Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic 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 (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.     

An Experimental Facility to Measure the Chemorheological Response of Inflated Elastomeric Membranes at High Temperature

An experimental facility for measuring the time-dependent deformation of an inflated elastomer membrane at elevated temperatures is presented. The facility controls the temperature and inflation volume of a membrane specimen and measures the pressure and deformation field. The finite deformation field is determined by comparing the configuration of the inflated membrane to the initially flat reference configuration, determined by photogrammetry of an array of dots printed on the surface of the membrane. The facility provides an effective method to investigate the changes in mechanical properties due to scission and cross-linking in the context of a simple elastomeric structure that has a distribution of multi-axial deformation states.     

Combined deformation- and temperature-induced scission in a rubber cylinder in torsion

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T_cr (near for natural rubber), it undergoes time and temperature dependent chemical changes consisting of scission and crosslinking of its macromolecular structure. The process continues until the temperature decreases below T_cr. Experiments carried out in uniaxial extension have shown that the chemical changes are independent of stretch ratio within moderate stretches. It is reasonable to expect that the chemical changes would be affected by sufficiently large deformations, an interaction referred to as ‘mechanochemistry’. A kinetic theory of the breakdown of solids by Zhurkov [Kinetic concept of strength of solids, Int. J. Fract. Mech. 1 (1965) 311-323. [15]] attributes this interaction to the lowering of activation energy by mechanical work.In a recent constitutive theory, an expression was developed that relates the chemical kinetics of scission of the original elastomeric network to time, temperature and activation energy. The kinetic theory of Zhurkov suggests a method for modifying this expression to account for the influence of deformation. This is explored in the case of simple shear deformations, such as those occurring during torsion of elastomeric cylinders held at fixed length. Using the approach of Penn and Kearsley [The scaling law for finite torsion of elastic cylinders, Trans. Soc. Rheology 20 (1976) 227-238. [16]], it is shown that experiments in torsion can be used to determine the influence of shear deformations on the chemical kinetics of scission.     

Experimental estimation of wall slip for filled rubber compounds

The phenomenon of wall slip during flow of rubber compounds through capillaries is investigated for a typical styrene-butadiene elastomer with carbon black. It was found that at low temperature (110°C) the dependencies of slip velocity V _c on shear stress are described by the power law but, additionally, V _c depends on radius of a channel. At high temperatures there is a critical shear stress below which sliding is absent. Sliding appears only at higher shear stresses where, again, V _c depends on shear stress and the radius of a channel.     

Prestretch effect on snap-through instability of short-length tubular elastomeric balloons under inflation

The inflated elastomeric balloon structures are widely used in engineering fields such as elastomeric actuators and artificial muscles. This study, involving both experiment and modeling, is focused on the prestretch effect on non-linear behavior of inflated short-length tubular elastomeric balloons. In the experiment, the prestretched tubular elastomeric balloon is subjected to air pressure while the two ends are fixed with rigid tubes. The shape evolutions of the tubular elastomeric balloons are illustrated. The non-axisymmetric bulging is observed in the inflated tubular balloon with small prestretch. An analytical model based on continuum mechanics is developed to investigate the inflation behavior of the tubular balloons, and the analytical results agree well with the experimental observation. Analysis shows that snap-through instabilities may happen during the inflation of the tubular balloon. Prestretch along the axis of the tubular balloon can suppress instability during inflation and regulate the reaction force along the axial direction. This work can guide the future application of tubular balloons in elastomeric actuators and artificial muscles.     

