Viscoelastic Stress Research Articles

A viscoelastic model of compression and relaxation behaviors in preforming process for carbon fiber fabrics with binder

The preforming process of fiber fabrics in liquid composite molding presents remarkable viscoelastic behaviors, and gives significant effect on the overall mechanical properties of composite components. Thus, here, a unified viscoelastic model to predict the compression and relaxation viscoelastic behaviors in preforming process for the carbon fiber fabrics with binder is originally proposed. The physical meaning of each model parameter is rationally defined. Experiments for typical carbon fiber fabrics are conducted to validate the proposed model. The theoretical curves match well with the experimental measurements, and the correlation factors for different contents of binder are larger than 0.9, demonstrating the proposed model can well capture the stress evolution. Besides, we clearly reveal that in compression, the elastic stress is the main stress, and the viscoelastic stress is very small. Elastic modulus increases non-linearly and rapidly with the loading time. As the content of the binder increases, the elastic modulus gradually decreases due to the binder layer. For the relaxation stage, the total stress relaxation ratio is enlarged, while the elastic stress relaxation ratio is reduced, indicating the addition of binder can significantly improve the relaxation ability of the fabrics. The relationship of delay time τ: τ0wt<τ4wt<τ8wt<τ12wt is experimentally confirmed, and is consistent with the theoretical prediction, suggesting the increasing binder enlarges the relaxation time. The proposed theoretical model here provides an approach to understand the viscoelastic responses in preforming process.

Modeling of delayed elasticity in glass

We have developed a numerical model based on finite element analysis (FEA) with a viscoelastic material model coupling stress relaxation and structural relaxation, using the Mauro-Allan-Potuzak (MAP) non-equilibrium viscosity equation as the shift function. A modeling study of the delayed elasticity behavior in glass under different equilibrium viscosity and non-equilibrium viscosity conditions is conducted. The delayed elastic response is found to be well described by a stretched exponential function with three parameters: the maximum delayed elasticity response, the retardation time of delayed elasticity response, and the stretching exponent of delayed elasticity response. The delayed elasticity magnitude is seen to increase with lower values of the stretching exponent bstress. At equilibrium viscosity, the retardation time shows a linear relationship with the stress relaxation time. However, when the temperature drops sharply in the non-equilibrium viscosity cases, the delayed elastic response may be frozen resulting in a lower magnitude for the delayed elasticity and the retardation time is not linear any more with the stress relaxation time. The delayed elasticity stretching exponent is seen to vary slightly at different relaxation times and normalized delayed elasticity response can roughly be collapsed into a single master curve. The impact of liquid fragility is also studied.

Drop breakup dynamics of dilute polymer solutions: Effect of molecular weight, concentration, and viscosity

The large extensional viscosity of dilute polymer solutions has been shown to dramatically delay the breakup of jets into drops. For low shear viscosity solutions, the jet breakup is initially governed by a balance of inertial and capillary stresses before transitioning to a balance of viscoelastic and capillary stresses at later times. This transition occurs at a critical time when the radius decay dynamics shift from a 2/3 power law to an exponential decay as the increasing deformation rate imposed on the fluid filament results in large molecular deformations and rapid crossover into the elasto-capillary regime. By experimental fits of the elasto-capillary thinning diameter data, a relaxation time of less than 100 μs has been successfully measured. In this paper, we show that, with a better understanding of the transition from the inertia-capillary to the elasto-capillary breakup regime, relaxation times close to 10 μs can be measured with the relaxation time resolution limited only by the frame rate and spatial resolution of the high speed camera. In this paper, the dynamics of drop formation and pinch-off are presented using dripping onto substrate capillary breakup extensional rheometry (CaBER-DoS) for a series of dilute solutions of polyethylene oxide (PEO) in water and in a viscosified water and glycerin mixture. Four different molecular weights between 100 k and 1 M g/mol were studied with varying solution viscosities between 1 and 22 mPa s and at concentrations between 0.004 and 0.5 times the overlap concentration, c*. The dependence of the relaxation time and extensional viscosity on these varying parameters was studied and compared to the predictions of dilute solution theory while simultaneously searching for the lower limit in solution elasticity that can be detected. For PEO in water, this limit was found to be a fluid with a relaxation time of roughly 20 μs. These results confirm that CaBER-DoS can be a powerful technique characterizing the rheology of a notoriously difficult material to quantify, namely, low viscosity inkjet printer inks.

