Biaxial Flow Research Articles

Mechanical Behavior of Lithium-Ion Battery Separators under Uniaxial and Biaxial Loading Conditions.

The mechanical integrity of two commercially available lithium-ion battery separators was investigated under uniaxial and biaxial loading conditions. Two dry-processed microporous films with polypropylene (PP)/polyethylene (PE)/polypropylene (PP) compositions were studied: Celgard H2010 Trilayer and Celgard Q20S1HX Ceramic-Coated Trilayer. The uniaxial tests were carried out along the machine direction (MD), transverse direction (TD), and diagonal direction (DD). In order to generate a state of in-plane biaxial tension, a pneumatic bulge test setup was prioritized over the commonly performed punch test in an attempt to eliminate the effects of contact friction. The biaxial flow stress-strain behavior of the membranes was deduced via the Panknin-Kruglov method coupled with a 3D Digital Image Correlation (DIC) technique. The findings demonstrate a high degree of in-plane anisotropy in both membranes. The ceramic coating was found to negatively affect the mechanical performance of the trilayer microporous separator, compromising its strength and stretchability, while preserving its failure mode. Derived from experimentally calibrated constitutive models, a finite element model was developed using the explicit solver OpenRadioss. The numerical model was capable of predicting the biaxial deformation of the semicrystalline membranes up until failure, showing a fairly good correlation with the experimental observations.

Molecular simulation of flow-enhanced nucleation of polyethylene crystallites in biaxial flows

Molecular simulation of flow-enhanced nucleation of polyethylene crystallites in biaxial flows

Mechanics and Stability of Force Chain Arch in Excavated Granular Material

Rock and soil masses in geotechnical engineering projects, such as tunnels, mines and slopes, undergo relative motion, exhibiting mechanical characteristics of solid–fluid transition under critical conditions. This work analyzes the characteristics of the solid–fluid transition interface and the mode of load transfer through biaxial compression particle flow photoelastic experiments on granular materials. The study documents that this interface forms an arch shape, marked by a force chain arch. The granular material exhibits two distinct states depending on its position: below the arch, the granular material is in a solid–fluid transitional state, with bearing capacity reduced, while above the arch, it is in a stable solid state, capable of bearing the overlying rock layer’s load. The presence of the force chain arch alters the direction of the originally downward-transferring load, redirecting it along the trajectory of the arch. Analysis of the force and stability of the force chain arch revealed that the arch shape parameters and boundary loads control the instability of the arch. Changes in the overlying and lateral loads lead to different types of instability of the force chain arch. The findings of the study are crucial for underground engineering construction and for the prevention of geological disasters related to granular material.

Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices

Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.

Structure-property correlation of polyvinyl alcohol films fabricated by different processing methods

Polyvinyl alcohol (PVA) films prepared by solution casting method or thermal processing techniques have been widely used in industrial applications. However, the relationship between processing methods and structural properties is still unclear. In this study, three film-forming techniques, namely solution casting, blown film extrusion and extrusion casting, were adopted to prepare PVA films and the influence of processing methods on the structural and physical properties of the films was studied. The results showed that blown film (BF) prepared under biaxial elongational flow had higher crystallinity, larger crystallite size and greater in-plane orientation compared to solution cast film (SCF) and extruded film (ETF). SCF showed the smallest crystallite size, slowest melting temperature, fewer defects, evident skin-core structure and in-plane orientation ascribing to its slow film forming process, stratified solidification and low initial macromolecular concentration. ETF displayed the lowest degree of crystallinity and orientation owing to the fast cooling outside the slit die and the absence of strong flow field. Hence, BF and SCF were endowed with high tensile strength (152.8 and 134.5 MPa), good puncture resistance (245.0 and 245.7 N/mm) and excellent oxygen barrier property (PO2 = 3.07 × 10−19 and 2.33 × 10−18 cm3 cm/(cm2·s·Pa)) while ETF exhibited inferior mechanical properties and oxygen barrier performance. These findings are of significance for building relationships between processing techniques, structural characteristics and practical properties of PVA films and help match appropriate film forming technology to the production of films for different application scenarios.

