Woven fabric permeability: From textile deformation to fluid flow mesoscale simulations

A two-step methodology is proposed in order to estimate from numerical simulations the permeability of deformed woven fabrics. Firstly, the shear deformation of a glass plain weave until the shear locking is studied from a mesoscale analysis achieved with a representative volume element (RVE) of the periodic plain weave. Simulations have been carried out within the scope of large transformations, accounting for yarn–yarn contacts, and assuming that yarns behave as hypoelastic materials with transverse isotropy. From the simulated deformed solid RVE, a complementary periodic fluid RVE is then built and the slow flow of an incompressible Newtonian fluid within it is investigated. This allows to compute, in a second step, the permeability of the deformed plain weave. The role of the shear deformation on the permeability of multi-layers or single layer preforms is discussed.     

Experimental and numerical investigation of fabric impact behavior

This paper presents experimental and numerical research regarding blunt trauma resistance of ten fabrics made of high strength fibers. Fabrics of various architecture were examined, including plain woven fabrics, unidirectional laminates and multiaxial fabrics. The fabrics were compared with respect to the depth of the depression formed and the amount of energy transferred to the backing during projectile impact. Absolute values of mentioned parameters were compared, as well as their values after normalization with respect to thickness and areal density of the fabrics. A numerical method for estimating the amount of energy transferred to the backing was proposed.Normalized results, obtained experimentally and numerically, proved that most of the analyzed fabrics provide a similar level of protection, but the best blunt trauma resistance is given by multiaxial fabrics and the least by plain woven fabrics. This study has also shown that the depth of the depression in the backing material is an insufficient parameter in describing protective properties of fabric against blunt trauma. It is possible that impacts into ballistic packages composed of different fabrics with the same depth of depression may cause completely dissimilar injuries because of the amount of energy transferred to the backing material.     

Simulation of coupling filtration and flow in a dual scale fibrous media

In this article, numerical simulation of suspension (particles filled-resin) flow through a fibrous media taking into account dual scale porosity in LCM (Liquid Composite Molding) processes is presented. During the flow, a strong interaction between the particle motion and the fluid flow takes place at the porous media wall (the fiber bundle surface). In this study, the Stokes–Darcy coupling is used to describe the resin flow at mesoscopic scale to treat the particles in suspension. A “fluid” model to describe the suspension flow, a “filtration” model to describe the particle capture and a “solid” model dedicated to the modeling of mass particles dynamics was used. The “solid” model is also operated to identify the particles retention.For validation, the numerical results of proposed model were compared with the experimental results from the literature and found in good agreement. Then, other numerical results studying the suspension’s rheological behavior are presented.     

Fabrication of carbon-based nanocomposite films by spin-coating process: An experimental and modeling study of the film thickness

Spin-coating is used for the fabrication of nanocomposite thin films, consisting of carbon nanoparticles embedded in epoxy matrix, on Mylar substrate. The final thickness of the heat-cured film was measured as a function of the spinning speed and nanoparticle concentration. Multi-walled carbon nanotubes with carboxyl functionalization (MWCNT-COOH) or exfoliated graphite nanoplatelets (xGnP) were used as fillers. Experimental results were in good agreement with the predictions from a model that considered the rheology and flow behavior of the reinforced resin fluids on a rotating disk. The model was differentiated for Newtonian and non-Newtonian regime of the spinning polymer fluid. In case of non-Newtonian behavior of the epoxy resin at high particle concentrations, a semi-empirical approach was used to determine the model constants from rheology measurements. Results from this analysis also indicate how rheological and wetting properties of the nano-reinforced polymer fluids depend on the aspect ratio of the graphene nanoplatelets.     

Enhanced Effective Thickness of multi-layered laminated glass

The stiffness and strength of laminated glass, a composite of glass layers bonded together by polymeric interlayers, depends upon shear coupling between the glass plies through the polymer. In the design practice, this effect is commonly considered by defining the effective thickness of laminated glass, i.e., the thickness of a monolith with equivalent bending properties. Various theories have been proposed to calculate such a value for a package of two layers of glass and one polymeric interlayer, but extrapolation to a higher number of layers gives in general inaccurate results. Here, the Enhanced Effective Thickness method, previously proposed for two-glass-layer composites, is extended to the case of laminated glass beams made (i) by three layers of glass of arbitrary thickness, or (ii) by an arbitrary number of equally-thick glass layers. Comparisons with numerical experiments confirm the accuracy of the proposed approach also in these cases.     

