate sensitive materials to be tested in new frequency ranges that more closely resemble service conditions. Finally, a need exists for an electrodynamic axial test setup that enables a single electrodynamic shaker to generate both axial and bending fatigue data to facilitate the comparison of fatigue data under various loading modes at similar frequencies.

[0010] Additionally, there exists a need to better understand the size and loading effects on fatigue results. An accurate understanding of these effects would improve designer confidence as well as potentially reducing testing time. There also exists a need to produce reliable fatigue results while increasing the throughput of a test setup. Development of resonance-based fatigue tests using sheet metal material could lead to time and money savings in specimen production, specimen preparation, and specimen testing.

Summary

[0011] Certain exemplary aspects of the invention are set forth below. It should be understood that these aspects are presented merely to provide the reader with a brief summary of certain forms the invention might take and that these aspects are not intended to limit the scope of the invention. Indeed, the invention may encompass a variety of aspects that may not be explicitly set forth below. [0012] Embodiments of the present invention are directed to a system and method for determining the relationship between applied axial stress and stress cycles to failure for AI-7075 T6 using resonance-based testing methods. The stress cycle range analyzed was 104 - 107 cycles. The goal was to use an electrodynamic shaker to collect axial fatigue data. Resonance-based axial fatigue tests typically operate in the 20 kHz frequency range using piezoelectric transducers. At this frequency, the fatigue strength of strain rate sensitive materials has been shown to be impacted. Development of an electrodynamic axial fatigue fixture allowed for axial fatigue tests to be done with reduced time, material cost, and energy requirements when compared to conventional methods. Additionally, the development of an electrodynamic axial fatigue test fixture that operated below ultrasonic frequencies allowed for strain rate sensitive materials to be tested in new frequency ranges that more closely resemble service conditions. Finally, the development of an electrodynamic axial test fixture allowed for one electrodynamic shaker to produce axial and bending fatigue data, and for comparisons fatigue data for different loading modes at a similar frequency to be made. The completion of this objective added to the body of knowledge in the literature and increased the throughput of axial fatigue tests.

[0013] Embodiments of the present invention are also directed to a system and method for determining the relationship between applied bending stress and stress cycles to failure for AI-7075 T6 using resonance-based testing methods. The stress cycle range analyzed was 104 - 107 cycles. This method differed from axial testing because alternating bending was a displacement-controlled test instead of force- controlled. To accomplish this objective, it was necessary to quantify the strain and qualify the vibrational mode during testing. The Krouse specimens used in this work were designed so that the bending stress on the top and bottom surfaces in the gauge section was constant. This constant stress situation was only valid for mode one vibrational bending. Previous work found that the strain per deflection of a strain- gauged specimen dwelling at a constant frequency did not match the strain per deflection of a strain-gauged specimen that was statically loaded. Completion of this objective allowed for accurate estimations of stress and strain to be used to populate bending fatigue data in the finite life region. [0014] According to one embodiment of the invention, an axial fatigue test system is disclosed. The axial fatigue test system includes a vibration source with a fixture, a control mass, and a test specimen with a first end attached to the vibration source and a second end attached to the control mass. The axial fatigue test system further includes an air bearing that is configured to receive the control mass, and a contactless engagement between the air bearing and the control mass maintains alignment of the control mass over the vibration source.

[0015] According to one aspect, the air bearing constrains movement of the control mass in a direction perpendicular to a movement axis defined by the vibration source. Movement of the control mass by the vibration source along the movement axis may be in a vertical direction, for example. Furthermore, the air bearing may be coaxially arranged with the movement axis. In another aspect, the air bearing may be static during operation of the axial fatigue test system.

[0016] In one aspect, the vibration source may be an electrodynamic shaker. Furthermore, the fixture may be located on a shaker table of the electrodynamic shaker. In another aspect, the fixture may include a spring. For example, the spring may be arranged between the fixture and the vibration source.

[0017] In another aspect, the axial fatigue test system may include a first instrument, such as an accelerometer, to measure the acceleration of the vibration source. The axial fatigue test system may also include a second instrument, such as an accelerometer, to measure the acceleration of the control mass. In yet another aspect, the axial fatigue test system may further include an imaging device directed at the test specimen to take images of the specimen during operation of the axial fatigue test system.

[0018] Embodiments of the present invention are also directed to a system and method for determining the effect of loading mode and specimen size on fatigue life. Previous authors have investigated the effect of size and loading mode on fatigue life, but often these effects were confounded together due to testing capabilities. This objective also tested the same material under the same nominal stress while using two different methods (stress-controlled, strain-controlled). The completion of this objective added to the body of knowledge surrounding the size effect and the fatigue performance of a material under different loading modes.

[0019] According to one embodiment of the invention, a method of conducting an axial fatigue test is disclosed. The method includes providing an axial fatigue test system that includes a vibration source with a fixture configured to receive a first end of a test specimen and a control mass attached to a second end of the test specimen. The vibration source is configured to impart movement to the test specimen and the control mass along a movement axis. The axial fatigue test system also includes an air bearing that is configured to receive the control mass, and a contactless engagement between the air bearing and the control mass maintains alignment of the control mass over the vibration source. The axial fatigue test system further includes one or more dynamic instrumentation for monitoring characteristics of the test specimen and a multiphysics non-destructive evaluation system operatively coupled to the vibration source and the one or more dynamic instrumentation to detect damage to the test specimen. The method includes operating the vibration source to cyclically move the test specimen at a resonance equal to a first resonance frequency; monitoring the test specimen for damage using the Multiphysics non-destructive evaluation system; and if damage to the test specimen is detected, varying the resonance of the test specimen to a second resonance frequency.

[0020] According to one aspect, the second resonance frequency may be less than the first resonance frequency. For example, the second resonance frequency may be zero.

[0021] In another aspect, the axial fatigue test system further includes an imaging device directed at the test specimen. If damage to the test specimen is detected, the method further includes operating the imaging device to monitor material characteristics of the test specimen.

[0022] In yet another aspect, the one or more dynamic instrumentation includes one or more of the following: an accelerometer; an imaging device; a laser displacement sensor; and an extensometer.

[0023] Various additional features and advantages of the invention will become more apparent to those of ordinary skill in the art upon review of the following detailed description of one or more illustrative embodiments taken in conjunction with the accompanying drawings.

Brief Description of the Drawings

[0024] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more embodiments of the invention and, together with the general description given above and the detailed description given below, serve to describe the one or more embodiments of the invention.

[0025] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings will be provided by the Office upon request and payment of the necessary fee.

[0026] Figs. 1 A and 1 B are a top view and a side view, respectively, illustrating a Tensile Specimen Geometry.

[0027] Figs. 2A and 2B are a top view and a side view, respectively, illustrating a Small Krouse Specimen Geometry.

[0028] Figs. 3A and 3B are a top view and a side view, respectively, illustrating a Large Krouse Specimen Geometry.

[0029] Figs. 4A and 4B are a top view and a side view, respectively, illustrating a Beam Specimen Geometry.

[0030] Fig. 5 schematically illustrates a vibration test setup for conducting alternating bending and fatigue tests.

[0031] Figs. 6A and 6B are a top view and a side view, respectively, illustrating a Small Axial Specimen Geometry.

[0032] Figs. 7A and 7B are a top view and a side view, respectively, illustrating a Large Axial Specimen Geometry.

[0033] Fig. 8 schematically illustrates an Axial Fatigue Setup according to an embodiment of the present invention.

[0034] Fig. 9 illustrates additional details of the axial fatigue setup of Fig. 8.

[0035] Fig. 10 illustrates Axial DIG Virtual Extensometers applied to a test specimen.

[0036] Fig. 11 illustrates a Highly Stressed Volume of Axial Specimens.

[0037] Fig. 12 illustrates Resonance-Based Modulus Results Estimated Using Euler-Bernoulli Beam Theory.

[0038] Fig. 13 illustrates an AI-7075 T6 Small Krouse Stress per Thickness Vs. Control Deflection Plot.

[0039] Fig. 14 illustrates an AI-7075 T6 Large Krouse Stress per Thickness Vs. Control Deflection Plot.

[0040] Fig. 15 illustrates Alternating Bending S-N Results.

[0041] Fig. 16A illustrates a Small Krouse Asymmetrical Resonance response curve. [0042] Fig. 16B illustrates a Resultant Control During the Small Krouse Fatigue Test of Fig. 16A.

[0043] Fig. 17A illustrates a Small Krouse Resonance response curve.

[0044] Fig. 17B illustrates a Resultant Control During the Small Krouse Fatigue

Test of Fig. 17A.

[0045] Fig. 18 illustrates a Box and Whisker Plot for Small Krouse Specimens at 35,000 psi.