A triple emulsion droplet in an extensional flow

In this theoretical report we analytically explore the deformation and breakup of an initially spherical triple emulsion drop undergoing an axisymmetric extensional creeping flow. The triple emulsion, suspended in an external fluid (fluid 1), is originally made from an inner spherical drop (fluid 4), engulfed by a spherical shell (fluid 3), which is subsequently engulfed by another spherical shell (fluid 2). The problem is described by eight dimensionless parameters: the external capillary number (Ca), three viscosity ratios (λ21, λ32, λ43), two radii ratios (K, k), and two surface tensions ratios (M, m). When the triple emulsion is subjected to an external uniaxial extensional flow (Ca > 0), the outer interface (21) and the inner drop interface (43) deform into prolate spheroids, while the interface between them (32) deforms into an oblate spheroid. The reverse occurs for an external biaxial flow (Ca < 0), the outer interface (21) and the inner drop interface (43) deform into oblate spheroids and the middle interface (32) becomes a prolate spheroid. Three types of breakup mechanisms are to be expected: when the outer and the middle interfaces are in contact, when the middle and the inner interfaces are in contact, and when the inner drop breaks while the two shell phases remain continuous. Finally, an analytical expression for the effective viscosity of a dilute emulsion containing spherical triple emulsion droplets is suggested. For a triple emulsion which behaves like a solid: a very viscous or a very thin outer shell (λ21→∞ or K→ 1), the effective viscosity reduces to Einstein’s formula, and when the triple emulsion behaves like a single drop: a very thick outer shell such that the inner shell and the inner drop disappear (K→ 0), Taylor’s expression is recovered.

A novel hydraulic bulge test in hot forming conditions

A novel hydraulic bulge test device was developed to evaluate high temperature biaxial stress–strain curves of quenchable boron steel sheets. The work mainly focuses on the resistance heating designed to assure a homogeneous temperature field in the dome area of the circular blank where the hydraulic pressure will be applied. The practical hot stamping conditions, including the heating and cooling steps, were reproduced to perform hydraulic bulge tests on the Usibor ®1500P steel for a temperature range between 700 to 900 °C, after an austenization step at 900 °C. Stress–strain curves were obtained from these expansion tests using the data extracted with a laser profilometer, due to the difficulties associated with the use of Digital Image Correlation at such high temperatures. Although the profilometer is a compromise solution, the comparisons between tensile and biaxial stress–strain results enable to verify the feasibility of the new device for the evaluation of the stress–strain curves at a high temperature in a biaxial state. The results point-out that, besides the difficulties with the acquisition of the strain fields and in the strain-rate control, there are also challenges in the interpretation of the metallurgical evolutions that can occur during the tests, which can affect the biaxial flow curves.

A method for characterizing the deformation localization in granular materials using the relative particle motion

The failure location identification of granular materials can be solved by capturing the deformation localization. Considering the relative translation and rotation among particles, a new concept named the relative particle motion (RPM) is proposed to describe the deformation localization of the granular materials. An approach is developed to realize the selection of particles that are used to calculate RPM. The number of particles involved in RPM calculation is controlled by two key parameters, i.e., grid spacing (U) and domain radius (R). Combining the proposed concept and the selection approach of particles, the method that can capture the region of the deformation localization in the granular material is established and implemented in PFC2D.The simulation of a uniaxial compression test is conducted to analyze the effect of parameters U and R on the calculation results of the RPM field, and a reasonable range of U and R is given. Three typical conditions, including the biaxial compression, trapdoor, and particle flow tests, are taken as examples to validate the proposed method under different loading conditions. Regions of the deformation localization characterized by RPM have a good agreement with the shear band presented in the published literature.

Deformation behavior and formability of friction stir processed DP600 steel

Abstract The effect of friction stir processing (FSP) on the formability of DP600 steel was experimentally investigated and the basic relationships between biaxial deformation behavior and FSP-induced evolutions in microstructural and mechanical properties were established. FSP formed a microstructure that consists of lath martensite with increased volume fraction compared to as-received (AR) microstructure that mainly consisted of well-distributed fine martensite particles in a ferrite matrix. Consequently, AR yield strength (301 MPa) and ultimate tensile strength (621 MPa) increased to about 811 and 1054 MPa, respectively. This strength enhancement achieved accompanied by adequate uniform elongation and elongation to failure values of 6.3 and 13.0%, respectively. Under biaxial loading conditions, good strain hardenability of the AR DP600 steel brought about a large membrane stretching regime leading to high punch force for biaxial flow. After FSP, both punch displacements within the membrane stretching regime decreased due to the increased volume fraction of lath martensite leading to higher cracking tendency. In result, cup depth and peak punch force of FSPed DP600 decreased from 8.7 mm and 33.2 kN to 7.1 mm and 28.1 kN, respectively. The obtained results simply indicate that FSP can be employed to enhance the strength of dual-phase steels with a reasonable level of formability.

