Mechanical Properties Of Viscoelastic Materials Research Articles

Mechanical property tests and physics-informed data-driven modeling of viscoelastic materials subjected to thermal-oxidative aging

The purpose of this paper is to investigate and characterize the performance changes of viscoelastic materials (VEMs) in viscoelastic (VE) devices used for structure vibration control due to the influence of aggressive environmental conditions during long-term service. To this end, a series of thermal-oxidative (TO) aging experiments are conducted on the developed VEMs, variation of microstructure and macroscopic mechanical behaviors of TO aged VEMs are tested and analyzed. The molecular chain network of VEMs that can be simplified into elastic chain network and free chain network is described by the architecture of microsphere model, a physics-informed data-driven model is proposed to reflect the mechanical properties of TO aged VEMs, in which the physics-informed neural network (PINN) theory is incorporated to describe the statistical characteristics of molecular chains and the reaction rate of TO aging. Based on the experimental data, implementation and validation of the proposed model are conducted on the mechanical properties of VEMs under varying aging levels. The experimental results suggest that TO aging could alter molecular chain structure of VEMs from the microscopic level, leading to an increase in crosslinking degree and modulus, and the degeneration of deformation ability and energy-dissipation capacity for VEMs. The verifications reveal that the proposed model possesses high accuracy in characterizing the mechanical properties and energy-dissipation capability of VEMs under different aging levels, which preliminarily proofs the potential of PINN theory in reflecting the complex mechanical behaviors of VEMs.

Mechanical properties of viscoelastic materials subjected to thermal‐oxidative aging: An experimental and theoretical study

AbstractViscoelastic materials (VEMs) made from rubber polymer will inevitably age due to the interactions with the harmful environment during service life, thus reducing the reliability of viscoelastic (VE) damping equipment installed in building structures. In order to understand and be able to predict the degradation of VE damping equipment, it is imperative to comprehensively study the influence of aging on the mechanical properties of VEMs. In this paper, a series of thermal‐oxidative (TO) aging tests and mechanical property tests are conducted on our previously developed VEMs to study effects of TO aging on the molecular chain structure and corresponding changes of macroscopic mechanical properties of VEMs. By classifying molecular chains of VEMS into elastic chains and free chains, the effects of different chemical reactions during TO aging on these two main chains and corresponding changes on macroscopic mechanical behaviors of VEMs are analyzed. This facilitates formulating a mathematical model that can characterize the mechanical behavior of TO aging VEMs. In conjunction with the experimental data, the accuracy and applicability of the proposed model are compared and verified. Sensitivity analyses of parameters involved in the proposed model are then performed. The experimental results demonstrate that the TO aging can degrade the deformation capability and harden the modulus of VEMs, which may adversely affect the performance of VE damping devices. The parameter analyses depict that the TO aging affects the macroscopic mechanical behavior of VEMs by altering the relative number and configuration of free chains and elastic chains as well as their respective contributions to the total stress of VEMs. The results point to the high accuracy of the proposed model in representing the strain–stress behavior of VEMs under different aging conditions.

TTS package: Computational tools for the application of the Time Temperature Superposition principle

The TTS package has been developed in R software to predict the mechanical properties of viscoelastic materials, at short and long observation times/frequencies by applying the Time Temperature Superposition (TTS) principle. TTS is a physical principle used in material science to estimate mechanical properties beyond the experimental range of observed times/frequencies by shifting data curves obtained at other temperatures relative to a reference temperature in the dataset. It is a methodology related to accelerated life-tests and reliability, whereas the TTS library is one of the first open source computational tool to apply the TTS principle. This R package provides free computational tools to obtain master curves that characterize materials from a thermal-mechanical approach. The TTS package also proposes, implements and explains our own method to obtain the shift factors and the master curve in a TTS analysis, based on horizontal shifting of the first derivative function of viscoelastic properties. This procedure provides shift factors estimates and smooth master curve estimates using B-spline fitting, in a fully automatic way, without assuming any parametric expression. Williams-Landel-Ferry (WLF) and Arrhenius TTS parametric models are also implemented in the TTS package. They can be fitted from shifts obtained by the our first derivative based method.

