Transient Stress Relaxation Research Articles

Origin of Two Distinct Stress Relaxation Regimes in Shear Jammed Dense Suspensions.

Many dense particulate suspensions show a stress induced transformation from a liquidlike state to a solidlike shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the bulk remains unknown. Here, we study transient stress relaxation behaviour of SJ states formed by a well-characterized dense suspension under a step strain perturbation. We observe a strongly nonexponential relaxation that develops a sharp discontinuous stress drop at short time for high enough peak-stress values. High resolution boundary imaging and normal stress measurements confirm that such stress discontinuity originates from the localized plastic events, whereas system spanning dilation controls the slower relaxation process. We also find an intriguing correlation between the nature of transient relaxation and the steady-state shear jamming phase diagram obtained from the Wyart-Cates model.

Correction to: Transient Stress Relaxation Test to Identify Material Constants in Dislocation Density Model

Correction to: Transient Stress Relaxation Test to Identify Material Constants in Dislocation Density Model

A New Method to Characterize and Model Stress-Relaxation Aging Behavior of Aluminum Alloys Under Age Forming Conditions

A new method that utilizes theories of thermally activated deformation and repeated transient stress-relaxation tests has been proposed and validated in this study for the characterization and modeling of the stress-relaxation aging (SRA) behavior of aluminum alloys and its dependence on stress and temperature. Using the new method, key deformation-related variables, i.e., stress components, activation volume, and activation energy, of the aerospace grade heat-treatable aluminum alloy AA7B04 have been obtained as a function of aging temperature (388 K, 413 K and 438 K), stress (both elastic and plastic), and SRA time (up to 4 hours). It has been found that the apparent activation energy Qa of the material remains constant in the elastic region but decreases with the increase in strain in the plastic region, and also decreases with the increase in temperature for all initial loading stresses. These characteristics contribute to a much higher degree of stress relaxation in the plastic region and at higher temperatures than in the elastic region and/or at lower temperatures. The obtained changing activation volume V and Qa indicate that the deformation rate is controlled by forest dislocation interactions in the elastic region (V decreases from over 200b3 to less than 100b3), and by a cross-slip mechanism at high stress levels in the plastic region (V decreases to a few tens of b3). Based on these theories and results, a novel and simple constitutive model has been proposed, with which the stress-relaxation behavior of AA7B04 at different aging temperatures (388 K to 448 K), preloaded from elastic to plastic regions for up to 16 hours has been successfully predicted. The proposed model eliminates the limitations of conventional SRA models which mainly deals with elastic loading and isothermal conditions, and provides a foundation to effectively predict the springback after advanced non-isothermal SRA forming of aluminum alloy structures in the aerospace industry.

Investigations on ductility improvement and reloading yielding during stress relaxation of dual phase Ti–6Al–4V titanium alloy

Transient stress relaxation test can be used to estimate activation volume for plastic deformation. The analysis is complicated due to the non-constancy of mobile dislocation density during relaxation. The reloading yielding post stress relaxation has a direct correlation with the change in mobile dislocation density during relaxation. However, this feature is ignored in the past studies. In the present work, the reloading yielding phenomenon in dual phase (α+β) titanium alloy (Ti–6Al–4V) is investigated using phenomenological stress relaxation model. Based on indirect experimental evidences, it is shown that the reloading yielding is due to regeneration of new dislocations and not due to unpinning of sessile dislocations, as assumed previously. The improvement of ductility due to stress relaxation follows a similar trend reported in literature. The ductility improvement is analyzed using both microstructure changes and thermal gradient. Fractographs of failed samples were investigated to understand the fracture characteristics and quantitative analyses were performed using image processing to correlate the microstructure mechanisms responsible for enhanced ductility. Thermal history at select locations were recorded using thermocouple and were used to analyze the contribution of thermal gradient in ductility. The necessity of a comprehensive approach to model ductility improvement in non-monotonic stress relaxation test is explored.

Viscoelastic properties of PLA/PCL blends compatibilized with different methods

The aim of this study was to observe changes in the viscoelastic properties of PLA/PCL (80/20) blends produced using different compatibilization methods. Reactive extrusion and high-energy radiation methods were used for blend compatibilization. Storage and loss moduli, complex viscosity, transient stress relaxation modulus, and tan δ of blends were analyzed and blend morphologies were examined. All compatibilized PLA/PCL blends had smaller dispersed particle sizes than the non-compatibilized blend, and well compatibilized blends had finer morphologies than poorly compatibilized blends. Viscoelastic properties differentiated well compatibilized and poorly compatibilized blends. Well compatibilized blends had higher storage and loss moduli and complex viscosities than those calculated by the log-additive mixing rule due to strong interfacial adhesion, whereas poorly compatibilized blends showed negative deviations due to weak interfacial adhesion. Moreover, well compatibilized blends had much slower stress relaxation than poorly compatibilized blends and didn’t show tan δ plateau region caused by slippage at the interface between continuous and dispersed phases.