Topological Transition in Multicyclic Chains with Structural Symmetry Inducing Stress-Overshoot Phenomena in Multicyclic/Linear Blends under Biaxial Elongational Flow

Blends of multicyclic and linear polymers under biaxial elongational flow were analyzed using coarse-grained molecular dynamics simulations. The multicyclic/linear blends displayed overshoot in the normal stress difference at the start-up of biaxial elongational flow. This overshoot was steeper for multicyclic/linear blends than for our previously reported monocyclic/linear blends [T. Murashima, K. Hagita, and T. Kawakatsu, Macromolecules, 2021, 54, 7210]. Investigation of the origin of the overshoot in the multicyclic/linear blends revealed a different mechanism than that previously observed in our monocyclic/linear blends. Specifically, a "topological transition" mechanism comprising a morphological change from the open- to closed-ring state was observed in the multicyclic chains, but not in the monocyclic chains. This topological transition drastically changes the stress of the rings. Although the topological transition was also observed in asymmetric-multicyclic/linear blends, no stress overshoot appeared, owing to the asymmetry in the multicyclic chains. Therefore, we hypothesized that the structural symmetry in multicyclic chains is indispensable for overshoot behavior to occur. We determined that the topological transition in multicyclic chains with structural symmetry induces stress-overshoot behavior in multicyclic/linear blends under biaxial elongational flow.

Cryogenic deformation behavior of 6061 aluminum alloy tube under biaxial tension condition

Cryogenic forming has been proposed for the fabrication of complex aluminum alloys tubular components to overcome the shortcomings of traditional forming processes. It is difficult to evaluate the cryogenic biaxial deformation behavior. In this study, a novel cryogenic hydro-bulging device was established to evaluate cryogenic deformation behavior and verify the feasibility of the new forming process. The cryogenic biaxial stress-strain relations were determined using a new analytical model to quantitatively characterize the hardening behavior. The cryogenic deformation mechanism was revealed by microstructure characterization. It is found that the maximum expansion rate of 6061 aluminum alloy tube at − 196 ℃ increases to 34.0% ± 0.6%, being 99.8% higher than that at room temperature. The obtained cryogenic biaxial flow curve exhibits the significantly improved plasticity and hardening ability with a strain hardening exponent of 0.43 at − 196 ℃. The high cryogenic strain hardening rate contributes to the stable uniform deformation. The improved cryogenic plasticity is associated with the diminished dislocations accumulation at grain boundaries. The enhanced cryogenic hardening ability is attributed to the impeded movable dislocations slip. The research demonstrates that cryogenic medium pressure forming has great potential for the fabrication of complex aluminum alloy tubular components. • A novel cryogenic hydro-bulging device was established for evaluating the cryogenic biaxial deformation behavior oftubes. • The cryogenic biaxial mechanical properties and hardening behavior were quantitatively evaluated by a new analytical model. • Excellent cryogenic biaxial formability can be obtained, contributing to the fabrication of complex tubular parts. • Microstructure was characterized to reveal the cryogenic deformation mechanism.

Viscosity Overshoot in Biaxial Elongational Flow: Coarse-Grained Molecular Dynamics Simulation of Ring–Linear Polymer Mixtures

Viscosity overshoot of entangled polymer melts has been observed under shear flow and uniaxial elongational flow, but has never been observed under biaxial elongational flow. We confirmed the presence of viscosity overshoot under biaxial elongational flows observed in a mixed system of ring and linear polymers expressed by coarse-grained molecular dynamics simulations. The overshoot was found to be more pronounced in weakly entangled melts. Furthermore, the threshold strain rate $\dot{\varepsilon}_{\rm th}$ distinguishing linear and nonlinear behaviors was found to be dependent on the linear chain length as $\dot{\varepsilon}_{\rm th}(N)\sim N^{-1/2}$, which differs from the conventional relationship, $\dot{\varepsilon}_{\rm th}(N) \sim N^{-2}$, expected from the inverse of the Rouse relaxation time. We have concluded that the cooperative interactions between rings and linear chains were enhanced under biaxial elongational flow.

