Voigt Units Research Articles

Improvement of the creep resistance of glycidyl azide polyol energetic thermoplastic elastomer-based propellant by nitrocellulose filler and its mechanism

To investigate the effects of nitrocellulose (NC) content on the creep properties of glycidyl azide polyol energetic thermoplastic elastomer (GAP-ETPE)-based propellant, creep behaviour was studied by rotary rheometer under various shear stress and temperatures. Experimental results showed that creep strain and creep rate of samples increase with the increasing shear stress level, and similar creep behaviour tendency was observed under elevated temperature. When filled with 1 and 2 wt% NC, the creep strain and creep rate of GAP-ETPE/NC-based propellant were significantly less than the unfilled state, indicating that the NC contents partly inhibited the mobility of the binder segment and improved the creep resistance of GAP-ETPE-based propellant. Moreover, the constitutive equations of the creep curves were obtained from the four-element mechanical model, and the fitting results coincided well with the experimental data. Among the fitting parameters, the elastic modulus of high elastic deformation, E2, and the viscosity of Voigt units, η2, were sensitive and promising for the evaluation of creep strain of the GAP-ETPE-based propellant. Finally, the creep resistance model was established and verified by Fourier transform infrared spectroscopy, glass temperature and physical crossing point density of GAP-ETPE/NC-based propellant. Upon analysis of the experimental data, we concluded that the creep resistance mechanism of GAP-ETPE/NC-based propellant came from NC altering the flow lines of the continuous phase and restricted chain mobility in the propellant, which improved the creep resistance.

Electro-rheological description of solids dielectrics exhibiting electrostriction

An electro-rheological model based in Voigt units which takes into consideration the variation in volume promoted by electrostriction is developed. The model was based on a mean field approximation as an averaging of the mechanical and electrical properties. The electro-rheological coupling which describes the effects of the electrical excitation on the mechanical response and the effects of the mechanical excitation on the electrical response of the dielectric is studied. In the case of an alternating electrical excitation the model reveals the appearance of harmonics in the current through the dielectric promoted by the electrostriction phenomenon. In contrast, for the case of an oscillating mechanical excitation, a current which overtakes the driving mechanical oscillation was resolved to appear. The correlation of the new model with experimental results, obtained from dynamic mechanical analysis tests conducted under high electric field, in polyamide, was found out.

Finite element method on fractional visco-elastic frames

In this study the Finite Element Method (FEM) on viscoelastic frames is presented. It is assumed that the Creep function of the constituent material is of power law type, as a consequence the local constitutive law is ruled by fractional operators. The Euler Bernoulli beam and the FEM for the frames are introduced. It is shown that the whole system is ruled by a set of coupled fractional differential equations. In quasi static setting the coupled fractional differential equations may be decomposed into a set of fractional viscoelastic Kelvin–Voigt units whose solution may be obtained in a very easy way.

Study of the Volume Change in an Electrorheological Representation for Semicrystalline Polymers

We have studied the problem of the change in volume in a dielectric material due to the deformation process promoted by the application of an alternating electric field. The classical electrodynamics, the mechanic of continuous media and the formalism of the rheology were coupled in the present study. By considering a dielectric material through a mean field approximation as an effective dipole described by means of a rheological Voigt unit, we have resolved the behavior of the electrical current through the dielectric. A second harmonic is found when the material is subjected to a sinusoidal electric field.

Fractional Tajimi–Kanai model for simulating earthquake ground motion

The ground acceleration is usually modeled as a filtered Gaussian process. The most common model is a Tajimi–Kanai (TK) filter that is a viscoelastic Kelvin–Voigt unit (a spring in parallel with a dashpot) carrying a mass excited by a white noise (acceleration at the bedrock). Based upon the observation that every real material exhibits a power law trend in the creep test, in this paper it is proposed the substitution of the purely viscous element in the Kelvin Voigt element with the so called springpot that is an element having an intermediate behavior between purely elastic (spring) and purely viscous (dashpot) behavior ruled by fractional operator. With this choice two main goals are reached: (i) The viscoelastic behavior of the ground may be simply characterized by performing the creep (or the relaxation) test on a specimen of the ground at the given site; (ii) The number of zero crossing of the absolute acceleration at the free field that for the classical TK model is $$\infty $$ for a true white noise acceleration, remains finite for the proposed model.