Settlement Analysis of Fractional-Order Generalised Kelvin Viscoelastic Foundation under Distributed Loads

A solution is proposed for ground surface settlement induced in fractional-generalised Kelvin semi-infinite space by distributed loads, based on the fractional differential theory. The effects of four main parameters—the differential order, the two shear moduli and the coefficient of viscosity—on the settlements are analysed using a numerical example, and a parametric-sensitivity analysis is conducted. The results show that the fractional-order generalised Kelvin model is more flexible than the conventional integer-order generalised Kelvin model since it can account for the rate of the deceleration creep phase; therefore, a wider range of mechanical properties of viscoelastic materials can be described with fewer parameters, and the differential order has a higher sensitivity than the other three parameters. Finally, the model is used to identify and fit the parameters to the data of the field-bearing plate rheological tests. The fit results of the fractional-order generalised Kelvin model, unlike those of the integer-order generalised Kelvin model, are closer to the measured results and can more accurately describe the rock’s rheological behaviour at the test location.

Mechanical properties of metal and polymeric viscoelastic materials and their applications

Nowadays, With the wide application of metals and polymeric materials, how to describe the property of Viscoelastic material and how to apply them in engineering has become more and more critical. Due to the lack of insight into the mechanical properties of viscoelastic materials, many scholars have done a lot of experiments in studying the behavior of viscoelastic materials. Axial tensile tests were conducted on specimens to derive different mechanical behaviors of metals, polymers, and other materials at different temperatures and loading rates. Metal can generally be divided into elastic and plastic parts, while polymeric materials have the phases of the linear elastic region, drawing region, and oriented molecular strength region. This paper also shows a test conducted by Argon, Ali S., and M. I. Bessonov of four different kinds of polymers at different circumstances of temperature. After that, the paper shows the application of viscoelastic materials as CLD in damping and some engineering problems caused by the mechanical properties of viscoelastic materials. Currently, research on viscoelasticity should mainly focus on the application of Finite Element Methods and the acquisition of more experimental data to establish a complete theoretical system.

Sliding Mode Control for Two-Degree-of-Freedom Fractional Zener Oscillator

Abstract Fractional-order derivatives provide a powerful tool for the characterization of mechanical properties of viscoelastic materials. Fractional oscillators are mechanical models of viscoelastically damped structures, the viscoelastic damping of which is described by fractional-order constitutive equations. This paper proposes sliding mode control for a two-degree-of-freedom fractional Zener oscillator. Firstly, a virtual fractional oscillator is generated by means of a state transformation. Then, the total mechanical energy in the virtual oscillator is determined as the sum of the kinetic energy, the potential energy, and the fractional energy. Furthermore, sliding mode control for the fractional Zener oscillator is designed, in which the Lyapunov function is defined by the total mechanical energy. Finally, numerical simulations are conducted to validate the effectiveness of the proposed controllers.

Mathematical modeling and test verification of viscoelastic materials considering microstructures and ambient temperature influence

Micro structures of viscoelastic materials (VEM) play an important role in their mechanical properties and energy dissipation capacities. This work shows a mathematical modeling of VEMs considering molecular chain-network configurations, and the temperature effects on mechanical properties of VEMs can also be characterized based on the equivalent relationship between temperature and frequency. The Dynamic Thermomechanical Analyzer (DMA) test is carried out to observe dynamic behaviors of the VEM and prove the accuracy of the proposed new mathematical model. The experimental data of viscoelastic damper (VED) are utilized to further verify the correctness of the proposed model with different ambient temperatures.

Analysis of blood flow characteristics in fractal vascular network based on the time fractional order

Fractional calculus has shown good adaptability in describing the mechanical properties of viscoelastic materials. Based on fractional order theory, the characteristics of blood flow in the fractal network of blood vessels are analyzed, and experiments are carried out by using a mixed solution to prove the results of simulation analysis that contains glycerol, gelatin, sodium chloride, etc. Under different time of fractional order conditions, the effects of Reynolds number, vascular network fractal dimension, and bifurcation series conditions, the blood flow characteristics in fractal vascular network are analyzed. The analysis results show that the blood flow increases with the increase in time fractional order and the flow resistance decreases with the increase in time fractional order. The blood flow law curve based on the equivalent Casson fluid theory has the same trend between the orders α = 0.9 and α = 1.0 of the time fractional order curve, so the order of time fractional order can describe the blood flow characteristics of equivalent Casson fluid. The experimental data are distributed on both sides of the theoretical calculation curve and the relative error is small, which is in good agreement with the effect of vascular fractal parameters obtained by integer order on blood.

