The work was supported by projects: "Research Centre of University of &#381;ilina - 2nd phase", ITMS 313011D011, Scientific Grant Agency of the Ministry of Education, Science and Sports of the Slovak Republic and Slovak Academy of Sciences, grants No.: 1/0045/17, 1/0951/17 and 1/0123/15 and Slovak Research and Development Agency, grant No. APVV-16-0276.

Note: Each specimen&#39;s geometry has to be selected and calculated according to the mechanical and physical properties of the tested material, so that it has an identical resonance frequency as the ultrasonic testing system.

1. Determination of the Fatigue Test Specimen Dimensions
Note: The standard &#34;hourglass&#34; tension-compression specimen geometry, with defined main dimensions, is shown in Figure 1. Dimensions d, D, and r are user defined (independent), while l and L dimensions have to be calculated, according to the conditions of the correct resonance frequency (dependent). The gauge length l results only from the geometry ratio between d, r, and D, and can be calculated easily or obtained from a component model; thus, it will not be an object of further discussion.
<ol>
	<li>Determination of Independent Dimensions 
	Note: The main dimensions of the specimen (d, D, r) are chosen according to the material parameters and the test conditions.
	<ol>
		<li>Determine the gauge diameter d according to the required volume of material for testing. In the case of a homogenous microstructure with no internal defects, a smaller gauge diameter is preferred. In the case of a material with significant internal defects (such as voids and shrinkages in cast materials), a bigger gauge diameter is necessary. The gauge diameter d is usually from 3&#160;mm to 5 mm.</li>
		<li>Determine the head diameter D according to available experimental material size. The used head diameter D is usually from 10 mm to 15 mm. 
		Note: The larger the D is, the shorter the head length (L) will be.</li>
	</ol>
	</li>
	<li>Determine the gauge radius r according to the required mechanical stress distribution in the specimen&#39;s gauge length. The larger the gauge diameter r is, the smoother is the mechanical stress distribution. A commonly used gauge radius is r = 20 mm or r = 32 mm. 
	Note: The larger the r is, the longer the specimen will be.</li>
	<li>Determination of Dependent Dimensions
	<ol>
		<li>Determine the wave number K according to the following formula9,18: 
		<img alt="Equation 1" src="/files/ftp_upload/57007/57007eq1.jpg" /> 
		Note: Here the fr is the resonance frequency of the ultrasonic system (Hz), &#961; is the volume density (kg m-3), and Ed is the dynamic modulus of elasticity (kg m-3).</li>
		<li>Determine the hyperbolic approximation of the gauge radius, according to the following formula9,19: 
		<img alt="Equation 2" src="/files/ftp_upload/57007/57007eq2.jpg" /> 
		Note: Here l is the gauge length (m), D is the head diameter (m), and d is the gauge diameter (m) (Figure 1).</li>
		<li>Determine the effective eccentricity according to following formula9,18: 
		<img alt="Equation 3" src="/files/ftp_upload/57007/57007eq3.jpg" /> 
		Note: Here A is the hyperbolic approximation (m-1) determined by equation (2), and K is the wave number (-) determined according to expression (1).</li>
		<li>Determine the length of head (L) according to the following equation9,18: 
		<img alt="Equation 4" src="/files/ftp_upload/57007/57007eq4.jpg" /> 
		Note: Here K is the wave number (-) determined according to expression (1) in point 1.2.1, &#946; is the effective eccentricity (m-1) determined by equation (3), and l is the gauge length (m) (Figure 1).</li>
	</ol>
	</li>
</ol>
2. Calculation of the Mechanical Stress in the Gauge Length of the Specimen
<ol>
	<li>Determine the norming geometrical factor <img alt="Equation 5" src="/files/ftp_upload/57007/57007eq5.jpg" /> according to the following equation9,18: 
	<img alt="Equation 6" src="/files/ftp_upload/57007/57007eq6.jpg" /></li>
	<li>Determine the deformation amplitude &#603; according to the following equation9,18: 
	<img alt="Equation 7" src="/files/ftp_upload/57007/57007eq7.jpg" /> 
	Note: Here&#160;<img alt="Equation 5" src="/files/ftp_upload/57007/57007eq5.jpg" /> is the geometrical factor (-) and u is the required displacement amplitude of the free end of the specimen (m).</li>
	<li>Determine the mechanical stress amplitude &#963;a according to the following equation9,18: 
	<img alt="Equation 8" src="/files/ftp_upload/57007/57007eq8.jpg" /> 
	Note: Here &#603; is the deformation amplitude (-) determined according to expression (5), and Ed is the dynamic modulus of elasticity (kg m-3). If the calculated mechanical stress is too low, it is necessary to increase the displacement amplitude u (m), and vice versa.</li>
</ol>
3. Manufacturing of the Specimen with Machining Operations
<ol>
	<li>Due to various small deviations of the machined specimens from an ideal shape, manufacture specimens with longer heads, usually L + 0.5 mm.</li>
</ol>
4. Harmonizing of the Resonance Frequency of the Specimen with the Ultrasonic System
Note: Harmonizing is the process of compensating various small deviations of the real specimen from the ideal, calculated shape, to obtain the correct resonance frequency, which is in harmony with the ultrasonic acoustic sonotrode.
<ol>
	<li>Choose the proper type of acoustic sonotrode, according to the required displacement range, which is able to provide proper mechanical stress in the specimen. 
	Note: Each type of sonotrode is designed and calibrated for a different displacement range, thus the proper sonotrode is chosen according to the required displacement amplitude calculated according to section 2.</li>