Puncture characterization of rubber membranes

Puncture resistance is among the major mechanical properties of rubber membranes, yet the intrinsic material parameters controlling the puncture of these materials are still unknown. To evaluate puncture resistance, the ASTM F1342 standard test is currently the most commonly used method. Using a conical puncture probe, this test is designed for any type of protective clothing, including coated fabrics, laminates, textiles, plastics, elastomeric films or flexible materials. This work aims to investigate the quantitative material parameters that control the puncture resistance of thin rubber membranes. Three commercial rubbers commonly used in protective gloves are investigated. The results demonstrate that the probe-tip geometry strongly affects the results in puncture characterization. The maximum puncture force depends on the contact surface between the elastomer membrane and the probe tip. The indentation force has been calculated for elastomer membranes with large deformations in the absence of friction, using the Mooney strain-energy function. The puncture strengths of elastomer membranes are much lower than their tensile and biaxial strengths. The puncture of rubber membranes is controlled by a maximum local deformation that is independent of the indentor geometry.     

Inflation of spherical rubber balloons

When a spherical rubber balloon of the sort used in meteorological applications is inflated, the onset of aspherical deformation is observed after the pressure maximum has been attained. Upon further inflation the balloon regains its spherical shape. Here, the rubber balloon is idealized as an elastic membrane and inflation is taken to be accomplished by a prescribed increase in enclosed volume. The axisymmetric equilibrium states of slightly imperfect membranes are determined numerically by means of the Ritz-Galerkin method. Several particular material models representative of the behavior of rubberlike solids are employed in order to illustrate a number of feautres associated with the aspherical deformation.     

Analytical solutions for inflation of pre-stretched elastomeric circular membranes under uniform pressure

Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics. For convenience of the structural design, it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings. However, both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution. In this paper, we focus on the inflation of a prestretched elastomeric circular membrane under uniform pressure, and derive an approximate analytical solution of the pressure–volume curve based upon a reasonable assumption on the shape of the inflated membrane. Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure–volume curve with prescribed peak point and initial slope. This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.     

On the bursting of linear polymer melts in inflation processes

Molten LLDPE and HDPE plates (thickness 2 mm) have been inflated into a circular cylinder (inner radius 31 mm) under isothermal conditions. Low deformation rates allow the plates to be inflated considerably into the cylinder, and at high inflation rates an early burst is observed.Axis-symmetric numerical simulation of the inflations have been performed, using a constitutive equation in the form of a separable memory integral where the strain dependence is described by the Linear Molecular Stress Function (L-MSF) model with dissipative convective constraint release. The material parameters in the constitutive model are obtained using liner viscoelastic (oscillatory shear) and uni-axial elongational measurements.The numerical simulations were performed for inflation of a flat plate and a perturbed plate, where a small circular cone was removed from the centre of the surface of the plate. This was done in order to investigate the stability of the inflations. It is shown that all of the inflations are hydrodynamically unstable, though the effect on the occurrence of the burst is limited. One exception is at slow inflation, where an unexpected burst may appear as a consequence of minute deviations from an ideal flat plate. All of the numerical calculations show quantitative agreement with the experiments for a wide range of experimental conditions. This strongly suggests that the initiation of the burst is a hydrodynamic phenomenon.The critical parameters in the inflation of molten linear polymers have been investigated using the Gel equation as a memory function (M(s)=Ans ^–(1+n)) and inflating the plate with a constant velocity for the top of the plate. The hydrodynamic burst in a linear polymer is mainly associated with the linear viscoelastic properties and only slightly with the non-linear strain dependence. Increased (linear) elasticity reduces the inflated volume, at the same inflation velocity, before the burst occurs. Furthermore, the critical parameter for the occurrence of the burst (whether or not the burst occurs) is related to the crossover point (G=G) in linear viscoelasticity.     

Bifurcation condition of crack pattern in the periodic rectangular array

Bifurcation condition of crack pattern in the periodic rectangular array plays an important role in determining the final failure pattern of rock material. An approximation for the critical crack size/spacing ratio is established for a uniformly growing periodic rectangular array yields to a non-uniform growing pattern of crack growth. Numerical results show that the critical crack size/spacing ratio λ_cr depends on the number of cracks, the crack spacing, the perpendicular distance between two adjacent rows, as well as the loading conditions. In general, λ_cr increases with the number of lines. It is observed that the critical crack size/spacing ratio λ_cr for the periodic rectangular array decreases with an increase in the perpendicular distance between two adjacent rows. It is clear that the critical crack size/spacing ratio λ_cr for the periodic rectangular array under shear stress increases with increasing the crack spacing.     