[0046] Fig. 19 illustrates a Typical Krouse Deflection and Frequency Trends Vs.

Fatigue Life % For Tolerance Bound Failures.

[0047] Fig. 20 illustrates a Typical Krouse Deflection and Frequency Trends Vs.

Fatigue Life % for Max Input Acceleration Failures.

[0048] Fig. 21 illustrates a Box and Whisker Plot for Large Krouse Specimens Tested at 35,000 psi.

[0049] Fig. 22 illustrates a Small Krouse Major Crack Length Vs. Frequency Drop % plot.

[0050] Fig. 23 illustrates a Large Krouse Major Crack Length Vs. Frequency Drop % plot.

[0051] Fig. 24 illustrates a AI-7075 T6 Small Axial Sample Measured Vs Applied

Stress plot.

[0052] Fig. 25 illustrates a AI-7075 T6 Large Axial Sample Measured Vs Applied Stress plot.

[0053] Fig. 26 illustrates Axial Fatigue Data.

[0054] Fig. 27 illustrates an Axial Fatigue Specimen Acceleration + Frequency Vs. Time plot.

[0055] Fig. 28 illustrates a Fatigue Life Vs. Transmissibility During Axial Tests plot.

[0056] Fig. 29 illustrates a Pareto Chart for Factorial Experiments.

[0057] Fig. 30 illustrates a Boxplot of Fatigue Life for all Geometries.

[0058] Fig. 31 illustrates a Cumulative Probability of Failure Vs. Large Krouse

Fatigue Data with Predicted and Actual Weibull Distribution Parameters plot.

[0059] Fig. 32 illustrates a Cumulative Probability of Failure Vs. Large Axial Fatigue Data with Predicted and Actual Weibull Distribution Parameters plot. Detailed Description

[0060] One or more specific embodiments of the present invention will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers’ specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

[0061] All the specimens described herein with respect to certain embodiments of the invention were cut from the same sheet of material to remove the variation in material properties between production batches. The specimens were wire EDM cut by Sure Tool & Manufacturing of Dayton, Ohio. Table 1 below lists the chemical composition of the material used as provided in the material test report. AI-7075 T6 was chosen because the fatigue strength in the 10⁴ - 10⁶ cycle range was well below the published yield stress. This meant that the range of stresses used for fatigue testing was likely to be below the materials proportional limit. It was important for the range of stresses used in fatigue testing to be below the proportional limit because the governing equation for stress in the Krouse specimen gage section was only valid for stresses below the proportional limit.

[0062] Table 1 : AI-7075 T6 Chemical Composition:

[0063] Tensile testing was completed to characterize the static material properties of AI-7075 T6. Figs. 1 A and 1 B illustrates an exemplary tensile specimen 10 geometry used in the tests set forth below. The specimen 10 was designed to be milled from existing beam specimens. An Instron 5567 test station was used to load the specimen. The force was measured using an Instron 2525-810 load cell and the elongation was measured with an Instron 2630-109 extensometer. An Aramis 2.3M system was used to capture images during tensile testing for use with digital image correlation (DIG). DIG allowed for the strain field of the entire tensile specimen gage section to be calculated.

[0064] Resonance-based methods were used to identify the flexural modulus of the material. The modulus estimation ratio between the small Krouse (Krouse 2.0) specimens 12 (Figs. 2A and 2B) and Beam specimens 14 (Figs. 4A and 4B) was roughly 0.8 for brass and titanium. The modulus of a cantilevered beam in mode 1 bending can be estimated as a function of the natural frequency, density, and physical dimensions of the beam 14. Equation (2) set forth below gives the equation for estimating the Modulus of Elasticity for a specimen from the physical properties, dimensions, and resonance characteristics.

[0065] In equation (2), p is the specimen density, a>_n is the resonant frequency, L is the cantilevered length, and t is the thickness of the specimen. The specimens were density tested using Archimedes’ principle as outlined in ASTM B311 . Three different geometries of specimens were subjected to resonance sweeps and impulse excitation tests to identify the resonant frequency of each specimen design. Figs. 2A and 2B illustrate the Small Krouse Specimen 12 Geometry, the wide end being fixed during testing and narrow end free. Figs. 3A and 3B illustrates a Large Krouse Specimen 16 Geometry. The Large Krouse specimen 16 dimensions are twice the dimensions of the small Krouse specimen 12; however, the thickness T is the same. Figs. 4A and 4B illustrate the Beam Specimen 14 geometry. Three specimens 10, 12, 14, 16 of each geometry were tested.

[0066] Impulse excitation was done by clamping the wide end of the Krouse specimen 12, 16 to a stationary fixture and striking the free end of the specimen 12, 16 with the ball end of a tuning fork. A Keyence LK-H087 laser displacement sensor was used to measure the displacement of the specimens’ 12, 16 free end over several seconds following the impulse. Since the free end motion was sinusoidal, the resonant frequency was calculated by counting the number of peaks that occurred in each amount of time. Impulse excitation was performed five times on each specimen 12, 16. Resonance sweeps were conducted using a Sentek L0111 A-PAS102 vibration test system controlled by a Vibration Research VR9500 controller. The output motion of the specimen 12, 16 was measured using a Keyence LK-H082 laser displacement sensor and the input motion of the shaker head was measured with a PCB Piezotronics accelerometer. Vibration VIEW software was used to input parameters to perform a resonance sweep. The resonance sweeps were run with an input acceleration of 2 G’s and a sweep speed of 1 octave/minute. The resonant frequency for each sweep was the frequency that corresponds to the peak transmissibility value on a transmissibility vs. frequency plot. Three upward sweeps and three downward sweeps were conducted for each specimen.

[0067] Small Krouse 12 and Large Krouse 16 specimen geometries were used for the alternating bending fatigue tests that will now be described. The Krouse specimen 12, 16 design was chosen so that the stress was constant throughout a gauge section 12a, 16a of each specimen, respectively. To avoid surface finish effects on fatigue life, the specimens 12, 16 were polished to an average roughness < 8 pin using a Pace Technologies polishing wheel with SiC polishing disks. The final polish was done in the longitudinal direction of the specimen 12, 16 to increase the visibility of cracks propagating through the gauge section 12a, 16a.

[0068] Fig. 5 schematically illustrates a vibration test setup 18 in accordance with an embodiment of the invention. The vibration test setup 18 is used to complete the alternating bending DIG and fatigue testing and may comprise as a L0111 A-PAS102 vibration test system controlled by a Vibration Research VR9500 controller 30. The output motion of the specimen 12, 16 being tested was measured using a laser displacement sensor 20, such as a Keyence LK-H082, that was positioned at a precise control distance from a fixture 22 configured to clamp one end edge of the specimen 12, 16. The laser displacement sensor 20 may be mounted to a micrometer for accurate adjustment of the control distance. The input motion is provided by a shaker head 24 of an electrodynamic shaker 26. Input motion of the shaker head 24 may be measured with a PCB Piezotronics accelerometer 28, for example. In one embodiment, the laser displacement sensor 20 may be used to control the output deflection of the specimens 12, 16 while dwelling. The vibration test setup 18 may also be used for the impulse excitation testing described above as well.

[0069] An imaging device 32, such as an Aramis 2.3IVI stereo DIG system, was used to take images during a series of dwells at various displacement levels. As shown schematically in Fig. 5, the imaging device is directed at the specimen 12, 16 being tested and is configured to capture DIG images as the system 18 is operated to run alternating bending fatigue tests. The images may be processed in GOM Correlate software to find the bending strain in the gage section 12a, 16a at each deflection level, which produced plots of Strain/Thickness Vs. Control Deflection for the small Krouse and large Krouse specimens 12, 16. Plots of Stress/Thickness Vs. Control Deflection were created by multiplying the strain/thickness axis by the material modulus. Linear regression of the Stress/Thickness Vs. Control Deflection level plot was used to calculate the stress levels for testing.

[0070] Alternating bending fatigue tests were then performed by dwelling the Krouse specimens 12, 16 at their resonant frequency while controlling the output deflection of the Krouse specimens 12, 16. Fourteen Krouse specimens 12, 16 of each Krouse geometry were tested at the 35,000 psi alternating stress level to study the effect of specimen size on fatigue life. Six additional Krouse specimens 12, 16 of each Krouse geometry were run at stress levels from 25,000 psi to 40,000 psi to publish stress-life (S-N) curves. Resonance-based alternating bending fatigue tests show a drop in resonant frequency as fatigue cracks propagate through the gage section 12a ,16a. Therefore, the alternating bending fatigue tests were terminated when the resonant frequency dropped by 20% of the initial resonant frequency or if the controller 30 was unable to control the output deflection to within ± 6 db. The frequency range of all fatigue tests completed in this work were within 500 Hz. This was done to minimize any frequency effects on fatigue life.