Analytical approach à la Newmark for curved laminated glass

A method of solution that extends to the case of curved laminated structures the traditional approach developed by Newmark et al. for straight beams is presented. The method is specialized to curved laminated glass, a composite formed by two external glass layers that sandwich a very thin polymeric interlayer. The effect of curvature on the shear coupling of glass plies through the interlayer is examined in the paradigmatic example of a laminated beam with constant moderate curvature under radial loading with different boundary conditions, varying the initial camber, the end constraints and the elastic properties of the polymer. Comparisons with numerical experiments confirm the accuracy of the proposed modeling. In general the response of a curved structure is greatly influenced by the axial force it undergoes, and such internal action is mainly governed, for fixed applied loads, by the boundary conditions at the extremities. The axial force produces the arch-response of the structure, which is not substantially affected by the shear coupling of glass through the interlayer. On the other hand, such coupling has major effects on the bending properties.     

Three-dimensional reconstruction of resin flow using capacitance sensor data assimilation during a liquid composite molding process: A numerical study

Liquid composite molding (LCM) is a method to manufacture fiber-reinforced composites, where dry fabric reinforcement is impregnated with a resin in a molding apparatus. However, the inherent process variability changes resin flow patterns during mold filling, which in turn may cause void formation. We propose a method to reconstruct three-dimensional resin flow in LCM, without embedding sensors into the composite structure. Capacitance measured from pairs of electrodes on molding tools and the stochastic simulation of resin flow during an LCM process are integrated by a sequential data assimilation method based on the ensemble Kalman filter; then, three-dimensional resin flow and permeability distribution are estimated simultaneously. The applicability of this method is investigated by numerical experiments, characterized by different spatial distributions of permeability. We confirmed that changes in resin flow caused by spatial permeability variations could be captured and the spatial distribution of permeability could be estimated by the proposed method.     

Numerical prediction of in-plane permeability for multilayer woven fabrics with manufacture-induced deformation

A unit cell based Computational Fluid Dynamics model is presented for predicting permeability of multilayer fabric structures. In Liquid Composites Moulding processes, fabric lay-ups undergo significant manufacture-induced deformation, combining compression, shear, and inter-layer nesting. Starting from the configuration of un-deformed fabric, the deformation is simulated geometrically by accounting for self-imposed kinematic constraints of interweaving yarns. The geometrical modelling approach is implemented in the open-source software TexGen. The permeability tensor is retrieved from flow analysis in ANSYS/CFX, based on TexGen voxel models. Using only measured geometrical data for un-deformed fabrics, deformed plain weave fabric and twill weave fabric lay-ups were modelled and their permeability tensors predicted. Comparison with experimental data demonstrates the generally good accuracy of predictions derived from the proposed numerical method.     

Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions

In this paper, the thermal effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution and employing a semi analytical differential transform method (DTM) for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying DTM. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, mode number and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behavior of an FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.     

Numerical evaluation for debonding failure phenomenon of adhesively bonded joints at cryogenic temperatures

In the present study, material characteristics, such as inelastic constitutive behaviour and debonding failure, of an adhesively bonded joint (ABJ) at cryogenic temperature have been evaluated using a computational approach. The modified Bodner-Partom model (BP model) has been introduced to describe the material nonlinearities of ABJ. The Gurson-Tvergaard model (GT model) has also been implemented into the constitutive model in order to analyse the phenomenon of debonding failure. An ABAQUS user-defined subroutine UMAT is developed using a damage-coupled constitutive model based on an implicit formulation. The numerical results are compared with a series of lap shear tests of ABJ at cryogenic temperature in order to verify the proposed method.     

