Stress Relaxation Time Research Articles

Influence of molecular weight on rheological, thermal, and mechanical properties of PEEK

AbstractThis study focuses on the influence of molecular weight on the rheological, thermal, and mechanical behavior of poly(ether‐ether‐ketone) (PEEK), a semicrystalline high‐performance polymer. The results show that the molecular weight of PEEK has significant influence on its rheological, thermal, and mechanical behavior. It was found that PEEK has the unique characteristic of two shear‐thinning regions. The shear viscosity and the stress relaxation time of PEEK increase significantly as molecular weight increases. In general, the Cox‐Merz rule is valid for all grades of PEEK. As molecular weight increases, the melting temperature of PEEK decreases slightly, but its isothermal and nonisothermal crystallization temperatures drop dramatically. As molecular weight increases, the crystallinity, the crystallization rate, and the magnitude of crystallization activation energy decrease. The crystallization kinetics study indicates that PEEK tends to form spherical crystalline structures, regardless of its molecular weight. As molecular weight increases, the tensile strength at yield, the tensile modulus, and the flexural modulus of PEEK decrease slightly, whereas the tensile strength at break, the tensile strain at break, the modulus of toughness, and the impact strength of PEEK increase significantly. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers

Rheological properties of cereal starch gels and Mesona Blumes gum mixtures

AbstractThe effect of Mesona Blumes gum (MBG) was examined on steady and dynamic shear of MBG/rice starch and MBG/wheat starch gels. In addition, stress relaxation and creep tests were performed for two types of cereal starch gels. The flow curves of both MBG/starch gels exhibited pseudoplastic behavior at shear rates between 0.01 and 10 s−1, and the data were fitted into the power law model (R2 = 0.91–0.98). Dynamic mechanical spectrum showed that all gels were strong gels in frequency between 0.1 and 10 Hz. Stress relaxation data at different strains indicated a strain‐softening phenomenon for both gels. Data were fitted into Maxwell model (R2 = 0.91–0.98). Creep curves were conducted at the shear stress 6.4 Pa within linear viscoelastic region of both MBG/starch gels. Data were fitted into Burgers model (R2 = 0.91–0.98). Apparent viscosity η, storage moduli G′, equilibrium stress relaxation modulus Ge and zero apparent viscosity η0 of MBG/rice starch gels decreased in the following order: 6/0>6/0.5>6/0.35>6/0.1 (starch/gum w/w). Whereas η, G′, Ge, and η0 of MBG/wheat starch gels increased gradually along side the increase of MBG contents. The stress relaxation time λ of MBG/rice starch gels increased in the following order: 6/0<6/0.5<6/0.35<6/0.1 (starch/gum w/w) while λ of MBG/wheat starch gels decreased gradually with the increase of MBG level. The influence of MBG on two examined cereal starch is totally opposite.

Photoacoustic generation by multiple picosecond pulse excitation

The purpose of this work is to demonstrate that higher amplitude of ultrashort laser induced photoacoustic signal can be achieved by multiple-pulse excitation when the temporal duration of the pulse train is less than the minimum of the medium's thermal relaxation time and stress relaxation time. Thus, improved signal-to-noise ratio can thus be attained through multiple-pulse excitation while minimizing the energy of each pulse. The authors used a Michelson interferometer together with a picoseconds laser system to introduce two 6 ps pulses separated by a controllable delay by introducing a path length difference between the two arms of the interferometer. The authors then employed a series of three interferometers to create a pulse train consisting of eight pulses. The average pulse energy was 11 nJ and the temporal span of the pulse train was less than 1 ns. The detected peak-to-peak amplitude of the multiple-pulse induced photoacoustic waves were linearly dependent on the number of pulses in the pulse train and such a linearity held for different optical absorption coefficients. The signal-to-noise ratio improved when the number of pulses increased. Moreover, nonlinear effects were not detected and no photoacoustic saturation effect was observed. The authors have shown that multiple-pulse excitation improves the signal-to-noise ratio through an accumulated energy deposition effect. This method is invaluable for photoacoustic measurements that require ultrashort laser pulses with minimized pulse energy to avoid laser damage.

