Unit Cell Approach Research Articles

Deformation of PEM fuel cell gas diffusion layers under compressive loading: An analytical approach

In the PEM fuel cell stack, the fibrous porous gas diffusion layer (GDL) provides mechanical support for the membrane assembly against the compressive loads imposed by bipolar plates. In this study, a new mechanistic model is developed using fundamental beam theory that can accurately predict the mechanical deflection of GDL under compressive loads. The present analytical model is built on a unit cell approach, which assumes a simplified geometry for the complex and random GDL microstructure. The model includes salient microstructural parameters and properties of the fibrous porous medium including: carbon fiber diameter, fiber elastic modulus, pore size distribution, and porosity. Carbon fiber bending is proved to be the main deformation mechanism at the unit cell level. A comprehensive optical measurement study with statistical analysis is performed to determine the geometrical parameters of the model for a number of commercially available GDL samples. A comparison between the present model and our experimental stress–strain data shows a good agreement for the linear deformation region, where the compressive pressure is higher than 1 MPa.

Analytical Modeling of PEM Fuel Cell Gas Diffusion Layers Deformation Under Compression: Part 2 - Nonlinear Behaviour Region

In the Proton exchange membrane PEM fuel cell stack, transport characteristics of the porous gas diffusion layer (GDL) change due to the GDL microstructural parameters variation in a result of compressive loading during the fuel cell assembly and operation. The GDL is a carbon fiber based highly porous media in the form of paper or cloth. In addition to the reactants and reactions products transportation, GDL provides mechanical support for the membrane assembly against the compressive loads imposed by bipolar plates. GDL mechanical behaviour can be divided into two regions; nonlinear and linear. In the compressive loads smaller than a critical pressure, GDL has a nonlinear mechanical behaviour and its compressive modulus is a function of deformation level. Using assumption of existing gap between the fibers in GDL micro-structure, the analytical model proposed in first part of this study for linear region, based on the unit cell approach, is extended to predict the nonlinear mechanical behaviour of GDL. The present unit cell model covers salient microstructural parameters and properties of the fibrous porous medium including: carbon fiber diameter, elastic modulus, pore size distribution, and gap size distribution between fibers. Bending of carbon fibers and closing the gaps between fibers are proved to be the main deformation mechanism of GDL deformation in nonlinear region. The statistical parameters of the gap distribution between carbon fibers in the GDL structure are calculated using experimental stress-strain data for a number of commercially available GDL samples. A comparison between the present model and the GDL stress-strain data shows that the model can predict accurately the mechanical behaviour of the GDL material. In addition to the mechanical behaviour, the proposed model provides useful information about the microstructural properties of the GDL during compression such as gap distribution between fibers that can be used in the GDL transport properties prediction. Keywords: Gas Diffusion Layer, Porous media, Fuel cell,analytical modeling, mechanical behaviour, compression

Analytical Modeling of PEM Fuel Cell Gas Diffusion Layers Deformation Under Compression: Part 1 - Linear Behaviour Region

In the Proton exchange membrane PEM fuel cell stack, transport characteristics of the porous gas diffusion layer (GDL) change due to the GDL microstructural parameters variation in a result of compressive loading during the fuel cell assembly and operation. The GDL is a carbon fiber based highly porous media in the form of paper or cloth. In addition to the reactants and reactions products transportation, GDL provides mechanical support for the membrane assembly against the compressive loads imposed by bipolar plates. According to the results of compression tests, GDL mechanical behaviour can be divided into regions; nonlinear and linear. In the compressive loads smaller than a critical pressure, GDL has a nonlinear mechanical behaviour and its compressive modulus is a function of deformation level. After reaching the critical pressure, the compressive strain increases linearly with the applied stress. Using unit cell approach and assuming a simplified geometry for the complex and random microstructure of the GDL, a new mechanistic model is developed that can accurately predict the mechanical behaviour of GDL. The unit cell model covers salient microstructural parameters and properties of the fibrous porous medium including: carbon fiber diameter, elastic modulus, and pore size distribution. Bending of carbon fibers is proved to be the main deformation mechanism of GDL deformation in linear region. A comprehensive optical measurement study with statistical analysis was performed to determine the effective geometrical parameters of the model for a number of commercially available GDL samples. A comparison between the present model and the GDL stress-strain data shows that the model can predict accurately the mechanical behaviour of the GDL material. The nonlinear behaviour of GDL will be addressed in the second part of this study. Keywords: Gas Diffusion Layer, Porous media, Fuel cell,analytical modeling, mechanical behaviour, compression