Analytical Expression of Complex Modulus for Viscoelastic Material

Transfer functions in the linear dynamic system theory are applied to characterize dynamic mechanical properties of viscoelastic materials. Correlation between transfer functions and typical rheological models and fractional derivative ones are briefly introduced. The transfer function of a rheological model may be expressed in terms of multiplication of factored polynomials. The frequency–response data are presented in the form of a Bode plot of magnitude, from which a transfer function can be established. The characteristic times can be conveniently identified via the corner frequencies of asymptotes of the magnitude curve. Dynamic frequency sweep results for a typical viscoelastic solid are presented to illustrate the use of the Bode diagram method for parameter identification.

A new high frequency dynamic mechanical analysis system: An approach to direct high frequency testing of tire tread rubber

Dynamic Mechanical Analysis (DMA) systems are measurement devices for obtaining master curves and complex modules of viscoelastic materials, such as rubbers. The conventional DMAs measurement systems in market have several limitations, which restrict their ability for operating at high frequencies. Thus, Williams, Landel and Ferry (WLF) relation is used to produce master curves and predict the material properties at high frequencies. In conventional DMAs, experiments are done in a range of temperatures, and then a master curve is made for a chosen reference temperature by shifting the measurements data to high frequencies. Therefore, the obtained results, which are not based on direct measurements, can be inaccurate. In order to overcome this problem a new simple shear high-frequency DMA (HFDMA) system is designed and built to directly measure the dynamic mechanical properties of viscoelastic material at high frequencies and the strain levels sufficient for tire manufacturers. The new HFDMA can be used to test any viscoelastic materials which have glass transmission temperature (Tg) lower than room temperature (about 23 °C) such as the Styrene-butadiene rubber (SBR). The SBR is the base material for tire tread. The designing process of this new HFDMA is presented in this paper. The rubber specimen shape is chosen by taking into account the shear elastic wave effect, bending, buckling effect and heat generation in the specimen. The repeatability test is accomplished to ensure that the results obtained from the new HFDMA are repeatable and the repeatability uncertainty is about 0.04%. The new HFDMA is validated by comparing to the direct test results of conventional DMA at 100 Hz. The direct high frequency (5 kHz) complex shear modulus and damping factor are compared with the master curve of the conventional DMA developed by the use of WLF relation for SBR. This comparison revealed that the complex shear modulus and damping factor of the SBR obtained from the HFDMA at 5 kHz and 0.05% strain amplitude are about 7% and 6.5% higher than those obtained from the conventional DMA, respectively.

Complex plane analysis of fractional derivative model and its use for parameter determination of viscoelastic material

The mechanical properties of viscoelastic materials are usually described by a rheological model composed of spring and dashpot in series or in parallel or their combination. The complex modulus as a function of angular frequency was firstly deduced, when fractional derivative rheological model is subjected to a sinusoidal perturbation in dynamic mechanical analysis (DMA) measurements. Then, the algebraic equations between the storage and loss moduli of the fractional Zener model in complex plane have been developed. The curve on the complex plane, a plot of loss modulus against storage modulus, is a repressed or distorted semicircle with its center below the real axis. The parameters of mechanical elements can be graphically estimated from its complex plane plot. The dynamic mechanical test of bituminous mixtures was carried out by frequency sweep over a wide range of 200 Hz to 0.02 Hz and its mechanical response can be described adequately by the fractional Zener model, whose element parameters are determined via geometric method.

The influence of the rheological parameters on the dispersion of the flexural waves in a viscoelastic bi-layered hollow cylinder

The paper investigates the influence of the rheological parameters which characterize the creep time, the long-term values of the mechanical properties of viscoelastic materials and a form of the creep function around the initial state of a deformation of the materials of the hollow bi-layered cylinder on the dispersion of the flexural waves propagated in this cylinder. Constitutive relations for the cylinder\'s materials are given through the fractional exponential operators by Rabotnov. The dispersive attenuation case is considered and numerical results related to the dispersion curves are presented and discussed for the first and second modes under the first harmonic in the circumferential direction. According to these results, it is established that the viscosity of the materials of the constituents causes a decrease in the flexural wave propagation velocity in the bi-layered cylinder under consideration. At the same time, the character of the influence of the rheological parameters, as well as other problem parameters such as the thickness-radius ratio and the elastic modulus ratio of the layers\' materials on the dispersion curves, are established.