Creep Behavior of Catheter Reinforced with Braids: Analytical Simulation of Uniaxial Tension under Two-Stage Step Stress

This paper describes the creep deformation behavior of catheter which is made of soft nylon resin and is reinforced with thin stainless wires called braid. In this research, the creep deformation behavior of uniaxial tension generated under two-stage step stress is examined as the most fundamental case that the principal axis of stress is fixed in a space. And the mechanical model, which is composed of a Voigt unit and a single spring element, is proposed for representing the creep deformation behavior. Then, the numerical simulation is carried out, and the validity of this model is verified by comparing the analytical results with the experimental results under two-stage step stress.

Shape memory polymer foams from emulsion templating

Shape memory polymers (SMPs) change their shape under a stimulus (thermal, chemical, light) and return from an imposed temporary shape to their permanent, original shape. SMPs usually contain “permanent” domains that determine the permanent shape (chemical or physical crosslinks) and “reversible” domains that determine the temporary shape, usually by heating above a glass transition temperature or a melting point (Tm). Compared to fully dense SMPs, SMP foams can undergo higher temporary deformations and can exhibit higher deformations when they recover. In this paper, SMP foams based upon (meth)acrylates with crystallizable long side-chains were synthesized through emulsion-templating within nanoparticle-stabilized high internal phase Pickering emulsions where the nanoparticles also served as crosslinking centers. The nature of the polymer backbone affected the nature of the crystalline phase for identical side chains. The SMP foams at room temperature maintained the temporary shape (a strain of 0.7) imposed above the Tm and exhibited good recovery upon reheating for all four compression–recovery cycles. While the methacrylate-based SMP exhibited a single-stage recovery, the acrylate-based SMP, with identical side-chains, exhibited a two-stage recovery that can be associated with the existence of two crystalline phases. The recovery behavior was described using Kelvin–Voigt units in series with the dependence of viscosity on temperature described using a WLF-like relationship.

Performance of diamond-like carbon-protected rubber under cyclic friction. II. Influence of substrate viscoelasticity on the friction evolution

In this paper, the influence of the mechanical properties of rubber substrate on frictional behavior of DLC-protected rubber is studied by numerical methods. The viscoelastic contribution to the friction during a tribotest was simulated according to a “mattress” approach composed by Voigt or standard linear solid units. The latter approach demonstrated more accurate predictions. In both cases, the results show an increase of the contact depth, which is in agreement with the experimental observations. The simulations also show a progressive reduction of the viscoelastic contribution of the coefficient of friction (CoF) with the number of laps due to the elongation of the front part of the contact area. This prediction does not agree with the experimentally observed increase of CoF, and suggests a dominant contribution of the adhesive component to the friction under real conditions.

An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators

In this paper, a model that can precisely portray hysteresis and creep in piezoelectric actuators is proposed. The model, which is originally constructed using bond-graph representation, describes the actuator’s various physical effects and energy interaction between physical domains. Specifically, the model utilizes a parallel connection of Maxwell-slip elements and a nonlinear spring to describe hysteresis, and a series connection of Kelvin–Voigt units to describe creep. Using the experimental data, the constitutive relation of the nonlinear spring and the parameters of linear, physical elements in the model can be systematically identified via the linear programming method. To further account for the frequency-dependent hysteresis behavior, a dynamic damper is incorporated. By analyzing the model, the influence of initial strain/charges on the creep response is revealed and an initialization procedure is devised to eliminate such an influence. An inverse model control, in the sense of feedback linearization, is constructed based on the identified model to make the actuator track reference trajectories. Experiments show that both creep and hysteresis are effectively cancelled and accurate tracking of selected reference trajectories is achieved.

Impedance spectroscopy analysis in a complex system: Sodium dodecyl sulfate solutions

Impedance measurements in the range 10–107 Hz were carried out in water solutions of sodium dodecyl sulfate for concentrations below and above critical micellar concentration (cmc). The results were analysed using a series combination of two Voigt units, describing bulk and interface process and, additionally, an unexpected inductive one, problably due to inertial effects of an adsorbed layer of SDS molecules at the electrode. The interface processes, including the inductive one, show transition at a concentration somewhat below cmc.

