With the development of new materials, it is now known that there is no such thing as a fatigue endur- ance limit, i.e. materials do not have infinite life when the stress level is such that there is no fracture up to 10 million (1E7) cycles. The problem of testing materials above this number of cycles is that most testing equipment operates well below 150 Hz, making testing up to 1 billion (1E9) cycles or above is an impracticality. The recent developments of ultrasonic testing machines where frequencies can go as high as 20 kHz or above enabled tests to be extended to these ranges in just a few days. This is known as very high cycle fatigue (VHCF). On the other hand, critical components used in engineering applications are usually subjected to multi-axial loads, as is the case of the fuselage and wings of aircrafts which are subjected to biaxial states of stress. In this paper, VHCF cruciform test specimens purposely designed to develop orthogonal biaxial stresses with different biaxiality ratios will be analysed. The specimens are composed from Aluminium 6082-T651, a medium strength alloy used in many highly stressed engineer- ing applications, including trusses, cranes, bridges and transportation. The specimens work as tuning forks with determined mode shapes at 20±0.5 kHz, where maximum principal stresses are developed at the centre of the specimen. Finite element analysis (FEA) is used to assess the dynamic behaviour of the specimens. The framework on how to design and manufacture cruciform specimens with different biaxiality ratios will be explained in a clear way so it can be used by other engineers in the field.
Biaxial Stresses; Cruciform Specimens; Very High Cycle Fatigue; Ultrasonic Testing
 Suryanarayana, C., Experimental Techniques in Materials and Mechanics, CRC Press: Boca Raton, 2011.
 Anes, V., Montalvão, D., Ribeiro, A., Freitas, M. & Fonte, M., Design and instrumen- tation of an ultrasonic fatigue testing machine. Proceedings of the 5th International Conference on Very High Cycle Fatigue, Berlin, Germany, 2011.
 Freitas, M., Anes, V., Montalvão, D., Reis, L. & Ribeiro, A., Design and assembly of an ultrasonic fatigue testing machine. Proceedings of the 28th Encuentro del Grupo Español de Fractura (Anales de Mecânica de la Fractura), Gijón, Spain, 2011.
 Wycisk, E., Siddique, S., Herzog, D., Walther, F. & Emmelmann, C., Fatigue Perfor- mance of Laser Additive Manufactured Ti–6Al–4V in Very High Cycle Fatigue Regime up to 109 Cycles. Frontiers in Materials, 2, article 72, 2015. https://doi.org/10.3389/ fmats.2015.00072
 Bathias, C., There is no infinite fatigue life in metallic materials. Fatigue and Fracture of Engineering Materials and Structures, 22, pp. 559–566, 1999. https://doi.org/10.1046/ j.1460-2695.1999.00183.x
 Pyttel, B., Schwerdt, D. & Berger, C., Very high cycle fatigue – Is there a fatigue limit? International Journal of Fatigue, 33, pp. 49–58, 2011. https://doi.org/10.1016/j.ijfa- tigue.2010.05.009
 Frederick, J., Ultrasonic Engineering, John Wiley & Sons: New York, NY, 1965.
 Lage, Y., Ribeiro, A., Montalvão, D., Reis, L. & Freitas, M., Automation in strain and temperature control on VHCF with an ultrasonic testing facility. Journal of ASTM Inter- national, ASTM STP 1571, pp. 80–100, 2014. https://doi.org/10.1520/stp157120130079
 Costa, P., Vieira, M., Reis, L., Ribeiro, A. & De Freitas, M., New specimen and horn design for combined tension and torsion ultrasonic fatigue testing in the very high cycle fatigue regime. International Journal of Fatigue, 103, pp. 248–257, 2017. https://doi. org/10.1016/j.ijfatigue.2017.05.022
 Cláudio, R., Freitas, M., Reis, L., Li, B., Guelho, I., Antunes, V. & Maia, J., In-Plane Biaxial Fatigue Testing Machine Powered by Linear Iron-Core Motors. Journal of ASTM International, ASTM STP 1571, 2014. https://doi.org/10.1520/stp157120130078
 Montalvão, D., Shengwen, Q. & Freitas, M., A study on the influence of Ni–Ti M-Wire in the flexural fatigue life of endodontic rotary files by using Finite Element Analysis. Materials Science and Engineering: C, 40, pp. 172–179, 2014. https://doi.org/10.1016/j. msec.2014.03.061
 Reis, L., Li, B. & De Freitas, M., A multiaxial fatigue approach to Rolling Contact Fatigue in railways. International Journal of Fatigue, 67, pp. 191–202. 2014, https:// doi.org/10.1016/j.ijfatigue.2014.02.001
 Baptista, R., Cláudio, R. A., Reis, L., Guelho, I., Freitas, M. & Madeira, J.F.A., Design optimization of cruciform specimens for biaxial fatigue loading. Frattura ed Integritá Strutturale, 30, pp. 118–126, 2014. https://doi.org/10.3221/igf-esis.30.16
 Montalvão, D. & Wren, A., Redesigning Axial-Axial (Biaxial) Cruciform Specimens for VHCF Ultrasonic Testing Machines, Heliyon, 3(11), 2017. https://doi.org/10.1016/j. heliyon.2017.e00466
 Costa, P.R., Montalvão, D., Freitas, M., Baxter, R. & Reis, L., Cruciform Specimen’s Analysis and Experiments in Ultrasonic Fatigue Testing. Proceedings of the 18th Inter- national Conference on New Trends in Fatigue and Fracture, Lisbon, Portugal, 2018.
 Bathias, C., Piezoelectric fatigue testing machines and devices. International Journal of Fatigue, 28, pp. 1438–1445, 2006. https://doi.org/10.1016/j.ijfatigue.2005.09.020
 Montalvão, D., Freitas, M., Reis, L. & Fonte, M., Design of cruciform test specimens with different biaxiality ratios for VHCF. Proceedings of the 8th International Confer- ence on Engineering Failure Analysis, Budapest, Hungary, 2018.
 Blaskovics, A., Development of Cruciform Specimens for Biaxial VHCF Testing, BEng Project, Bournemouth University, June 2019 (in progress).
 Silva, J.M.M. & Maia N.M.M. (eds), Theoretical and Experimental Modal Analysis, Research Studies Press: Taunton, 1997.