	<li>Mount the sonotrode on the piezo-electric converter.
	<ol>
		<li>Screw the connection screw inside the central hole on the sonotrode until it reaches the bottom.</li>
		<li>Spread acoustic gel on the face of the sonotrode. 
		Note: A small amount of gel is used, just enough to fill the irregularity of the surfaces, which improves the transfer of the mechanical wave between piezo-electric converter and the sonotrode.</li>
		<li>Screw the sonotrode into the piezo-electric converter.</li>
	</ol>
	</li>
	<li>Run the ultrasonic system with a piezo electric converter with mounted sonotrode to measure the resonance frequency of the particular system at actual temperature.
	<ol>
		<li>Run the ultrasonic testing software (e.g., Win20k).</li>
		<li>Choose the type of the used sonotrode in the drop-down menu in the &#34;Model&#34; box.</li>
		<li>Enter the lowest possible displacement amplitude for the particular sonotrode into the &#34;Amplitude&#34; box.</li>
		<li>Click the &#34;Start&#34; button.</li>
		<li>Read the actual resonance frequency of the system in the &#34;Frequency&#34; box.</li>
		<li>Click the &#34;Stop&#34; button.</li>
	</ol>
	</li>
	<li>Mount the specimen at the end of the sonotrode.
	<ol>
		<li>Screw the connection screw into the central hole of the specimen until it reaches the bottom.</li>
		<li>Screw the specimen to the sonotrode.</li>
	</ol>
	</li>
	<li>Run the ultrasonic system with a piezo electric converter with mounted sonotrode and specimen to measure the resonance frequency of the particular system at actual temperature.
	<ol>
		<li>Run the ultrasonic testing software.</li>
		<li>Choose the type of sonotrode used in the drop-down menu in the &#34;Model&#34; box.</li>
		<li>Enter the lowest possible displacement amplitude for the particular sonotrode into the &#34;Amplitude&#34; box.</li>
		<li>Click the &#34;Start&#34; button.</li>
		<li>Read the actual resonance frequency of the system in the &#34;Frequency&#34; box.</li>
		<li>Click the &#34;Stop&#34; button.</li>
	</ol>
	</li>
	<li>When the resonance frequency of the system with mounted specimen is lower than that without the specimen, reduce the mass of the specimen by cutting off the faces of the specimen&#39;s head. 
	Note: If the resonance frequency with a mounted specimen is higher, it would be necessary to reduce the gauge diameter d, which would change the conditions of the test. This is the reason 0.5 mm is added to length of the heads in the manufacturing process.
	<ol>
		<li>Dismount the specimen from the sonotrode.</li>
		<li>Mount the specimen into a lathe and turn down 0.1 mm of the face of the first head.</li>
		<li>Mount the specimen into a lathe and turn down 0.1 mm of the face of the second head.</li>
		<li>Repeat step 4.6 until the resonance frequency is within tolerance of &#177; 10 Hz.</li>
	</ol>
	</li>
</ol>
5. Final Mounting of the Specimen to the Sonotrode before the Fatigue Test
<ol>
	<li>Apply acoustic gel on the faces to create connections between the sonotrode and the specimen.
	<ol>
		<li>Screw the connection screw into the central hole of the specimen until it reaches the bottom.</li>
		<li>Spread the acoustic gel on the face of the specimen. 
		Note: Just a small amount of acoustic gel is used to fill in the irregularities on the surface to improve the acoustic wave transfer from the sonotrode to the specimen.</li>
		<li>Screw the specimen to the sonotrode.</li>
	</ol>
	</li>
</ol>
6. Run the Cooling System for Specimen
<ol>
	<li>If air cooling is used, focus the air stream directly on the middle of the gauge length of the specimen, and wait for about 20 s, so the flow of the air stream saturates the specimen.</li>
	<li>If water cooling is used, focus the water nozzles at the top head of the specimen, and adjust the stream intensity so the water flows smoothly along the gauge length, to avoid cavitation. 
	Note: Submerging the specimen into water or oil is possible as well, however this can be used only for short time tests due to the significant cavitation effect, which accelerates the fatigue crack initiation process.</li>
</ol>
7. Run the Cooling System of the Piezo Electric Converter
<ol>
	<li>Open the valve of the air stream and adjust the pressure in the interval between 0.5 and 1 bar.</li>
</ol>
8. Run the Test at Required Displacement Amplitude
<ol>
	<li>Run the ultrasonic testing software.</li>
	<li>Choose the type of the used sonotrode in the drop-down menu in the &#34;Model&#34; box.</li>
	<li>Enter the requested displacement amplitude for the particular sonotrode into the &#34;Amplitude&#34; box.</li>
	<li>Click the &#34;Start&#34; button.</li>
</ol>
9. Fatigue Crack Initiation and Propagation
<ol>
	<li>Observe that after the fatigue crack initiation and propagation through a part of the cross section, the system is shifted out of the resonance frequency and the test is naturally terminated.</li>
	<li>If the test does not end with a fracture, after reaching requested number of loading cycles, (the test is a run-out) terminate using the &#34;Stop&#34; button in the ultrasonic testing software.</li>
</ol>
10. Dismount the Specimen from the Sonotrode
<ol>
	<li>Screw off the specimen from the ultrasonic sonotrode.</li>
</ol>
11. Static Loading Force Fracturing
<ol>
	<li>Use static loading force to fracture the rest of the cross section with use of a static loading machine. 
	Note: The vector and type of the loading force for the static fracture should correspond with the type of the fatigue loading so that the fracture surface has consistent character.</li>
</ol>