STUDY ON THE PRINCIPLE OF THE VISCOSITY MEASUREMENT OF LIQUIDS WITH A FORCED-VIBRATION TORSION PENDULUM

The principle of the viscosity measurement of liquids with a forced vibration torsion pendulum is studied in this paper-The parameters of the testing system was determined by a 3-parameter model containing a Voigt unit,and the feasibility of the corresponding 4-parameter model of the measuring system,in which a liquid sample has been introduced to measure its viscosity,is then verified-It is proposed,based on the experimental results,that the measuring system is reliable-

Viscoelastic characterization of solid foods from creep compliance data: application to potato tissues

Two software systems were developed to simplify acquisition and analysis of data describing creep behavior of viscoelastic solid foods and to determine the magnitude of instantaneous elastic compliance, viscoelastic compliances and viscosity associated with Newtonian flow. The first of these systems was used to store information on the experiment, to collect the data generated during the experiment, to present these in real time and to create files containing the experimental data for subsequent analysis. The second system was used to fit data to discrete Kelvin-Voigt models with four, six or eight constants. The systems were tested in the calculation of rheological properties of fresh and cooked potato tissues. A six-element Burgers model containing two discrete Voigt units proved the most suitable for defining tissue creep behavior, suggesting that different structural components could be related to each unit. The instantaneous elastic modulus could be associated with internal cell pressure. Gelatinization of starch and viscoelastic units appeared to reflect the viscoelastic properties of pectic substances and hemicelluloses, respectively.

Change in the two-step flow behavior on aging the ternary mixture comprising monoalkyl cationic surfactant, long-chain alcohol and water II. Analysis of the creep behavior

A two-step development of the internal structure on aging the ternary mixture comprising cetyltrimethylammonium chloride (C 16CA), cetyl alcohol (C 16OH), and water was elucidated from the change in the creep behavior. The system was expressed by a six-element model comprising two Voigt units in series with a Maxwell unit. A similar increase in the instantaneous elastic modulus G 0, the Newtonian viscosity η 0, and the elastic modulus and viscosity of the Voigt units ( G 1, η 1) with a longer retardation time τ 1 were observed on aging up to 1–3 days, followed by a leveling off. Conversely, the elastic modulus and viscosity of the Voigt units ( G 2, η 2) with a shorter retardation time τ 2 were constant at the beginning, followed by an increase on aging. From a cryo-SEM observation, we confirm that the two-step development considered from the creep properties on aging was caused by an initial coagulation to form a network of multilamellar vesicles, and a subsequent phase transition from vesicles to lamelae.

The Viscoelastic Deformation of Some Tableting Materials as Assessed by Indentation Rheology

AbstractThe time-dependent deformation of compacts prepared from four tablet compression bases has been assessed by microindentation rheology. Compacts were made from Avicel PH101, Emcompress, Emdex, and Starch 1500 at compaction pressures of 30, 60, and 90 MPa. A spherical indenter, 1.55 mm diameter, was allowed to indent into the compacts under a fixed load of 5.89 N (600 g) and the changing depth of indentation was recorded. The corresponding creep compliance versus time curve was calculated and analyzed by discrete mechanical analysis to yield Maxwell and Voigt “spring and dashpot” mechanical models. This yielded quantitative data on instantaneous elastic compliance and modulus, the time-dependent viscoelastic compliances, viscosities, and retardation times of each Voigt unit, and the Newtonian viscosity of the compacts. In general, the deformation of the compacts was in the rank order Starch 1500 > Avicel PH101 > Emdex > Emcompress. Emcompress showed negligible viscoelasticity and plasticity. For the...

Viscoelastic Analysis of Shear Adhesion Test for Pressure-Sensitive Adhesive Tape

Abstract A new shear adhesion tester of a pressure-sensitive adhesive tape is developed, by which the slippage of the tape under shearing force can be measured as accurately as 1 μm or 0.1 μm per digit by the aid of a linear variable differential transformer. When shearing force is exerted on a tape applied on an adherend, two kinds of slippages are expected, that is, the one between the surface of the adhesive and the adherend and the other of the shearing strain of the adhesive. In order to separate the two kinds of slippages, slippage under shearing force and the recovery displacement after removing the force are measured. Analysing the results of measurements it becomes clear that viscoelastic models of Voigt units connected in series are suitable for both of the slippages.