Viscoelastic effect on steady wavy roll cells in wall-bounded shear flow

An alternative step in understanding the flows of near wall drag-reducing turbulence can be examining the flow in a well-organized streamwise vortex with a laminar background. Herein, we studied the flow behaviors of the Giesekus viscoelastic fluid in a rotating plane Couette flow system, which is accompanied by steady roll cell structures. By fixing the Reynolds and rotation numbers at values that provide as steady wavy roll cell, i.e., an array of meandering streamwise vortices, the Weissenberg number was increased up to 2000 (where the relaxation time was normalized by the wall speed and the kinematic viscosity). We observed that, in the viscoelastic flows, the secondary flow (wall-normal and spanwise velocity fluctuations) are suppressed while the streamwise component is maintained, and the wavy roll cells are modulated into streamwise-independent straight roll cells. The kinetic energy transports among the mean shear flow, Reynolds stresses due to the roll cell, and viscoelastic stress are investigated in the non-turbulent background. We further discussed the modulation mechanism and its relevance to the drag reduction phenomenon in the viscoelastic wall turbulence.

Simulations of 3D bioprinting: predicting bioprintability of nanofibrillar inks

3D bioprinting with cell containing bioinks show great promise in the biofabrication of patient specific tissue constructs. To fulfil the multiple requirements of a bioink, a wide range of materials and bioink composition are being developed and evaluated with regard to cell viability, mechanical performance and printability. It is essential that the printability and printing fidelity is not neglected since failure in printing the targeted architecture may be catastrophic for the survival of the cells and consequently the function of the printed tissue. However, experimental evaluation of bioinks printability is time-consuming and must be kept at a minimum, especially when 3D bioprinting with cells that are valuable and costly. This paper demonstrates how experimental evaluation could be complemented with computer based simulations to evaluate newly developed bioinks. Here, a computational fluid dynamics simulation tool was used to study the influence of different printing parameters and evaluate the predictability of the printing process. Based on data from oscillation frequency measurements of the evaluated bioinks, a full stress rheology model was used, where the viscoelastic behaviour of the material was captured. Simulation of the 3D bioprinting process is a powerful tool and will help in reducing the time and cost in the development and evaluation of bioinks. Moreover, it gives the opportunity to isolate parameters such as printing speed, nozzle height, flow rate and printing path to study their influence on the printing fidelity and the viscoelastic stresses within the bioink. The ability to study these features more extensively by simulating the printing process will result in a better understanding of what influences the viability of cells in 3D bioprinted tissue constructs.

Temperature-dependent modelling of a HNBR O-ring seal above and below the glass transition temperature

Sealing products can undergo many different atmospheric conditions and hence large variations in the in-service temperatures. These products, typically made of elastomer, are known to have heat sensitive mechanical characteristics. Since the reliability of sealing systems can be affected by cyclic temperature conditions, it is essential to predict seal performances depending on the temperature in order to prevent the occurrence of interfacial leaks. The aim of the present study is to simulate the thermo-mechanical behavior of a HNBR O-ring seal during a temperature cycle ranging from room temperature to low temperatures down to −34 °C. The main objective is to present the construction and the thermal dependency of a hyperelasto-visco-hysteresis (HVH) model so as to be able to predict the mechanical behavior of the elastomer in function of temperature. This phenomenological model is designed in the form of a combination of hyperelastic, viscoelastic and elasto-hysteretic stress contributions. The relevant parameters are identified using a material database based on the results of classical homogeneous isothermal relaxation tests and anisothermal relaxation tests. The predictions of the HVH model obtained shows good agreement with the experimental contact force during a 20% squeezed O-ring test under cyclic thermal loading below the glass transition temperature.