[0071] A uniaxial fatigue test method and system will now be described with respect to Figs. 6A-9. In that regard, Figs. 6A and 6B show a small axial fatigue specimen 34 and Figs. 7A and 7B show a large axial fatigue specimen 36, both of which were tested in accordance with embodiment of the invention described below. To avoid surface finish effects on fatigue life, the specimens 34, 36 were polished to an average roughness < 8 pin using a Pace Technologies polishing wheel with SiC polishing disks.

[0072] Fig. 8 schematically illustrates an axial fatigue test setup 40, which may comprise a Sentek L0111 A-PAS102 vibration test system controlled by a Vibration Research VR9500 controller 42, used to conduct axial fatigue tests in accordance with one embodiment of the invention. The test setup 40 includes an electrodynamic shaker 44 having a shaker head 46 (otherwise referred to as a shaker table or shaker armature) with a fixture 48 configured to receive a first end 50 of the specimen 34, 36 being tested. In addition to securing one end 50 of the specimen, the fixture 48 serves as a planar spring 52. That is, a portion of the fixture 48 is configured as a planar spring 52. The specimen 34, 36 is configured to be secured between the fixture 48 and a control mass 54. In that regard, the control mass 54 is configured to receive a second end 56 of the specimen 34, 36. The weight of the control mass 54 is generally borne by the specimen 34, 36. The control mass 54 is coaxially arranged within an air bearing 58 that is supported above the shaker head 46 by a support frame 60. As will be described in further detail below, certain movements of the control mass 54 are constrained by the air bearing 58 in a contactless or frictionless manner to maintain alignment of the control mass 54 over the shaker head 46. To that end, the shaker 44 is configured to cyclically move or shake the shaker head 46 in a direction along a movement axis A1 to impart movement to the test specimen 34, 36 and the control mass 54. The movement axis A1 may be a vertical axis that aligns with a local gravity vector. The air bearing 58 is generally coaxially arranged with the movement axis A1 to support the control mass 54.

[0073] With reference to Figs. 8 and 9, certain movement of the control mass 54 is constrained by the air bearing 58 that is attached to the frame 60. In one embodiment of the test setup 40, the frame 60 may be supported from a static surface 62 of the shaker 44, such as a top surface adjacent the shaker head 46, for example. Thus, the frame 60 is generally static during operation of the shaker 44. The fixture 48 (spring 52), control mass 54, specimen 34, 36, and mounting cylinders 64, 66 were connected to the shaker head 46. The axial fatigue system 40 was designed to operate like a one-dimensional M-C-K vibrational system as described by equation (1 ). The porous media air bearing 58 provides axial alignment of forces on the specimen 34, 36 by restricting the motion of the control mass 58 to one linear movement axis A1 . That is, the air bearing 58 restricts or prevents movement of the control mass 54 in a horizontal movement direction that is generally perpendicular to the vertical movement axis A1 . However, the air bearing 58 allows for frictionless motion of the control mass 54 along the movement axis A1 . To that end, the air bearing 58 minimizes metal-on-metal sliding friction between the bearing 58 and the control mass 54 that is irregular and random. The random spikes in friction may result in the VibrationVIEW controller 42 being unable to control the output acceleration during resonance. Furthermore, damping due to friction may decrease the transmissibility during resonance to a level that limits the stress range of the uniaxial tests.

[0074] With reference to Fig. 9, the air bearing 58 is a porous media air bearing that allows for frictionless and uniaxial motion between the control mass 54 and the air bearing 58. In that regard, the air bearing 58 includes a housing 70 defined by a first half 72 and a second half 74 configured to fit together around a porous bushing 76, which defines a bearing surface 78 of the air bearing 58. The housing 70 is attached to the frame 60 in the testing setup 40, as shown. The bushing 76 may be formed of a sintered metal or other permeable material(s), such as graphite, for example, capable of allowing air to pass through the bushing 76 to create a uniform pressure distribution over the bearing surface 78. Each housing half 72, 74 includes a pair of channels that provide the housing with a pair of annular channels 80 configured to extend circumferentially about the bushing 76. One or both housing halves 72, 74 may include air passageways 82 to provide airflow from an air source 84 connected to an air inlet 86 to the channels 80. In that regard, airflow passes through passageways 84 within the housings 72, 74 to each annular channel 80 to form an air band between the housing 70 and around the bushing 76 and thus a constant airflow through the porous bushing 76, as indicated by the directional arrows 88. The bearing 58 may include one or more gaskets 90, such as O-rings, arranged between the bushing 76 and the housing 70 to prevent airflow from escaping the annular channels 80.

[0075] During use, compressed air is forced through microscopic pores 89 in the bushing 76 which creates a uniform even layer of pressurized air in a region or gap 92 between the bearing surface 78 of the bushing 76 and the cylinder arranged within the bushing 76, such as the control mass 54. The layer or band of compressed air in the region 92 provides concentric alignment of the metallic cylinder, such as the control mass 54, to the bushing 76. Thus, the air bearing 58 allows for uniaxial, frictionless motion between the two concentric cylinders in the current application. Uniaxial motion is required in axial fatigue testing systems because this uniaxial motion creates uniaxial stresses. Frictionless motion is required to use the resonance-based system with an electrodynamic shaker. Unstable friction within a vibrational system is difficult to control especially at high frequencies which is typically where electrodynamic shakers operate. This implementation of an air bearing 58 into a resonance-based fatigue testing system 40 allows for an electrodynamic shaker 44 to be used to produce axial fatigue data. Thus, implementation of an air bearing 58 into an axial fatigue testing system 40 to create frictionless linear motion allows for a resonance-based axial fatigue testing system 40 to be used with an electrodynamic shaker 44. This further allows for resonance-based axial fatigue testing systems 40 to achieve much higher testing frequencies which greatly decreases the time required to run a fatigue test. This reduces the cost and time required to produce axial fatigue data which is highly sought after in many industries.

[0076] In the test setup 40, a first instrument, such as an accelerometer 94 which may be a PCB Piezotronics accelerometer, may be used to measure the acceleration of the shaker head 46, while a second instrument, such as an accelerometer 96 which may be a DYTRAN Instruments accelerometer, may be used to measure the acceleration of the control mass 54. The first and second instruments 94, 96 may be replaced with a Linear Variable Differential Transformer (LVDT) for measuring linear displacement or position. Induction may also be used to measure linear displacement or position of the test setup 40 components. In either case, the force on the specimen is calculated using Newton’s second law shown below in equation (3):

F — mA

[0077] In equation (3), Pis the force in Ibf., m is the mass of the control mass 54 and upper mounting cylinder 66 in lb., and A is the acceleration of the control mass 54 in G’s. The mass was measured with an A&D GX-6100 scale. The force acting on the specimen 34, 36 was used to calculate the stress on the axial specimen. To validate the stresses imposed on the specimens 34, 36, three specimens of each axial geometry were subjected to a series of resonance dwells at various stress levels. As shown schematically in Fig. 8, the testing setup 40 may also include an imaging device 98, such as a using a Chronos 1 .4 high speed camera, to capture DIG images during these dwells. In one embodiment, three virtual extensometers 100 were applied using GOM correlate software and the strain amplitude during one cycle was recorded. Fig. 10 shows the location of the virtual extensometers 100 on an exemplary axial specimen 34, 36. Virtual extensometers 100 may be located on both sides of the specimen 34, 36. All extensometers 100 were located in a gage section 102 of each specimen 34, 36 and were the same length and facet size for calculation. The average axial strain was then multiplied by the material modulus to calculate stress. This allowed for a direct comparison between the desired stress calculated using the output acceleration level and the measured stress calculated using the DIC strain.

[0078] To study the effects of specimen 34, 36 size on fatigue life and to analyze load effects between axial and bending tests, 14 of each axial specimen 34, 36 geometry were tested at 35,000 psi. Six additional specimens 34, 36 of each axial geometry were run at stress levels from 25,000 - 40,000 psi to publish S-N curves. The axial fatigue tests were designed to be terminated when the resonant frequency of the specimen 34, 36 dropped by 20% of the initial resonant frequency or when the controller 42 was unable to maintain stable control. It was observed in this work that the axial fatigue tests ran to final fracture and separation before the controller 42 lost control or the frequency dropped below the 20% threshold.