Coil-stretch-like transition of elastic sheets in extensional flows.

The conformation of a long linear polymer dissolved in fluid and exposed to an extensional flow is well-known to exhibit a "coil-stretch" transition, which for sufficiently long chains can lead to bistability. The present work reports computations indicating that an analogous "compact-stretched" transition arises in the dynamics of a thin elastic sheet. Sheets of nominally circular, square or rectangular shape are simulated in planar and biaxial flows using a finite element method for the sheet conformations and a regularized Stokeslet method for the fluid flow. If a neo-Hookean constitutive model is used for the sheet elasticity, the sheets will stretch without bound once a critical extension rate, as characterized nondimensionally by a capillary number, is exceeded. Nonlinear elasticity, represented with the Yeoh model, arrests the stretching, leading to a highly-stretched steady state once the critical capillary number is exceeded. For all shapes and in both planar and biaxial extension, a parameter regime exists in which both weakly stretched (compact) and strongly stretched states can be found, depending on initial conditions. I.e. this parameter regime displays bistability. As in the long-chain polymer case, the bistable behavior arises from the hydrodynamic interaction between distant elements of the sheet, and vanishes if these interactions are artificially screened by use of a Brinkman model for the fluid motion. While the sheets can transiently display wrinkled shapes, all final shapes in planar and biaxial extension are planar.

Texture attributes of acid coagulated fresh cheeses as assessed by instrumental and sensory methods

A series of commercial acid coagulated fresh cheeses was examined as far as their texture characteristics were concerned using instrumental and sensory methods. Instrumental tests employed were determination of Young's modulus of elasticity and lubricated squeeze flow viscosimetry. Sensory tests by trained panellists assessed mouthfeel perception of the cheeses. Two attributes were selected: in mouth thickness and smoothness. Statistical analysis of the instrumental and sensory data revealed that the attribute thickness correlated fairly well with results obtained from the determination of Young's modulus, whereas the attribute smoothness with results obtained from determination of elongational viscosity at low biaxial flow rate. It is suggested that the two tests can be employed successfully for texture assessment of acid fresh cheeses regardless of their composition and the processing conditions employed during production.

Design and Characterization of a Novel Biaxial Bionic Hair Flow Sensor Based on Resonant Sensing.

This paper presents the design, theoretical analysis, simulation verification, fabrication and prototype characterization of a novel biaxial bionic hair flow sensor based on resonant sensing. Firstly, the device architecture, mainly consists of a polymer hair post, a silicon micro signal transducer and a glass substrate, is described, the theoretical simplified model is established and the mechanical sensitivity to air flow is deducted. Then, the structure simulations based on Ansys software are implemented to preliminarily verify the feasibility of the proposed sensor conception and optimize the structure parameters simultaneously. Subsequently, a closed-loop control scheme based on digital phase-locked loop and an amplitude demodulation algorithm of oscillatory flow velocity based on the least mean square method are proposed to transform and extract the air flow signal, and then verify it by circuit simulations based on SIMULINK. Finally, the fabricated prototype is illustrated and comprehensively tested. The tested prototype possesses an x-axis scale factor of 1.56 Hz/(m/s)2 and a y-axis scale factor of 1.81 Hz/(m/s)2 for the steady air flow and an x-axis detection threshold of 43.27 mm/s and a y-axis detection threshold of 41.85 mm/s for the oscillatory air flow.

New Multistage Sheet-Bulk Metal Forming Process Using Oscillating Tools

A new sheet-bulk metal forming process for the production of bulk components out of a flat sheet has been developed. Superimposed oscillation has been applied to the new process. By this means, process limits regarding better mould filling were expanded, and forming forces could be reduced. In order to investigate the effects of superimposed oscillation on material behaviour, plane strain and ring compression tests were carried out. The superimposed oscillated plane strain compression test showed a reduction in biaxial flow stress and thus in plastic work. Furthermore, reduced friction and roughness were verified in ring compression tests using superimposed oscillation.

