Development of a Very High Cycle Fatigue (VHCF) multiaxial testing device

M. Vieira et alii, Frattura ed Integrità Strutturale, 37 (2016) 131-137; DOI: 10.3221/IGF-ESIS.37.18 Focussed on Multiaxial Fatigue and Fracture Development of a Very High Cycle Fatigue (VHCF) multiaxial testing device M. Vieira, M. de Freitas, L. Reis, A. M. R. Ribeiro IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal, , http://orcid.org/0000-0003-3525-9218 http://orcid.org/0000-0001-9848-9569 http//orcid.org/0000-0001-2345-6789 M. da Fonte Escola Superior Náutica Infante D. Henrique, Av. Eng. Bonneville Franco 2770-058 Paço d'Arcos, Portugal http://orcid.org/0000-0002-2345-6790 ABSTRACT. The very high cycle region of the S-N fatigue curve has been the subject of intensive research on the last years, with special focus on axial, bending, torsional and fretting fatigue tests. Very high cycle fatigue can be achieved using ultrasonic exciters which allow for frequency testing of up to 30 kHz. Still, the multiaxial fatigue analysis is not yet developed for this type of fatigue analyses, mainly due to conceptual limitations of these testing devices. In this paper, a device designed to produce biaxial fatigue testing using a single piezoelectric axial exciter is presented, as well as the preliminary testing of this device. The device is comprised of a horn and a specimen, which are both attached to the piezoelectric exciter. The steps taken towards the final geometry of the device are presented. Preliminary experimental testing of the developed device is made using thermographic imaging, strain measurements and vibration speeds and indicates good behaviour of the tested specimen. KEYWORDS. Multiaxial fatigue; Very high cycle fatigue; Fatigue testing machines; Strain measurements. INTRODUCTION F atigue damage has special relevance on the life span of mechanical components and structures, as it takes responsibility for the majority of the registered structural failures. Although its mechanisms have been the subject of continuous research, the growing need for greater lifespans forced the understanding of the behavior of materials under very high cycle loadings [1], also known as the Very High Cycle Fatigue (VHCF) regime. This field of research, which studies the mechanical behavior of materials for fatigue lives over 10E7 cycles, has recently gained notoriety [2], largely due to the appearance of ultrasonic fatigue testing machines, working at 20-30 kHz and due to the acquisition and control equipment capable of handling signals at such high frequencies. In this context, the results found in the bibliography [1, 2], which usually focus on either axial or torsional fatigue tests, allow us to understand the behavior of materials on the very high cycle region of the S-N curves, remarking the absence, 131 M. Vieira et alii, Frattura ed Integrità Strutturale, 37 (2016) 131-137; DOI: 10.3221/IGF-ESIS.37.18 for some materials, of the fatigue limit that used to be considered on mechanical design. However, these results only refer to uniaxial loadings when, in real conditions, mechanical components are usually loaded under multiaxial loadings. Because of the axial character of the excitation created by the piezoelectric exciter, only axial, bending or fretting specimen testing were able to be performed up to now. The appearance of torsional piezoelectric exciters allowed for VHCF testing on torsional conditions, as well. But, for multiaxial conditions, no VHCF results have been described on the literature due to conceptual limitations of these devices. Multiaxial loading fatigue has been the subject of intense research for low and high cycle regimes, but not on the VHCF region, due to the inexistence of machines capable of operating on ultrasonic frequencies and submit specimens to multiaxial loadings. For the high cycle regime, the von Mises criterion on biaxial loading has been questioned since experimental data does not correlate well, either for in-phase or out-of-phase loadings [3]. In this paper, the development of a fatigue testing machine for biaxial conditions working at VHCF is presented. The device is comprised of a horn and a specimen, which are both attached to an ultrasonic piezoelectric axial exciter. BIAXIAL FATIGUE TESTING MACHINE FOR VHCF T he present work describes the processes of creation and development of a VHCF testing device for biaxial conditions, using a single axial piezoelectric exciter. The device is comprised of a horn and a specimen, being the latter the component to be tested on biaxial conditions, with a loading that was predefined to have in-phase sinusoidal components of axial and shear stress in R=-1. The horn Since the horn receives a sinusoidal axial displacement from the piezoelectric exciter, and it is intended to induce also torsional loadings on the specimen, the horn has to be responsible for the generation of the rotational movement which will be imposed on the specimen and will promote shear stresses in it. This implies that the horn takes special importance on the behavior of the device, specifically on the relationship between axial and torsional loadings imposed on the specimen. The computational modal analysis made to this geometry proved that a certain dynamic vibrational mode could be achieved in which the horn would vibrate in a hybrid mode composed by the first axial mode and the first torsional mode, where axial and rotational displacements were amplified on the smaller free end. Still, there was a need for a horn that would possess this specific mode on the frequency at which the exciter operates (20 kHz). The iterative process to obtain the final geometry was produced using finite element software, and a schematic representation is shown on Fig. 1: Figure 1: 2D representation of the developed biaxial horn. The final horn geometry consists of a conical shaped piece possessing two groups of oblique slits responsible for the generation of the rotational character of the horn, which in turn will promote sinusoidal rotations on the specimen that will add to the already existent sinusoidal axial excitation. The specimen Before introducing the final geometry of the used specimen, it might be interesting to analyze the dynamic equation for a generic bar, Eq. 1, [1]: 132 M. Vieira et alii, Frattura ed Integrità Strutturale, 37 (2016) 131-137; DOI: 10.3221/IGF-ESIS.37.18  2u E  2u t  x 2  2 (1) where u is the displacement, t is time, E is the Young Modulus, x is the associated coordinate system and  is the specific mass of the material. The mathematical solution of Eq. 1 is:  nx   ct  u( x )  A0 cos  sen    l   l  (2) where A0 is the generic amplitude of vibration, l is the bar length and c is the wave propagation speed. Eq. 2 represents the axial displacement along the generic bar, respective to a certain nth mode, while Eq. 3 represents the natural non-damped frequency, n for the nth mode. n  n l E (3)  The solution (...truncated)