Multiscale Numerical Simulations of Branched Polymer Melt Viscoelastic Flow Based on Double-Equation XPP Model

The double-equation extended Pom-Pom (DXPP) constitutive model is used to study the macro and micro thermorheological behaviors of branched polymer melt. The energy equation is deduced based on a slip tensor. The flow model is constructed based on a weakly-compressible viscoelastic flow model combined with DXPP model, energy equation, and Tait state equation. A hybrid finite element method and finite volume method (FEM/FVM) are introduced to solve the above-mentioned model. The distributions of viscoelastic stress, temperature, backbone orientation, and backbone stretch are given in 4 : 1 planar contraction viscoelastic flows. The effect of Pom-Pom molecular parameters and a slip parameter on thermorheological behaviors is discussed. The numerical results show that the backbones are oriented along the direction of fluid flow in most areas and are spin-oriented state near the wall area with stronger shear of downstream channel. And the temperature alongy=-1is little higher in entropy elastic case than one in energy elastic case. Results demonstrate good agreement with those given in the literatures.

Reconstruction of kernel depending also on space variable

The paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic type. This problem describes uniaxial deformations u of a cylindrical domain (0,π) × Ω, which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on Ω‐sections perpendicular to the x axis. Various types of boundary conditions in [0,T] × {0,π} × Ω are prescribed, whereas Dirichlet conditions are assumed in [0,T] × (0,π) × ∂Ω. To reconstruct both u and k, we suppose of knowing for any time tand any x ∈ (0,π) the flux of the viscoelastic stress vector through the boundary of the Ω‐section. The main novelty is that the unknown kernel k is allowed to depend, not only on the time variable t but also on the space variable x.

Did the 2008 Mw 7.9 Wenchuan Earthquake Trigger the Occurrence of the 2017 Mw 6.5 Jiuzhaigou Earthquake in Sichuan, China?

AbstractThe 2017 Mw 6.5 Jiuzhaigou earthquake occurred at the southeastern boundary of the Bayankala block in Tibetan Plateau. Here we investigate the spatial and temporal seismicity rate changes in the Jiuzhaigou region using the finite‐source epidemic‐type aftershock sequence model and stochastic declustering method. The background probabilities of all events are obtained, and the cumulative background seismicity is extracted and fitted by a linear function. Following from this, we argue that there was a decrease of background seismicity in Jiuzhaigou region immediately after the occurrence of the 2008 Mw 7.9 Wenchuan earthquake. On the other hand, we also calculate the static and viscoelastic stress changes in the area around the hypocenter of the Jiuzhaigou earthquake induced by the Wenchuan earthquake. Although opposite results are resolved by previous studies, we infer a negative Coulomb failure stress change under reasonable assumptions of parameters for this case. Combining these two observed empirical relationships, we conclude that the 2017 Jiuzhaigou earthquake is delayed by the Wenchuan earthquake and the former event possibly results from the southeastward movement of the Bayankala block, which in turn arises from the collision of Indian‐Australian Plate and the Eurasian Plate. These findings indicate that Bayankala block and its adjacent tectonic faults are still in the highly active seismic period that started in the 1990s.

Viscoelastic finite element analysis of residual stresses in porcelain-veneered zirconia dental crowns.

The main problem of porcelain-veneered zirconia (PVZ) dental restorations is chipping and delamination of veneering porcelain owing to the development of deleterious residual stresses during the cooling phase of veneer firing. The aim of this study is to elucidate the effects of cooling rate, thermal contraction coefficient and elastic modulus on residual stresses developed in PVZ dental crowns using viscoelastic finite element methods (VFEM). A three-dimensional VFEM model has been developed to predict residual stresses in PVZ structures using ABAQUS finite element software and user subroutines. First, the newly established model was validated with experimentally measured residual stress profiles using Vickers indentation on flat PVZ specimens. An excellent agreement between the model prediction and experimental data was found. Then, the model was used to predict residual stresses in more complex anatomically-correct crown systems. Two PVZ crown systems with different thermal contraction coefficients and porcelain moduli were studied: VM9/Y-TZP and LAVA/Y-TZP. A sequential dual-step finite element analysis was performed: heat transfer analysis and viscoelastic stress analysis. Controlled and bench convection cooling rates were simulated by applying different convective heat transfer coefficients 1.7E-5 W/mm2 °C (controlled cooling) and 0.6E-4 W/mm2 °C (bench cooling) on the crown surfaces exposed to the air. Rigorous viscoelastic finite element analysis revealed that controlled cooling results in lower maximum stresses in both veneer and core layers for the two PVZ systems relative to bench cooling. Better compatibility of thermal contraction coefficients between porcelain and zirconia and a lower porcelain modulus reduce residual stresses in both layers.