Mechanisms of brittle-ductile transition in toughened thermoplastics

The objective of this work was to investigate the mechanism of brittle-ductile transition in toughened polymers. Two systems, namely, a rubber-toughened nylon 66 (Zytel ST-801) and a high impact polystyrene (HIPS), were chosen for this study. The samples were prepared by injection molding and were tested in three-point bending under various loading rates and temperatures. The brittle-ductile transition temperature (T_b–d) was determined from the observed fracture behavior as a function of temperature. Molecular relaxation temperatures of the polymers were measured by mechanical spectroscopy at various frequencies. The correlation between temperature and loading rate was estimated using the Arrhenius equation. The results show that T_b–d of Zytel ST-801 is only slightly affected by the loading rate, whereas T_b–d of HIPS strongly increases with deformation rate. It is found that for the former, within the experimental errors, an increase in T_b–d with loading rate corresponds to the shift in the secondary relaxation temperature T_b of the nylon 66 matrix. For the latter however, the increase in T_b–d is related to the glass/rubber relaxation of the polystyrene matrix. It seems that the type of molecular relaxation controlling the brittle-ductile transition corresponds to that with lower activation energy.     

Influence of stress triaxiality and temperature on void growth and ductile/brittle transition behavior of 40 Cr steel

Examined experimentally are the influence of stress triaxiality and temperature on the growth of microvoids and the ductile/brittle transition (DBT) macrobehavior of 40 Cr steel subjected to two different heat treatments. This is accomplished by testing more than 300 smooth and notched specimens over a temperature range of 20°C to −196°C. Changes in the microstructure morphology are examined by scanning electron microscopy (SEM) and identified with fracture data on a surface constructed from the uniaxial strain ε_c at fracture, the stress triaxiality R_σ and the temperature T. While stress triaxiality has a significant influence on the DBT temperature T_c, it does not affect the ratio of the average radius of voids R_o to that of inclusions R_i. The ratio R_o/R_i is found to increase with temperature and remains constant in specimens with different notch radii regardless of the temperature. Empirical relations between T_c and R_σ⁻ and R_o/R_i and T are proposed to better understand how macrofracture parameters are influenced by microstructure entities.     

On the dynamic electromechanical loading of dielectric elastomer membranes

Dielectric elastomer actuators (DEAs) have received considerable attention recently due to large voltage-induced strains, which can be over 100%. Previously, a large deformation quasi-static model that describes the out-of-plane deformations of clamped diaphragms was derived. The numerical model results compare well with quasi-static experimental results for the same configuration. With relevance to dynamic applications, the time-varying response of initially planar dielectric elastomer membranes configured for out-of-plane deformations has not been reported until now. In this paper, an experimental investigation and analysis of the dynamic response of a dielectric elastomer membrane is reported. The experiments were conducted with prestretched DEAs fabricated from 0.5 mm thick polyacrylate films and carbon grease electrodes. The experiments covered the electromechanical spectrum by investigating membrane response due to (i) a time-varying voltage input and (ii) a time-varying pressure input, resulting in a combined electromechanical loading state in both cases. For the time-varying voltage experiments, the membrane had a prestretch of three and was passively inflated to various predetermined states, and then actuated. The pole strains incurred during the inflation were as high as 25.6%, corresponding to slightly less than a hemispherical state. On actuation, the membrane would inflate further, causing a maximum additional strain of 9.5%. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum polar strain of 28%. The results from these experiments reveal that the response of the membrane is a departure from the classical dynamic response of continuum membrane structures. The dynamic response of the membrane is that of a damped system with specific deformation shapes reminiscent of the classical membrane mode shapes but without same-phase oscillation, that is to say all parts of the system do not pass through the equilibrium configuration at the same time. Of particular interest is the ability to excite these deformations through a varying electrical load at constant mechanical pressure.     