Multiscale modeling of unsaturated flow in dual-scale fiber preforms of liquid composite molding III: reactive flows

The woven, stitched or braided fabrics used in liquid composite molding (LCM) display partial saturation behind moving flow-front in an LCM mold which is caused by delayed impregnation of fiber tows. In this part 3 of the present series of three papers, a novel multiscale approach proposed in parts 1 and 2 [1] and [2] is adapted for modeling the unsaturated flow observed in the dual-scale fabrics of LCM under non-isothermal, reactive conditions. The volume-averaged species or resin cure equation, in conjunction with volume-averaged mass, momentum and energy (temperature) equations, is employed to model the reactive resin flow in the inter-tow (gap) and intra-tow (tow) regions with coupling expressed through several sink and source terms in the governing equations. A coarse global-mesh is used to solve the global (gap) flow over the entire domain, and a fine local mesh in form of the unit-cell of periodic fabrics is employed to solve the local (tow) flows. The multiscale algorithm based on the hierarchical computational grids is then extended to solve the dual-scale flow under reactive conditions. The simulation is compared with a two-color experiment and a previously published two-layer model. Significant differences between the temperatures and cures of the gap and tow regions of the dual-scale porous medium are observed. The ratio of pore volumes in the tow and gap regions, the effective thermal conductivity in the tows, and the reaction rate are identified as the important parameters for temperature and cure distributions in the gap and tow regions.     

Data assimilation through integration of stochastic resin flow simulation with visual observation during vacuum-assisted resin transfer molding: A numerical study

This study investigated data assimilation through integration of visual observation with a stochastic numerical simulation of resin flow during vacuum-assisted resin transfer molding. The data assimilation was performed using the four-dimensional asynchronous ensemble square root filter and a stochastic numerical simulation by means of the Karhunen–Loève expansion of the permeability field. Through numerical experiments of linear flow, it was verified that the estimation accuracy of the resin impregnation behavior improved compared to that when using conventional data assimilation and that the permeability field could be estimated simultaneously, although it is not explicitly related to the observation. We also investigated the applicability of the proposed method to radial-injection VaRTM by varying the model thickness. The proposed method successfully estimated the resin impregnation behavior and permeability field. Additionally, the required condition for the number of ensemble members was clarified.     

Mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air voids

In random-chopped fiber-reinforced polymer (FRP) composites used as a retrofit material, a high volume fraction of voids is inevitable due to the manufacturing characteristics. In this paper, the mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air porosity are investigated through experiments and numerical analysis. Coupon-shaped specimens with various material compositions were manufactured to examine the uniaxial tensile performance, and the air voids in the composites were measured by a microscope camera. In order to predict the overall performance of the composites, a micromechanical formulation that accounts for porosity was newly developed. The derived model was incorporated into a finite element (FE) code, and the model parameters were estimated by comparing uniaxial tensile test results for various systems of random-chopped FRP composites. In addition, concrete beams strengthened with the composites were produced to evaluate their load-carrying capacity. The FE predictions of the composite structures were then compared with experimental data to verify the predictive capability of the proposed numerical framework.     

A numerical investigation into the influence of fabric construction on ballistic performance

The use of high-performance fibres has made it possible to produce lightweight and strong personal body armour. Parallel to the creation and use of new fibres, fabric construction also plays an essential role for performance improvement. In this research, finite element (FE) models were built up and used to predict the response of woven fabrics with different structural parameters, including fabric structure, thread density of the fabric and yarn linear density. The research confirmed that the plain woven fabric exhibits superior energy absorption over other structures in a ballistic event by absorbing 34% more impact energy than the fabric made from 7-end satin weave. This could be explained that the maximum interlacing points in this fabric which help transmit stress to a larger fabric area, enabling more secondary yarns to be involved for energy dissipation. It was found that fabric energy absorption decreases as fabric is made denser, and this phenomenon becomes more pronounced in a multi-ply ballistic system than in a single-ply system. The research results also indicated that the level of yarn crimp in a woven fabric is an effective parameter in influencing the ballistic performance of the fabrics. A low level of yarn crimp would lead to the increase of the fabric tensile modulus and consequently influencing the propagation of the transverse wave. In addition, it was found that for fabrics with the same level of yarn crimp, low yarn linear density and high fabric tightness were desirable for ballistic performance improvement.     

Finite element simulation of delamination growth in composite materials using LS-DYNA

In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (η) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.     

