Rate dependent modelling of the forming behaviour of viscous textile composites

A predictive approach to modelling the forming of viscous textile composites has been implemented in two finite element codes; Abaqus Standard™ and Abaqus Explicit™. A multi-scale energy model is used to predict the shear force–shear angle–shear rate behaviour of viscous textile composites, at specified temperatures, using parameters supplied readily by material manufacturers, such as fibre volume fraction, weave architecture and matrix rheology. The predictions of the energy model are fed into finite element simulations to provide the in-plane shear properties of two different macro-scale constitutive models implemented in the finite element codes. The manner of coupling predictions of the multi-scale energy model with the macro-scale models is shown to affect the rate-dependent material response in the simulations. These coupling methods are evaluated using picture frame test simulations.     

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.     

Press forming a 0/90 cross-ply advanced thermoplastic composite using the double-dome benchmark geometry

A pre-consolidated thermoplastic advanced composite cross-ply sheet comprised of two uniaxial plies orientated at 0/90° has been thermoformed using tooling based on the double-dome bench-mark geometry. Mitigation of wrinkling was achieved using springs to apply tension to the forming sheet rather than using a friction-based blank-holder. The shear angle across the surface of the formed geometry has been measured and compared with data collected previously from experiments on woven engineering fabrics. The shear behaviour of the material has been characterised as a function of rate and temperature using the picture frame shear test technique. Multi-scale modelling predictions of the material’s shear behaviour have been incorporated in finite element forming predictions; the latter are compared against the experimental results.     

Finite element modeling of ballistic impact on multi-layer Kevlar 49 fabrics

This paper presents a material model suitable for simulating the behavior of dry fabrics subjected to ballistic impact. The developed material model is implemented in a commercial explicit finite element (FE) software LS-DYNA through a user defined material subroutine (UMAT). The constitutive model is developed using data from uniaxial quasi-static and high strain rate tension tests, picture frame tests and friction tests. Different finite element modeling schemes using shell finite elements are used to study efficiency and accuracy issues. First, single FE layer (SL) and multiple FE layers (ML) were used to simulate the ballistic tests conducted at NASA Glenn Research Center (NASA-GRC). Second, in the multiple layer configuration, a new modeling approach called Spiral Modeling Scheme (SMS) was tried and compared to the existing Concentric Modeling Scheme (CMS). Regression analyses were used to fill missing experimental data – the shear properties of the fabric, damping coefficient and the parameters used in Cowper-Symonds (CS) model which account for strain rate effect on material properties, in order to achieve close match between FE simulations and experimental data. The difference in absorbed energy by the fabric after impact, displacement of fabric near point of impact, and extent of damage were used as metrics for evaluating the material model. In addition, the ballistic limits of the multi-layer fabrics for various configurations were also determined.     

Finite element modelling of plastic instability during ECAP processing of flow-softening materials

A finite element analysis of the equal channel angular pressing (ECAP) of flow-softening materials is presented in this paper. A very fine mesh was used in the simulations, allowing a detailed analysis of the development of localized shear phenomena. Two different flow curves were used in the simulations; one displayed an initial flow-softening followed by perfect plastic behavior, whereas the other followed a constant flow-softening behavior. The flow-softening rate affects the intensity of shear localization. The deformation zone, that is usually concentrated around a fixed shear plane during processing of perfect plastic or strain hardening materials, splits into two parts and its position varies cyclically during the process, leading to oscillations in the punch load during processing. A comparison of the finite element predictions with those from the slip line field theory is also presented.     

Numerical investigation of elastic mechanical properties of graphene structures

The computation of the elastic mechanical properties of graphene sheets, nanoribbons and graphite flakes using spring based finite element models is the aim of this paper. Interatomic bonded interactions as well as van der Waals forces between carbon atoms are simulated via the use of appropriate spring elements expressing corresponding potential energies provided by molecular theory. Each layer is idealized as a spring-like structure with carbon atoms represented by nodes while interatomic forces are simulated by translational and torsional springs with linear behavior. The non-bonded van der Waals interactions among atoms which are responsible for keeping the graphene layers together are simulated with the Lennard-Jones potential using appropriate spring elements. Numerical results concerning the Young’s modulus, shear modulus and Poisson’s ratio for graphene structures are derived in terms of their chilarity, width, length and number of layers. The numerical results from finite element simulations show good agreement with existing numerical values in the open literature.     

Mixed-interpolated finite elements for functionally graded cylindrical shells

In this paper cylindrical shells made of functionally graded materials (FGMs) are studied. A two-constituent material distribution through the thickness is considered, varying with a simple power rule of mixture. The equations governing the FGMs shells are determined using a variational formulation arising from the Naghdi theory. Moreover a strategy to achieve an improved transverse shear factor is investigated by energy equivalence. To approximate the problem a family of mixed-interpolated finite elements is used. It is based on a suitable reduction of the shear and membrane energy. Several numerical simulations are carried out in order to show the capability of the proposed elements to capture the properties of shells of various gradings, subjected to thermo-mechanical loads.     