Study on the structure and properties of SSBR with large-volume functional groups at the end of chains

Solution polymerized styrene-butadiene rubber (SSBR) and SSBR with tert-Butylchlorodiphenylsilane (TBCSi, large-volume functional groups) at the two ends of macromolecular chains (T-SSBR) were prepared by anionic polymerization. The molecular structure parameters of T-SSBR and SSBR were characterized and the ratio of the amount of macromolecular chain ends connected with TBCSi to total macromolecular chain ends (i.e., end-capping efficiency) was calculated. The comprehensive properties of T-SSBR and SSBR composites filled with carbon black (CB) were investigated. The results showed that T-SSBR composites presented lower Payne effect (namely better CB dispersion) than those of SSBR composites, which led to decrease in hardness, internal friction, dynamic compression heat built-up and permanent set of T-SSBR composites, significant increase in tensile strength, elongation at break, tear strength and resilience of T-SSBR composites, and excellent balance between wet-skid resistance and rolling resistance. However, compared with SSBR composites, T-SSBR composites presented longer stress-relaxation time, bigger die-swell and higher apparent viscosity, as well as slightly inferior dynamic-cutting resistance. All the above, owing to the end-capping of TBCSi, which could immobilize the free chain ends of T-SSBR (i.e., to reduce the friction loss of molecular chains and create a greater degree of orientation in the force field), and adsorb CB, the comprehensive performances of T-SSBR were better than those of SSBR and T-SSBR terminated with styrene-TBCSi (TS-SSBR) were far superior to those of T-SSBR terminated with butadiene-TBCSi (TB-SSBR). Accordingly, the former was suitable for the tread of green tires.

Slow dynamics of wormlike micelles

We present an extensive rheology study of the wormlike micelle system lecithin-water-cyclohexane. In this system the micelles are really wormlike, meaning that there are no signs of micellar branching, as it has previously been demonstrated by NMR self-diffusion experiments (R. Angelico, U. Olsson, G. Palazzo and A. Ceglie, Phys. Rev. Lett., 1998, 81, 2823). Wormlike micelles break and recombine, processes that are important for the stress relaxation. When branching is highly unfavorable, micelle recombination reactions only involve micelle ends, the concentration of which are very low when the micelles are very long. Hence, the break and recombination kinetics is very slow for true wormlike micelles. In the present system, the stress relaxation times are of the order of an hour. This is about three to four orders of magnitude longer than what commonly is observed in systems claimed to contain wormlike micelles. We conclude that systems with true wormlike micelles are very rare. An exponential stress relaxation is observed except at lower concentrations, where the micellar breaking time appears to exceed the reptation time. Because of the slow dynamics, the linear elastic modulus can be obtained from small rapid shear deformations, for which the system obeys Hooke's law. Larger deformations result in a fracture of the micellar network at a critical strain γ* ∼ ϕ−1, where ϕ is the micelle volume fraction. For γ < γ* we may still obtain fracture, although with a lag time, τ*, that decreases with increasing γ, and vanishes when γ = γ*. Extrapolating τ* to zero deformation we obtain the estimate ≈250 s at the highest concentration ϕ = 0.29. We interpret this time as the equilibrium micellar breaking time at rest, a quantity not previously measured.

Thermodynamic approach to rheology of complex fluids: Flow-concentration coupling

In this work, the generalized Bautista-Manero-Puig (BMP) model derived from extended irreversible thermodynamics (EIT) is used to analyze the coupling of stress with concentration in complex fluids. It is shown that this model is consistent with previous analyses that predict mechanical and thermodynamic instabilities in the shear-banding regime. In particular, for simple shear flows, the model presented here predicts the structure factor in the plane of shear and the onset of instabilities in the gradient-vorticity plane. Furthermore, the model predicts distinctive features of the models of Brochard-de Gennes and Schmitt as particular cases. For finite stress relaxation time, the generalized BMP model allows the prediction of transient structures normal to the vorticity axis. Instabilities are predicted in the regions of high viscosity, which suggest that the induction of a more viscous phase in a shear-thickening solution can lead the system to instability, in this case, the layering is predicted perpendicular to the vorticity direction. These transient structural patterns within the shear-thickening region correspond to spinodal phase separation. When the mechanical and thermodynamic instabilities are uncoupled, the model predictions agree with experiments and with the transient-gel model of Brochard and de Gennes.