<ol>
	<li>Moore, H. F., Kommers, J. B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> The fatigue of metals. , 321 (1927).</li><li>Nicholas, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> High Cycle Fatigue: A Mechanics of Materials Perspective. , (2006).</li><li>Schijve, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Fatigue of Structures and Materials. , (2008).</li><li>Murakami, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions. , (2002).</li><li>Trsko, L., Bokuvka, O., Novy, F., Guagliano, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effect+of+severe+shot+peening+on+ultra-high-cycle+fatigue+of+a+low-alloy+steel.">Effect of severe shot peening on ultra-high-cycle fatigue of a low-alloy steel.</a> Mater. Design. 57, 103-113 (2014).</li><li>Stanzl, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Fracture+mechanisms+and+fracture+mechanics+at+ultrasonic+frequencies.">Fracture mechanisms and fracture mechanics at ultrasonic frequencies.</a> Fatigue. Fract. Eng. M. 22 (7), 567-579 (1999).</li><li>Bathias, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=There+is+no+infinite+fatigue+life+in+metallic+materials.">There is no infinite fatigue life in metallic materials.</a> Fatigue. Fract. Eng. M. 22 (7), 559-565 (1999).</li><li>Ritchie, R. O., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=High-cycle+fatigue+of+Ti-6Al-4V.">High-cycle fatigue of Ti-6Al-4V.</a> Fatigue. Fract. Eng. M. 22 (7), 621-631 (1999).</li><li>Bathias, C., Paris, P. C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Gigacycle Fatigue in Mechanical Practice. , (2004).</li><li>Bokuvka, O., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Ultrasonic Fatigue of Materials at Low and High Frequency Loading. , (2015).</li><li>Almaraz, G. M. D., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ultrasonic+Fatigue+Testing+on+the+Polymeric+Material+PMMA,+Used+in+Odontology+Applications.">Ultrasonic Fatigue Testing on the Polymeric Material PMMA, Used in Odontology Applications.</a> Procedia Structural Integrity. 3, 562-570 (2017).</li><li>Flore, D., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Investigation+of+the+high+and+very+high+cycle+fatigue+behaviour+of+continuous+fibre+reinforced+plastics+by+conventional+and+ultrasonic+fatigue+testing.">Investigation of the high and very high cycle fatigue behaviour of continuous fibre reinforced plastics by conventional and ultrasonic fatigue testing.</a> Compos. Sci. Technol. 141, 130-136 (2017).</li><li>Tr&#353;ko, L., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Influence+of+Severe+Shot+Peening+on+the+Surface+State+and+Ultra-High-Cycle+Fatigue+Behavior+of+an+AW+7075+Aluminum+Alloy.">Influence of Severe Shot Peening on the Surface State and Ultra-High-Cycle Fatigue Behavior of an AW 7075 Aluminum Alloy.</a> J. Mater. Eng. Perform. 26 (6), 2784-2797 (2017).</li><li>Mayer, H., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Cyclic+torsion+very+high+cycle+fatigue+of+VDSiCr+spring+steel+at+different+load+ratios.">Cyclic torsion very high cycle fatigue of VDSiCr spring steel at different load ratios.</a> Int. J. Fatigue. 70, 322-327 (2015).</li><li>Bathias, C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Piezoelectric+fatigue+testing+machines+and+devices.">Piezoelectric fatigue testing machines and devices.</a> Int. J. Fatigue. 28 (11), 1438-1445 (2006).</li><li>Mayer, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ultrasonic+torsion+and+tension-compression+fatigue+testing:+Measuring+principles+and+investigations+on+2024-T351+aluminium+alloy.">Ultrasonic torsion and tension-compression fatigue testing: Measuring principles and investigations on 2024-T351 aluminium alloy.</a> Int. J. Fatigue. 28 (11), 1446-1455 (2006).</li><li>Brugger, C., Palin-Luc, T., Osmond, P., Blanc, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+new+ultrasonic+fatigue+testing+device+for+biaxial+bending+in+the+gigacycle+regime.">A new ultrasonic fatigue testing device for biaxial bending in the gigacycle regime.</a> Int. J. Fatigue. 100, Part 2, 619-626 (2017).</li><li>Wagner, D., Cavalieri, F. J., Bathias, C., Ranc, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ultrasonic+fatigue+tests+at+high+temperature+on+anaustenitic+steel.">Ultrasonic fatigue tests at high temperature on anaustenitic steel.</a> J. Propul. Power. 1 (1), 29-35 (2012).</li><li>Kohout, J., Vechet, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+new+function+for+fatigue+curves+characterization+and+its+multiple+merits.">A new function for fatigue curves characterization and its multiple merits.</a> Int. J. Fatigue. 23 (2), 175-183 (2001).</li></ol>