[0079] The size and load effects on fatigue life were analyzed using a full 2² factorial experiment. Factor A was the specimen size and factor B was the load type. Table 2 below shows the factorial experimental design with the corresponding specimen geometry. Alpha was equal to 0.05 for this factorial experiment. Fourteen replicates of each treatment combination were fatigue tested at 35,000 psi. The results of Table 2 were analyzed using Minitab to determine which factors significantly affect fatigue performance. This factorial experiment tested the following null hypotheses: (1 ) The main effects of specimen size on mean fatigue life were equal to 0; (2) The main effects of loading type on mean fatigue life were equal to 0; and (3) The interaction effects of specimen size and load type on mean fatigue life were equal to 0.

[0080] Table 2: Fatigue Specimen Geometry by Treatment Combination.

[0081 ] The two-parameter Weibull distribution was fit to the 14 replicates fatigue tested at 35,000 psi for each specimen geometry. Equation (4) set forth below gives the two-parameter Weibull cumulative distribution function for fatigue life.

[0082] In equation (4), p is the scale parameter, a is the shape parameter, and N is the number of cycles. The maximum likelihood estimation function in MATLAB was used to find the unrestricted Weibull distribution parameters for each geometry. This function calculates the optimal shape and scale parameters by maximizing the likelihood function for a vector of fatigue lives given different input parameters.

[0083] Computer aided design models for each specimen geometry were analyzed using SOLIDWORKS Finite Element Analysis (FEA). The goal of this task was to quantify the amount of highly-stressed volume (HSV) for each geometry. FEA was run with decreasing plate element sizes until convergence in the amount of HSV was found. Fig. 11 shows a highly stressed volume 104, 106 of each axial specimen, 34, 36, respectively. HSV ratios were then calculated by dividing the HSV of a large geometry 36 by the HSV of a small geometry 34. The previously found Small Krouse distribution parameters and HSV ratio were used to produce a predicted scale parameter for the Large Krouse.

[0084] The accuracy of the predicted scale parameter for the Large Krouse specimen 16 was analyzed using the likelihood ratio test. Likelihood ratio tests evaluate how well a restricted set of parameters fit a data set in comparison to an unrestricted set of parameters. Equation (5) set forth below gives the test statistic for the likelihood ratio test.

[0085] In equation (5), Li represents the likelihood of the data given that both the shape and scale parameters were found using unrestricted MLE. Lo represents the likelihood of the data with at least one restricted parameter, and all unrestricted parameters found using MLE. For Lo, the scale parameter was restricted to the value found using equation (10). Restricted MLE was then used to find the shape parameter that maximized the likelihood of the Large Krouse data set given the restricted scale parameter of the Weibull distribution, to was then calculated as the likelihood of the Large Krouse data set evaluated using the parameters found with restricted MLE. The likelihood ratio test statistic was then calculated using Loand Li. The null and alternate hypotheses for the likelihood ratio test were: (1 ) The unrestricted model does not provide a statistically significant improvement in likelihood over the restricted model, and (2) The unrestricted model does provide a statistically significant improvement in likelihood over the restricted model.

[0086] The null hypothesis was rejected if the test statistic found was greater than the critical value of x²(a, v), where a was the significance level of the comparison and vis the number of restricted parameters. Alpha was 0.05 for the likelihood ratio test. [0087] This method of predicting the effect of highly stressed volume on Weibull distribution parameters and testing with the likelihood ratio test was applied to several geometry combinations. This model is commonly used to predict the performance of large specimens given the performance of small specimens. Therefore, the small Krouse specimen 12 Weibull distribution was used to predict the Weibull distribution of the large Krouse specimen 16. This process was then repeated to predict the Weibull distribution of the larger axial specimen 36 using the distribution of the smaller axial specimen 34. Lastly, the small Krouse specimen 12 distribution was then used to predict the performance of the large axial specimen 36. The HSV ratio between the large Krouse 16 and small Krouse 12 geometries was 8.3 and the HSV ratio between the large axial 36 and small axial 34 geometries was 10.8. The HSV ratio between the large axial specimen 36 and small Krouse specimen 12 was 1135.7. MATLAB code for implementing this data per the steps described above, comprises the following sequence of operations: provide HSV of each specimen geometry; calculate the Weibull parameters for each specimen geometry; predict the scale parameter based on the size effect which includes predicting scale parameter for axial 2.0 from axial 3.0 distribution (predict large axial from small axial); Perform Likelihood Ratio Test on Axial 2.0 Data using Axial 3.0 Data; Find unrestricted shape parameter based on predicted scale parameter; calculate LRT parameters for axial sample; perform test and display results; Perform Likelihood Ratio Test on Krouse 3.0 Data using Krouse 2.0 prediction; Find unrestricted shape parameter based on predicted scale parameter; calculate LRT parameters for axial sample; perform test and display results; Perform Likelihood Ratio Test on Axial 2.0 Data using Krouse 2.0 prediction; Find unrestricted shape parameter based on predicted scale parameter; calculate LRT parameters for axial sample; perform test and display results; Plot Fatigue Data.

[0088] The mean and standard deviation (STD) results of tensile testing are shown in Table 3 below. The strain rate of testing was chosen to determine yield properties according to ASTM E8. The tensile results agree well with the material test report provided by SureTool. Three 16mm virtual extensometers 100 were placed in the gage section 102 of the specimen 34, 36 using GOM correlate. One virtual extensometer 100 was placed in the middle of the specimen 34, 36 and two were placed on opposing sides and the results were averaged. The facet size used for these virtual extensometers 100 was 21 . The noise measured with these extensometers 100 was ±45 micro strain. When using DIG to calculate strain, there was a 0.60% difference between the yield strength found during testing and the yield strength provided in the material test report. Similarly, there was a 0.96% difference in the ultimate tensile strength and a 3.1% difference in elongation at failure between the DIG tensile results and material test report.

[0089] For the tensile properties calculated using the extensometer 100, the yield strength was 3.1 % different than the value published in the material test report. The ultimate tensile strength was 0.96% different and the elongation at failure was 0.3% different compared to the material test report. Sample two of the tensile testing battery displayed extensometer slippage in the stress strain curve. This resulted in the material properties for this sample to be altered when calculated using the extensometer strain values. For this reason, the material properties used throughout this work were the results calculated using the DIG strain values.

[0090] Table 3: Average Tensile Properties.

[0091] The modulus of elasticity calculated using the extensometer 100 showed better agreement with published values compared to the modulus calculated using DIG. The stress range for calculating modulus was found using the strain deviation method as mentioned in ASTM-E111 . This method relies on many measurements being taken in the elastic region of the stress-strain graph. The sampling frequency for the extensometer 100 was 50 Hz and the imaging frequency for DIG was 1 Hz. This resulted in far fewer points being used for the strain deviation method with DIG, which limited the accuracy of fit. The standard error of the regression on DIG data points was on the same order of magnitude as the standard deviation for all three tensile specimens, which indicates that the standard deviation for the modulus found using DIG data was dictated by the quality of regression. For the modulus value found using the extensometer, the standard error of regression was two orders of magnitude lower than the standard deviation for all three tensile specimens. This indicates that the standard deviation for the modulus was dominated by the variation in modulus between samples and the potential extensometer 100 slippage that occurred with specimen 2.

[0092] Fig. 12 shows the average results of resonance sweeps and impulse excitation for the three geometries tested. The impulse excitation tests resulted in higher average modulus estimates. It was found that the small Krouse 12 and large Krouse 16 provided similar estimates of modulus for resonance sweeps and impulse excitation. The average ratio of moduli found between small Krouse 12 and large Krouse 16 specimens was 0.99. The beam specimens 14 provided an estimate of modulus that agrees with the results of tensile testing. The average ratio of moduli between small Krouse 12 and beam specimens 14 was 0.84. The average ratio of moduli between large Krouse 16 and beam specimens 14 was also 0.84. The impulse excitation tests provided a higher average estimation of modulus compared to resonance sweeps. Appendix A lists the resonance-based modulus estimates for all the specimens used in this work.

[0093] Figs. 13 and 14 show the stress per thickness plots that resulted from performing DIG on the small Krouse 12 and large Krouse 16 specimens. With respect to Fig. 13, strain was measured during resonance dwells at given deflection levels using DIC and converted into stress/thickness. Linear regression of 14 data points given in legend. Deflection was measured 0.375” from clamped section. With respect to Fig. 19, strain was measured during resonance dwells at given deflection levels using DIC and converted into stress/thickness. Linear Regression of 23 data points given in legend. Deflection was measured 0.9” from clamped section. Virtual extensometers with a facet size of 21 were used to measure the strain in the gage section. The average noise level of the DIC system used for measurement resulted in ±130 micro strain. The range of strains measured during resonance dwells for the small Krouse specimen 12 was 1770 to 4585 micro strains. The measured strains resulted in stresses from 17,000 - 44,000 psi. The range of strains measured during resonance dwells for the large Krouse specimen 16 was 1020 to 4050 micro strain. The measured strains for the large specimens 16 resulted in stresses from 10,000 - 40,000 psi. The DIC images were captured with an Aramis 2.3M camera system with a maximum imaging frequency of 140 Hz. The resonant frequencies of the small Krouse 12 and large Krouse 16 specimens were 470 Hz and 170 Hz, respectively. Aliasing was used to capture the full sinusoidal motion of the specimen during each dwell.

