PSI - Issue 42

Rita Dantas et al. / Procedia Structural Integrity 42 (2022) 1676–1683 Rita Dantas / Structural Integrity Procedia 00 (2019) 000–000

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this conventional fatigue limit during their service life. For example, according to Murakami (2002), during ten years of service, a high speed Japanese Shunkansen Train experiences more than 10 7 cycles. For that reason, the region beyond 10 7 cycles, usually named as very high cycle fatigue (VHCF), and the concept of fatigue limit have been matter of study and interest in the last decades (Sharma et al., 2020) (Zimmermann, 2018). In order to overcome the time e ff ort required, the ultrasonic fatigue testing machine has been developed and widely used, since this technology is capable of performing fatigue tests in higher frequencies such as 20 kHz . Nevertheless, ultrasonic testing introduces new challenges and topics of research, such as the e ff ect of frequency, the overheating due to high testing frequencies, and new mechanisms of failure (internal crack initiation)(Furuya et al., 2002) (Furuya et al., 2012) (Palin-Luc and Jeddi, 2018). Usually, in hardened steel, for lower number of loading cycles the fatigue crack initiates at the surface, while for longer lives the initiation mechanism will be internal (Nishijima and Kanazawa, 1999).

Nomenclature

E

Young’s modulus

Density

ρ ν u v

Poisson’s ratio

Displacement along x Displacement along y Displacement along z

w

t

Time variable

e c S

Volume dilatation

Velocity of wave propagation

Cross-section area

f

Force acting in the cross section

U ω

Amplitude of vibration

Frequency of vibration L 1 Length of specimen’s cylindrical part L 2 Length of half specimen’s bowstrings L Total length of the specimen

R 1 Specimen’s minimum radius R 2 Specimen’s maximum radius α

Variable to adjust the hyperbolic cosine A 0 Displacement wave amplitude at the end of the specimen ε Strain at a certain location of the specimen σ Stress at a certain location of the specimen σ u Ultimate tensile strength σ y Yield tensile strength σ a Stress amplitude

Moreover, for ultrasonic fatigue tests, the specimen’s geometry is a critical point, since it must be designed to resonate at the operating frequency of the ultrasonic testing machine. Besides, the geometry defines the range of stress which is possible to test in this kind of fatigue machine. Thus, the procedure of designing the specimen can be complex and an iterative process, which di ffi culty will depend on the geometry chosen and on the type of test. For certain geometries, the specimen’s dimensions can be calculated by an analytical method (Bathias and Paris, 2004). Thus, during this work, a methodology to design a smooth specimen was established based on an analytical formu lation, to carry on ultrasonic fatigue tests in S690 steel. Then, the specimens were manufactured and an experimental campaign of twenty specimens was performed in an ultrasonic testing machine at 20 kHz . At the end of this work, a mean curve for S690 steel was obtained.