Analysis of axisymmetric instability in polymer melt electrospinning jet

The linear stability analysis is carried out for the straight jet of a polymer melt in an electrospinning process. The stability of axisymmetric disturbances is examined in order to comprehend the onset of fiber morphology with diametric variations or bead formation along the fiber under non-isothermal electrospinning conditions. As the polymeric fluid (polylactic acid melt) is a low conductivity fluid with unentangled polymer molecules, the viscoelasticity is described using the non-linear rheological Giesekus constitutive model assuming very small axial conduction current. The non-periodic axisymmetric disturbances are imposed on the non-uniform radius jet, obtained as the solution of the 1-D slender filament governing equations and the eigenspectrum for the disturbance growth rate is constructed under the realistic melt electrospinning conditions. The growth rate corresponding to the leading mode in the eigenspectrum is found to increase with increasing surface tension forces and decrease with the enhanced external electric field. Thus, the leading growth rate behavior suggests that the classical Rayleigh–Plateau instability dominates over the conducting mode of instability for melt electrospinning. Further, the role of non-isothermal conditions in the stability behavior is examined. The convective heat transfer from electrified jet to the cooling ambiance leads to thicker fibers with greater stability to axisymmetric disturbances. The stabilizing effect of heat transfer is attributed mainly to the temperature sensitive fluid rheology. In particular, the enhancement in polymer viscosity in the jet propagation direction is responsible for the build up of stabilizing viscoelastic stress. The fluid elasticity, denoted by the flow Deborah number, also tends to stabilize the electrified jet as temperature drop along the flow increases the relaxation time of the polymer chains leading to high polymeric stress associated with the stretched chains. As crystallization of polymeric chains under non-isothermal condition is not considered, the analysis holds for either amorphous polymers or polymers with slow crystallization kinetics compared to the short residence time during the spinning flow.

Mechanical Characterization of a Thick-Walled Viscoelastic Hollow Cylinder under Multiaxial Stress Conditions

A brief review of the mechanical characterization of viscoelastic materials under uniaxial, biaxial and multiaxial stress condition is carried out in this paper. Parametric analytical studies have been done in a simulated tubular specimen with different internal pressure loadings at various material properties. We observed that the relaxation modulus values obtained from the thick-walled hollow cylinder analyses are higher that the traditional uniaxial and biaxial test data under the same strain level. We noticed that during the initial period, the relaxation-modulus values are almost identical and later the relaxation modulus obtained from the thick-walled hollow cylinder analysis is found significantly higher than the uniaxial and the strip biaxial test data. We conjectured that in the initial stage the stress–strain ratios are almost independent of the geometry of the test specimen and subsequently the stress conditions vary according to the shape of the specimen because the relaxation modulus is found geometry dependent when loading time advances. Note that the main objective of this characterization is not to determine the magnitude of the stress actually present in the test specimen, but to help the designer to decide the best geometry in a realistic way according to the industrial applications from the viscoelastic stress relaxation point of view.