We have nothing to disclose.

Ultrasonic fatigue testing is one of the few methods which allows testing of the structural materials in the ultra-high cycle region. However, the specimen shape and size are very limited with respect to the resonance frequency. For instance, testing of thin sheets in the mode of axial loading is generally not possible. In addition, testing of large specimens is usually not possible, because the testing machines do not provide such power and it would require the design of a special ultrasonic system. 
<p class="jove_...

Fatigue damage of structural materials is strongly connected with industrialization and mainly with use of steam engine and steam locomotives for railway transport, where a lot of metal components, mainly iron based, have been used and had to withstand various types of cyclic loading. One of the earliest tests was done by Albert (Germany 1829)1 on welded chains for mine hoists. The loading frequency was 10 bends per minute, and the maximal tests recorded reached 100,000 loading cycles1. Another important work was carried out by William Fairbairn in 1864. Tests were performed on wrought-iron girders with use of a static load, which was lifted by a lever and then dropped causing vibrations. The girder was loaded with gradually increasing loading stress amplitude. After reaching several hundred thousand cycles on various loading stress amplitudes, in the end the girder failed after just about five thousand loading cycles at a loading amplitude of two fifths of the ultimate tensile strength. The first comprehensive and systematic study of the influence of repeated stress on structural materials was done by August W&#246;hler in 1860-18701. For these tests, he was using torsion, bending, and axial loading modes. W&#246;hler designed many unique fatigue testing machines, but their disadvantage was low operation speeds, for example the fastest rotating bending machine operated at 72 rpm (1.2 Hz), thus completion of the experimental program took 12 years1. After performing these tests, it was considered that after reaching a loading amplitude at which the material withstands 107 cycles, the fatigue degradation is negligible and the material can withstand an infinite number of loading cycles. This loading amplitude was named the &#34;fatigue limit&#34; and became the main parameter in industrial design for many years2,3.
Further development of new industrial machines, which required higher efficiency and cost savings, had to provide the possibility of higher loading, higher operation speeds, higher durations, and high reliability with low maintenance requirements. For example, components of the high-speed train Shinkanzen, after 10 years of operation, have to withstand approximately 109 cycles and failure of a main component can have fatal consequences4. Furthermore, components of jet engines often operate at 12,000 rpm, and components of turbo blowers often exceed 17,000 rpm. Those high operation speeds increased requirements for fatigue life testing in the so-called ultra-high cycle region, and to assess if the fatigue strength of a material could be really considered constant for more than 10 million cycles. After the first tests performed by exceeding this endurance, it was obvious that fatigue failures can occur even at applied stress amplitudes lower than the fatigue limit, after a number of cycles much more than 107, and that the damage and failure mechanism could be different from the usual ones5.
Creating a fatigue test program aimed at investigating the ultra-high cycle region required the development of new testing devices to strongly increase the loading frequency. A symposium focused on this topic was held in Paris in June 1998, where experimental results were presented which were obtained by Stanzl-Tschegg6 and Bathias7 at 20 kHz loading frequencies, by Ritchie8 with the use of 1 kHz closed loop servo-hydraulic testing machine, and by Davidson8 with a 1.5 kHz magneto-strictive testing machine4. From that time, many solutions were proposed, but still the most commonly used machine for this kind of test is based on the concept of Manson from 1950 and uses frequencies close to 20 kHz9. These machines exhibit a good balance between strain rate, the determination accuracy of the number of cycles, and the time of the fatigue test (1010 cycles are achieved in approximately 6 days). Other devices were able to provide even higher loading frequencies, like the one used by Girald in 1959 - 92 kHz and Kikukawa in 1965 - 199 kHz; however, these are rarely used because they create extremely high deformation rates and, since the test lasts for only few minutes, a remarkable error in the cycle counting is expected. Another important factor limiting the loading frequency of resonance devices for fatigue testing is the size of the specimen, which is in direct relation with the resonance frequency. The larger the requested loading frequency, the smaller the specimen. This is the reason why frequencies above 40 kHz are rarely used10.
Since the displacement amplitude is usually limited within the interval between 3 and 80 &#181;m, ultrasonic fatigue testing can be successfully applied on most metallic materials, though techniques for the testing of polymeric materials such as PMMA11 and composites12 were also developed. Generally, ultrasonic fatigue testing is possible to perform in modes of axial loading: tensile - compression symmetrical cycle13,14, tension - tension cycle15, three-point bending15, and there are also a few studies with special modifications of the system for torsion testing15,16 and biaxial bending17. It is not possible to use arbitrary specimens, because for this method, the geometry is strictly related to achieving the resonance frequency of 20 kHz. For the axial loading, several types of specimens have been commonly used, usually with an hour-glass shape with a gauge length diameter from 3 to 5 mm. For the three-point bending, thin sheets are commonly used, and for other methods special types of specimens are designed, according to the method type and testing conditions. The method was designed for evaluation of fatigue life in the high and ultra-high cycle region, and this means that at 20 kHz loading, a million cycles is obtained in 50 s; therefore, this is usually considered the bottom limit of loading cycles which can be investigated with reasonable accuracy, with respect to the number of cycle determination. Each specimen has to be harmonized with the ultrasonic horn by changing the specimen&#39;s mass to provide the right resonance frequency of the system: ultrasonic horn with specimen.

