PSI - Issue 42

Pedro R. da Costa et al. / Procedia Structural Integrity 42 (2022) 1560–1566 Pedro R. da Costa/ Structural Integrity Procedia 00 (2019) 000 – 000

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A brief introduction to the present study ultrasonic machines and applied experimental methodologies is now made. The most common method to induce an ultrasonic fatigue setup into resonance is a piezoelectric transducer. All three constructed and here presented methods use an axial piezoelectric transducer. A designed set of components are sequentially attached to the transducer, each with a certain resonant mode at the working frequency of the transducer (20 kHz considering the present study). An ultrasonic setup is usually composed by a booster and a horn. For the tension-compression ultrasonic machine, the booster and horn's primary purpose is to amplify the axial displacements from the transducer. A cylindrical hourglass-shaped specimen is then attached to the horn. A single point of displacement measurement was applied in the opposite specimen base from the horn (the specimen free base). In the pure torsion ultrasonic setup two different horns are transversely connected by a pin. The first is the longitudinal horn (LH), similar to the booster and horn of the tension-compression ultrasonic setup. The LH is attached directly to the transducer. The second horn is the torsional horn (TH) with a torsional resonance at 20kHz. The transverse pin connection allows for the LH to excite the torsional resonance of the TH. Again, the specimen has a cylindrical hourglass shape. Two groves were machined on the specimen free base to measure the its rotation displacement amplitude. Simultanously, a roseate strain gauge was applied in the specimen fatigue testing region for measuring the induced shear strain amplitude. The designed tension-torsion ultrasonic setup by Costa et al. (2017) follows the tension-compression setup basis: axial piezoelectric transducer, booster horn and a cylindrical specimen. The horn and the specimen's innovative geometries allow the machine to reach a multiaxial tension-torsion at 20kHz. A set of slits were introduced to the horn geometry that transform the axial transducer displacement into an axial/rotation displacement combination. The specimen has not one but three hourglass-shaped sections. The purpose of the specimen's distinctive shape is to have the ability to be excited into two different resonance modes simultaneously at the same 20kHz frequency, the first longitudinal and the third torsional modes. A combination of the tension and pure torsion experimental methodologies were followed to measure the multiaxial displacement and strain amplitudes. The axial displacement was measured similarly to the tension-compression ultrasonic test, while the rotational displacement was measured with similar machined groves to the free base of the specimen. Since the specimen has a multiaxial stress state at the fatigue testing region, a rosette strain gauge was applied. Figure 1 shows a schematic of the tension-torsion and pure torsion setups with the laser conducted measurements. The made groves are also present to better illustrate their shape and how they allowed for rotational measurement.

Fig. 1. Displacement vibrometer laser experimental methodology and setup representation: (A) multiaxial Tension/Torsion; (B) detail from A; (C) pure torsion. Figure 1 also identifies the ultrasonic pure torsion LH and TH horns and the point of connection. All conducted measurements were compared to numerical modal analysis of the three setups. The finite element conducted analysis in free-free no boundary conditions steady-state modal provided a displacement stress ratio that was compared to the experimentally obtained. Analytically determined stress amplitudes from the measured displacements were also computed. All followed equations for tension-compression can be perceived in Bathias and Paris book (2005), while for pure torsion the Japanese Welding Engineering Society standard WES 1112 was followed (2017).