Chemorheological response of elastomers at elevated temperatures: Experiments and simulations

An experimental study and a method for simulating the constitutive response of elastomers at temperatures in the chemorheological range (90-150 °C for natural rubber) are presented. A comprehensive set of uniaxial experiments for a variety of prescribed temperature histories is performed on natural rubber specimens that exhibit finite elasticity, entropic stiffening with temperature, viscoelasticity, scission, and oxygen diffusion/reaction effects. The simulation approach is based on a multi-network framework for finite elasticity, isothermal incompressibility, thermal expansion, and temperature-induced degradation. The model extends previous work to account for kinetics of scission for arbitrary time-varying temperature histories and incorporates the effects of viscoelastic relaxation and diffusion-limited oxidative scission. The model is calibrated to experiments performed on a commercially-available filled natural rubber material, and numerical simulations are compared favorably to experiments for a variety of temperature histories.     

Finite inflation of a hyperelastic toroidal membrane over a cylindrical rim

The present paper is devoted to the study of finite inflation of a hyperelastic toroidal membrane on a cylindrical rim under uniform internal pressure. Both compliant and rigid frictionless rims have been considered. The compliant cylindrical rim is modeled as a linear distributed stiffness. The initial cross-section of the torus is assumed to be circular, and the membrane material is assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The problem is formulated as a two point boundary value problem and solved using a shooting method by employing the Nelder–Meads search technique. The optimization function is constructed on a two (three) dimensional search space for the compliant cylinder (rigid cylinder). The effect of the inflation pressure, material properties and elastic properties of the rim on the state of stretch and stress, and on the geometry of the inflated torus have been studied, and some interesting results have been obtained. The stability of the inflated configurations in terms of occurrence of the impending wrinkling state in the membrane has also been studied.     

On a Free Convection Problem Over a Vertical Flat Surface in a Porous Medium

The problem of the free convection boundary-layer flow over a semi-infinite vertical flat surface in a porous medium is considered, in which the surface temperature has a constant value T₁ at the leading edge, where T₁ is above the ambient temperature, and takes a value T₂ at a given distance L along the surface, varying linearly between these two values and remaining constant afterwards. Numerical solutions of the boundary-layer equations are obtained as well as solutions valid for both small and large distance along the surface. Results are presented for the three cases, when the temperature T₂ is greater, equal or less than the ambient temperature T_∞. In the first case, T₂ > T_∞, a boundary-layer flow develops along the surface starting with a flow associated with the temperature difference T₁ − T_∞ at the leading edge and approaching a flow associated with the temperature difference T₂ − T_∞ at large distances. In the second case, T₂ = T_∞, the convective flow set up on the initial part of the surface drives a wall jet in the region where the surface temperature is the same as ambient. In the final case, T₂ < T_∞, a singularity develops in the numerical solution at the point where the surface temperature becomes T_∞. The nature of this singularity is discussed.     

Issue Information

Three‐dimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical set‐up, which restricts the development of intrinsic wake structure, leads to an over‐prediction of the onset point of the secondary wake instability (Re_cr). A best practice of the numerical set‐up is presented for the accurate prediction of Re_cr by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Re_cr, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical set‐up. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Re_cr, while the periodic boundary condition is recommended for simulating the wake structures above Re_cr. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.     

The peculiarities of the rheological behaviour of coal tars

The results are discussed of rheological studies of coal tars with different concentrations of substances insoluble in toluene at periodical, steady-state and combined periodical-steady shear deformations in a wide range of deformation frequencies, rates and amplitudes in the temperature region from 223 to 333 K. The temperatures of structural and mechanical glassingT _g , the activation energies of viscous flow and initial viscoelastic constants of these systems have been determined. Temperature and temperature-frequency dependencies of dynamical parameters have been obtained, the pre-steady-state and the steady-state flow modes of permanent deformation have been studied and thixotropic parameters have been evaluated at the combined action of vibration and permanent deformation.