<table><tbody><tr><td>Ultrasonic fatigue testing device</td><td>Lasur</td><td>-</td><td>20 kHz, used for fatigue tests</td></tr><tr><td>Nyogel 783</td><td>Nye Lubricants</td><td>-</td><td>Used as acoustic gel for connection of the parts of the ultrasonic system</td></tr><tr><td>Win 20k software</td><td>Lasur</td><td>-</td><td>Software for operation of the Lasur fatigue testing machine</td></tr></tbody></table>

ultrasonic fatigue testing in the tension-compression mode

Ultrasonic fatigue testing is one of a few methods which allow investigating fatigue properties in the ultra-high cycle region. The method is based on exposing the specimen to longitudinal vibrations on its resonance frequency close to 20 kHz. With use of this method, it is possible to significantly decrease the time required for the test, when compared to conventional testing devices usually working at frequencies under 200 Hz. It is also used to simulate loading of material during operation in high speed conditions, such as those experienced by components of jet engines or car turbo pumps. It is necessary to operate only in the high and ultra-high cycle region, due to the possibility of extremely high deformation rates, which can have a significant influence on the test results. Specimen shape and dimensions have to be carefully selected and calculated to fulfill the resonance condition of the ultrasonic system; thus, it is not possible to test the full components or specimens of arbitrary shape. Before each test, it is necessary to harmonize the specimen with the frequency of the ultrasonic system to compensate for deviations of the real shape from the ideal one. It is not possible to run a test until a total fracture of the specimen, since the test is automatically terminated after initiation and propagation of the crack to a certain length, when the stiffness of the system changes enough to shift the system out of the resonance frequency. This manuscript describes the process of evaluation of materials' fatigue properties at high-frequency ultrasonic fatigue loading with use of mechanical resonance at a frequency close to 20 kHz. The protocol includes a detailed description of all steps required for a correct test, including specimen design, stress calculation, harmonizing with the resonance frequency, performing the test, and final static fracture.

Fatigue test results include loading stress, number of loading cycles, and the test termination character (fracture or run-out) can be seen in Table 1, where results of fatigue life of the 50CrMo4 quenched and tempered steel are provided. The most common interpretation of the fatigue life test results is the so-called S - N plot (S - stress, N - number of cycles), also known as the W&#246;hler&#39;s plot. The dependence of fatigue life on the applied loading stress is plo...

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Ultrasonic Fatigue Testing in the Tension-Compression Mode

A protocol for ultrasonic fatigue testing in the high and ultra-high cycle region in axial tension-compression loading mode.

Ultrasonic fatigue testing is one of a few methods which allow investigating fatigue properties in the ultra-high cycle region. The method is based on ...

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10.6K Views.  University of Žilina. A protocol for ultrasonic fatigue testing in the high and ultra-high cycle region in axial tension-compression loading mode.

