Determination of dynamic properties of elastomers over broad frequency range

Support excitation of a small spring-mass system, consisting of a massm and two thin wafers in shear, is used as a simple and reliable method to determine the dynamic properties (storage-modulus and complex-modulus loss factor) of elastomeric materials over a fairly broad frequency range. No special equipment or instrumentation is required since ordinary vibration equipment is used. Microminiature accelerometers are used to monitor the support and mass accelerations which eliminates the measurement of small forces and displacements. The frequency range of interest over which experimental data can be obtained fromone specimen can be varied by the thicknessh of the elastomeric waters and/or the size of the massm. The method discussed has been used to determine the dynamic properties of a wide variety of elastomers with frequencies as high as 6000 Hz. Typical results demonstrating repeatability of the method are shown for a carboxyl-terminated butadiene acrylonitrile (CTBN) specimen over the frequency range of 500–3000 Hz. The small test setup is easily adaptable for use in small temprature-controlled chambers for temperature/frequency studies of elastomers. The mathematical model developed for reduction of experimental data is based on the complex shear modulus for the damping model of the elastomer where the spring-mass system is subjected to support excitation.     

Development of a Novel Experimental Device to Investigate Swelling of Elastomers in Biodiesel Undergoing Multiaxial Large Deformation

The lifetime of an elastomeric product depends on the nature of mechanical loading and the environmental condition during the service. In this context, at least two important aspects contribute to the degradation of the elastomeric parts in service: diffusion of aggressive liquids leading to swelling and fluctuating multiaxial mechanical loading leading to fatigue failure. Moreover, the amount of swelling of elastomers in solvent is affected by the presence of mechanical loading. Hence, it is essential to understand the interactions between the two phenomena for durability analysis of the component. The present study investigates the swelling of elastomers due to diffusion of palm biodiesel in the presence of static multiaxial large deformation. For this purpose, new experimental device and specimen are developed. The device consists of a hollow diabolo elastomeric specimen attached to specially-designed circular metallic grips and plates such that immersion tests can be conducted while the specimens are simultaneously subjected to various mechanical loadings: simple tension, simple torsion and combined tension-torsion. Thus, diffusion of liquids takes place in the material which concurrently undergoes multiaxial large deformation. Two types of elastomers are investigated: Nitrile Rubber (NBR) and Polychloroprene Rubber (CR). The particular features of the device and specimen are discussed and perspectives for further improvement are drawn.     

Filled elastomers: A theory of filler reinforcement based on hydrodynamic and interphasial effects

Experimental evidence has by now established that (i) the hydrodynamic effect and (ii) the presence of stiff interphases (commonly referred to as bound rubber) “bonding” the underlying elastomer to the fillers are the dominant microscopic mechanisms typically responsible for the enhanced macroscopic stiffness of filled elastomers. Yet, because of the technical difficulties of dealing with these fine-scale effects within the realm of finite deformations, the theoretical reproduction of the macroscopic mechanical response of filled elastomers has remained an open problem.The object of this paper is to put forward a microscopic field theory with the capability to describe, explain, and predict the macroscopic response of filled elastomers under arbitrarily large nonlinear elastic deformations directly in terms of: (i) the nonlinear elastic properties of the elastomeric matrix, (ii) the concentration of filler particles, and (iii) the thickness and stiffness of the surrounding interphases. Attention is restricted to the prominent case of isotropic incompressible elastomers filled with a random and isotropic distribution of comparatively rigid fillers. The central idea of the theory rests on the construction of a homogenization solution for the fundamental problem of a Gaussian elastomer filled with a dilute concentration of rigid spherical particles bonded through Gaussian interphases of constant thickness, and on the extension of this solution to non-Gaussian elastomers filled with finite concentrations of particles and interphases by means of a combination of iterative and variational techniques.For demonstration purposes, the theory is compared with full 3D finite-element simulations of the large-deformation response of Gaussian and non-Gaussian elastomers reinforced by isotropic distributions of rigid spherical particles bonded through interphases of various finite sizes and stiffnesses, as well as with experimental data available from the literature. Good agreement is found in all of these comparisons. The implications of this agreement are discussed.     

Macroscopic response of particle-reinforced elastomers subjected to prescribed torques or rotations on the particles

Particle-reinforced rubbers are composite materials consisting of randomly distributed, stiff fibers/particles in a soft elastomeric material. Since the particles are stiff compared to the embedding rubber, their deformation can be ignored for all practical purposes. However, due to the softness of the rubber, they can undergo rigid body translations and rotations. Constitutive models accounting for the effect of such particle motions on the macroscopic response under prescribed deformations on the boundary have been developed recently. But, in some applications (e.g., magneto-active elastomers), the particles may experience additional torques as a consequence of an externally applied (magnetic) field, which, in turn, can affect the overall rotation of the particles in the rubber, and therefore also the macroscopic response of the composite. This paper is concerned with the development of constitutive models for particle-reinforced elastomers, which are designed to account for externally applied torques on the internally distributed particles, in addition to the externally applied deformation on the boundary of the composite. For this purpose, we propose a new variational framework involving suitably prescribed eigenstresses on the particles. For simplicity, the framework is applied to an elastomer reinforced by aligned, rigid, cylindrical fibers of elliptical cross section, which can undergo finite rotations in the context of a finite-deformation, plane strain problem for the composite. In particular, expressions are derived for the average in-plane rotation of the fibers as a function of the torques that are applied on them, both under vanishing and prescribed strain on the boundary. The results of this work will make possible the development of improved constitutive models for magneto-active elastomers, and other types of smart composite materials that are susceptible to externally applied torques.     