Impact resistant polymeric glasses using compressive pre‐stress

AbstractThe application of an externally applied pre‐stress on impact properties is studied on polymethyl methacrylate (PMMA) organic glass. Samples are tested under equi‐biaxial compression, simple shear and a combination of biaxial compression and shear. Equi‐biaxial compression is shown to increase the threshold stress level for projectile penetration whereas shear pre‐stress has a large effect on the overall energy absorbed during an impact. There is also an apparent interaction observed between compression and shear to dramatically increase the threshold stress. Pre‐stressed laminates show an increase in damage area because of the unique formation of a secondary cone. Higher levels of compressive equi‐biaxial pre‐stress significantly increase the stress relaxation time because of the corresponding increase in hydrostatic stress. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Mechanical Behavior and Failure Mode of Unidirectional Fiber Composites at Low Strain Rate Level

The rate responses of unidirectional fiber composites at low strain rate level (range from 2E-5 to 2E-2 s-1), including tensile mechanical and stress relaxation behaviors, were investigated in this article. The results obtained showed that the ultimate tensile stress increases as strain rate increases, and the stress relaxation time decreases as pre-tensile strain rate increases. And besides, the macro-failure modes of fiber composites changed from ductile fracture feature to brittle fracture feature as strain rate increasing. Furthermore, the micro-failure modes of multi-fiber composite were investigated originally, with the results indicating that fiber-fiber interactions decreased while increasing tensile strain rate.

An Eulerian finite‐volume scheme for large elastoplastic deformations in solids

AbstractConservative formulations of the governing laws of elastoplastic solid media have distinct advantages when solved using high‐order shock capturing methods for simulating processes involving large deformations and shock waves. In this paper one such model is considered where inelastic deformations are accounted for via conservation laws for elastic strain with relaxation source terms. Plastic deformations are governed by the relaxation time of tangential stresses. Compared with alternative Eulerian conservative models, the governing system consists of fewer equations overall. A numerical scheme for the inhomogeneous system is proposed based upon the temporal splitting. In this way the reduced system of non‐linear elasticity is solved explicitly, with convective fluxes evaluated using high‐order approximations of Riemann problems locally throughout the computational mesh. Numerical stiffness of the relaxation terms at high strain rates is avoided by utilizing certain properties of the governing model and performing an implicit update. The methods are demonstrated using test cases involving large deformations and high strain rates in one‐, two‐, and three‐dimensions. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Absence of reptation in highly confined polymers

We present results of mechanical stress relaxation measurements on polymers confined at the air-water interface in the form of a monolayer. Systematic measurements allow, to our knowledge, for the first time, observation of the scaling of the stress relaxation time of the highly confined polymers as a function of both surface concentration and molecular weight. The observed scaling is found to be very close to that expected for motion of unentangled polymer solutions with hydrodynamic interactions. Our experimental observations thus clearly rule out the possibility of entanglement and hence reptation as a mode of relaxation in such highly confined polymeric systems.

Interplay between Covalent and Physical Interactions within Environment Sensitive Hydrogels