[0094] Given the lensing, lighting, and sensor resolution of the Aramis 2.3M system, the system was incapable of measuring low stress levels for the small Krouse specimen 12 compared to the large Krouse specimen 16. The small Krouse specimen 12 had a greater velocity, covered less of the sensors’ field of view, and had smaller amplitudes of motion compared to the large Krouse specimen 16. All these factors restricted the current DIC system from resolving distortion of the speckle pattern for the small Krouse specimen 12 at deflection levels below 0.005 inches pk-pk. The vertical offset of the regression line for the stress/thickness vs. deflection level plots should be zero as there should be zero stress on the specimen when there was no imposed deflection. The vertical offsets in Fig. 13 and Fig. 14 are near the bounds of the standard error of regression for each regression. The larger deflection range as well as the larger number of points used in regression for the large Krouse specimen 16 produced a lower non-linearity, lower vertical offset, and lower standard error of regression compared to the small Krouse specimen 12. The smaller deflection level range as well as the fewer number of points used in regression for the small Krouse specimen 12 likely contributed to the larger offset and nonlinearity.

[0095] The range of stresses used for fatigue testing the large Krouse 16 and small Krouse 12 specimens was 25,000 - 40,000 psi. This stress range was chosen to avoid extrapolation of the stress/thickness Vs. control deflection level plots. Fig. 15 shows the alternating bending fatigue testing results of both Krouse geometries. In particular, the large Krouse specimens 16 had a longer fatigue life at 35,000 psi than the smaller Krouse specimens 12 according to the Basquin curve fit. Fourteen specimens of each geometry were tested at 35,000 psi. Six specimens of each geometry were then used to populate S-N data from 25,000 - 40,000 psi in 2500 psi increments. The fatigue data was linearized by taking the logarithm of each point. Least squares was used to perform linear regression on the linearized data to find the Basquin equation coefficients for each specimen geometry. The fatigue data points at 35,000 psi were averaged for each geometry and the mean value was used in place of all 14 replicates to prevent the 14 replicates from dominating the Basquin coefficients. The Basquin curve predicts the small Krouse specimens 12 failing at 59,000 cycles and the large Krouse specimens 16 failing at 11 1 ,000 cycles. The slopes of the Basquin curve for each bending specimen were similar in the range of fatigue lives that were analyzed.

[0096] When running the small Krouse specimens 12, it was observed that the initial sweep and dwell of the specimens produced a skewed resonance sweep curve and poor control at the desired deflection level. Fig. 16A shows the asymmetrical resonance sweep of a small Krouse specimen 12. The resonance sweep curve displayed a sharp decrease in deflection at frequencies just below the peak and a much more gradual decrease in deflection at frequencies just above the peak. Fig. 16B shows the quality of deflection control during the start of fatigue testing that occurred right after the first resonance sweep shown in Fig. 16A. The deflection of the Krouse specimen 12 exhibited poor control in the moments immediately after the deflection ramped up to the target level.

[0097] It was then observed that if the same specimen was re-resonant swept and fatigue testing was resumed, the resonance sweep curve was more symmetrical and there was a greater quality of deflection control for the fatigue test. Fig. 17A shows the resonance sweep curve of a specimen that was subjected to a second resonance sweep. The deflection response was more symmetrical about the peak frequency for the specimen that was subjected to a second resonance sweep. Fig. 17B shows the resultant initial deflection control of the specimen after a second resonance sweep. There was less overshoot of the target deflection level after the second resonance sweep than after the first resonance sweep. The large Krouse specimens 2+ used in this work showed symmetrical resonance response curves and accurate control during ensuing resonance dwells. The large Krouse specimens 16 were run entirely before the small Krouse specimens 12. AI-6061 T6 small Krouse specimens 12 that were used for initial data testing did not exhibit skewed resonance sweeps in the small Krouse specimens 12.

[0098] In alternating bending testing, the specimen was cantilevered with a control mass mounted on the free end. The specimen’s resistance to bending provided the spring constant that makes the bending fatigue tests perform according to equation (4). As the fatigue test progressed, cracks initiated and propagated throughout the specimen which weakened the specimen’s resistance to deflection. A decreased resistance to deflection decreased the spring constant, K, in equation (4) which changed in the vibrational characteristics of the specimen. The resonant frequency and transmissibility were the most affected characteristics and were shown to drop during each bending fatigue test.

[0099] For the small Krouse specimens 12 it was found that none of the specimens experienced a drop in resonant frequency below 20%, which was one of the desired termination criteria. All of the small Krouse 12 fatigue tests were terminated due to the output deflection falling outside of the ± 6db tolerance bounds or when the shaker exceeded its maximum input acceleration limit. Fig. 18 shows a box and whisker plot of fatigue life vs. termination condition for the small Krouse specimens 12 tested at 35,000 psi. Fig. 18 shows that exceeding the tolerance bounds resulted in a greater spread of fatigue life than terminating due to max input acceleration. Rapid changes to the vibrational characteristics resulted in failure due to the output deflection spiking outside of the tolerance bounds. Fig. 19 shows the end of test trends when the test was terminated due to exceeding tolerance bounds. Notice the steady deflection control from 75% to 95% of the specimen’s fatigue life where the frequency increasingly decreases. It appeared that rapid changes caused the controller to enter a positive feedback loop which led to the deflection exceeding the tolerance bounds. [00100] Gradual changes to the vibrational characteristics caused the output deflection of the specimen to steadily decrease which prompted the controller to increase the input deflection to maintain the desired output deflection. This led to the shaker reaching its maximum input acceleration level. Fig. 20 shows the characteristic deflection and frequency trends when a Krouse specimen 12, 16 failed due to exceeding the max input acceleration. Notice the rapid drop in displacement near the end of the test. Max Input Acceleration Failures also show a period of smooth control over the output deflection near 75%-95% of total fatigue life. In both modes of failure, it appears that there existed a period of the specimen’s fatigue life where the output deflection level was controlled very accurately. This period is shown in Fig. 19 and Fig. 20 near the 75%-95% fatigue life. It is possible that stable crack growth occurred from 75%-95% of the fatigue life and unstable crack growth occurred from 95%-100%.

[00101] The shaker had a minor system resonance at 500 Hz which appeared to cause several of the small Krouse specimens 12 tested at 35,000 psi to terminate due to exceeding the tolerance bounds. A t-test was used to compare the mean fatigue life of the specimens that failed with frequencies near the system resonance to the specimens that failed with frequencies far from the system resonance. The null hypothesis stated that the mean fatigue life of the specimens that failed near the system resonance was equal to the mean fatigue life of the specimens that failed away from the system resonance. The results of the t-test failed to reject the null hypothesis with a p-value of 0.37, indicating that the failures near the system resonance did not statistically affect the mean fatigue life.

[00102] The large Krouse 16 fatigue tests were terminated when the output deflection fell outside of the tolerance bounds, when the shaker exceeded its maximum input acceleration limit, or when the resonant frequency dropped below the lower frequency bound set in VibrationVIEW. To run fatigue tests in VibrationVIEW, a resonance sweep was run to find the resonant frequency for each specimen. The fatigue test then started at this resonant frequency and the controller adjusted the input excitation frequency to maximize the transmissibility of the specimen. It was desired to have the fatigue tests terminated when the resonant frequency dropped below 20% of the resonant frequency. However, VibrationVIEW automatically terminated tests when the frequency of testing exceeded the bounds of the initial resonance sweep. The large Krouse specimens 16 had a resonant frequency near 170 Hz and the initial resonance sweep had a lower frequency bound of 150 Hz. It was found that five of the large Krouse 16 fatigue tests run at 35,000 psi were terminated when the testing frequency dropped below 150 Hz which corresponded to roughly a 13% drop in resonant frequency.

[00103] A t-test was run to see if terminating the fatigue tests when the frequency fell below 150 Hz had an effect on the mean fatigue life of large Krouse specimens 16 tested at 35,000 psi. The five specimens terminated due to this lower frequency bound were compared to the nine other specimens that failed due to the other termination conditions. The null hypothesis stated that the mean fatigue life of the early termination condition was equal to the mean fatigue life for the other termination conditions. The results of the t-test failed to reject the null hypothesis with a p-value of 0.25 which indicated the early stop condition did not affect the mean fatigue life of large Krouse specimens 16 at 35,000 psi. Fig. 21 shows a box and whisker plot of fatigue life vs. the termination condition for the small Krouse specimens 12 tested at 35,000 psi. Fig. 21 shows that failure due to exceeding the tolerance bounds produces a wider range of fatigue lives which agrees with the results in Fig. 18.