Viscoelastic shear properties of porcine temporomandibular joint disc.

To investigate the intrinsic viscoelastic shear properties in porcine TMJ discs. Twelve fresh porcine TMJ discs from young adult pigs (6-8months) were used. Cylindrical samples (5mm diameter) with uniform thickness (~1.2mm) were prepared from five regions of the TMJ disc. Torsional shear tests were performed under 10% compressive strain. Dynamic shear was applied in two methods: 1) a frequency sweep test over the frequency range of 0.1-10rad/s with a constant shear strain amplitude of 0.05rad and 2) a strain sweep test over the range of 0.005-0.15rad at a constant frequency of 10rad/s. Transient stress relaxation tests were also performed to determine the equilibrium shear properties. As the frequency increased in the frequency sweep test, the dynamic shear complex modulus increased, with values ranging from 7 to 17kPa. The phase angle, ranging from 11 to 15 degrees, displayed no pattern of regional variation as the frequency increased. The dynamic shear modulus decreased as the shear strain increased. The equilibrium shear modulus had values ranging from 2.6 to 4kPa. The posterior region had significantly higher values for dynamic shear modulus than those in the anterior region, while no significant regional difference was found for equilibrium shear modulus. Our results suggest that the intrinsic region-dependent viscoelastic shear characteristics of TMJ disc may play a crucial role in determining the local strain of the TMJ disc under mechanical loading.

Rheological Behavior of the Melts for Polyethylene-based Montmorillonite Nanocomposites

The viscoelastic properties of melts of nanocomposites with partially exfoliated structures, which were composed of low-density polyethylene (LDPE), ethylene vinyl acetate copolymer (EVA), and montmorillonite and modified by cetyltrimethyl ammonium bromide and octadecyltrimethyl ammonium bromide, were studied. The results obtained through measurements of the dynamic storage modulus G', the dynamic loss modulus G”, and the transient stress relaxation modulus G(t) of the composites, reveal that the viscoelastic properties of the composites strongly depend on the amount of montmorillonite that is exfoliated into the composites. With the increase in montmorillonite content, the composites show an obvious property of pseudo solid-like materials within the region of lower frequencies (ω). The montmorillonite layers are aligned along the stress direction, and the dependence of dynamic modulus on ω, appears quite different for the composites before and after being exposed to a large amplitude oscillatory shears.

INFLUENCE OF SURFACTANT PROTEIN C IN β-SHEET CONFORMATION ON THE SURFACE DILATATIONAL BEHAVIOR OF PULMONARY SURFACTANT COMPONENTS SPREAD ON THE SURFACE OF A CAPTIVE BUBBLE

Surfactant protein C (SP-C) exists in α-helical and β-sheet conformation. The influence of these conformations on the surface behavior of spread layers containing dipalmytoyl phosphatodylcholine and the surfactant protein B was investigated. The β-sheet conformation of SP-C, which is formed during the preparation procedure at high lipid/protein concentrations, was confirmed by using circular dichroism (CD) and FTIR spectroscopy. Using a captive bubble device, the surface pressure/area isotherms, the surface dilatational elasticity and viscosity, and the main relaxation times of a transient stress relaxation were determined. Surface layers containing SP-C in β-sheet have no protein squeeze-out plateau. The surface dilatational elasticity is increased, which leads to a film of low compressibility. The relaxation times were increased by more than one order of magnitude, and the decays after surface compression and dilatation did not approach each other. Therefore, the surface behavior of layers containing SP-C in β-sheets remarkably differs from those containing SP-C in α-helical conformation. The presence of β–SP-C prevents the film from meeting the function of a pulmonary surfactant layer.

