High-speed compression of single alginate microspheres

A recently developed high strain-rate micro-compression tester was used for the mechanical characterization of alginate microspheres produced by emulsification/internal gelation. Single microparticles with diameters of 80- were compressed to a wide range of deformations at different speeds (10-), and then released, or held at constant deformation to permit them to relax. The higher speeds allowed compressions with minimal time-dependent behaviour of the particles, whether due to viscoelasticity or water loss. During compressions the force imposed on the particles was also measured so that force-deformation curves could be generated and analysed. A high-speed camera (500 f.p.s.) was used to capture images during compression and the subsequent release. Image analysis showed that the particles recovered fully when the gross deformation was 50% of the initial diameter, or less. This was taken to be the elastic limit for the particles. A 30% deformation was therefore chosen for compression/hold experiments. The faster the compression speed, the higher the force at a given deformation, implying that there was time-dependent behaviour. However, there was a plateau in the (reduced) elastic modulus-compression speed curve, which indicated that above a certain compression speed, time-dependent behaviour during compression might be neglected. Using such high speeds, the elastic modulus of microspheres was shown to be 330±4  kPa at 2% w/v (initial) alginate concentration. The force relaxation behaviour of the microspheres was characterized using the half relaxation time T_1/2. This new high-speed micro-compression tester, with complementary high-speed video, is a powerful tool for investigating the mechanical properties of alginate particles and similar hydrated materials at the microscale.     

Uniaxial extension of polyvinyl chloride in the high-elastic state

The dependence of true stress on the extension ratio of PVC threads has been determined for a wide range of extension rates. Since the polymer subjected to deformation was in the high-elastic state (at temperatures from 90 to 160°), the deformations were predominantly high-elastic. The dependence of true stress on the amount of high-elastic deformation is described by the Mooney-Rivlin equation. Relaxation moduli have been found on the basis of measurements of stress relaxation at constant deformation after various extension ratios were attained at different rates. Within the limits of deformation regimes at which the true stress is an increasing function of extension ratio the relaxation moduli do not depend on extension ratio and rate of extension. This enables one to arrive at a master curve of the relaxation modulus versus relaxation time with the reservation indicated above concerning the increasing character of the dependence of true stress on extension ratio. The relaxation spectrum represented by the high-elasticity plateau has been determined from the relaxation moduli according to the first approximation. The experimental data for a very wide range of deformation regimes and temperatures are presented in the form of an invariant dependence of the ratio of true stress to the rate of deformation on the product of deformation time by extension ratio. The ultimate strength of the specimens frozen rapidly after the attainment of definite extension ratios is determined by the accumulated high-elastic deformation.     

The effect of time and temperature on the mechanical behavior of a “plasticized” epoxy resin under different loading modes

Epoxy–Versamid specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine mode of failure, yield stress and strain, and tangent and relaxation moduli. Stress-strain curves were used to define brittle, ductile, ductile-rubbery, and rubbery modes of behavior which prevailed in different temperature-strain rate regions. The time-temperature superposition principle was applied to yield stress, initial tangent moduli, and relaxation moduli data for all three types of loading. The transition regions, tangent and relaxation moduli, and shift factors were the same in tension, compression, and flexure. Thus the most convenient mode of loading can be used to determine the general time-temperature dependence. The ratio of compressive-to-tensile yield stress was almost constant over the entire ductile region. Flexural yielding data were used to predict yield stress in tension and compression, and stress relaxation master curves were shown to be related to elastic modulus vs. strain rate curves. The yielding phenomenon was interpreted using Eyring's theory of non-Newtonian viscoplastic flow. The apparent activation energy and activation volume were larger for tension than compression. A theory is offered to explain why yielding can occur in a cross-linked system.     