[00104] The large Krouse specimens 16 that failed due to exceeding the tolerance bounds and exceeding the maximum input acceleration of the shaker showed the same failure trends that are pictured in Fig. 19 and Fig. 20, respectively. The drop in resonant frequency as a percent of the initial resonant frequency and the drop in resonant frequency in Hz were calculated for each Krouse specimen 12, 16. The mean drop in resonant frequency (%) for the specimens tested at 35,000 psi was 3.1% for the small Krouse specimens 12 and 11 .9% for the large Krouse specimens 16. Similarly, the mean drop in resonant frequency (Hz) for the specimens tested at 35,000 psi was 15.9 Hz for the small Krouse specimens 12 and 20.6 Hz for the large Krouse specimens 16. A Keyence microscope was used to measure the length of the largest crack for each Krouse specimen 12, 16. Fig. 22 and Fig. 23 show the correlation between the major crack length and the frequency drop % for the small and large Krouse specimens 12, 16 tested at 35,000 psi, respectively. The mean crack length for the small Krouse specimens 12 was 0.11 inches and was 0.39 for the large Krouse specimens 16. Fig. 22 and Fig. 23 both show a direct relationship between the major crack length and the percent drop in resonant frequency. With respect to Fig. 23, The five data points near 13% frequency drop were terminated due to the lower sweep bound. The table in Appendix B lists the results of each bending fatigue test including the drop in frequency, major crack length, and cycles to failure.

[00105] To validate the stresses imposed on the axial specimens, three axial specimens of each geometry were dwelled at stress levels from 10,000 - 42,000 psi. The applied stress level was chosen by multiplying the weight of the control mass 54 by the output acceleration and dividing by the cross-sectional area of the specimen. Virtual extensometers 100 were placed in the specimen’s gage section 102 using GOM Correlate. Facet sizes of 21 were used for the extensometers 100. Three extensometers 100 were equally spaced across the gage section 102 width and the average strain was calculated. The calculated strain in the gage section 102 was multiplied by the material modulus to convert to stress. Fig. 24 and Fig. 25 show the measured stress vs. applied stress for the small and large axial specimens 34, 36, respectively. In both plots, the measured stress was calculated using both the modulus found with DIG and the modulus found with the extensometer during tensile testing. In Fig. 24 and Fig. 25 the modulus found with the extensometer during tensile testing produced a higher measured stress value. With respect to Fig. 24, The applied stress was set using Applied Stress = (mass * acceleration)/(Cross sectional area). The measured stress was calculated using Measured stress = (E - material modulus)*(e - DIG measured strain). Two different moduli were used to calculate measured stress. With respect to Fig. 25, the applied stress was set using Applied Stress = (mass * acceleration)/(Cross sectional area). The measured stress was calculated using Measured stress = (E - material modulus)*(e - DIG measured strain). Two different moduli were used to calculate measured stress. The higher measured stress values produced a slope closer to one for both the small and large axial specimens 34, 36. A slope of one reflects a perfect agreement between the measured and applied stress. In both axial geometries, it was observed that the measured stress was higher than expected at the 10,000 and 14,000 psi stress levels. An analysis of the axial DIG system found that there was ± 450 micro strains from background noise which equated to ±4500 psi of stress.

[00106] Fig. 26 shows the results of axial fatigue testing for the small and large axial specimens 34, 36. Fourteen specimens of each geometry were tested at 35,000 psi. Six additional specimens of each geometry were tested from 25,000 - 30,000 psi in 2500 psi increments. The large axial specimens 36 had a longer fatigue life than the small axial specimens 34 at the 35,000 psi stress level. The Basquin fit curve predicted the small axial specimens 34 failing at 25,300 cycles where the large specimens 36 were predicted to fail at 29,500 cycles at the 35,000 psi stress level. The Kt values for the small and large axial specimens 36 were 1.12 and 1.10, respectively. The fatigue data was linearized by taking the logarithm of each point. Least squares regression was performed on the linearized data to find the Basquin equation coefficients for each specimen geometry. The fatigue data points at 35,000 psi were averaged for each geometry and the mean value was used in place of all 14 replicates. The average value was used prevent the 14 replicates from dominating the Basquin coefficients. The Basquin curve for the small specimens 34 showed a steeper decrease in fatigue strength as the number of cycles to failure increased. [00107] The axial fatigue specimens 34, 36 did not display any consistent trends before failure. Fig. 27 shows the frequency and acceleration plots for a specimen 34, 36 over the course of a fatigue test. There was no consistent drop in frequency unlike the bending specimens. Unlike the Krouse specimens 12, 16, the axial fatigue specimens 34, 36 did not act as a spring in this vibrational system. The spring 52 that provided resonance in the axial system 40 was an external spring that mounted to the shaker head 46. The specimens 34, 36 were a linkage that connected the control mass 54 to the planar spring 52. Therefore, when a fatigue crack propagated through an axial specimen 34, 36 there was little effect on the spring constant that defined the resonance characteristics of the axial system 40. This means that there was no warning before specimen 34, 36 failure. All axial specimens 34, 36 failed by complete separation of the specimen 34, 36 in the gage section 102. Given the current design of the axial fatigue tester, there was no way to keep the specimen 34, 36 failure surfaces from colliding after separation. This prevented any meaningful conclusions from being drawn by studying the specimen 34, 36 failure surfaces. [00108] The axial test setup 40 used in this work displayed an increase in transmissibility during testing compared to previous iterations. The increased transmissibility reflected more stable control during testing, lower dampening due to friction, lower energy required for testing, and a higher stress testing capability for the axial test setup. Fig. 28 shows the fatigue life of axial specimens 34, 36 tested at the 35,000 psi stress level vs. the average transmissibility during testing. Fig. 28 shows that for both the small and large axial geometries there were no obvious trends in the data that indicate the fatigue life was affected by the transmissibility during testing. It was previously hypothesized that a larger transmissibility during testing reflected an improved specimen 34, 36 alignment and would produce a higher fatigue life. The large axial specimens 36 displayed less variation in the transmissibility during testing compared to the small axial specimens 34. The overall average transmissibility during testing for the small specimens 34 was 202.8 and was 151 .9 for the large axial specimens 36. The increase in overall average transmissibility for the small axial specimens 34 did not result in a longer fatigue life at 35,000 psi.

[00109] A 2² factorial experiment was used to test the effects of size and load type on the mean fatigue life at a common stress level. Table 4 shows the results of this experiment. It was found that the size and load factors had a statistically significant effect on the mean fatigue life of AI-7075 T6. The interaction effect between size and load type was found to not have a statistically significant effect on the mean fatigue life. However, the P value for the interaction effects was 0.058 which was close to the 0.05 alpha level. Fig. 29 shows a Pareto chart for the factorial experiment. Fig. 29 shows that the load type factor has a larger standardized effect on fatigue life than the specimen size.

[00110] Table 4: Two Factor ANOVA Results.

[00111] A student’s T-test was done in Minitab to compare the mean fatigue lives of the small and large Krouse specimens 12, 16. The null hypothesis stated that the mean fatigue lives were equal for both Krouse specimens 12, 16. The alternative hypothesis stated that the mean fatigue lives were not equal. It was found that there was a statistically significant difference in the mean fatigue lives for the Krouse specimens 12, 16 with a p-value of 0.017. Fig. 30 shows a boxplot of the fatigue lives for the small Krouse and large Krouse specimens 12, 16. An increase in the mean fatigue life can be seen for the large Krouse specimens 16. An F test was completed for the fatigue life of the Krouse specimens 12, 16 at 35,000 psi. The null hypothesis stated that the variance in fatigue life was equal for the Krouse specimens 12, 16. The alternative hypothesis stated that the variance in fatigue life was not equal for the Krouse specimens 12, 16. The results of the F test reject the null hypothesis with a p-value of 5.72E-5. An outlier can be seen in the Krouse 3 specimens which could have greatly influenced the variance.

