Test MethodExperimental assessment of stiffness and energy dissipation properties of disk-shaped polymer-based composite specimens by in-plane torsion testing
Introduction
The increasing demand for structural weight lightning in response to ever stricter requirements related to fuel efficiency and emission restrictions have brought researchers to focus their attention on composite material engineering in several fields of transportation industry and especially in aerospace and automotive sectors [1]. Nowadays, composite materials are employed extensively in a wide variety of industrial applications as a powerful alternative to conventional metal materials, such as steel or aluminium alloys. In this context, carbon fibre reinforced polymers (CFRP) represent a significant category of composites owing to the possibility to tailor relevant material properties, such as stiffness and strength, on specific engineering requirements, while achieving a considerable weight reduction [2].
In addition to the above-mentioned static properties, CFRP are becoming increasingly attractive for their intrinsic capability of reducing vibrations, which they inherit from their polymeric matrix [3]. Mechanical vibrations may compromise both reliability and safety of structures in many areas of mechanical, civil and aerospace engineering. Classical examples are offshore platforms subject to oscillations under the action of sea currents, blades of a wind turbine or helicopter rotors, bridges and buildings under the action of wind or earthquakes, or road vehicle vibrations caused by the dynamic excitation coming from the engine or from other external sources, such as irregularities on the road surface. The main challenge is that vibrations can be triggered by either cyclic or suddenly applied external forces, leading to unexpected dynamic conditions of the entire mechanical system, thus diminishing reliability, fatigue-life expectations or at worst causing unexpected damages [4].
In a vibrating system, the phenomenon of energy dissipation into other forms of energy, like heat, is referred to as damping property [5] and occurs as a consequence of dynamic deformation. In structural dynamics, damping is due to multiple physical causes such as friction in the joints, due to interface interactions between different components, or more complex internal friction phenomena triggered by structural deformation of multi-layers materials. Indeed, composites materials offer very high dissipative capacities as compared to conventional metallic alloys, and polymer-based composites complement the mentioned advantages with more favourable weight-to-strength and better resistance ratio. Existence of such material paves the way to a paradigm shift in the design of mechanical systems: incorporating CFRP structural elements within existing systems may result in a substantial and more effective mitigation of noise and vibration issues.
This paper aims at characterising the dynamic behaviour of CFRP disk-shaped specimens, under torsional vibrations, thus offering a quantitative indication for the design of CFRP inserts aiming at mitigating vibrations in rotor dynamics applications such as powertrain systems using gearbox or more in general systems with large rotating elements.
The research presents a novel approach to assess torsional stiffness and damping of CFRP specimens. Specifically, a steel mechanism was designed as a special fixture of a universal testing machine (UTM) in order to hold the disk-shaped samples while enabling the desired displacement-controlled torsional loading. In this way, higher loads than the traditional torsion testing machines can be applied on the specimens.
Damping phenomena and properties in CFRP have been widely described in literature through the analysis of different mechanical aspects, based on numerical predictive models and experimental characterisation [6,7]. Energy dissipation in vibrating composites with a polymer matrix is related to several sources, such as the viscoelastic behaviour of either the matrix or the fibre materials, damping due to the interphase, visco-plastic and thermoelastic damping [8]. Among all possible sources, the most relevant and dominant contribution is related to the viscoelastic nature of the matrix [9]. Differently from traditional metal materials, which usually exhibit limited structural damping, viscoelasticity comprises the combination of both elastic (solid) and viscous (fluid) behaviours producing significant damping phenomena that are typically dependent on temperature and excitation frequency.
Experimental tests and measurements are essential to estimate damping properties of composites to be used as input parameters for simulations aimed at analysing the dynamic behaviour of a given structure. Generally, three main techniques are used to characterise the damping capacity of a material [10]. The first relies on the transient response of the system and it is called the logarithmic decrement method. It consists in deducing damping from the rate of oscillation reduction during an exponential decay [11]. This technique has been used in Ref. [12] to analyse and enhance the damping properties of carbon fibre reinforced epoxy composites. The second is known as the half-power bandwidth method, which derives the loss factor of the system, as a measure of the level of damping from the sharpness of the peak in the frequency response function (FRF) at a resonant frequency. Specifically, the loss factor of the structure is defined as a function of the quality factor of resonance Q [11]. In Ref. [13] this method has been applied to cantilever beam specimens excited by an external source to evaluate material damping, while in Ref. [14] the loss factor has been calculated for a beam specimen made of flax fibre-reinforced polymer. Finally, the third method for the characterisation of damping in a structure is related to the dynamic mechanical analysis (DMA) technique. It consists in computing the energy dissipated during a cyclic force-displacement (or stress-strain) test, thus evaluating the area of the typical elliptic steady-state hysteretic cycle [15].