Structural changes in CTAB/H2O mixtures using a rheological approach

A complete, rheometrical analysis (steady, oscillatory and transient stress-relaxation experiments) may be performed to indirectly elucidate the inner structure of surfactant solutions over a wide range of physicochemical conditions. In this paper, structure and structural changes in cetyltrimethylammonium bromide (CTAB)/H2O mixtures have been studied by a set of rheological experiments as a function of composition (2–40 wt% CTAB) and temperature (20–70 °C). This system was chosen for several reasons: firstly, it forms elongated micelles and exhibits a strong viscoelasticity at low concentrations (ca. 2 wt%); secondly, it has a low critical micellar concentration and a Krafft temperature close to the room temperature; third, a nematic phase (type-I, N) is formed in the concentration range 25–29 wt% with a clearing temperature of ca. 40 °C. The nematic phase is intermediate to a micellar isotropic phase (L1), at low concentration, and to a normal hexagonal lyomesophase (H1) at high concentration of CTAB. The L1 phase, consisting of a very large region, exhibited different rheological properties. At 30 °C, viscoelastic data revealed a sphere-to-cylinder transition in shape of micelles in mixtures above 14 wt% CTAB. By increasing further the composition, a fast micellar growth was observed without reaching an entangled phase. The evolution of micellar morphology was also recorded with increasing temperature. The nematic and hexagonal phases, made by similar structural units (i.e. unconnected cylindrical aggregates), behaved like shear thinning materials and showed a comparable viscoelastic spectrum consisting of fast and slow relaxation processes. The slower relaxation times were interpreted as a relaxation of a shear-induced orientation that involved large lyotropic domains. Faster relaxation times (<1 s), on the contrary, could be related to dynamics or kinetics of stiff cylindrical aggregates.

Surface Dilatational Behavior of Pulmonary Surfactant Components Spread on the Surface of a Captive Bubble. 3. Dipalmitoyl Phosphatidylcholine, Surfactant Protein C, and Surfactant Protein B

Spread monolayers containing dipalmitoyl phosphatidylcholine (DPPC), surfactant protein C (SP-C), and surfactant protein B (SP-B) were characterized by dynamic and equilibrium surface pressure/area isotherms, surface dilatational rheological measurements, and transient stress relaxation. The maximum surface pressure which can be realized by monolayer compression depends significantly on the compression rate. The surface rheological behavior is strongly influenced by the presence of SP-B, which reduces the characteristic time of stress relaxation. Therefore the surface pressure of a layer containing SP-B (DPPC + SP-B or DPPC + SP-B + SP-C) changes within some seconds after a transient surface pressure jump to a constant value which corresponds to an equilibrium surface pressure plateau at about 51 mN/m, whereas DPPC + SP-C relaxes within tens of seconds to a steady-state value of surface pressure. In the frequency range of human breathing, the surface dilatational viscosity is weak and nearly independent of surface pressure and frequency for all systems investigated. The surface rheological behavior of the phospholipid/surfactant layers in this range is mainly elastic, with maximum elasticity at a surface pressure slightly below the equilibrium surface pressure plateau, whereas the compressibility of the pulmonary film in the surface pressure range of breathing crosses a stationary compressibility maximum. This study suggests that the presence of SP-B is essential for expiration and the presence of both proteins, SP-B and SP-C, is essential for the inspiration process of the breathing cycle.

Stress Relaxation Behavior of Unidirectional CFRP at Elevated Temperature and Analysis Using a Viscoplasticity Model.

Off-axis stress relaxation behavior of a unidirectional carbon fiber-reinforced composite (T 800 H/3631) has been examined at high temperature. Stress relaxation tests are performed at 100°C on plain coupon specimens with various off-axis angles: θ=0, 10, 30, 45, and 90°. For each of these off-axis angles, the stress relaxation tests are carried out at three different strain levels. Just after the total strain is kept constant, the stress rapidly relaxes with time in a short period. Then, the relaxation rate of the composite stress tends to vanish. The extent of the transient stress relaxation is significantly dependent on the total strain kept constant and the fiber orientation angle. Simulation of the off-axis stress relaxation behavior is performed using a macromechanical viscoplasticity model based on an overstress. It is demonstrated that the model succeeds in moderately reproducing the time-dependent behavior of this system.

Transient stress relaxation around a spherical inclusion: the role of the combination of interfacial diffusion and sliding

Transient stress relaxation around a spherical inclusion caused by the combination of interfacial diffusion and sliding is examined. The inclusion is rigid while the matrix is elastic. It is assumed that only the matrix atoms can be relocated on the interface. With the help of Papkovitch–Neuber’s displacement potentials, the time-dependent stress distribution in the matrix is obtained analytically. It is found that significant stress relaxation occurs only in the region very close to the inclusion. In addition, the radial stress component is relaxed non-monotonically. A brief explanation for this unexpected phenomenon is also given.