Modeling viscoelastic dielectrics

Dielectric elastomers, as an important category of electroactive polymers, are known to have viscoelastic properties that strongly affect their dynamic performance and limit their applications. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principles of non-equilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. The mechanism of instantaneous instability, which corresponds to the pull-in instability often observed on dielectric elastomers, is studied in a general non-equilibrium state. The current theoretical framework is able to adopt most finite-deformation constitutive relations and evolution laws of viscoelastic solids. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate, pre-stress, and relaxation. The dynamic response, as well as the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields, is also studied.     

介电弹性材料的机电耦合性能研究

作为一种新型的电活性聚合物,介电弹性材料可被用作柔性致动器。其中材料的介电性能和机械性能是影响其机电耦合致动性能的关键因素。通过实验方法研究了一种典型的介电弹性材料VHB4910在不同温度和频率下的介电常数和弹性模量,基于实验结果分析了该材料的机电耦合性能。结果表明:依赖于频率和温度的弹性模量是影响该介电弹性材料致动变形的主要因素,对致动性能的影响最大可达4个数量级,材料的介电常数对其致动性能的影响相对较小。     

Mechanics of mechanochemically responsive elastomers

Mechanochemically responsive (MCR) polymers have been synthesized by incorporating mechanophores – molecules whose chemical reactions are triggered by mechanical force – into conventional polymer networks. Deformation of the MCR polymers applies force on the mechanophores and triggers their reactions, which manifest as phenomena such as changing colors, varying fluorescence and releasing molecules. While the activation of most existing MCR polymers requires irreversible plastic deformation or fracture of the polymers, we covalently coupled mechanophores into the backbone chains of elastomer networks, achieving MCR elastomers that can be repeatedly activated over multiple cycles of large and reversible deformations. This paper reports a microphysical model of MCR elastomers, which quantitatively captures the interplay between the macroscopic deformation of the MCR elastomers and the reversible activation of mechanophores on polymer chains with non-uniform lengths. Our model consistently predicts both the stress–strain behaviors and the color or fluorescence variation of the MCR elastomers under large deformations. We quantitatively explain that MCR elastomers with time-independent stress–strain behaviors can give time-dependent variation of color or fluorescence due to the kinetics of mechanophore activation and that MCR elastomers with different chain-length distributions can exhibit similar stress–strain behaviors but very different colors or fluorescence. Implementing the model into ABAQUS subroutine further demonstrates our model's capability in guiding the design of MCR elastomeric devices for applications such as large-strain imaging and color and fluorescence displays.     

Chemo-thermomechanical ageing of elastomers based on multiphase continuum mechanics

This article concerns the constitutive representation of one of the chemical ageing processes that occur in elastomers, chemo-thermomechanical ageing, which takes place as an irreversible, time-delayed chemical reaction when a medium diffuses into an unlike solid. This process is inhomogeneous in component parts of finite thickness, and as it can be thermally activated, ageing is accelerated on an increase in temperature. The application of multiphase continuum mechanics to these basic characteristics enables a thermodynamically coupled material model to be formulated, which is able to describe not only the viscoelasticity, but also the chemical decomposition and reformation processes that occur in the polymer network. The evolution principle of Liu-Müller is used to evaluate the thermomechanical consistency of the model obtained. Subsequent to this, the finite element method is applied to solve the resulting set of partial equations, which corresponds to a coupled multifield problem. The article closes with convincing simulations of illustrative examples.     

Sub-surface fracture of a thin metallic foil under impact loading

We examine here sub-surface fracture of a thin metallic foil sandwiched between two elastomeric layers under impact. In particular we generate a vertical stack consisting of alternate layers of soft elastomers and thin aluminum foils and place it on a rigid substrate; we then allow a rigid sphere to impact the stack from a small vertical height. We show that under impact the foil at the top of the stack undergoes buckling deformation; however the foil sandwiched between the two elastic layers undergoes both deformation and fracture. We show that because of friction at the contacting interfaces with the elastomer, the sandwiched foil is subjected to in-plane stretching which when exceeds a threshold limit causes fracture. Experiments show that this threshold condition is reached within a range of critical thicknesses of the top and bottom elastomeric layers, for a given height of impact of the rigid spherical indenter. We present a theoretical analysis to predict the critical thickness of the stack below which the foil is expected to undergo fracture and also the critical heights within this stack at which the foil would fracture.     

Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers

Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality.     

Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes

When an elastomeric material is deformed and subjected to temperatures above some chemorheological value T _cr (near 100°C for natural rubber), its macromolecular structure undergoes time and temperature dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (often a reduced stiffness) and permanent set on removal of the applied load. A recently proposed constitutive theory is used to study the influence of chemorheological changes on the inflation of an initially isotropic spherical rubber membrane. The membrane is inflated while at a temperature below T _cr. We then look at the pressure response assuming the sphere's radius is held fixed while the temperature is increased above T _cr for a period of time and then returned to its original value. The inflation pressure during this process is expressed in terms of the temperature, representing entropic stiffening of the elastomer, and a time dependent property that represents the kinetics of the chemorheological change in the elastomer. When the membrane has been returned to its original temperature, it is shown to have a permanent set and a modified pressure-inflated radius relation. Their dependence on the initial inflated radius, material properties and kinetics of chemorheological change is studied when the underlying elastomeric networks are neo-Hookean or Mooney–Rivlin.     

Mathematical modeling of magneto-sensitive elastomers

Magneto-sensitive (MS) elastomers are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. These materials typically consist of micron-sized ferrous particles dispersed in an elastomer. The full system of equations for deformable MS solids in an electro-magnetic field is first considered. Then, the strain-energy functions for isotropic MS elastomers are presented and a simple phenomenological model is suggested. Finally, to illustrate some of the features of the derived model, a MS elastomer confined by parallel top and bottom plates is subjected to shear deformation under the influence of a magnetic field normal to the plates. An acceptable agreement is illustrated between numerical simulation and experimental observation.     

Temperature dependent bulge test for elastomers

The bulge test is a particularly convenient testing method for characterizing elastomers under biaxial loading. In addition, it is convenient to utilize this test for validating material models in simulation due to the heterogeneous strain field induced during inflation. During the bulge test the strain field for elastomers covers uniaxial tension at the border to pure shear and equibiaxial tension at the pole. Elastomeric materials exhibit a hyperelastic material behavior, with a dependency on temperature and loading rate. The temperature effect on the mechanical behavior during biaxial loading is considered in the present study. A bulge test setup combined with a temperature chamber is developed in order to characterize this effect, and an exemplary temperature dependent characterization of a poly(norbornene) elastomer is performed with this setup. The equibiaxial stress–strain curves measured at 60 °C, 20 °C and −20 °C are presented.     

Free-energy density functions for nematic elastomers

The recently proposed neo-classical theory for nematic elastomers generalizes standard molecular-statistical Gaussian network theory to allow for anisotropic distributions of polymer chains. The resulting free-energy density models several of the novel properties of nematic elastomers. In particular, it predicts the ability of nematic elastomers to undergo large deformations with exactly zero force and energy cost—so called soft elasticity. Although some nematic elastomers have been shown to undergo deformations with unusually small applied forces, not all do so, and none deform with zero force. Further, as a zero force corresponds to infinitely many possible deformations in the neo-classical theory, this non-uniqueness leads to serious indeterminacies in numerical schemes. Here we suggest that the neo-classical free-energy density is incomplete and propose an alternative derivation that resolves these difficulties. In our approach, we use the molecular-statistical theory to identify appropriate variables. This yields the choice for the microstructural degrees of freedom as well as two independent strain tensors (the overall macroscopic strain plus a relative strain that indicates how the deformation of the elastomeric microstructure deviates from the macroscopic deformation). We then propose expressions for the free-energy density as a function of the three quantities and show how the material parameters can be measured by two simple tests. The neo-classical free-energy density can be viewed as a special case of our expressions in which the free-energy density is independent of the overall macroscopic strain, thus supporting our view that the neo-classical theory is incomplete.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

Mullins effect in elastomers filled with particles aligned by a magnetic field

Magnetorheological elastomers (MRE) are particulate composite materials, whose fillers are structured by a magnetic field during curing. These particles are brought in quasi-contact by the field, in a chain-like unidirectional structure. Due to this organization the local stresses between the particles is high and debonding between particles and elastomer occur at low strain. We have experimentally studied and analytically modeled the progressive breaking of the polymer-to-particle bonds. The two cases of strong and weak bonds between elastomers and particles have been studied. The analytical model correctly reproduces the stress strain curve in the presence of a debonding process although overestimating the size of the debonding cavity which is obtained by comparison between experiments and FEM simulations. The extension of the model to a chain of spheres allows to well explain the Mullins effect on MRE. Furthermore it is shown that the quality of the bonds between the particles and the elastomer does not influence the change of stiffness brought by the application of a magnetic field.     

The Stability of Laminated Elastomer Coatings Under Surface Loading

The stability of laminated elastomer coatings at normal and high temperatures is considered in a three-dimensional formulation. The problem is formulated and the basic characteristic equations are derived. Graphs of the physicomechanical parameters of some elastomers against temperature are experimentally obtained. Specific examples for a three-layer coating are considered