[00112] A T-test was conducted to determine if the specimen size influenced the mean fatigue life for the axial specimens 34, 36. The null hypothesis stated that specimen size had no effect on the mean fatigue life for the axial specimens 34, 36. The alternative hypothesis stated that specimen size had a significant effect on the fatigue life. The T-test results showed a statistically significant difference between the mean fatigue life between the small and large axial specimens 36 with p-value of 0.003. Fig. 30 shows an increased fatigue life for the large axial specimens 36. Fig. 30 also shows that the larger specimen 36 for both loading types showed and increased fatigue life and increased variance compared to the respective smaller specimen 34. An F test was conducted for the axial specimens 34, 36. The null hypothesis stated that the variance in fatigue life was equal for both axial specimen 34, 36 geometries. The alternative hypothesis stated that the variance was different between the two axial specimen 34, 36 geometries. The results of this test reject the null hypothesis with a p-value of 0.0046 which indicates that the variances were different. The mean fatigue life of the large Krouse specimens 16 was 1 .67 times greater than the mean fatigue life of the small Krouse specimens 12. Similarly, the mean fatigue life of the large axial specimens 36 was 1 .42 times greater than the mean fatigue life of the small axial specimens 34.

[00113] Table 5 below gives the highly stressed volume for each specimen geometry that was found with finite element analysis. The highly stressed volume in Table 5 was used to predict a shift in the Weibull distribution scale parameter when two different size specimens were tested under the same alternating stress. After the small Krouse specimens 12 were fatigue tested, the fatigue data at 35,000 psi were fit to a Weibull distribution. The Weibull distribution scale parameter for the small Krouse 12, as well as the highly stressed volume, were used to predict the large specimens’ 16 Weibull distribution scale parameter. After fatigue testing the large Krouse specimen 16, the fatigue data at 35,000 psi were fit to a Weibull distribution. [00114] Fig. 31 shows the predicted scale parameter as well as the post-test fit scale parameter in relation to the fatigue data for the large Krouse specimens 16. Fig. 31 shows that the predicted scale parameter was much smaller than the posttest fit scale parameter. This was because the large Krouse specimens 16 had longer fatigue lives than the small Krouse specimens 12 to predict that the scale parameter will decrease as the highly stressed volume increases. Consequentially, the likelihood ratio test comparing the predicted parameters and the post-test fit parameters rejected the null hypothesis that the that post-test fit parameters did not provide a significant increase in the likelihood of the fatigue data. This means that the predicted parameters did not provide a good estimate for the fatigue data of the large Krouse specimens 16. The model predicts a decrease in fatigue life as highly stressed volume increases which is the opposite of what happened with the Krouse specimens 12, 16. It was identified that the small Krouse specimens 12 failed with an average major crack length of 0.11 inches where the large Krouse specimens 16 had an average major crack length of 0.39 inches. It is possible that the fatigue lives of the Krouse specimens 12, 16 were affected by the length of crack that causes failure in resonance-based bending tests. In traditional bending fatigue tests, the Krouse specimen 12, 16 tip is forced into fully reversed deflection until complete separation of the specimen. It is possible that the prediction used with this model would be more accurate if the specimens 12,16 were tested using traditional methods, which would remove any effect of crack length on fatigue life.

[00115] Table 5: Highly Stressed Volume for Each Specimen. Highly stressed volume was found using SolidWorks finite element analysis.

[00116] After the small axial specimens 34 were fatigue tested, the fatigue data was fit to a Weibull distribution. The Weibull scale parameter of the large axial specimens 36 given the small axial specimen 34 fatigue data at 35,000 psi was determined. Fig. 32 shows the predicted scale parameter plotted with the post-test fit scale parameter and the large axial 36 fatigue data. Like with the Krouse specimens 12, 16, the larger axial specimens 36 had a longer fatigue life than the smaller axial specimens 34. This again meant that the shift in scale parameter produced a shift in the opposite direction as what occurred in the fatigue test. Again, the likelihood ratio test comparing the predicted scale parameter to the post-test fit scale parameter rejected the null hypothesis that the post-test fit scale parameter did not provide a significantly better fit to the experimental data. This means that the predicted axial parameter did not fit the axial data found during testing.

[00117] The large axial scale parameter was also calculated and the small Krouse 12 fatigue data at 35,000 psi. Fig. 32 shows this predicted scale parameter. The prediction of the large axial parameter made using the small Krouse 12 data was done because this provided the largest ratio of highly stressed volumes between any of the specimen geometries. This also predicted the parameter for an axial specimen based on bending fatigue data which was done previously in the literature. The predicted scale parameter for the large axial specimens, made using the small Krouse 12 fatigue data, was not within the scatter of the axial fatigue data which indicated a poor prediction. This prediction was affected by the small Krouse 12 fatigue data which unexpectedly had shorter fatigue lives than the large Krouse specimens 16. This means that the predicted scale parameter could have affected by the accuracy of the model used as well as the small Krouse data used with the model.

[00118] The first objective was to analyze the relationship between resonancebased axial stress and stress cycles to failure for AI-7075 T6. Forty axial fatigue specimens 34, 36 were run to failure with fully reversed stress levels from 40,000 psi to 25,000 psi with the input motion provided by an electrodynamic shaker. The axial fatigue tests produced fatigue lives ranging from 12,600 cycles to 153,200 cycles. The second objective of this study was to analyze the relationship between resonance-based bending stress and stress cycles to failure for AI-7075 T6 with the input motion provided by an electrodynamic shaker 44. Forty bending fatigue specimens were run to failure with fully reversed stress levels from 40,000 psi to 25,000 psi. The bending fatigue tests resulted in fatigue lives ranging from 10,900 cycles to 2,006,500 cycles, fulfilling the requirements of objective two. Resonancebased methods for obtaining the modulus of the Krouse specimens 12, 16 were implemented to assess the applicability of a literature model to new geometries. The final objective of this study was to compare the results of the bending and axial fatigue tests using a 22 factorial experiment. Two axial geometries were chosen, and two bending geometries were chosen to analyze the effects of size and load type on the fatigue life of AI-7075 T6. Fourteen replicates of each geometry were run to failure at a constant stress level of 35,000 psi. The replicates were analyzed using Minitab factorial analysis to fulfill the requirements of objective three. Additionally, a statistical model was used to attempt to predict the effect of highly stressed volume on the fatigue life distribution of AI-7075 T6.

[00119] The results of the resonance-based modulus testing conclude that the small Krouse and large Krouse specimens 12, 16 produce similar estimations of modulus for AI-7075 T6. The ratio of moduli between the Krouse 12, 16 and beam specimens was found to be 0.84 using Euler-Bernoulli beam theory. This work found that impulse excitation provided a higher average modulus estimate than resonance sweeps.

[00120] Using DIG to create stress/thickness vs. control deflection plots provided an improved method for estimating the stress imposed on a specimen during fatigue testing compared to previous methods. Previous methods to quantify bending strain during resonance used strain gages which often fatigued or unbonded from the specimen surface rapidly. The DIO system used was highly adaptable and allowed for rapid generation of strain data after setup and calibration. Since the Aramis 2.3M system was not built for very high-speed applications, aliasing had to be used to capture the full deflection waveform of the Krouse specimens 12, 16.

[00121] The alternating bending fatigue tests were supposed to be terminated when the resonant frequency dropped by 20% or when the VR9500 controller was unable to control within its tolerance bounds of ± 6 db of output acceleration, whichever was first. During testing, the small Krouse specimens 12 failed due to the shaker 44 reaching its maximum input acceleration or when the output acceleration exceeded the tolerance bounds. The large Krouse 16 fatigue tests were terminated when the shaker 44 reached its maximum input acceleration, when the output acceleration exceeded the tolerance bounds, or when the resonant frequency drifted below the lower limit of the initial resonance sweep. It was found that the mean resonant frequency drop (%) for the small and large Krouse specimens 12, 16 tested at 35,000 psi was 3.1% and 11 .9%, respectively. Analysis of the Krouse specimens 12, 16 tested at 35,000 psi found that the average major crack length was 0.11 inches for the small Krouse specimens 12 and 0.39 for the Large Krouse specimens 16. A direct correlation between the major crack length in Krouse specimens 12, 16 and the % resonant frequency drop was identified in Fig. 22 and Fig. 23.

[00122] The axial fatigue test setup 40 used in this work provided a novel method for producing resonance-based axial fatigue data which successfully fulfilled the requirements of objective one. The air bearing 58 produced average transmissibility values of 202.8 and 151 .9 for the small and large axial specimens 34, 36, respectively. It will be understood that the control mass 54 and planar spring 52 can be resized to enable testing of stronger materials at different frequencies. Increasing the control mass 54 of the system 40 lowers the acceleration level required from the shaker 44 to stress the specimen 34, 36 if the transmissibility values do not change. The frequency of testing can then be tuned by changing the planar spring 52 stiffness.