Characterising and modelling variability of tow orientation in engineering fabrics and textile composites

Variability of tow orientation is unavoidable for biaxial engineering fabrics and their composites. Since the mechanical behaviour of these materials is strongly dependent on the fibre direction, variability should be considered and modelled as exactly as possible for more realistic estimation of their forming and infusion behaviour and their final composite mechanical properties. In this study, a numerical code, ‘VariFab’, has been written to model realistic full-field variability of the tow directions across flat sheets of biaxial engineering fabrics and woven textile composites. The algorithm is based on pin-jointed net kinematics and can produce a mesh of arbitrary perimeter shape, suitable for subsequent computational analysis such as finite element forming simulations. While the shear angle in each element is varied, the side-length of all unit cells within the mesh is constant. This simplification ensures that spurious tensile stresses are not generated during deformation of the mesh during forming simulations. Variability is controlled using six parameters that can take on arbitrary values within certain ranges, allowing flexibility in mesh generation. The distribution of tow angles within a pre-consolidated glass–polypropylene composite and self-reinforced polypropylene and glass fabrics has been characterised over various length scales. Reproduction of the same statistical variability of tow orientation as in these experiments is successfully achieved by combining the VariFab code with a simple genetic algorithm.     

Modeling of heat transfer and unsaturated flow in woven fiber reinforcements during direct injection-pultrusion process of thermoplastic composites

This paper provides a methodology for the modeling of heat transfer and polymer flow during direct thermoplastic injection pultrusion process. Pultrusion was initially developed with thermosets which have low viscosity. But the impregnation becomes a critical point with thermoplastics which exhibit higher viscosity. There are very few reported works on direct thermoplastic impregnation with injection within the die. In addition, the rare studies have not adequately addressed the issue of unsaturated flow in woven fiber reinforcements. The solution proposed here, models the polymer flow through dual-scale porous media. A heat transfer model is coupled to a flow model enriched with a sink term. Specific changes of variables are made so as to model the steady state solution of unsaturation along a continuous process. The sink term, added to the continuity equation, represents the absorption rate of polymer by the bundles. Data were measured on a pultrusion line and micrographs confirmed the modeling strategy with an unsaturated flow approach. The flow modeling coupled to heat transfer of the thermoplastic pultrusion process aims at determining the saturation evolution through the die so as to manufacture pultruded profiles with the lowest residual porosity.     

Experimental and finite element study on the spring back of double curved aluminum/polypropylene/aluminum sandwich sheet

The most prominent feature of sheet material forming process is an elastic recovery phenomenon during unloading which leads to spring back and side wall curl. Metal–polymer laminate sheets are emerging materials that have many potential applications. Therefore evaluation of spring back is mandatory for production of precise products from these new sheet materials. In this paper, the results of spring back evaluation of AA3105/polypropylene/AA3105 sandwich sheet materials have been presented after being subjected to double-curvature forming. Numerical simulation of double-curvature forming process has also been carried out using both implicit and explicit finite element programs. The influences of some geometrical parameters on spring back such as thickness of sandwich sheet and tool curvatures radii have been evaluated.     

A discrete spectral model for intermediate crack debonding in FRP-strengthened RC beams

One of the common failure modes of reinforced concrete (RC) beams strengthened in flexure with a bonded fibre-reinforced polymer (FRP) is intermediate crack (IC) debonding, which is originated at a critical section in the vicinity of flexural cracks and propagates to a plate end. Despite considerable research over the last years, few reliable and simplified IC debonding strength models have been developed. This paper firstly presents a one-dimensional model based on the discrete crack approach for concrete and the spectral element method for the numerical simulation of the IC debonding process. The progressive formation of flexural cracks and subsequent concrete–FRP interfacial debonding is formulated by the introduction of a new element able to represent both phenomena simultaneously without perturbing the numerical procedure. Furthermore, with the proposed model, high frequency dynamic response for these kinds of structures can also be obtained in a very simple and non-expensive way, which makes this procedure very useful as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in local dynamic characteristics.     

Thermal flow permeametry – A rapid method for finding local changes in flow channels

Solid bodies with flow channels can have very heterogeneous structure, whose local variations are difficult to analyze. Yet, this can play an important role affecting characteristics, such as, fluid flow property, strength and heat conductivity. This article presents a method named thermal flow permeametry (TFP) that is applicable for a quick analysis of variations in flow channels, even in meter-sized structures. For illustrating the method, we analyzed the local permeability levels of a large and extremely complex fiber structure. In TFP, hot air is ejected through a structure, while thermal camera measures local surface temperature variations during heating. Gray values of the thermal image are then plotted versus the structures local thickness, density and permeability. We showed that gray values link with local permeability, affected by thickness, density and flow channel tortuousness. We also found out that TFP is very sensitive to local changes in flow channels.