Aeroelastic analysis of sandwich cylinder with fractional viscoelastic core described by Zener model

The flutter of a sandwich circular cylindrical shell, with the fractional order Zener constitutive relationship is studied. Based on the Donnell–Mushtari theory for facing layers and first order shear deformation theory for viscoelastic layer, the structural formulation of the sandwich cylinder is obtained and the aerodynamic pressure due to the fluid flow is evaluated by piston theory. The Lagrange method along with Rayleigh–Ritz method is implemented to derive and solve the governing equations. To determine the stability margin of three-layered cylinder the obtained set of ordinary differential equations are solved. In the following, the effects of variation of the geometric parameters such as length to radius ratio, radius to total thickness ratio and thickness of core layer, constraining layer and mechanical properties of viscoelastic material on flutter boundaries of sandwich cylindrical shell are investigated.

Analysis and implementation of chatter frequency dependent constrained layer damping tool holder for stability improvement in turning process

The machining stability is closely affected by dynamics behavior of the tool holder in turning operation. In this paper, the constrained layer damping (CLD) tool holder with chatter frequency dependent dynamics is analyzed to further improve machining stability. The dynamics behavior of CLD tool holder is first considered to be influenced by the chatter frequency due to the viscoelastic material. The mechanical properties of viscoelastic materials are determined by the testing frequency. Analytical models are built to calculate the modal parameters such as damping ratio. The chatter frequency dependence further increases the critical depth of cuts in stability lobes. Then, dimensions of the CLD structure are simulated and selected to increase damping where the chatter frequency is assumed to approximate the natural frequency, after that the developed CLD tool holder is manufactured. Lastly, modal tests and cutting experiments are performed for verification. The damping ratio of developed CLD tool holder are increased by 99% compared to that of conventional steel tool holder. It has been proved that the developed CLD tool holder can further improve machining stability with better damping performance especially when the chatter frequency is farther from the natural frequency.

Identification of the parameters of the Maxwell model using self-excited oscillation

In the present paper, a method for identifying the parameters of the Maxwell model using self-excited oscillation is proposed. Viscoelastic materials have the properties of both elasticity and viscosity and are generally used in dynamic systems to reduce vibration and noise. We herein focus on the measurement of linear viscoelasticity and investigate the widely used Maxwell model. The conventional measurement method for obtaining the dynamic mechanical properties of viscoelastic materials is easily affected by the friction and inertia of the measurement instrument. The proposed method uses the positive velocity feedback control to produce the self-excited oscillation, and the measurement results are not affected by these effects. The validity of the proposed method is confirmed experimentally using a prototype measurement system.

Study on the Dynamic Mechanical Properties of Viscoelastic Materials Based on Asymmetrical Sandwich Beams

A modified estimation method for the dynamic mechanical properties of viscoelastic materials via asymmetrical sandwich specimens is presented. In contrast to the traditional vibrating cantilever beam test method (VCBTM), the proposed method allows asymmetrical base beams in sandwich specimens. Based on the complex stiffness method, complex parameters are introduced for general sandwich configurations. Calculation formulas for loss factor and shear modulus of the core material are presented. The effectiveness of this approach is validated numerically and experimentally by analysis of one symmetrical sandwich beam specimen and two specimens with asymmetrical thicknesses and materials. It is shown that dynamic mechanical parameters of the core material can be obtained regardless of sandwiches’ symmetry. The proposed method breaks the symmetrical criteria for sandwich specimens and may provide a wider application to measure viscoelastic materials’ dynamic properties.