Numerical analyses of bending fatigue of four-step three-dimensional rectangular-braided composite materials from unit cell approach

This paper reports the numerical analyses of three-point bending fatigue behavior of four-step three-dimensional braided composite with three types of representative unit cell (RUC) model. The three types of unit cell models are the unit cell model for the interior, surface, and corner regions of the three-dimensional braided composite. A user-defined material subroutine was developed to characterize the stiffness matrix and fatigue damage evolution of the unit cells and furthermore the braided composite. The fatigue bending behaviors were calculated from the unit cell model with finite element method. It is found that the stress concentration and large deflection located at the middle of the braided composite specimen and both the ends of the bottom areas. As the increase of the stress level, the braided composite is subjected to larger deformation and faster damage accumulation, resulting in a fast fatigue failure. The RUC model could be extended to predict and design the bending fatigue performance of other three-dimensional braided composite structures.

Transverse conductivity and longitudinal shear of elliptic fiber composite with imperfect interface

The paper addresses the problem of calculating the local fields and effective transport properties and longitudinal shear stiffness of elliptic fiber composite with imperfect interface. The Rayleigh type representative unit cell approach has been used. The micro geometry of composite is modeled by a periodic structure with a unit cell containing multiple elliptic inclusions. The developed method combines the superposition principle, the technique of complex potentials and certain new results in the theory of special functions. An appropriate choice of the potentials provides reducing the boundary-value problem to an ordinary, well-posed set of linear algebraic equations. The exact finite form expression of the effective stiffness tensor has been obtained by analytical averaging the local gradient and flux fields. The convergence of solution has been verified and the parametric study of the model has been performed. The obtained accurate, statistically meaningful results illustrate a substantial effect of imperfect interface on the effective behavior of composite.

A finite element unit-cell method for homogenised mechanical properties of heterogeneous plates

This paper presents a 3D unit-cell approach which enables estimations of all bending, in-plane and coupling properties in the sense of the classical laminated plate theory for heterogeneous plates. For this reason, periodic boundary conditions which simultaneously allow in-plane as well as bending/twisting deformation modes are introduced. In contrast to existing approaches, the 3D unit-cell is connected with the macroscopic plate theory by means of prescribed loads and the extraction of strains/curvatures. Novel bending experiments at large curvatures of E-glass-fibre/epoxy cross-ply laminate with cracking outer ply at the bending tension side are conducted. Subsequently, numerical results are validated by comparing them to the measured bending stiffness degradation. Further, the effects of the single-sided transverse cracks on relevant stiffness properties are computed.

Effect of impactor shapes and yarn frictional effects on plain woven fabric puncture simulation

Research in modeling and simulation of woven fabrics has been quite intensive in the past decade. The simulation studies presented confined consideration of crimp and extension roles in the damage deformation process, in particular tensile and puncture. Most simulation works are struggling to relate internal yarn interactions with respective damage modes due to the unit cell approach. Hence, in the present study, an alternative finite element analysis approach was proposed to model yarn crimp and extension response during puncture based on the validated uniaxial tensile and puncture models. Puncture stress–strain, post-impact kinetic energy and damage evolution of full-scale woven fabrics models were evaluated with two impactor shapes and three friction levels. The results show that puncture damage behavior is the critical dependent of the magnitude of impactor shapes and yarn frictional contacts. Good comparisons with the experimental and previous studies demonstrate the approach’s suitability for modeling textile in composites.