A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates

This paper reports the development of a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behaviour within the framework of the first-order shear deformation theory. The approach incorporates the strain smoothing method for mesh-free conforming nodal integration into the conventional finite element techniques. The membrane-bending part of the element stiffness matrix is calculated by the line integral on the boundaries of the smoothing elements while the shear part is performed using an independent interpolation field in the natural co-ordinate system. Numerical results show that the element offered here is locking-free for extremely thin laminates, reliable and accurate, and easy to implement. Its convergence properties are insensitive to mesh distortion, thickness-span ratios, lay-up sequence and degree of anisotropy.     

Effect of fiber arrangement on mechanical properties of short fiber reinforced composites

The present paper developed a three-dimensional (3D) “tension–shear chain” theoretical model to predict the mechanical properties of unidirectional short fiber reinforced composites, and especially to investigate the distribution effect of short fibers. The accuracy of its predictions on effective modulus, strength, failure strain and energy storage capacity of composites with different distributions of fibers are validated by simulations of finite element method (FEM). It is found that besides the volume fraction, shape, and orientation of the reinforcements, the distribution of fibers also plays a significant role in the mechanical properties of unidirectional composites. Two stiffness distribution factors and two strength distribution factors are identified to completely characterize this influence. It is also noted that stairwise staggering (including regular staggering), which is adopted by the nature, could achieve overall excellent performance. The proposed 3D tension–shear chain model may provide guidance to the design of short fiber reinforced composites.     

Thermo-Oxidative Induced Damage in Polymer Composites: Microstructure Image-Based Multi-Scale Modeling and Experimental Validation

A multi-scale modeling approach is presented to simulate and validate thermo-oxidation shrinkage and cracking damage of a high temperature polymer composite. The multi-scale approach investigates coupled transient diffusion-reaction and static structural at macro- to micro-scale. The micro-scale shrinkage deformation and cracking damage are simulated and validated using 2D and 3D simulations. Localized shrinkage displacement boundary conditions for the micro-scale simulations are determined from the respective meso- and macro-scale simulations, conducted for a cross-ply laminate. The meso-scale geometrical domain and the micro-scale geometry and mesh are developed using the object oriented finite element (OOF). The macro-scale shrinkage and weight loss are measured using unidirectional coupons and used to build the macro-shrinkage model. The cross-ply coupons are used to validate the macro-shrinkage model by the shrinkage profiles acquired using scanning electron images at the cracked surface. The macro-shrinkage model deformation shows a discrepancy when the micro-scale image-based cracking is computed. The local maximum shrinkage strain is assumed to be 13 times the maximum macro-shrinkage strain of 2.5 × 10^?5, upon which the discrepancy is minimized. The microcrack damage of the composite is modeled using a static elastic analysis with extended finite element and cohesive surfaces by considering the modulus spatial evolution. The 3D shrinkage displacements are fed to the model using node-wise boundary/domain conditions of the respective oxidized region. Microcrack simulation results: length, meander, and opening are closely matched to the crack in the area of interest for the scanning electron images.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

Localized remeshing techniques for three‐dimensional metal forming simulations with linear tetrahedral elements

The localized remeshing technique for three‐dimensional metal forming simulations is proposed based on a mixed finite element formulation with linear tetrahedral elements in the present study. The numerical algorithm to generate linear tetrahedral elements is developed for finite element analyses using the advancing front technique with local optimization method which keeps the advancing fronts smooth. The surface mesh generation using mesh manipulations of the boundary elements of the old mesh system was made to improve mesh quality of the boundary surface elements, resulting in reduction of volume change in forming simulations. The mesh quality generated was compared with that obtained from the commercial CAD package for the complex geometry like lumbar. The simulation results of backward extrusion and bevel gear and spider forgings indicate that the currently developed simulation technique with the localized remeshing can be used effectively to simulate the three‐dimensional forming processes with a reduced computation time. Copyright © 2006 John Wiley & Sons, Ltd.     

A new hybrid smoothed FEM for static and free vibration analyses of Reissner–Mindlin Plates

A new smoothed finite element method (S-FEM) is proposed using hybrid smoothing operations based on nodes and edges of the mesh for static and free vibration analyses of plates governed by the Reissner–Mindlin plate theory. In the present approach, both the node-based smoothed finite element method (NS-FEM) and edge-based smoothed finite element method (ES-FEM) are utilized in a careful designed manner to overcome the shear locking. The formulations use 3-node triangular elements for easy automatic mesh creation, and linear interpolation functions are used for simplicity and robustness. The bending strains field are smoothed by the means of gradient smoothing technique over smoothing domains constructed by element edges, while the shear strains filed is smoothed based on the combination of NS-FEM and ES-FEM with a proper weightage controlled by a coefficient. A simple formula is developed for automatic selection of the coefficient by considering mesh size and thickness of the plate. For easy reference, the present technique is termed as NS+ES-FEM. The numerical examples demonstrate that the proposed method passes the shear-locking test and improves accuracy of the solution.     