Ferroelastic deformation of La0.58Sr0.4Co0.2Fe0.8O3−δ under uniaxial compressive loading

The mechanical deformation of lanthanum strontium cobalt ferrite under uniaxial compression was investigated at various temperatures. The material revealed a rather complex mechanical behaviour related to its ferroelasticity and stress–strain curves obtained in the 1st and 2nd loading cycles were completely different. A distinctive ferroelastic creep was observed at 293 K whilst typical ferroelastic stress–strain curves were obtained in the temperature range from 473 K to 873 K. At 1073 K, high-temperature creep deformation was observed instead of the ferroelastic deformation. The apparent Young's modulus was evaluated in various ways; the modulus determined from the last unloading curve ranged between 85 and 120 GPa. The obtained critical stress monotonically decreases from about 80 MPa to zero with increasing temperature, corresponding to the behaviour of the remnant strain. The presented results indicate that the importance of an appropriate consideration of the loading history in the practical application of these ferroelastic materials.     

Mechanical and electronic properties of ultrathin nanodiamonds under uniaxial compressions

Mechanical and electronic properties of ultrathin hydrogenated nanodiamonds (with diameters from 0.71 nm to 1.4 nm) under uniaxial compression have been investigated by means of density functional theory calculations. The computed Young's moduli of nanodiamonds are lower than the bulk value and increase with size, which can be fitted to an empirical function of diameter. Similar to the bulk diamond, the HOMO–LUMO gaps of nanodiamond reduces under uniaxial strain, implying tunable electronic properties via mechanical deformations.     

Time-dependent properties of versamid cured epoxies

Versamid cured-epoxy specimens were loaded in tension, compression, and flexure at different strain rates and temperatures to determine the yield stress and strain, and tangent, secant, and relaxation moduli. A torsion pendulum was used to measure the dynamic properties as a function of temperature and frequency. The time-temperature superposition principle was used to reduce this data to master curves. It was concluded that the time-temperature shift factors for secant moduli up to the yield point, for stress relaxation and for dynamic moduli were identical and were independent of the mode of loading. It was also shown that the presence of fillers or reinforcing agents likewise had no effect on the shift factors.     

Compressive recovery behaviour of a polycarbonate

Polycarbonate samples were subjected to large compression strains (beyond yielding) and were unloaded after some degree of stress relaxation. The subsequent deformation recovery was measured for several values of strain, loading rate and duration of stress relaxation. All the data could be reported as a single curve by normalizing the recovered strain with the stress at the end of the relaxation period.     

Determination of mechanical properties of polymeric microspheres used in controlled drug delivery systems by nanoindentation

In this study, we synthesized poly (vinyl acetate-co-divinyl benzene) microspheres with various monomer/cross-linker contents for oral/topical sustained drug release applications and determined the micromechanical properties by nanoindentation. Compression elastic moduli of materials were calculated by using the limited depth of indentation according to Hertz elastic deformation model and presented as the histogram of multiple data. In terms of drug release practices, poly (VAc-co-DVB) microspheres with a high DVB content, especially in topical applications, are expected to carry drugs under mechanical stresses of less than 1.0 GPa.     

Relaxation of the axial strain induced stresses in double–coated optical fibers

The axial strain induced stresses in double‐coated optical fibers are analyzed by the viscoelastic theory. A closed form solution of the axial strain induced viscoelastic stresses is obtained. The viscoelastic stresses are a function of the radii, Young's moduli, relaxation times and Poisson's ratios of the polymeric coatings. If the applied axial strain linearly increases, the induced stresses increase with the time. On the other hand, if the axial strain is fixed, besides the axial stress in the glass fiber, the stresses exponentially decrease with the time. The relaxation of stresses is strongly dependent on the relaxation times of the polymeric coatings. If the relaxation time of the polymeric coating is very long, the viscous behavior of the polymeric coatings will not appear, and the axial strain induced stresses solved by the viscoelastic theory are the same as those solved by the elastic theory. On the other hand, if the relaxation time of the polymeric coating is very short, the relaxation of stresses is very apparent. A compressive radial stress at the interface of the glass fiber and primary coating will result in an increase of the transmission losses, and a tensile interfacial radial stress will possibly produce debonding at the interface of the glass fiber and primary coating. To minimize this interfacial radial stress, the radius, Young's modulus and Poisson's ratio of the polymeric coatings should be appropriately selected, and the relaxation time of the primary coating should be shortened. Finally, the stresses in single‐coated and double‐coated optical fibers are discussed.     