Dynamics of capsules enclosing viscoelastic fluid in simple shear flow

Previous studies on capsule dynamics in shear flow have dealt with Newtonian fluids, while the effect of fluid viscoelasticity remains an unresolved fundamental question. In this paper, we report a numerical investigation of the dynamics of capsules enclosing a viscoelastic fluid and which are freely suspended in a Newtonian fluid under simple shear. Systematic simulations are performed at small but non-zero Reynolds numbers (i.e. $Re=0.1$) using a three-dimensional front-tracking finite-difference model, in which the fluid viscoelasticity is introduced via the Oldroyd-B constitutive equation. We demonstrate that the internal fluid viscoelasticity presents significant effects on the deformation behaviour of initially spherical capsules, including transient evolution and equilibrium values of their deformation and orientation. Particularly, the capsule deformation decreases slightly with the Deborah number De increasing from 0 to $O(1)$. In contrast, with De increasing within high levels, i.e. $O(1{-}100)$, the capsule deformation increases continuously and eventually approaches the Newtonian limit having a viscosity the same as the Newtonian part of the viscoelastic capsule. By analysing the viscous stress, pressure and viscoelastic stress acting on the capsule membrane, we reveal that the mechanism underlying the effects of the internal fluid viscoelasticity on the capsule deformation is the alterations in the distribution of the viscoelastic stress at low De and its magnitude at high De, respectively. Furthermore, we find some new features in the dynamics of initially non-spherical capsules induced by the internal fluid viscoelasticity. Particularly, the transition from tumbling to swinging of oblate capsules can be triggered at very high viscosity ratios by increasing De alone. Besides, the critical viscosity ratio for the tumbling-to-swinging transition is remarkably enlarged with De increasing at relatively high levels, i.e. $O(1{-}100)$, while it shows little change at low De, i.e. below $O(1)$.

Impact of Heat Moisture Treatment and Hydration Level of Flours on the Functional and Nutritional Value-Added Wheat-Barley Blended Breads

The impact of heat moisture treatment (HMT) of flours on the techno-functional and nutritional patterns of binary flour bread matrices (wheat/barley, WT/CB, 60:40, w/w) was investigated in untreated (−) and HMT (+) samples made at 160 and 170 dough yield (DY) levels. Assessment was performed by determining viscoelastic (stress relaxation test) and mechanical (double compression test) behaviours, volume (seed displacement), colour (Photoshop system), crumb grain (digital image analysis), starch digestibility (enzyme hydrolysis) and staling kinetics (Avrami equation), bioaccessible polyphenol content (digestive enzymatic mild extraction) and anti-radical activity (DPPH●). A superior functional profile was provided by HMT of CB flour in the blend WT−CB+ when hydrated at DY 170 compared to the untreated control WT−CB−. The sample exhibited a similar specific volume, more cohesive, springier, more resilient crumb, with similar rate and extent of crumb firming on ageing, and similar colour pattern but finer and more uniformly sized cell structure, and deserved similar sensory ratings as the control WT−CB− concerning cell uniformity, smoothness and typical smell and taste. Digestible starch kinetic curves of blended breads pointed out samples WT−CB+ and WT+CB+ as matrices expliciting a lower degree and slower rate of starch hydrolysis when mixed at low and high DY, respectively. A similar anti-radical activity for composite bread matrices was evidenced regardless of either HMT or DY.

Viscoelastic Stresses in the Plates Containing Inclusions with Cracks

We study viscoelastic stresses in the plates containing inclusions weakened by cracks by the method of boundary integral equations and the Laplace integral transformation. The case in which the rheological relations between stresses and strains are written in the differential form is analyzed in detail. To solve the boundary problem of viscoelasticity, we use the well-known approach in which the corresponding problem of the theory of elasticity is studied by replacing the differential operators with constant quantities. The solution of the auxiliary problem is obtained by the method of boundary integral equations reduced to a system of algebraic equations. After replacing the elastic quantities in this system by the corresponding differential operators, we solve the system obtained as a result by using the Laplace integral transformation and then applying the improved numerical-analytic inversion formula adapted to this class of problems.