A systematic study is carried out to understand how physical and covalent crosslinks affect the mechanical properties of an eight-arm poly(ethyleneglycol)-based hydrogel. Heparin and heparin-binding peptide are used as a physical crosslinker, and an enzymatically cleavable peptide with a cysteine on each end serves as a covalent crosslinker. While physical crosslinks alone do not induce gelation due to the low binding affinity between heparin and heparin-binding peptide, the addition of covalent crosslinks leads to gel formation. Strikingly, the addition of the covalent crosslinks not only leads to gel formation, but also enhances the contribution from the physical crosslinks to the overall shear moduli, which are negligible in the absence of covalent crosslinks. The gels, which contain both covalent and physical crosslinks, are able to reversibly respond to external stimuli such as temperature and oscillatory shear unlike the purely covalent gel in which the moduli remain largely insensitive to such stimuli. Two explanations are provided for this striking phenomenon. First, the addition of covalent crosslinks increased the stress relaxation time of the gel enabling the physical interactions to contribute to the moduli. This is contrasted to the case of physically crosslinked material, which relaxes the stress too quickly, preventing the physical interactions from contributing to the low frequency moduli. Second, it is believed that the physical interactions within the covalent network were further enhanced by "macromolecular confinement", which favors the formation of compact conformational structures in the confined space. Quartz crystal microbalance (QCM) was used to measure the dissociation constant (K(d)) within the hydrogel and to demonstrate that the binding between heparin and heparin-binding peptide is stronger within the gel compared to that within the solution phase. Because extracellular matrix (ECM) contains both covalent and physical interactions between its constituents, and the mechanical properties of the ECM are important factors to control cell functions, the findings of this research may have important implications in various fields of tissue engineering and cell biology.

The influence of the stress relaxation and creep recovery times on the viscoelastic properties of open cell foams

AbstractThe aim of this work is to study the mechanical behavior of flexible polyurethane foams used in cushioning applications. In particular, the differences between slow recovery (SR) and fast recovery (FR) foams are highlighted. To characterize the flexible polyurethane foams, creep and hysteresis tests were performed at different strain rate, stress levels, and temperatures. Significant differences were observed between the SR and FR foams, particularly in terms of residual deformation after unloading, hysteresis area, and creep behavior at different stress levels. Creep compliance at different stress levels was compared with a Voigt‐Kelvin model. Stress–strain loading curves were compared with a phenomenological model originally modified to account for the strain rate dependence. In both cases, it is possible to show that the main differences observed in the behavior of the foams are due to the different relaxation and recovery times of the foams. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Finite element modeling of polymer hot embossing using a glass‐rubber finite strain constitutive model

AbstractA hyperelastic–viscoplastic constitutive model for amorphous polymers was used in finite element simulations of micro‐hot embossing across the glass transition. The model was selected for its ability to capture finite strain temperature and rate dependence over a wide range of temperatures, including across the glass transition. The simulations focused on the glass transition temperature regime, and particularly probed the effects of time and temperature during cooling and mold release. The results show that strong temperature sensitivity of the material across the glass transition leads to a wide range of required embossing force and springback. The interplay between changes in material properties upon cooling and stress relaxation can lead to significant increases in embossing force during the cooling stage, especially when high cooling rates are employed. The effects of thermal expansion also complicate the problem during rapid cooling. Nonlinear material behavior is shown to affect results in parametric hot embossing studies. Careful tailoring of embossing temperature, cooling rate, and demolding temperature is critical in acceptable feature replication. The best results are found for moderate cooling rates, which allow adequate time for stress relaxation in the material prior to mold release. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

Determination of the viscoelastic properties of hydrogels based on polyethylene glycol diacrylate (PEG-DA) and human articular cartilage

In this work, a systematic study of the viscoelastic properties of hydrogels based on polyethylene glycol diacrylate (PEG-DA) is presented. In addition to artificial PEG-DA-based hydrogels, natural hydrogels in the form of human articular cartilage were examined. Specimens were (unconfined) compression tested under static and dynamic load. Besides this, instrumented indentation tests with different indenter geometries (cylindrical, spherical) and load ranges (macro- and nano-indentation) were carried out and relaxation tests for the determination of moduli and relaxation time were performed. Tensile tests completed the list of measurement techniques. The measured initial moduli of the evaluated hydrogels range from 104?107 Pa. Spherical indentation was used in testing human articular cartilage in phosphate buffered saline (PBS). Cartilage samples were measured shortly after explantation, being stored at room temperature. The influence of freezing and shock-freezing was evaluated. It turned out that freezing has a massive impact on sample properties, especially on the stress relaxation time and the ratio of initial to equilibrium modulus.