Transient stress relaxation around spherical inclusions by interfacial diffusion and sliding

Stress relaxation in composites reinforced by hard, spherical inclusions by interfacial diffusion and interfacial sliding are studied separately. Somigliana dislocations are used to model the misfits at the matrix-inclusion interface. By adopting Papkovitch-Neuber displacement potentials, the transient fields of displacement and stress in the system of a single inclusion embedded in an infinite matrix under uniaxial tension are obtained explicitly. The overall anelastic behaviors of the composites are then analyzed on the basis of Mori-Tanaka mean-field approximation. Numerical results are illustrated, and some interesting concerns are discussed.

Origin of MeV ion irradiation-induced stress changes in SiO2

The 4 MeV Xe ion irradiation of a thin thermally grown SiO2 film on a Si substrate leads to four different effects in which each manifests itself by a characteristic change in the mechanical stress state of the film: densification, ascribed to a beam-induced structural change in the silica network; stress relaxation by radiation-enhanced plastic flow; anisotropic expansion and stress generation; and transient stress relaxation ascribed to the annealing of point defects. Using sensitive wafer-curvature measurements, in situ measurements of the in-plane mechanical stress were made during and after ion irradiation at various temperatures in the range from 95 to 575 K, in order to study the magnitude of these effects, the mechanism behind them, as well as their interplay. It is found that the structural transformation leads to a state with an equilibrium density that is 1.7%–3.2% higher than the initial state, depending on the irradiation temperature. Due to the constraint imposed by the substrate, this transformation causes a tensile in-plane stress in the oxide film. This stress is relaxed by plastic flow, leading to densification of the film. The anisotropic strain-generation rate decreases linearly with temperature from (2.5±0.4)×10−17 cm2/ion at 95 K to (−0.9±0.7)×10−17 cm2/ion at 575 K. The spectrum of irradiation-induced point defects, measured from the stress change after the ion beam was switched off, peaks below 0.23 eV and extends up to 0.80 eV. All four irradiation-induced effects can be described using a thermal spike model.

Shear Mechanical Properties of Human Lumbar Annulus Fibrosus

Function, failure, and remodeling of the intervertebral disc are all related to the stress and strain fields in the tissue and may be calculated by finite element models with accurate material properties, realistic geometry, and appropriate boundary conditions. There is no comprehensive study in the literature investigating the shear material properties of the annulus fibrosus. This study obtained shear material properties of the annulus fibrosus and tested the hypothesis that these properties are affected by the amplitude and frequency of shearing, applied compressive stress, and degenerative state of the tissue. Cylindrical specimens with an axial orientation from seven nondegenerated and six degenerated discs were tested in torsional shear under dynamic and static conditions. Frequency sweep experiments over a physiological range of frequencies (0.1-100 rad/sec) at a shear strain amplitude of 0.05 rad were performed under three different axial compressive stresses (17.5, 25, and 35 kPa). At the largest compressive stress, shear strain sweep experiments (strain amplitude range: 0.005-0.15 rad at a frequency of 5 rad/sec) and transient stress-relaxation tests (shear strain range: 0.02-0.15 rad) were performed. The annulus fibrosus material was less stiff and more dissipative at larger shear strain amplitudes, stiffer at higher frequencies of oscillation, and stiffer and less dissipative at larger axial compressive stresses. The dynamic shear modulus, /G*/, had values ranging from 100 to 400 kPa, depending on the experimental condition and degenerative level. The shear behavior was also predominantly elastic, with values for the tangent of the phase angle (tandelta) ranging from 0.1 to 0.7. The annulus material also became stiffer and more dissipative with degenerative grade; however, this was not statistically significant. The results indicated that nonlinearities, compression/shear coupling, intrinsic viscoelasticity, and, to a lesser degree, degeneration all affect the shear material behavior of the annulus fibrosus, with important implications for load-carriage mechanisms in the intervertebral disc. These material complexities should be considered when choosing material constants for finite element models.

1732 一方向炭素繊維強化複合材料の高温における応力リラクセーション挙動

Short-term off-axis stress relaxation behavior of unidirectional carbon fiber-reinforced composite (T800H/Epoxy) has been examined at high temperature. Stress relaxation tests were performed at 100℃ on plain coupon specimens with various off-axis angles : θ=0,10,30,45,and 90°. For each of these off-axis angles, the stress relaxation tests were carried out at three different strain levels. The stress relaxation phenomenon was clearly observed for all off-axis angles, including θ=0° Just after the total strain was kept constant, the stress rapidly relaxed with time in a short period. Then, the relaxation rate of the composite stress tended to vanish. The extent of the transient stress relaxation was significantly dependent on the total strain kept constant and the fiber orientation angle.