A virtual framework for simulation of complex viscoelastic flows

A framework is presented and demonstrated in which extrusion and laydown of viscoelastic fluids can be simulated. Examples include application of seam sealing and adhesive material, and additive manufacturing processes. A state of the art fluid flow solver is used to solve the flow equations and various rheological constitutive models are supported, such as shear thinning viscosity models or more complex viscoelastic stress models. With connection to robot path planning software the framework can be used in the product preparation phase to improve quality, reduce material consumption and commissioning time.

Validation of Reynolds-stress model for turbulent viscoelastic-fluid flow over backward facing step

The prediction of viscoelastic-fluid turbulent flows within the RANS (Reynolds-Averaged Navier-Stokes) computational framework is required for engineering applications. For such flows the modelling of an additional non-linear term Λij, correlated with the viscoelastic stress dissipation in Reynolds-averaged constitutive equation, is of decisive importance for the flow prediction accuracy. In this paper, a Reynolds-stress model (RSM) was adopted as a background turbulence model within the RANS framework for computing a drag-reducing turbulent flow over a backward-facing step (BFS). Two different model formulations for Λij were investigated by computing three BFS configurations differing in terms of geometry expansion, i.e. expansion ratio (ER). The turbulent intensities were overestimated within the separated shear layer just behind the step edge for the case with ER = 1.25, while they were slightly underestimated for the case with ER = 1.75, irrespective of the Λij modelling. As a result, the reattachment length predicted by RANS became rather short exhibiting an opposite dependency on the ER-parameter compared to the complementary DNS data. In summary, the overall models’ predictive performance in terms of presently investigated Λij-term formulations differs only marginally within the separated shear layer.

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Abstract Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

Contact mechanics of isotactic polypropylene: Effect of pre-stretch on the frictional response

Polymers are increasingly used in applications where relative moving parts are in contact. The dissipation of energy due to friction, i.e. heat production, reduces a product's lifetime significantly. Since in processing often an extrusion or injection moulding step is used in product formation, the induced anisotropic microstructure leads to a spatial variation of mechanical properties, for example frictional resistance. In this work we compare the scratch response of isotropic isotactic polypropylene (iPP) to the response of various oriented iPP systems. Subjected to single-asperity contact with a rigid diamond, the surface penetration and lateral force are measured. For various combinations of applied normal load and sliding velocity, the surface penetration and lateral force are measured. Optical profilometry measurements are used to explain the (large) differences in residual scratch profile between tests performed in the direction parallel and transverse to the orientation direction, respectively. As the anisotropy increases with the amount of orientation, both the maximum tensile stress and the strain hardening increase substantially. The penetration depth, for oriented systems governed by the transverse viscoelasticity and yield stress, is comparable for all loading angles and decreases with increasing amount of orientation. The direction of lowest frictional resistance is shown to be the direction parallel to the oriented crystals. The combination of decreasing global deformation and friction reduction as a result of pre-stretch decelerates strain localization, therewith delaying crack initiation which eventually leads to abrasive wear. Along with that, the substantial amount of elastic recovery after scratching in the transverse direction is related to the pre-tension of the perpendicular crystal network.

Characteristics of Viscoelastic Crustal Deformation Following a Megathrust Earthquake: Discrepancy Between the Apparent and Intrinsic Relaxation Time Constants

The viscoelastic deformation of an elastic–viscoelastic composite system is significantly different from that of a simple viscoelastic medium. Here, we show that complicated transient deformation due to viscoelastic stress relaxation after a megathrust earthquake can occur even in a very simple situation, in which an elastic surface layer (lithosphere) is underlain by a viscoelastic substratum (asthenosphere) under gravity. Although the overall decay rate of the system is controlled by the intrinsic relaxation time constant of the asthenosphere, the apparent decay time constant at each observation point is significantly different from place to place and generally much longer than the intrinsic relaxation time constant of the asthenosphere. It is also not rare that the sense of displacement rate is reversed during the viscoelastic relaxation. If we do not bear these points in mind, we may draw false conclusions from observed deformation data. Such complicated transient behavior can be explained mathematically from the characteristics of viscoelastic solution: for an elastic–viscoelastic layered half-space, the viscoelastic solution is expressed as superposition of three decaying components with different relaxation time constants that depend on wavelength.