Dewetting as an investigative tool for studying properties of thin polymer films

Employing mass conservation, time-resolved dewetting experiments of thin polymer films allow to determine in real time the dynamic contact angle and the slippage length. Moreover, based on a systematic variation of interfacial properties of a polymer brush, dewetting makes it possible to calculate the force it needs to extract a single polymer chain from its own melt. In the visco-elastic regime close to the glass transition, the temperature and molecular weight dependence of the relaxation time of residual stresses resulting from film preparation by spin-coating can be obtained from the evolution of the shape of the dewetting rim. The presented examples demonstrate that dewetting represents a powerful approach for a sensitive characterization of rheological, frictional and interfacial properties of thin polymer films.

Cartilage stress-relaxation proceeds slower at higher compressive strains

Articular cartilage is the connective tissue which covers bone surfaces and deforms during in vivo activity. Previous research has investigated flow-dependent cartilage viscoelasticity, but relatively few studies have investigated flow-independent mechanisms. This study investigated polymer dynamics as an explanation for the molecular basis of flow-independent cartilage viscoelasticity. Polymer dynamics predicts that stress-relaxation will proceed more slowly at higher volumetric concentrations of polymer. Stress-relaxation tests were performed on cartilage samples after precompression to different strain levels. Precompression increases the volumetric concentration of cartilage biopolymers, and polymer dynamics predicts an increase in relaxation time constant. Stress-relaxation was slower for greater precompression. There was a significant correlation between the stress-relaxation time constant and cartilage volumetric concentration. Estimates of the flow-dependent timescale suggest that flow-dependent relaxation occurs on a longer timescale than presently observed. These results are consistent with polymer dynamics as a mechanism of cartilage viscoelasticity.

The mechanical properties of individual, electrospun fibrinogen fibers

We used a combined atomic force microscopic (AFM)/fluorescence microscopic technique to study the mechanical properties of individual, electrospun fibrinogen fibers in aqueous buffer. Fibers (average diameter 208 nm) were suspended over 12 μm-wide grooves in a striated, transparent substrate. The AFM, situated above the sample, was used to laterally stretch the fibers and to measure the applied force. The fluorescence microscope, situated below the sample, was used to visualize the stretching process. The fibers could be stretched to 2.3 times their original length before breaking; the breaking stress was 22 × 10 6 Pa. We collected incremental stress–strain curves to determine the viscoelastic behavior of these fibers. The total stretch modulus was 17.5 × 10 6 Pa and the relaxed elastic modulus was 7.2 × 10 6 Pa. When held at constant strain, electrospun fibrinogen fibers showed a fast and slow stress relaxation time of 3 and 55 s. Our fibers were spun from the typically used 90% 1,1,1,3,3,3-hexafluoro-2-propanol (90-HFP) electrospinning solution and re-suspended in aqueous buffer. Circular dichroism spectra indicate that α-helical content of fibrinogen is ∼70% higher in 90-HFP than in aqueous solution. These data are needed to understand the mechanical behavior of electrospun fibrinogen structures. Our technique is also applicable to study other nanoscopic fibers.

Viscoelastic properties of Nafion at elevated temperature and humidity

AbstractTensile stress–strain and stress relaxation properties of 1100 equivalent weight Nafion have been measured from 23 to 120 °C at 0–100% relative humidity. At room temperature, the elastic modulus of Nafion decreases with water activity. At 90 °C, the elastic modulus goes through a maximum at a water activity of ∼ 0.3. At temperatures ≥90 °C, hydrated membranes are stiffer than dry membranes. Stress‐relaxation was found to have two very different rates depending on strain, temperature, and water content. At high temperature, low water activity, and small strain, the stress relaxation displays a maximum relaxation time with stress approaching zero after 103–104s. Water absorption slows down stress‐relaxation rates. At high water activity, the maximum stress relaxation time was &gt;105s at all temperatures. No maximum relaxation time was seen atT≤ 50 °C. Increasing the applied strain also resulted in no observed upper limit to the stress relaxation time. The results suggest that temperature, absorbed water, and imposed strain alter the microstructure of Nafion inducing ordering transitions; ordered microstructure increases the elastic modulus and results in a stress relaxation time of &gt;105s. Loss of microphase order reduces the elastic modulus and results in a maximum stress relaxation time of 103–104s. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 11–24, 2009.