Video: Ultrasonic Fatigue Testing in the Tension-Compression Mode

A Testing Platform for Durability Studies of Polymers and Fiber-reinforced Polymer Composites under Concurrent Hygrothermo-mechanical Stimuli

The durability of polymers and fiber-reinforced polymer composites under service condition is a critical aspect to be addressed for their robust designs and condition-based maintenance. These materials are adopted in a wide range of engineering applications, from aircraft and ship structures, to bridges, wind turbine blades, biomaterials and biomedical implants. Polymers are viscoelastic materials, and their response may be highly nonlinear and thus make it challenging to predict and monitor their in-service performance. The laboratory-scale testing platform presented herein assists the investigation of the influence of concurrent mechanical loadings and environmental conditions on these materials. The platform was designed to be low-cost and user-friendly. Its chemically resistant materials make the platform adaptable to studies of chemical degradation due to in-service exposure to fluids. An example of experiment was conducted at RT on closed-cell polyurethane foam samples loaded with a weight corresponding to ~50% of their ultimate static and dry load. Results show that the testing apparatus is appropriate for these studies. Results also highlight the larger vulnerability of the polymer under concurrent loading, based on the higher mid-point displacements and lower residual failure loads. Recommendations are made for additional improvements to the testing apparatus.

The durability of polymers and fiber-reinforced polymer composites in service is a critical aspect for their designs and condition-based maintenance. We present a novel low-cost laboratory testing platform for the investigation of the influence of concurrent mechanical and environmental loadings, and may help design more efficient yet safer composite structures.

The durability of polymers and fiber-reinforced polymer composites under service condition is a critical aspect to be addressed for their robust designs ...

Experiments on Ultrasonic Lubrication Using a Piezoelectrically-assisted Tribometer and Optical Profilometer

Friction and wear are detrimental to engineered systems. Ultrasonic lubrication is achieved when the interface between two sliding surfaces is vibrated at a frequency above the acoustic range (20 kHz). As a solid-state technology, ultrasonic lubrication can be used where conventional lubricants are unfeasible or undesirable. Further, ultrasonic lubrication allows for electrical modulation of the effective friction coefficient between two sliding surfaces. This property enables adaptive systems that modify their frictional state and associated dynamic response as the operating conditions change. Surface wear can also be reduced through ultrasonic lubrication. We developed a protocol to investigate the dependence of friction force reduction and wear reduction on the linear sliding velocity between ultrasonically lubricated surfaces. A pin-on-disc tribometer was built which differs from commercial units in that a piezoelectric stack is used to vibrate the pin at 22 kHz normal to the rotating disc surface. Friction and wear metrics including effective friction force, volume loss, and surface roughness are measured without and with ultrasonic vibrations at a constant pressure of 1 to 4 MPa and three different sliding velocities: 20.3, 40.6, and 87 mm/sec. An optical profilometer is utilized to characterize the wear surfaces. The effective friction force is reduced by 62% at 20.3 mm/sec. Consistently with existing theories for ultrasonic lubrication, the percent reduction in friction force diminishes with increasing speed, down to 29% friction force reduction at 87 mm/sec. Wear reduction remains essentially constant (49%) at the three speeds considered.

We present a protocol for using a piezoelectrically-assisted tribometer and optical profilometer to investigate the dependence of ultrasonic wear and friction reduction on linear velocity, contact pressure, and surface properties.

Friction and wear are detrimental to engineered systems. Ultrasonic lubrication is achieved when the interface between two sliding surfaces is vibrated at ...

Ultrasonic Welding of Thermoplastic Composite Coupons for Mechanical Characterization of Welded Joints through Single Lap Shear Testing

This paper presents a novel straightforward method for ultrasonic welding of thermoplastic-composite coupons in optimum processing conditions. The ultrasonic welding process described in this paper is based on three main pillars. Firstly, flat energy directors are used for preferential heat generation at the joining interface during the welding process. A flat energy director is a neat thermoplastic resin film that is placed between the parts to be joined prior to the welding process and heats up preferentially owing to its lower compressive stiffness relative to the composite substrates. Consequently, flat energy directors provide a simple solution that does not require molding of resin protrusions on the surfaces of the composite substrates, as opposed to ultrasonic welding of unreinforced plastics. Secondly, the process data provided by the ultrasonic welder is used to rapidly define the optimum welding parameters for any thermoplastic composite material combination. Thirdly, displacement control is used in the welding process to ensure consistent quality of the welded joints. According to this method, thermoplastic-composite flat coupons are individually welded in a single lap configuration. Mechanical testing of the welded coupons allows determining the apparent lap shear strength of the joints, which is one of the properties most commonly used to quantify the strength of thermoplastic composite welded joints.

A straightforward procedure for ultrasonic welding of thermoplastic composite coupons for basic mechanical testing is described. Key characteristics of this ultrasonic welding process are the use of flat energy directors for simplified process preparation and the use of process data for the fast definition of optimum processing conditions.

This paper presents a novel straightforward method for ultrasonic welding of thermoplastic-composite coupons in optimum processing conditions. The ...