[00123] The small axial specimens 34 failed at a statistically significant lower mean fatigue life at 35,000 psi. It is possible that the small axial specimens 34 were unequally affected by misalignment due to the specimen design. The small axial specimens 34 had a higher relative stiffness compared to the large axial specimens 36. For the same amount of misalignment there would be a higher bending stress imposed on the small axial specimens 34. It will be understood that adjusting alignment of the specimen 34, 36 after it has been mounted in the testing fixture 48 may improve testing results. This would allow for alignment of the specimen 34, 36 before each test to ensure that the percentage of bending stress during testing is kept minimal. For example, the resonance system can be run at a large amplitude and very low frequency while DIG images are taken so that the degree of misalignment can be quantified throughout the full range of displacement.

[00124] The resonance-based axial fatigue tester 40 may also include the ability to impose mean stress ratios on a specimen 34, 36. This would allow for rapid generation of Goodman diagram data as well as fully reversed fatigue data which is of great importance to the scientific community. The ability to impose mean stress would also allow for fracture surface analysis. The resonance-based axial fatigue tester 40 may also include the ability to test cylindrical specimens as this would allow the same specimen geometry to be tested in axial fatigue and rotating bending fatigue. Positive stress ratios would allow for thin specimens to be used during testing without the fear of buckling.

[00125] The results of the factorial experiment indicate that there was a presence of a size effect and a load effect in the fatigue life of AI-7075 T6. The statistical model used predicted that there would be a decrease in fatigue life as the amount of highly stressed volume in a part increased. The results of testing showed that there was a statistically significant increase in mean fatigue life at 35,000 psi when highly stressed volume increased in the bending and axial specimens 34, 36. The p-value for size effect on mean fatigue life at 35,000 psi was 0.017 for bending specimens 12, 14, 16 and 0.003 for axial specimens 34, 36. It is believed that misalignment during axial testing and differing failure patterns in the Krouse specimens 12, 16 could have led to premature fatigue failure. These factors also influenced the statistical model used to predict the effect of HSV on fatigue life. The statistical model used did not accurately predict the effect of HSV on fatigue life of AI-7075 T6. This model was based on the expectation that greater highly stressed volumes contain more microstructural defects, which serve as crack initiation locations and increase the probability of crack initiation.

[00126] It is recommended that this model be used to predict the effect of highly stressed volume on crack initiation instead of fracture. This may be done by using a high-speed digital image correlation system to capture bursts of images at different points throughout the fatigue test of a part. Acoustic emission could also be used to identify crack initiation through analysis of the acoustic emission trends at different points in the specimen’s fatigue life. This would allow for the researcher to identify when fatigue cracks initiate in resonance-based fatigue tests. This would also allow the researcher to identify differences in crack propagation rates and failure in the Krouse specimens 12, 16. The acoustic emission trends can also be analyzed at different points in the specimen’s fatigue life to explain the deflection trends in Fig. 19 and Fig. 20.

[00127] According to embodiments of the present invention, a new closed-loop testing approach is provided that allows for the identification of crack initiation and/or the onset of fatigue failure, and employs one of several methods of observation of the phenomena for criteria related to the cause of the crack's initiation, and thereby also characterize the fatigue death of the part in more detail than is currently possible. In that regard, current approaches generally rely on either postmortem fractography and correlation to estimate initial causes and locations of crack initiation or changes in modulus or other bulk properties, which require a crack to already be present in the specimen, excluding the possibility of immediate assessment and observation of crack growth in its early stages. Non-destructive Evaluation (NDE) methods such as what we are applying to our high-cycle, high speed system have been applied to low-cycle tests in another fatigue regime, but on substantially different equipment, different geometries, and with systems not requiring the speed our resonance-based, closed-loop arrangement allows.

[00128] According to one embodiment of the present invention, the test system may be similar to the test system 40 described above with respect to Figs. 8-9, and include a vibration source 44, a mass 54, a spring 52, and a specimen (some embodiments of the design use the specimen as the spring), dynamic instrumentation (20, 28, 32, 100) for feedback control, and a controller 42 and amplifier to drive the vibration source. The vibration source, such as an electrodynamic shaker, causes vibrations to load the specimen either by resonating the specimen itself or by resonating the mass and spring together thereby loading the specimen in cyclical fashion. A multiphysics non-destructive evaluation system is used to detect damage with high speed feedback and computation (using various combinations of lasers, piezoelectric transducers (pzts), acoustic emissions, and imagery analysis (DIG)) and microprocessors for high-speed computation in order to analyze damage detection in real-time during the high cycle test. Upon the detection of crack initiation, the system can use several means for immediate conclusion or suspension of the test, including physical arrestors to brake the system, elements to rapidly change resonant characteristics and thereby immediately stop the sample from being loaded (i.e . , zero resonance is being imparted to the test specimen), or active control of the vibration source to stop relatively quickly. Alternatively, imagery analysis or other external sensors can be triggered to monitor material characteristics while continuing the test at high speed to study the effects of crack growth in-situ. To this end, the test system provides for the close study of the phenomena and material characteristics that lead to fatigue failures in high cycle fatigue tests.

[00129] In one embodiment, the system can be used with different loading modes, and there may be both axial and bending forms of this system in load-controlled and strain-controlled arrangements. For example, this may include torsional and combined-loading modes as well as the introduction and control of mean stresses in addition to the cyclical stresses on the part.

[00130] Appendix A:

[00131] Appendix B:

[00132] While the invention has been illustrated by the description of various embodiments thereof, and while the embodiments have been described in considerable detail, it is not intended to restrict or in any way limit the scope of the appended claims to such detail. Thus, the various features discussed herein may be used alone or in any combination. Additional advantages and modifications will readily appear to those skilled in the art. The invention in its broader aspects is therefore not limited to the specific details and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the scope of the general inventive concept.

[00133] WHAT IS CLAIMED IS:

Claims

1 . An axial fatigue test system, comprising: a vibration source including a fixture; a control mass; a test specimen having a first end attached to the vibration source and a second end attached to the control mass; and an air bearing configured to receive the control mass, wherein a contactless engagement between the air bearing and the control mass maintains alignment of the control mass over the vibration source.

2. The axial fatigue test system of claim 1 , wherein the air bearing constrains movement of the control mass in a direction perpendicular to a movement axis defined by the vibration source.

3. The axial fatigue test system of claim 2, wherein movement along the movement axis is in a vertical direction.

4. The axial fatigue test system of claim 2, wherein the air bearing is coaxially arranged with the movement axis.

5. The axial fatigue test system of claim 2, wherein vibration source is an electrodynamic shaker.

6. The axial fatigue test system of claim 5, wherein the fixture is located on a shaker table of the electrodynamic shaker.

7. The axial fatigue test system of claim 1 , wherein the fixture includes a spring.

8. The axial fatigue test system of claim 7, wherein the spring is arranged between the fixture and the vibration source.

9. The axial fatigue test system of claim 1 , further comprising a first instrument to measure the acceleration of the vibration source.

10. The axial fatigue test system of claim 9, further comprising a second instrument to measure the acceleration of the control mass.

11 . The axial fatigue test system of claim 1 , further comprising an imaging device directed at the test specimen to take images of the specimen during operation of the axial fatigue test system.

12. The axial fatigue test system of claim 1 , wherein the air bearing is configured to be static during operation of the axial fatigue test system.

13. The axial fatigue test system of claim 1 , wherein the control mass includes a mounting cylinder to receive the second end of the test specimen and the fixture includes a mounting cylinder to receive the first end of the test specimen.

14. A method of conducting an axial fatigue test, comprising: providing an axial fatigue test system, comprising: a vibration source including a fixture configured to receive a first end of a test specimen and a control mass attached to a second end of the test specimen, the vibration source being configured to impart movement to the test specimen and the control mass along a movement axis; an air bearing configured to receive the control mass, wherein a contactless engagement between the air bearing and the control mass maintains alignment of the control mass over the vibration source; one or more dynamic instrumentation for monitoring characteristics of the test specimen; and a multiphysics non-destructive evaluation system operatively coupled to the vibration source and the one or more dynamic instrumentation to detect damage to the test specimen; operating the vibration source to cyclically move the test specimen at a resonance equal to a first resonance frequency; monitoring the test specimen for damage using the Multiphysics nondestructive evaluation system; and if damage to the test specimen is detected, varying the resonance of the test specimen to a second resonance frequency.

15. The method of claim 14, wherein the second resonance frequency is less than the first resonance frequency.

16. The method of claim 15, wherein the second resonance frequency is zero.

17. The method of claim 14, wherein the axial fatigue test system further comprises an imaging device directed at the test specimen, and wherein if damage to the test specimen is detected, the method further comprises: operating the imaging device to monitor material characteristics of the test specimen.

18. The method of claim 14, wherein the one or more dynamic instrumentation comprises one or more of the following: an accelerometer; an imaging device; a laser displacement sensor; and an extensometer.