Various studies have already exploited DMA for the analysis of damping properties of composite laminates under longitudinal or flexural vibration. Abramovich et al. [15] validated the damping capacity of composite laminates for aerospace applications as a comparison with aluminium material. Montalvao et al. [16] applied harmonic axial loadings to quasi-isotropic laminate specimens and evaluated both the real and imaginary part of the complex Young's modulus.
With reference to flexural vibrations, elastic moduli and specific damping capacity have been investigated in Ref. [17] for beams made of carbon and flax fiber-reinforced polymers as a function of ply orientation and frequency, while in Ref. [18] the authors have described the temperature dependence of the storage modulus and loss factor of composite specimens tested in a cantilever configuration.
Although various papers have already investigated on DMA applied to CFRP, there is still a lack of experimental works addressing its application to the analyses of composite structures subject to dynamic torsional loads, which the research herein addressed intends to cover. Such loading conditions are common in rotating machinery, whose typical high-power demands require severe dynamic torques that are harmful in case of vibrational behaviours and may compromise the fatigue life of the system.
To this aim, the use of new hybrid structures is becoming more and more attractive [19], also in case of rotor dynamics applications. The use of hybrid rotating parts has been investigated in Ref. [20], where circular plate cutting tool structures were analysed and designed in a hybrid steel/composite configuration in order to reduce mass and improve dynamic stiffness thus shifting the natural frequencies towards higher values. More recently, Catera et al. [21], in 2017, described an innovative concept of hybrid gears, which combine the high contact stress and fatigue resistance of the steel used for the toothed part with the high strength-to-weight ratio of composite materials of the central part of the gear. Owing to its relatively higher damping properties, such a composite gear body is expected to disrupt the transmission path of the vibrations arising during meshing and travelling from the tooth contact areas to the rotating shafts, and, as a consequence, to reduce the dynamic excitation exerted onto the full structure.
In this work, a novel experimental approach was proposed targeting the assessment of the stiffness and damping capacity of disk-shaped CFRP specimens with different laminate layups. A novel experimental method was presented designing a dedicated steel structure to be used with a UTM. This equipment allows applying cyclic in-plane torsion with higher loads than the traditional machines.
The outline of the paper can be summarised as follow: Section 2 starts introducing the fundamental of viscoelasticity theory, paving the way for adopting DMA during cyclic torsional excitation of disk-shaped composite specimens. Besides, this section describes the designed experimental setup. Section 3 presents and discusses the experimental results comprising two CFRP disks with the same material composition, but two different lay-ups. Specifically, analyses of stiffness and global energy loss, as a function of varying amplitudes and frequencies, were shown. Finally, Section 4 concludes the paper highlighting the pros and cons of the proposed approach and providing an outlook of the envisaged future developments.
Section snippets
Materials and methods
Damping is a sort of black-box concept, related to the fact that part of the energy of a vibrating mechanical system is dissipated, owing to multiple physical reasons. Therefore, to maintain steady-state conditions, the energy loss must be balanced by external excitations. Specifically, the physics of damping phenomena comprises several mechanisms of energy dissipations such as internal molecular friction, sliding friction or fluid resistance. However, dealing with all the possible causes does
Experimental results
For the experimental tests, a MTS hydraulic linear testing machine with specific hydraulic wedge grips was employed. Each test was performed in displacement control imposing the desired harmonic displacement and recording it together with the resulting reaction force. Fig. 8 depicts a pair of typical hysteresis cycles obtained plotting the Load – Displacement along one of the steady-state cycles.
Table 2 summarises the experimental plan executed for each specimen, which comprises a set of tests
Conclusion and future works
This work presented an original approach to enable in-plane torsion testing of polymer-based composite material disks. The conceived testing approach aimed at a dynamic torsional characterisation. Specifically, the methodology as well as the experimental infrastructure and all the related choices for its construction were described. During the preliminary design, finite element analysis showed that the achievable torsional deformation on the disk-shaped specimens is considerable although a
CRediT authorship contribution statement
Francesco Cosco: Conceptualization, Methodology. Giuseppe Serratore: Software, Validation. Piervincenzo Giovanni Catera: Data curation. Francesco Gagliardi: Writing - original draft, Supervision. Eduardo Luberto: Visualization, Investigation. Domenico Mundo: Writing - review & editing, Supervision.
Acknowledgments
The research was partially funded by the European Commission, with the support of the European social fund (ESF) and the European regional development fund (ERDF), and the Ministry of Education, University and Research (MIUR), through the National Operational Program for Research and Innovation, PON R&I 2014-2020, Action I.2 Attraction and International Mobility, AIM1857122.
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