粘着テープの保持力試験装置の試作及び粘弾性力学モデルの解析

A new tester to measure micro shearing slippage of the tape is developed, in which an LVDT is used to measure the slippage at 1 or 0.1 μm a digit. By the tester not only the slippage under the application of shearing force but also the recovering slippage after the force is removed can be measured. Shearing and recovering slippage of a polyester tape coated with adhesive of polyacrilic acidester is measured under the following conditions : 0.98 N {100 gf} in shearing force, 0, 20, 40 and 60 min in leaving time, 30 min both in loading and recovering time, and 23 ± 0.5°C and 65 ± 5% RH in atmospheric condition. The results of the experiments and the analyses are concluded briefly as followes : (1) Combination of two Voigt units is effectively adapted for both of the cohesive and boundary slip. (2) The coefficients of the Voigt units in cohesive slip are kept constant throughout the applied leaving time. (3) The coefficients of the Voigt units of boundary slip in short leaving time show higher transient effect and larger terminal velocity of slip, but in the leaving time of 40 min little transient effect is observed, and in the leaving time of 60 min no boundary slip is recognized.

Rheological Study of Vanishing Cream

Dispersions of stearic acid in an aqueous phase containing polyhydric alcohol, stabilized by sodium and potassium soaps, so-called vanishing cream, have been studied by measuring their flow and creep properties. The stearic acid was a commercially available mixture of the long chain acids of C14, C16, C18 and C20; the polyhydric alcohol was a member of the series glycerin, propylene glycol, etc. All the systems examined showed complex flow properties, e.g., hysteresis loops and spur points in the flow experiments. The creep behavior of all the systems could be represented by a mechanical model composed of a Voigt unit and a Maxwell unit in series. The observed total compliance was markedly dependent on the formulation and the aging time of the systems. However, the retardation time did not change appreciably, indicating that there was no essential difference in the nature of the secondary bonds in the systems, which was break and reform during creep tests. These rheological properties may be explained by the presence of a network structure of the soap micelles in which fatty acid was solubilize partially, in the aqueous phase.

Rheological Study of Fatty Acid-Soap Systems

Stearic acid dispersions in the aqueous phase stabilized by sodium stearate or potassium stearate have been examined by their flow and creep curves. The flow curves, obtained by using a Couett type viscometer, showed hysteresis loops between "up" and "down" curves. The creep curves suggested that the systems can be represented by a mechanical model of one Voigt unit in series with a Maxwell unit. The compliances increased sharply with decreasing weight fraction of dispersed phase from 0.10 to 0.05, and also showed an increase by ageing over several weeks after the preparation. These rheological properties may be explained by the presence of a network structure of the soap micelles solubilized partially by fatty acid, in the aqueous phase.

The self-bodying action of the mixed emulsifier cetrimide-cetostearyl alcohol.

Liquid paraffin emulsions stabilized by the mixed emulsifier cetrimide/cetostearyl alcohol have been examined by microscopy, particle size analysis, continuous shear rheometry, and creep. The disperse phase of each emulsion was aggregated, and many of the nonspherical particles contained crystals of cetostearyl alcohol. The rheological properties of each emulsion were not related directly to the particle size distribution but to a gel network present in the continuous phase. This gel network was shown to be similar to that formed by dispersing cetrimide and cetostearyl alcohol in water so as to form a ternary system. All the systems showed complex flow properties in continuous shear experiments, e.g., hysteresis loops denoting irreversible shear breakdown. Additional complex flow properties, i.e., spur points and dilatancy, apparent in emulsions containing greater than 5% mixed emulsifier, were related to the structure in the continuous phase. In creep, mechanical models of three Voigt Units in series with a Maxwell Unit were deduced. In ternary systems and emulsions, the compliances decreased and the viscosities increased as the cetrimide/cetostearyl alcohol concetration increased. The creep parameters indicated that emulsions containing greater than 5% mixed emulsifier increased in consistency on aging, owing to the orientation of gel structure in the continuous phase.

The self bodying action of the mixed emulsifier sodium dodecyl sulfate/cetyl alcohol

Liquid paraffin emulsion stabilized by the mixed emulsifier sodium dodecyl sulfate/cetyl alcohol have been examined by microscopy, particle size analysis, continuous shear rheometry, and creep. The disperse phase was aggregated and included some nonspherical globules containing crystals of cetyl alcohol. Emulsions were thixotropic and the extent increased with emulsifier concentration. In creep, systems suggested a mechanical model of three Voigt units in series with a Maxwell unit; the compliances decreased and the viscosities increased with emulsifier concentration. Rheological properties are explained by the presence of a viscoelastic network in the continuous phase.