A compound drop in a nonlinear extensional flow

The fluid mechanics problem of an initially spherical compound drop suspended in another fluid undergoing a nonlinear extensional creeping flow, is the subject of this theoretical report. The compound drop is originally composed from an inner spherical drop positioned at the center of a spherical fluid shell. The problem is governed by six dimensionless parameters: the external capillary number (Ca), two viscosity ratios: shell over external (λ21) and internal over shell (λ32), the radii ratio: inner over outer (κ), the surface tensions ratio: inner-shell over outer-shell (Ω), and the nonlinear intensity of the flow (E). When the extensional flow is linear (E=0), a case already treated in the literature, a uniaxial flow (Ca > 0) deforms the outer surface into a prolate spheroid and the inner drop into an oblate spheroid, while the reverse occurs for the biaxial flow (Ca < 0). If the extensional flow is nonlinear (E≠ 0), the external fluid behaves different than the linear case suggesting sometimes closed circulations (E > 0) and always separating surfaces (E < 0). As a result, each surface of the compound drop may experience both uniaxial and biaxial flow simultaneously, and the number of shell and internal drop circulations may be doubled. This weird situation, suggests new and exciting deformation and breakup patterns, and it is the result of the inclusions of nonlinear terms to the flow field.

Modeling material behavior of AA5083 aluminum alloy sheet using biaxial tensile tests and its application in numerical simulation of deep drawing

Improvement in accuracy of the predicted results from numerical simulation results into a reduction of cost and time involved in tool design and experimental trials. However, the predicted results from finite element simulations are significantly affected by the chosen yield criterion and work hardening law. The selection of yield criterion and work hardening law depends on the characterization methods used for defining the material behavior. In this work, the mechanical behavior of AA5083-O aluminum alloy sheet is modeled by performing biaxial tensile tests using cruciform specimen and hydraulic bulging experiments in addition to uniaxial tensile tests. Biaxial to uniaxial yield stress ratios are determined using the equal plastic work principle from the flow curves obtained from these tests. The obtained ratios are used to find the coefficients of Yld2000-2d and Hill48 yield criteria which is then used in the numerical simulations of cylindrical cup deep drawing. Numerical simulations are also carried out using uniaxial and biaxial flow curves fitted with different isotropic hardening laws. Thickness distributions and the load-displacement curves are predicted and validated by performing cylindrical cup deep drawing experiments.

Numerical simulation of hydraulic bulging using uniaxial and biaxial flow curves and different yield criteria

In sheet metal forming industry, finite element analysis has become a necessary step before actual production of the parts. It helps in the improvement of part quality as well reduces the effort applied in experimental trials. However, the success of finite element simulation mainly depends on the constitutive model used for defining the plastic deformation behaviour of the sheet material. Material characterization in biaxial stress state helps in selecting advanced constitutive models in numerical simulations. In this work, aluminium alloy AA5083 sheet material is characterized in uniaxial and biaxial tension conditions. Hydraulic bulge tests are performed to obtain the flow curves and material properties which are then used to find the coefficients in different yield criteria. These coefficients and the flow curves, fitted using different work hardening laws, are used in finite element simulation of the hydraulic bulge test and the results are validated by experiments.

Extensional flow dynamics of polystyrene melt

A linear polystyrene melt with broad molecular weight distribution (CAS 0993-53-6 from Aldrich) was characterized in extensional flow using a filament stretching rheometer. A series of measurements were performed, including (1) the startup of uniaxial extensional flow until steady state; (2) the strain controlled reversed (i.e., biaxial) flow following the startup of uniaxial flow; and (3) stress relaxation (i.e., keeping the strain unchanged) also following the startup of uniaxial flow. The measurements were compared with the model by Narimissa and Wagner [J. Rheol. 60, 625–636 (2016)]. Good agreements at low extension rates and low strain values were observed. Higher deviations were observed at high rates under steady state conditions as well as during stress relaxation and reversed flow.A linear polystyrene melt with broad molecular weight distribution (CAS 0993-53-6 from Aldrich) was characterized in extensional flow using a filament stretching rheometer. A series of measurements were performed, including (1) the startup of uniaxial extensional flow until steady state; (2) the strain controlled reversed (i.e., biaxial) flow following the startup of uniaxial flow; and (3) stress relaxation (i.e., keeping the strain unchanged) also following the startup of uniaxial flow. The measurements were compared with the model by Narimissa and Wagner [J. Rheol. 60, 625–636 (2016)]. Good agreements at low extension rates and low strain values were observed. Higher deviations were observed at high rates under steady state conditions as well as during stress relaxation and reversed flow.