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

A novel measurement approach is used to reveal the cumulative deformation field at a sub-grain level and to study the influence of microstructure on the growth of microstructurally small fatigue cracks. The proposed strain field analysis methodology is based on the use of a unique pattering technique with a characteristic speckle size of approximately 10 &#181;m. The developed methodology is applied to study the small fatigue crack behavior in body centered cubic (bcc) Fe-Cr ferritic stainless steel with a relatively large grain size allowing a high spatial measurement accuracy at the sub-grain level. This methodology allows the measurement of small fatigue crack growth retardation events and associated intermittent shear strain localization zones ahead of the crack tip. In addition, this can be correlated with the grain orientation and size. Thus, the developed methodology can provide a deeper fundamental understanding of the small fatigue crack growth behavior, required for the development of robust theoretical models for the small fatigue crack&#160;propagation in polycrystalline materials.

Microstructurally small fatigue crack growth behavior is investigated using a novel methodological approach combining crack growth rate measurement and strain-field analysis to reveal the cumulative deformation field at sub-grain level.

A novel measurement approach is used to reveal the cumulative deformation field at a sub-grain level and to study the influence of microstructure on the ...

Intermediate Strain Rate Material Characterization with Digital Image Correlation

The mechanical response of a material under dynamic load is typically different than its behavior under static conditions; therefore, the common quasistatic equipment and procedures used for material characterization are not applicable for materials under dynamic loads. The dynamic response of a material depends on its deformation rate and is broadly categorized into high (i.e., greater than 200/s), intermediate (i.e., 10&#8722;200/s) and low strain rate regimes (i.e., below 10/s). Each of these regimes calls for specific facilities and testing protocols to ensure the reliability of the acquired data. Due to the limited access to high-speed servo-hydraulic facilities and validated testing protocols, there is a noticeable gap in the results at the intermediate strain rate. The current manuscript presents a validated protocol for the characterization of different materials at these intermediate strain rates. Strain gauge instrumentation and digital image correlation protocols are also included as complimentary modules to extract the utmost level of detailed data from every single test. Examples of raw data, obtained from a variety of materials and test setups (e.g., tensile and shear) is presented and the analysis procedure used to process the output data is described. Finally, the challenges of dynamic characterization using the current protocol, along with the limitations of the facility and methods of overcoming potential problems are discussed.

Here we present a methodology for the dynamic characterization of tensile specimens at intermediate strain rates using a high-speed servo-hydraulic load frame. Procedures for strain gauge instrumentation and analysis, as well as for digital image correlation strain measurements on the specimens, are also defined.

The mechanical response of a material under dynamic load is typically different than its behavior under static conditions; therefore, the common ...

Crack Monitoring in Resonance Fatigue Testing of Welded Specimens Using Digital Image Correlation

A procedure using digital image correlation (DIC) to detect cracks on welded specimens during fatigue tests on resonance testing machines is presented. It is intended as a practical and reproducible procedure to identify macroscopic cracks at an early stage and monitor crack propagation during fatigue tests. It consists of strain field measurements at the weld using DIC. Images are taken at fixed load cycle intervals. Cracks become visible in the computed strain field as elevated strains. This way, the whole width of a small-scale specimen can be monitored to detect where and when a crack initiates. Subsequently, it is possible to monitor the development of the crack length. Because the resulting images are saved, the results are verifiable and comparable. The procedure is limited to cracks initiating at the surface and is intended for fatigue tests under laboratory conditions. By visualizing the crack, the presented procedure allows direct observation of macrocracks from their formation until rupture of the specimen.

Digital image correlation is used in fatigue tests on a resonance testing machine to detect macroscopic cracks and monitor crack propagation in welded specimens. Cracks on the specimen surface become visible as increased strains.

A procedure using digital image correlation (DIC) to detect cracks on welded specimens during fatigue tests on resonance testing machines is presented. It ...

Biomechanical Characterization of Human Soft Tissues Using Indentation and Tensile Testing

Regenerative medicine aims to engineer materials to replace or restore damaged or diseased organs. The mechanical properties of such materials should mimic the human tissues they are aiming to replace; to provide the required anatomical shape, the materials must be able to sustain the mechanical forces they will experience when implanted at the defect site. Although the mechanical properties of tissue-engineered scaffolds are of great importance, many human tissues that undergo restoration with engineered materials have not been fully biomechanically characterized. Several compressive and tensile protocols are reported for evaluating materials, but with large variability it is difficult to compare results between studies. Further complicating the studies is the often destructive nature of mechanical testing. Whilst an understanding of tissue failure is important, it is also important to have knowledge of the elastic and viscoelastic properties under more physiological loading conditions.
This report aims to provide a minimally destructive protocol to evaluate the compressive and tensile properties of human soft tissues. As examples of this technique, the tensile testing of skin and the compressive testing of cartilage are described. These protocols can also be directly applied to synthetic materials to ensure that the mechanical properties are similar to the native tissue. Protocols to assess the mechanical properties of human native tissue will allow a benchmark by which to create suitable tissue-engineered substitutes.