Mechanical properties of single alginate microspheres determined by microcompression and finite element modelling

Calcium alginate microspheres have been studied extensively as carriers in drug delivery systems, for encapsulation of biological materials such as biocatalysts, and as matrices in tissue engineering. Understanding the mechanical properties of such microspheres is essential because they may be exposed to mechanical forces during processing and in end applications. In order to characterise their mechanical properties, microspheres may be compressed between two flat surfaces, and a theoretical model applied to the force-displacement and force-time data to extract mechanical property parameters. In previous work, single calcium alginate microspheres were compressed and then held at constant deformation, and the force being imposed on them was measured. It was found that the force increased with deformation, as expected, and that there was significant force relaxation during holding. In this work, force versus displacement/time data corresponding to compression and holding of a single (102 μm) calcium alginate microsphere were modelled by finite element analysis. Since the force relaxation might be due to water loss or microsphere viscoelasticity, a poroelastic material model was first used to assess the potential effect of water loss from the microsphere solid matrix during holding. Using image analysis, the volume loss during compression and relaxation of the microsphere was determined. Assuming all the change in volume was due to water loss, and assuming a literature value of alginate permeability, the poroelastic material model showed that the effect of water loss on the force behaviour was small enough during relaxation that it might be neglected. This allowed a compressible, isotropic and homogeneous linear viscoelastic material model to be evaluated against experimental relaxation data to obtain viscoelastic property parameters of the microsphere. A viscoelastic material model with two relaxation times showed excellent capability in modelling both compression and relaxation. The instantaneous elastic modulus, long-term elastic modulus and the two relaxation times were found to be 490, 68.6 kPa, and 0.013 and 0.085 s, respectively. Deformation parameters of the compressed microsphere such as the contact radius and central lateral extension were also obtained from finite element modelling, and were compared with experimental data, showing good agreement and confirming the validity of the model at least for the microsphere under test.     

Prediction of the relationship between the rate of deformation and the rate of stress relaxation in glassy polymers

Kim, et al. (Polymer, 54(15), 3949, 2013) recently reported on the unexpected relaxation behavior of an amorphous polymer in the T_g-region, where the rate of stress relaxation increased with deformation at a strain rate of 1.5 × 10⁻⁴ s⁻¹ but decreased at a strain rate of 1.2 × 10⁻⁵ s⁻¹. This inversion in the ordering with strain rate challenges the underlying structure of the existing nonlinear viscoelastic and viscoplastic constitutive models, where the key nonlinearity is a deformation dependent material clock. The nonlinear stress relaxation predictions of a recently developed stochastic constitutive model, SCM, (Medvedev, et al., J. Rheology, 57(3), 949, 2013) that acknowledge dynamic heterogeneity of the glass have been investigated. The SCM predicts the inversion in the ordering of the mobility with the loading strain rate as reported by the stress relaxation response. The change in perspective on the nonlinear viscoelastic behavior of glassy polymers engendered by the SCM is discussed.     

Tensile properties of TiO2-filled poly(vinyl acetate) in the transition region

The stress–strain properties of TiO₂-filled poly(vinyl acetate) have been studied at filler percentages of 0, 10, 20, 30, and 40% TiO₂ over a strain-rate range of 100–5000%/ min at 24°C. Tensile strength, Young's modulus, and offset yield strengths all were found to increase with higher strain rates and higher TiO₂ contents. Ultimate elongations decreased with greater TiO₂ content and higher strain rates. Shift factors for volume fraction of filler were estimated for tensile properties as function of test rate. Stress relaxation studies have shown a reduction in relaxation times with increasing TiO₂ content. Calculations of the out-of-phase Young's modulus were made as a function of filler content employing a box-type of distribution of relaxation times. A possible explanation for the stress–strain behavior observed is that introduction of TiO₂ changes the internal viscosity of the system, similar to the effect of temperature. This would also mean that the ultimate properties would be dependent on filler content and strain rate because viscous resistance to chain deformation would be altered. The effect of filler on stress relaxation could be thought of being due to an increase in short-range chain motion.     