Use of Artificial Neural Network and Theoretical Modeling to Predict the Effective Elastic Modulus of Composites with Ellipsoidal Inclusions

In this paper, a possible applicability of artificial neural networks to predict the elastic modulus of composites with ellipsoidal inclusions is investigated. Besides it, based on the general micromechanical unit cell approach, theoretical formula is also developed, for effective elastic modulus of composites containing randomly dispersed ellipsoidal in homogeneities. Developed theoretical model considers the ellipsoidal particles to be arranged in a three-dimensional cubic array. The arrangement has been divided into unit cells, each of which contains an ellipsoid. Practically in real composite systems neither isostress is there, nor isostrain, and besides it due to the effect of random packing of the phases, non-uniform shape of the particles, we are forced to include an empirical correction factor. We are forced to include an empirical correction factor in place of volume fraction which provided a modified expression for effective elastic modulus. Empirical correction factor is correlated in terms of the ratio of elastic moduli and the volume fractions of the constituents. Numerical simulations has also been done using artificial neural network and compared with the results of Halpin-Tsai and Mori-Tanaka models as well as with experimental results as cited in the literature. Calculation has been done for the samples of Glass fiber/nylon 6 composite (MMW nylon 6/glass fiber), Organically mod-ified montmorillonite (MMT)/High molecular weight (HMW) nylon 6 nanocomposite ((HE)2M1R1-HMW nylon 6), Epoxy-alumina composites and MXD6-clay nanocomposite. It is found that both the theoretical predictions by the proposed model and ANN results are in close agreement with the experimental results.

Effective electromechanical response of macro-fiber composite (MFC): Analytical and numerical models

Abstract An analytical model is proposed to predict the effective properties of macro-fiber composites (MFCs) using equivalent layered approach. The assumptions are based on “rule of mixtures”, series and parallel capacitance theory, along with uniform electric field across the electrodes. Also, a finite element (FE) model based on unit cell approach is carried out to evaluate the effective properties using periodic boundary conditions. Simulated results based on the proposed analytical and numerical approaches are validated with asymptotic expansion homogenization method (AHM) [1] , [2] and the data available for a particular fiber volume fraction from manufacturer.

Micro-mechanics of Foam using Unit Cell (Closed Cell) Approach

Micro-mechanics of Foam using Unit Cell (Closed Cell) Approach

Numerical Modelling of the Change in Stiffness Properties of Cross-Ply Laminates Subjected to Large Bending Curvatures

This paper presents a 3D unit-cell approach which enables the estimation of bending, inplaneand coupling stiffness properties in the sense of the classical laminated plate theory for arbitrarilyheterogeneous plates. Periodic boundary conditions which simultaneously allow for in-plane as wellas for bending and twist deformation modes are introduced. Additionally, bending experiments of glassfibre/epoxy cross-ply laminates with cracked outer layer at the tension side are conducted and the stiffnessdegradation due to these transverse cracks is compared to numerical results.

Micromechanical modeling of unidirectional composites with uneven interfacial strengths

Abstract Composite materials under loads normal to the fiber orientation often fail due to debonding between fibers and matrix. In this paper a micromechanical model is developed to study the interfacial and geometrical effects in fiber-reinforced composites using generalized plane strain by means of the finite element method. Assuming a periodic distribution of fibers in the matrix, a unit cell is chosen including two quarter-circular fibers. By using this unit cell approach the composite material is modeled rather realistically as the possibility of having different fiber–matrix strength exists. In the present study two different cases are considered: I) Two perfectly bonded interfaces. II) Two debonding interfaces of uneven strength. The fibers are purely elastic while the matrix is considered as isotropic with an elasto-plastic behavior. To model the fracture of the fiber–matrix interfaces, a trapezoidal cohesive zone model is used. A parametric study is carried out to evaluate the influence of the interfacial properties, fiber position and fiber volume fraction on the overall stress–strain response as well as the end-crack opening displacement and the opening crack angle. All the results presented are compared with corresponding perfectly bonded interfaces. Generally, different crack initiations and propagations at the two interfaces are seen, which result in an overall stress–strain response of the material that often first depict a rather smooth stress drop followed by a second sudden stress drop. This behavior is shown to be very sensitive to interface parameters as well as geometrical parameters. The interfacial dissimilarity shows for all the investigations, that decreasing the maximum cohesive strength leads to more stable interfacial crack growth, whereas increasing the critical interfacial separation causes a less distinct debonding at one interface before debonding at the other.