Identifying Mechanical Properties of Viscoelastic Materials in Time Domain Using the Fractional Zener Model

THE PRESENT PAPER AIMS AT PRESENTING A METHODOLOGY FOR CHARACTERIZING VISCOELASTIC MATERIALS IN TIME DOMAIN, TAKING INTO ACCOUNT THE FRACTIONAL ZENER CONSTITUTIVE MODEL AND THE INFLUENCE OF TEMPERATURE THROUGH WILLIAMS, LANDEL, AND FERRY€™S MODEL. TO THAT EFFECT, A SET OF POINTS OBTAINED EXPERIMENTALLY THROUGH UNIAXIAL TENSILE TESTS WITH DIFFERENT CONSTANT STRAIN RATES IS CONSIDERED. THE APPROACH IS BASED ON THE MINIMIZATION OF THE QUADRATIC DISTANCE BETWEEN THE EXPERIMENTAL STRESS-STRAIN CURVES AND THE CORRESPONDING ONES GIVEN BY THE THEORETICAL MODEL. IN ORDER TO AVOID THE LOCAL MINIMA IN THE PROCESS OF OPTIMIZATION, A HYBRID TECHNIQUE BASED ON GENETIC ALGORITHMS AND NON-LINEAR PROGRAMMING TECHNIQUES IS USED. THE METHODOLOGY IS APPLIED IN THE CHARACTERIZATION OF TWO DIFFERENT COMMERCIAL VISCOELASTIC MATERIALS. THE RESULTS INDICATE THAT THE PROPOSED METHODOLOGY IS EFFECTIVE IN IDENTIFYING THERMORHEOLOGICALLY SIMPLE VISCOELASTIC MATERIALS.

Multi-dimensional seismic response control of offshore platform structures with viscoelastic dampers (II-Experimental study)

Based on the change of traditional viscoelastic damper structure, a brand-new damper is designed to control simultaneously the translational vibration and the rotational vibration for platforms. Experimental study has been carried out on the mechanical properties of viscoelastic material and on its multi-dimensional seismic response control effect of viscoelastic damper. Three types of viscoelastic dampers with different shapes of viscoelastic material are designed to test the influence of excited frequency, strain amplitude and ambient temperature on the mechanical property parameters such as circular dissipation per unit, equivalent stiffness, loss factor and storage shear modulus. Then, shaking table tests are done on a group of single-storey platform systems containing one symmetric platform and three asymmetric platforms with different eccentric forms. Experimental results show that the simulation precision of the restoring force model is rather good for the shear deformation of viscoelastic damper and is also satisfied for the torsion deformation and combined deformations of viscoelastic damper. The shaking table tests have verified that the new-type viscoelastic damper is capable of mitigating the multi-dimensional seismic response of offshore platform.

Experimental research on aluminium–magnesium fuel-rich propellant under high strain rates

The aluminium–magnesium fuel-rich propellant is one of the classified propellant used in the solid rocket ramjet. The weapons with the rocket ramjet are under high overload by launching, the mechanical properties of the propellant should be studied under high strain rate. The uniaxial compressive mechanical curves of the aluminium–magnesium fuel-rich propellant under high strain rates have been obtained with the modified split Hopkinson pressure bar in this paper. Four groups of stress–strain curves were obtained at different strain rates of 2600, 3300, 4500 and 5100 s−1. The experimental results show that the mechanical properties of the aluminium–magnesium fuel-rich propellant are rate-dependent, and the Mg–Al fuel-rich propellant has the mechanical properties of viscoelastic material. With the increase of strain rate, the modulus of the aluminium–magnesium fuel-rich propellant obviously increases. The underlying mechanism of the significant rate sensitivity was investigated by adopting the scanning electron microscope from a micro-structure point of view.

Viscoelastic modeling of nanoindentation experiments: A multicurve method

ABSTRACTNanoindentation is an increasingly used method of extracting surface mechanical properties of viscoelastic materials, especially polymers. Recently, Hutcheson and McKenna used a viscoelastic contact mechanics model to analyze the contact problem between a nanosphere and polystyrene surface. In nanoindentation experiments, the ramp loading test is a similar problem to the particle embedment experiment except that the indentation load function differs. The motivation in this work is to expand the Hutcheson and McKenna analysis to the nanoindentation problem. In particular, we illustrate the limitations of analyzing only a single load‐indentation curve, which does not provide enough information to determine the full range of the viscoelastic response of a polymer, and we show that performing a test sequence that includes multiple loading rates or indentation rates spanning two or more orders of magnitude greatly improves the extracted viscoelastic properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 633–639