High‐Temperature Compression Deformation Behavior of Fine‐Grained Carbon‐Bonded Alumina

Carbon‐bonded alumina with 33 wt% residual carbon was tested in compression at room temperature and at temperatures between 700°C and 1500°C in quasi‐static tests, creep tests, and stress relaxation tests. Therefore, a new high‐temperature test set up with inert gas chamber and inductive heating was used. The tests were accomplished by investigations of microstructure and Young's modulus. At room temperature, the results exhibit a pronounced hysteresis for the first loading cycle, which almost completely disappeared in subsequent cycles. The creep tests showed characteristic curves for compression whereas primary and secondary (stationary) creep occurred. Above 1000°C, a strong increase in creep rate was detected, whereas almost no creep was observed below this temperature. All creep curves were approximated with the models of logarithmic and Andrade creep. The activation energy for creep was found to be 263 kJ/mol above 1150°C. The resistance against stress relaxation showed an anomaly with a minimum between 1000°C to 1200°C and a maximum between 1300°C and 1400°C.     

Determination of young's modulus of elastomers by use of a thermomechanical analyzer

This work used a conventional thermomechanical analyzer (TMA) to measure the depth of indentation at room temperature of elastomers and Finkin's equation to calculate Young's moduli of elastomers, which have been measured by Drutowski, from the radius of contact of an indentor on thin sheets of sample. Data obtained from the TMA are compared with those measured by radius of contact and Hertz contact theory and are found in good agreement. Measurements of Young's modulus as a function of temperature at different heating rates by TMA were made for an acrylic elastomer. The results are compared with theory and the deviations from theory are discussed.     

Porosity effect on microstructure,mechanical, and fluid dynamic properties of Ti2AlC by direct foaming and gel‐casting

In this study, Ti₂AlC foams were fabricated by direct foaming and gel‐casting using agarose as gelling agent. Slurry viscosity, determined by the agarose content (at a fixed solids loading), as well as surfactant concentration and foaming time were the key parameters employed for controlling the foaming yield, and hence the foam porosity after sintering process. Fabricated foams having total porosity in the 62.5‐84.4 vol% range were systematically characterized to determine their pore size and morphology. The effect of the foam porosity on the room‐temperature compression strength and elastic modulus was also determined. Depending on the amount of porosity, the compression strength and Young's modulus were found to be in the range of 9‐91 MPa and 7‐52 GPa, respectively. Permeability to air flow at temperatures up to 700°C was investigated. Darcian (k₁) and non‐Darcian (k₂) permeability coefficients displayed values in the range 0.30‐93.44 × 10^?11 m² and 0.39‐345.54 × 10^?7 m, respectively. The amount of porosity is therefore a very useful microstructural parameter for tuning the mechanical and fluid dynamic properties of Ti₂AlC foams.     

Nonlinear Elasticity of Silica Glass

In situ Brillouin light scattering measurements with a spatial resolution of ~1 μm have been carried out to study the elastic moduli of silica glass fibers in a single two‐point bend experiment to nominal strains of 7% in both tensile and compressive regions. Such data are necessary in order to convert the failure strains obtained from two‐point bend experiments into failure stress. For the first time, the neutral axis shift in a bent silica glass fiber was observed in our measurements, with more of the fiber deforming in compression than in tension, resulting from the nonlinear elastic behavior of silica glass. Understanding the neutral axis shift will improve the accuracy of strain and stress calculations in bent fibers. This study shows that an expression including a fifth‐order term is required to capture both the minimum in compression and the maximum in tension in the strain‐dependent Young's modulus of silica glass. A stress versus strain relation over a broad range of compressive and tensile strains was established for silica glass in this study, which will significantly improve our understanding of its deformation behavior.     