Molecular NMR T2 values can predict cartilage stress-relaxation parameters

Articular cartilage lines synovial joints and functions as a low-friction deformable tissue to enable smooth and stable joint articulation. The objective of this study was to determine the relationships between cartilage stress-relaxation properties and the collagen and GAG NMR transverse relaxation times ( T 2) toward understanding mechanisms of cartilage viscoelasticity. Stress-relaxation tests were performed on both cultured and enzymatically digested bovine cartilage, followed by measurements of both the collagen and GAG T 2 using the Call–Purcell–Meiboom–Gill pulse sequence. The peak and equilibrium stresses were correlated with the GAG T 2, and the stress-relaxation time constant was correlated with the collagen T 2. Multiple linear regression models were successful in using the specific T 2 values to predict the stress-relaxation properties. As a model of osteoarthritis, enzymatic digestion with collagenase and testicular hyaluronidase had weak effects on T 2 values. These data present a complex picture of cartilage mechanical behavior, with cartilage stiffness associated with the GAG T 2 values and the stress-relaxation time constant associated with the collagen T 2.

Effects of Particle Size and Starch Damage of Flour and Alkaline Reagent on Yellow Alkaline Noodle Characteristics

ABSTRACTA hard white spring wheat was milled to yield three patent flours with different starch damage levels by manipulating reduction grinding conditions, and each flour was sieved to give three different particle sizes (85–110, 110–132, 132–183 μm). Raw alkaline noodles were prepared using either 1% w/w kansui (sodium and potassium carbonates in 9:1 ratio) or 1% w/w sodium hydroxide. Noodles prepared with sodium hydroxide were significantly brighter, less red, and more yellow than those made with kansui. Differences in noodle color among flour treatments were evident but were attributable to differences in flour refinement rather to than particle size or starch damage. Noodles were rested for 1 hr after processing before cooking. Alkaline reagent was the main factor associated with cooking loss, being ≈50% greater for sodium hydroxide noodles because of higher pH compared with kansui noodles. Cooked sodium hydroxide noodles were thicker than kansui noodles, and cooked strands for both noodle types became thicker as starch damage increased and as particle size became coarser. Instrumental assessment of cooked noodle texture showed that maximum cutting stress (MCS), resistance to compression (RTC), recovery (REC), stress relaxation time (SRT), chewiness (CHE), and springiness (SPR) were influenced by the type of alkaline reagent. Flour particle size and starch damage also influenced noodle texture but the magnitude of the effects and the trends were dependent on alkaline reagent. MCS of kansui noodles was much greater than for sodium hydroxide noodles. MCS of kansui noodles increased as starch damage increased but, in contrast, MCS of sodium hydroxide noodles decreased with increasing starch damage. REC of kansui noodles increased with increasing starch damage and decreased with larger particle size, whereas for sodium hydroxide noodles REC decreased with increasing starch damage and declined dramatically with larger particle size. Kansui noodles exhibited significantly shorter SRT than sodium hydroxide noodles. SRT of kansui noodles was only moderately affected by starch damage and particle size, whereas for sodium hydroxide noodles, SRT became much shorter as flour became coarser and starch damage became higher. CHE of kansui noodles was greater than for sodium hydroxide noodles. CHE of kansui noodles increased as starch damage increased. In contrast, CHE of sodium hydroxide noodles decreased as starch damage increased and also decreased as flour became coarser. SPR of both noodle types decreased as flour became coarser and starch damage became greater. On the basis of these experiments, flour of smaller particle size is an asset to the cooking quality of sodium hydroxide noodles, but high starch damage is to be avoided. For kansui noodles, the impact of flour particle size on cooked noodle texture was less evident and low starch damage, rather than high starch damage, was an asset.