Solid-mechanics finite element simulations of the draping of fabrics: a sensitivity analysis

This paper covers numerical investigations of the draping of woven fabrics into a “hat” shape, combining a hemispherical cup with a wide flat rim. A mechanical approach is adopted using finite element analysis (FEA) methodology. In this, the fabric is considered as a solid sheet with mechanical properties and friction properties. In this study, a linear elastic anisotropic material model describes the deformation of fabrics. An explicit dynamic finite element analysis is applied and systematic parametric numerical studies are presented, which incorporate investigations of the effects of numerical parameters, material properties and processing conditions on the draping of fabrics. More specifically, the effects of the following variables and parameters are included: number of elements, number of time increments in the dynamic FEA analysis, punch speed, shear and tensile moduli of fabric, coefficient of friction for all interfaces and level of load on the fabric holder.     

Homogenisation Metamodelling of Perforated Plates

Abstract:  The use of finite element (FE)-based homogenisation has improved the study of composite material properties. However, it involves enormous computational effort when implemented in engineering design problems. Therefore an artificial neural network (ANN) surrogate model is proposed here to avoid this issue. In this study, a numerical homogenisation code was developed based on a commercial FE package. It is used to develop the ANN metamodel for an individual composite structure. The effectiveness of the metamodel was examined through an analytical optimisation procedure.     

On enhanced strain methods for small and finite deformations of solids

Numerical simulations of engineering problems require robust elements. For a broad range of applications these elements should perform well in bending dominated situations and also in cases of incompressibility. The element should be insensitive against mesh distortions which frequently occur due to modern mesh generation tools or during finite deformations. Possibly the elements should not lock in the thin limits and thus be applicable to shell problems. Furthermore due to efficiency reasons a good coarse mesh accuracy is required in nonlinear analysis. In this paper we discuss the family of enhanced strain elements in order to depict the positive and negative aspects related to these elements. Throughout this discussion we use numerical examples to underline the theoretical results.     

Analysis of a two-way tension-shear coupling in woven fabrics under combined loading tests: Global to local transformation of non-orthogonal normalized forces and displacements

Dependence of shear rigidity of woven fabrics on yarn pre-tension has been reported in the recent literature, however some conflict regarding the trend of this effect is observed. Sources of this conflict are discussed and resolved in the present article using a new characterization framework and a custom-design combined loading fixture. It is shown that in order to correctly characterize the tension-shear coupling behavior in woven fabrics, instead of using global measured data, local normalized forces and displacements should be driven via a non-orthogonal transformation procedure, while considering kinematic force coupling in the setup. In addition, the effect of fabric shear on the tensile behavior of yarns has been investigated, suggesting that the coupling under question is in fact two-way. In particular, results revealed that applying yarn pre-tension increases the shear resistance of the fabric reinforcement, while the tensile behavior of the material becomes more compliant when undergoing shear deformation.     

Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element

We present new numerical results in buckling failure analysis of cracked composite functionally graded plates subjected to uniaxial and biaxial compression loads. An accurate extended 3-node triangular plate element in the context of the extended finite element method (XFEM) is developed, integrating the discrete shear gap method (DSG) to eliminate shear-locking. The plate kinematics is based on the Reissner–Mindlin theory, and material properties are assumed to vary through thickness direction, obeying a power law distribution. The developed DSG-XFEM is found to be effective and accurate as it owns many desirable advantages: conveniently representing crack geometry which is independent of the mesh; shear-locking effect is no longer valid; mesh distortion is insensitive and controllable; thin plates is possible; triangular elements are easily generated for problems even with complex geometries; and high accuracy. All these arisen features are demonstrated through numerical examples and the effects of crack-length, material gradation, mesh distortion, inclined angles of cracks, boundary conditions, width-to-thickness ratio, length ratio, etc. on the critical buckling coefficient (CBC) are analyzed. Numerical results reveal that the material gradation, crack-length, thickness, length ratios, etc. have a strong effect on the behavior of CBC. This phenomenon is mainly attributed to the plate stiffness degradation due to the presence of local defects and material composition. Also, the boundary conditions greatly alter the CBC whereas the inclination of cracked angle is found to be insignificant.     

Inter-ply stitching optimisation of highly drapeable multi-ply preforms

An efficient finite element model has been developed in Abaqus/Explicit to solve highly non-linear fabric forming problems, using a non-orthogonal constitutive relation and membrane elements to model bi-axial fabrics. 1D cable-spring elements have been defined to model localised inter-ply stitch-bonds, introduced to facilitate automated handling of multi-ply preforms. Forming simulation results indicate that stitch placement cannot be optimised intuitively to avoid forming defects. A genetic algorithm has been developed to optimise the stitch pattern, minimising shear deformation in multi-ply stitched preforms. The quality of the shear angle distribution has been assessed using a maximum value criterion (MAXVC) and a Weibull distribution quantile criterion (WBLQC). Both criteria are suitable for local stitch optimisation, producing acceptable solutions towards the global optimum. The convergence rate is higher for MAXVC, while WBLQC is more effective for finding a solution closer to the global optimum. The derived solutions show that optimised patterns of through-thickness stitches can improve the formability of multi-ply preforms compared with an unstitched reference case, as strain re-distribution homogenises the shear angles in each ply.