Evaluation by various experimental approaches of the crosslink density of urethane networks based on hydroxyl‐terminated polybutadiene

Crosslink density (CLD) is an important characteristic for elastomeric polymer networks. The mechanical and viscoelastic properties of the elastomers are critically dependant on the CLD. Several methods have been adopted for its determination, but swelling and stress–strain methods continue to be more popular because of the convenience associated with these techniques. In this article, the determination of CLD of allophanate–urethane networks based on hydroxyl‐terminated polybutadiene and toluene diisocyanate with swelling and stress–strain methods is reported. The Flory–Rhener relationship was applied to calculate CLD from the swelling data. CLDs were also calculated from the initial slope of the stress–strain curve (Young's modulus), Mooney–Rivlin plots, equilibrium relaxation moduli, and dynamic mechanical properties. A comparison was drawn among the values obtained with the various methods. Although the CLD values obtained from Mooney–Rivlin plots were slightly lower than those obtained from swelling data, the values obtained with Young's modulus and storage modulus were considerably higher. The values obtained with swelling and equilibrium relaxation moduli data were very close to each other. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3129–3133, 2007     

Determination of the viscoelastic properties of synthetic yarns on the basis of short-term testing

Conclusions A method has been developed for determining the deformation characteristics of polycaproamide yarns, which differs from the previously known ones by allowing for relaxation contributions in loading the specimen.The parameters obtained by the indicated method permit one to calculate a family of relaxation curves at a deformation up to 25–30% of the breaking value, relaxation times up to 10³ sec, and with an error which does not exceed experimental error.Stretching diagrams and stress relaxation curves at long relaxation times can be calculated with an accuracy sufficient for engineering calculations.Translated from Khimicheskie Volokna, No. 2, pp. 24–25, March–April, 1988.     

Mechanical properties of phenolphthalein polyether ketone: Yield stress,young's modulus,and fracture toughness

A series of tensile and three-point bending studies was conducted at various temperatures and loading rates using phenolphthalein polyether ketone (PEK-C). Yield stress, Young's modulus, fracture toughness, and crack opening displacement data were obtained for various conditions. In general, both yield stress and Young's modulus increase with decreasing temperature. However, the relationships between fracture toughness, loading rate, and temperature are very complex. This behavior is due to the simultaneous intersection of viscoelasticity and localized plastic deformation. The increased yield stress is the main factor contributing to the reduction in fracture toughness and crack opening displacement. The relationship between fracture toughness and yield stress are discussed. © 1995 John Wiley & Sons, Inc.     

PNIPAM/锂藻土纳米复合凝胶微球的制备及其弹性力学性能

利用微流控技术,以锂藻土作为交联剂,成功制备得到温度响应型聚（N-异丙基丙烯酰胺）（PNIPAM）与锂藻土的纳米复合凝胶微球,并利用一种简单的微步进单轴压缩装置,分别在25℃和37℃下对具有不同锂藻土含量的PNIPAM/锂藻土纳米复合凝胶微球的弹性力学性能进行系统研究。该微步进单轴压缩装置主要包括三个部分：一个程控进样器用以实现对凝胶微球的微步进压缩,一套配有高分辨率数码相机的侧视光学系统用以记录凝胶微球受压时发生的形变,一台精密电子天平作为力传感器用来记录凝胶微球在特定形变下所受的外力。研究结果表明,纳米复合凝胶微球在25℃和37℃下的形变量H与所受压力F的实验数据与Hertz弹性接触理论方程呈现良好的拟合关系,证明了PNIPAM/锂藻土纳米复合凝胶微球在25℃和37℃下均具有弹性形变行为。同时,随着锂藻土含量的增加,PNIPAM/锂藻土纳米复合凝胶微球的温敏性降低,但其杨氏模量增大。具有相同锂藻土含量的纳米复合凝胶微球,由于温度升高凝胶体积收缩、凝胶结构变得致密,因此在37℃下的杨氏模量大于其在25℃下的杨氏模量。研究结果可为PNIPAM/锂藻土纳米复合凝胶微球的设计与实际应用提供指导。