Finite element analyses of tensile impact behaviors of co-woven-knitted composite from unit-cell approach

This paper reports finite element analyses of tensile impact behaviors of co-woven-knitted (CWK) composite from a unit-cell model. A unit-cell model was established to characterize the microstructure of the CWK composite. A vectorized user-defined material subroutine was written and connected with commercial finite element analysis (FEA) software package ABAQUS to calculate the tensile failure of the CWK composites. The FEA results were also compared with the experimental results of the CWK composites under high strain rate tension obtained from the split Hopkinson tension bar apparatus. The comparisons indicate that the FEA results agree well with the experimental results. The failure mechanisms of the CWK composite under the different strain rates are also discussed.

Numerical simulation of the influence of particle clustering on tensile behavior of particle-reinforced composites

The spatial distribution of reinforcement particles significantly influences the tensile behavior of particle-reinforced composites. In this study, the role of particle clustering on the macroscopic and microscopic behavior of these composites in the absence of damage was numerically investigated. An infinite material containing a periodic distribution of clustered, elastic, spherical particles was modeled using a unit cell approach. Three types of multi-particle unit cells were simulated with different arrangements of clustered particles as well as different cluster densities. The uniaxial stress–strain curves in tension were compared with the curves obtained from single-particle unit cell simulations. It was shown that clustering of particles increases the plastic strain accumulated in the matrix and slightly increases the work hardening rate. More importantly, it was observed that while the influence of the particle distribution on the overall behavior of the composite was not significant in uniaxial tension, the maximum principal stress inside the particles is acutely sensitive to the particle cluster morphology.

Isoelectronic and isolobal O, CH2, CH3+and BH3as electron pairs; similarities between molecular and solid-state chemistry

A topological analysis of the electron localization function (ELF) of a molecule of hexamethyldisiloxane, (H3C)3-Si-O-Si-(CH3)3, has been carried out, drawing a consistent picture of Si-O-Si bonding both in the linear and angular geometries. The ELF analysis confirms the idea that the O atom, in the linear geometry of (H3C)3-Si-O-Si-(CH3)3, is isolobal with the isoelectronic -CH3(+)- and -BH3- groups, the bonding in the Si-O-Si group being described as a two-electron, three-center (2e, 3c) bond. At the same time, the three oxygen lone pairs mirror the three C-H and B-H bonds, respectively. On the contrary, in the angular geometry the same O atoms form two Si-O bonds and its lone pairs mimic the geometry of the -CH2- group. In this model the O atoms would play the same role as the formally present O(2-) anions in the `so-called' ionic solids, such as in the skeletons of aluminate and silicate polyanions, thereby connecting molecular and solid-state chemistry as formulated by the `fragment formalism' or the `molecular unit-cell approach'. This unifying concept as well as the calculations we have carried out fully agree and also give support to earlier ideas developed by Bragg and Bent, among other authors. Bonding in the series of compounds P4, P4O6, P4O10, N4(CH2)6 (hexamethylenetetramine) and (CH)4(CH2)6 (adamantane) is discussed in the context of the isolobal model.

A statistically-based thermal conductivity model for fuel cell Gas Diffusion Layers

Many of the characterization and theoretical analyses of Gas Diffusion Layers (GDL) transport properties have to date been done as a function of porosity with little attention paid to other geometrical properties. In this paper, a statistical unit cell approach is presented for predicting the thermal conductivity of GDLs by introducing geometrical properties such as the intersecting fiber angles and characteristic distances/aspect ratios. These geometrical properties are deconvoluted analytically using optical and porometry data. The dependency of the thermal conductivity on the geometrical parameters is analyzed, and the GDL structure for optimal heat conduction is identified. It is shown that aspect ratio is as important as porosity in determining conductivity, and that the traditional notion that a porous medium with higher porosity has a lower thermal conductivity is not always true. The maximum thermal conductivity depends primarily on porosity and fiber angle, occurs at an aspect ratio of around unity, and shows negligible dependence on fiber diameter. The geometrical concepts and the measured data presented in this paper help unravel some unexplained trends reported in the literature and provide novel insights on avenues to optimize GDLs. The methodology can be extended to estimate other transport properties such as permeability.

Influence of contact resistance and natural convection effects on non-dimensional effective thermal conductivity estimation of two-phase materials

In this article, the development of geometry dependent resistance model by considering contact resistance and natural convection effects are used to estimate the effective thermal conductivity of two-phase materials based on the unit cell approach. The algebraic equations have been derived based on isotherm approach for 2-D and 3-D spatially periodic medium. Comparison study has been made between developed models and experimental data. The result agrees well with experimental values.