112 炭素繊維アングルプライ積層板の高温における応力リラクセーション挙動

Short-term stress relaxation behavior of angle-plied T800H/Epoxy [±θ] has been studied at high temperature. Stress relaxation tests were performed at 100℃ using plain coupon specimens with various fiber orientation angles : θ=0,30,45,60,and 90°. For each fiber orientation angle, the stress relaxation tests were carried out at three different total strain levels. The stress relaxation phenomenon was clearly observed for all kinds of angle-plied laminate, including θ=0°. Just after the total strain was kept constant, the stress rapidly relaxed with time in a short period. Then, the relaxation rate of the composite stress apparently vanished. The extent of the transient stress relaxation was significantly dependent on the total strain kept constant and the fiber orientation angle. Normalized relaxation curves eventually fell on a single relationship.

Shear mechanical properties of human lumbar annulus fibrosus.

Function, failure, and remodeling of the intervertebral disc are all related to the stress and strain fields in the tissue and may be calculated by finite element models with accurate material properties, realistic geometry, and appropriate boundary conditions. There is no comprehensive study in the literature investigating the shear material properties of the annulus fibrosus. This study obtained shear material properties of the annulus fibrosus and tested the hypothesis that these properties are affected by the amplitude and frequency of shearing, applied compressive stress, and degenerative state of the tissue. Cylindrical specimens with an axial orientation from seven nondegenerated and six degenerated discs were tested in torsional shear under dynamic and static conditions. Frequency sweep experiments over a physiological range of frequencies (0.1-100 rad/sec) at a shear strain amplitude of 0.05 rad were performed under three different axial compressive stresses (17.5, 25, and 35 kPa). At the largest compressive stress, shear strain sweep experiments (strain amplitude range: 0.005-0.15 rad at a frequency of 5 rad/sec) and transient stress-relaxation tests (shear strain range: 0.02-0.15 rad) were performed. The annulus fibrosus material was less stiff and more dissipative at larger shear strain amplitudes, stiffer at higher frequencies of oscillation, and stiffer and less dissipative at larger axial compressive stresses. The dynamic shear modulus, /G*/, had values ranging from 100 to 400 kPa, depending on the experimental condition and degenerative level. The shear behavior was also predominantly elastic, with values for the tangent of the phase angle (tandelta) ranging from 0.1 to 0.7. The annulus material also became stiffer and more dissipative with degenerative grade; however, this was not statistically significant. The results indicated that nonlinearities, compression/shear coupling, intrinsic viscoelasticity, and, to a lesser degree, degeneration all affect the shear material behavior of the annulus fibrosus, with important implications for load-carriage mechanisms in the intervertebral disc. These material complexities should be considered when choosing material constants for finite element models.

Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions

Predictions for double-step strain flows are presented using a newly proposed reptation theory that accounts for segment connectivity, chain-length breathing, segmental stretch and constraint release in a self-consistent, full-chain theory. In this part of the work emphasis is on double-step shear strains where the second step is reversed and the imposition time of the second strain is earlier than the estimated retraction time, for which the Doi–Edwards model and single-integral models have been found to be incapable of describing experimental trends. Transient stress relaxation properties of two types of reversing flows, types B and C, have been examined and compared to the predictions obtained from the Doi–Edwards model and a single-integral model. The simulations show excellent agreement with the experimental trends based on recent mechanical and optical measurements.

Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. I. Theory and single-step strain predictions

A self-consistent reptation theory that accounts for chain-tube interactions, segment connectivity, chain-length breathing, segmental stretch, and constraint release is proposed. Simulation results are compared semiquantitatively to experimental observations in single-step strain flows. Since stochastic simulation techniques are used, no approximations, such as independent alignment or consistent averaging are needed to obtain results. The simulation results show excellent agreement with experimental trends in shear and normal stress relaxations, including the second normal stress difference, well into the nonlinear regime. For most of these experiments, the original Doi and Edwards theory, which incorporates independent alignment or consistent averaging, is not satisfactory. In the following companion paper, we show how the model is capable of describing double-step-strain flows for all stress components. Subsequent papers show excellent agreement for the inception of steady shear flow, and steady shear flow.