Tissue biomechanics is important for maintaining cell shape and function and for determining phenotype. This report demonstrates non-destructive mechanical protocols for characterizing elastic and viscoelastic properties of human soft tissues, which can be directly applied to tissue-engineered substrates to allow a close matching of engineered materials to native tissue.

Regenerative medicine aims to engineer materials to replace or restore damaged or diseased organs. The mechanical properties of such materials should ...

Bioengineering

Biomechanical Testing of Murine Tendons

Tendon disorders are common, affect people of all ages, and are often debilitating. Standard treatments, such as anti-inflammatory drugs, rehabilitation, and surgical repair, often fail. In order to define tendon function and demonstrate efficacy of new treatments, the mechanical properties of tendons from animal models must be accurately determined. Murine animal models are now widely used to study tendon disorders and evaluate novel treatments for tendinopathies; however, determining the mechanical properties of mouse tendons has been challenging. In this study, a new system was developed for tendon mechanical testing that includes 3D-printed fixtures that exactly match the anatomies of the humerus and calcaneus to mechanically test supraspinatus tendons and Achilles tendons, respectively. These fixtures were developed using 3D reconstructions of native bone anatomy, solid modeling, and additive manufacturing. The new approach eliminated artifactual gripping failures (e.g., failure at the growth plate failure rather than in the tendon), decreased overall testing time, and increased reproducibility. Furthermore, this new method is readily adaptable for testing other murine tendons and tendons from other animals.

The protocol describes efficient and reproducible tensile biomechanical testing methods for murine tendons through the use of custom-fit 3D printed fixtures.

Tendon disorders are common, affect people of all ages, and are often debilitating. Standard treatments, such as anti-inflammatory drugs, rehabilitation, ...

Cortical Bone Assessment Using the Ultrasonic BDAT Device

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population

Fragility fractures are still a worldwide health burden in the context of population aging. In particular, the global number of hip fractures is expected to double between 2020 and 2050. Therefore, it is essential to detect patients at risk of fragility fracture at the population scale. The current golden standard is dual X-ray absorptiometry (DXA), providing the areal bone mineral density (aBMD). Ultrasonic devices, usually more portable and cheaper than X-ray devices, represent interesting DXA alternatives as screening tools. However, operator dependency is usually recognized as their main drawback. In this study, the measurement protocol of the bi-directional axial transmission (BDAT) ultrasonic device is presented in detail. The dedicated ultrasonic probe is placed at the one-third distal radius of the non-dominant forearm using conventional coupling gel. The guided interface provides in quasi-real time (about 2 Hz) four parameters of interest: velocities of the first arriving signal (vFAS) and the A0 mode (vA0),&#160;cortical thickness (Ct.Th) and porosity (Ct.Po), as well as four quality parameters. The operator moves the probe slowly at the measurement site, carefully observing the feedback provided by the interface until finding a stable position and starting a series of 10 acquisitions. When at least four consistent series are obtained, the measurement ends, and an automatic report is generated. The measurement usually takes about 5 min to complete. To determine the robustness of this protocol, a reproducibility study was conducted among 3 operators (one expert and two novices) and 14 healthy participants (6 women, 8 men, 21-53 years old). The intraclass correlation coefficients (ICC) were found good for vA0 (0.76), Ct.Po (0.80) or excellent for Ct.Th (0.87) and vFAS (0.91). The standard deviations were found to be less than 10% of the total ranges in clinical practice.

Here, we present the measurement protocol of the bi-directional axial transmission (BDAT) ultrasonic device in detail and test it in a reproducibility study, considering 14 healthy participants and 3 operators. Reliability, measured with the intraclass correlation coefficients (ICC), was good to excellent for four parameters of interest.

Fragility fractures are still a worldwide health burden in the context of population aging. In particular, the global number of hip fractures is expected ...

Stress-Strain Characteristics of Aluminum

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
Aluminum is one of the most abundant materials in our lives, as it is omnipresent in everything from soda cans to airplane components. Its widespread use is relatively recent (1900AD), primarily because aluminum does not occur in its free state, but rather in combination with oxygen and other elements, often in the form of Al2O3. Aluminum was originally obtained from bauxite mineral deposits in tropical countries, and its refinement requires very high-energy consumption. The high cost of producing quality aluminum is another reason why it is a very widely recycled material.
Aluminum, especially when alloyed with one or more of several common elements, has been increasingly used in architectural, transportation, chemical, and electrical applications. Today, aluminum is surpassed only by steel in its use as a structural material. Aluminum is available, like most other metals, as flat-rolled products, extrusions, forgings, and castings. Aluminum offers superior strength-to-weight ratio, corrosion resistance, ease of fabrication, non-magnetic properties, high thermal and electrical conductivity, as well as ease of alloying.

Uniaxial Tensile Strength and Stress-Strain Test of Aluminum

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
Aluminum is one of the most abundant materials ...

Ultrasonic Fatigue Testing in the Tension-Compression Mode

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