A unit cell approach to compute thermal conductivity of uncured silicone/phosphor composites

Composites of silicone matrix filled with phosphor are widely used in light emitting diodes (LEDs) packaging. Its thermal conductivity is one of the important properties for LED thermal analysis. In this paper, a unit cell model (UCM) that includes interface resistance between phosphor and silicone matrix was built and applied to predict the thermal conductivity of uncured silicone/phosphor composites at different phosphor volume fractions. The thermal conductivities of seven uncured silicone/phosphor composites samples were measured for comparison with modeling results. The comparison shows that the model result matches to the experimental data within ±6% at the low volume fraction from 3.8% to 25%. Both the experiment and modeling results show that thermal conductivity of the composite has a sudden increase when volume fraction increases to near 40%, which can be explained by the percolation theory. For higher volume fraction, the effect of the interface resistance Rb between the phosphor fillers and silicone matrix cannot be neglected.

CFD analysis of the fluid flow behavior in a reverse electrodialysis stack

Abstract Salinity Gradient Power by Reverse Electrodialysis (SGP-RE) technology allows the production of electricity from the different chemical potentials of two differently concentrated salty solutions flowing in alternate channels suitably separated by selective ion exchange membranes. In SGP-RE, as well as in conventional ElectroDialysis (ED) technology, the process performance dramatically depends on the stack geometry and the internal fluid dynamics conditions: optimizing the system geometry in order to guarantee lower pressure drops (ΔP) and uniform flow rates distribution within the channels is a topic of primary importance. Although literature studies on Computational Fluid Dynamics (CFD) analysis and optimization of spacer-filled channels have been recently increasing in number and range of applications, only a few efforts have been focused on the analysis of the overall performance of the process. In particular, the proper attention should be devoted to verify whether the spacer geometry optimization really represents the main factor affecting the overall process performance. In the present work, realized within the EU-FP7 funded REAPower project, CFD simulations were carried out in order to assess the effects of different parameters on the global process efficiency, such as the choice of spacer material and morphology, and the optimization of feed and blowdown distribution systems. Spacer material and morphology can affect the fluid dynamics inside each channel. In particular, the appropriate choice of net spacer material can influence the slip/no-slip condition of the flow on the spacer wires, thus significantly affecting the channel fluid dynamics in terms of pressure drops. A Unit Cell approach was adopted to investigate the effect of the different choices on the fluid flow along the channel. Also, the possibility of choosing a porous medium to substitute the net spacer was theoretically addressed. Such investigation focused on the porosity and the fiber radius required to respect the process constrains of pressure drops and mechanical stability. On the other hand, the overall pressure drops of a SGP-RE or ED stack can be considered as resulting from different contributions: the pressure drop relevant to the feed distributor, the pressure drop inside the channel, and the pressure drop in the discharging collector. The choice of the optimal stack geometry is, therefore, strongly related to the need of both minimizing each of the above terms and obtaining the most uniform feed streams distribution among the stack channels. In order to investigate such aspects, simulations were performed on a simplified ideal planar stack with either 50 spacer-less or 50 spacer-filled channels. The effect of the distribution/collector channel thickness and geometry on single-channel flow rates and overall pressure drops in the system was analyzed and a significant influence of distributor layout and size on the overall process performance was found.

Numerical simulation of three-point bending fatigue of four-step 3-D braided rectangular composite under different stress levels from unit-cell approach

This paper reports the three-point bending fatigue behavior of 3-D carbon/epoxy braided composite in experimental and finite element analyses (FEAs) approaches. In the experimental approach, the stiffness degradation and maximum deflection curves were obtained to illustrate the relationship between applied stress levels and number of cycles to failure. In FEA approach, a user-defined material subroutine UMAT which characterizes the stiffness matrix and fatigue damage evolution of the 3-D braided composite was developed. It was incorporated with a finite element code ABAQUS/Standard to calculate the stiffness degradation and maximum deflection of the 3-D braided composite during each loading cycle. From the comparisons between experimental and FEA results, good agreements prove the validity of the unit cell model and the subroutine UMAT.