Mechanical properties of hybrid composites using finite element method based micromechanics

A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.     

Investigation into three-layered HMA mixtures

Hot-mix asphalt (HMA) mixtures consist of three phases: aggregate, asphalt binder (mastic) and air voids, of which the first two (aggregate and asphalt binder) provide the structure that withstands various kinds of loading.

Due to the nature of high inhomogeneity between aggregate and asphalt binder, significant stress and strain concentration occurs at the interface between the two phases, which causes adverse effect to HMA mixtures and potentially contributes to pavement distresses/failure.

This paper presents a novel idea to mitigate the stress and strain concentration by introducing an intermediate layer between aggregate and asphalt binder in HMA mixture. Microstructural analyses of layered system indicated that the three-layered composite HMA mixture would greatly improve the performance of asphalt mixture. The composite mixture showed more than 10% reduction in internal stress and strain and consequently its performance could be potentially improved. To validate the theoretical analyses, a laboratory experiment was conducted to compare the performance of a conventional mixture to that of a conceptual three-layered composite HMA mixture, which was formed by incorporating a stiff natural asphalt (gilsonite) as the intermediate layer. The results of the limited laboratory experiment confirmed the findings from the theoretical analyses.     

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.     

Numerical study of the effects of reinforcement/matrix interphase on stress-strain behavior of YAl2 particle reinforced MgLiAl composites

For the potential influence produced by the reinforcement/matrix interphase in particle reinforced metal matrix composites (PMMCs), a unit cell model with transition interphase was proposed. Uniaxial tensile loading was simulated and the stress/strain behavior was predicted. The results show that a transition interphase with both appropriate strength and thickness could affect the failure mode, reduce the stress concentration, and enhance the maximum strain value of the composite.     

Predicting microdroplet force response using a multiscale modeling approach

An axisymmetric microscale finite element model of a microdroplet test specimen is developed where the structural response of the fiber–droplet interface is accounted for by surface-based cohesive behavior. In this study, the interface cohesive response is estimated using a nanoscale interface finite element model that explicitly includes the effects of fiber surface topography and the interphase region. The interphase behavior in the nanoscale interface model is calibrated using indirect experimental data. Once calibrated, the fiber surface topography in the nanoscale interface model is modified in order to estimate the parameters defining the surface-based cohesive behavior of similar fiber–matrix systems with different fiber topography. The effect of altering the fiber topography on the force response of the microdroplet test can then be predicted by the microdroplet FE model. Comparing the simulation results with experimental data from the literature shows that this multiscale modeling approach gives accurate predictions for the interfacial shear stress.     

Delamination modelling of GLARE using the extended finite element method

In this paper, an application of the Extended Finite Element Method (XFEM) for simulation of delamination in fibre metal laminates is presented. The study consider a double cantilever beam made of fibre metal laminate in which crack opening in mode I and crack propagation were studied. Comparison with the solution by standard Finite Element Method (FEM) as well as with experimental tests is provided. To the authors’ knowledge, this is the first time that XFEM is used in the fracture analysis of fibre metal laminates such as GLARE. The results indicated that XFEM could be a promising technique for the failure analysis of composite structures.     

Sandwich buckling formulas and applicability of standard computational algorithm for finite strain

Although, for homogeneous columns, the differences between Engesser's and Haringx's formulas for shear buckling have been explained in 1971 by the dependence of shear modulus on the axial stress, for soft-core sandwich columns the choice of the correct formula has baffled engineers for half a century. Recently, Ba ant explained this difference by a variational analysis which showed that an agreement is achieved if the shear modulus of the light core is considered to depend on the compressive stress in the skins even when small-strain elasticity applies. To clarify this paradoxical dependence, first the variational framework is briefly reviewed. Subsequently, the mathematical results from Ba ant's recent study are physically reinterpreted, with the conclusion that only the Engesser-type theory (rather than Haringx-type theory) corresponds to constant shear moduli as obtained, for example, by the torsional test of a tube made from the foam. This is a rather fundamental point for applications because the discrepancy between these two theories can be very large in the case of short columns with thin skins. The implications for standard finite element programs are then explored by computing the critical loads of several sandwich columns with different material and geometric properties. The finite element computations show agreement with the Engesser-type formula predictions, while the Haringx-type prediction can be obtained with the finite element program somewhat artificially—by updating the core modulus as a function of the axial stress in the skins.     

Experimental and finite element studies on hot sizing process for L-shaped composite beams

This work aims at developing a hot sizing process on composite materials to correct the profiles of composite structures during manufacture. Hot sizing experiments were carried out at 150 °C with different sizing loads and hot sizing periods for L-shaped composite beams made of carbon fiber plain-weave fabric and epoxy resin. To predict the springback in hot sizing process, a corresponding finite element simulation method was developed using stress relaxation equations determined at the same temperature. Excellent agreements between the predicted and observed results were obtained. The effects of the component thickness and 45° ply percentage on the springback rate were investigated by simulation. Springback rate in hot sizing process on composite materials ranges from 60% to 95%. In conclusion hot sizing process is proved to be a valid method for compensation for the process-induced deformation (PID) of L-shaped composite beams.     

Interphase effect on the macroscopic elastic properties of non-bonded single-walled carbon nanotube composites

Compared to the small diameter of a carbon nanotube (CNT), the thickness of the CNT–matrix interphase in a CNT–composite is considerable. Hence, the interphase property can significantly influence the macroscopic properties of the composite. This paper applies an effective multi-scale method to explore such an interphase effect on the properties of nano-composites reinforced by single-walled CNTs. The method integrates the van der Waals (vdW) gap interphase, the dense interphase, and the randomly distributed wavy CNTs in a matrix to realize an accurate prediction of macroscopic properties with a nanoscopic resolution, by using a conventional finite element code commercially available. The study concluded that with the same volume fraction, increasing CNT waviness and diameter reduces the composite Young's modulus, and that ignoring either the vdW gap interphase or the dense interphase can lead to an erroneous characterization, and that both interphases can be ignored in some circumstances.     

Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method

Here, asymmetric free vibration characteristics and thermoelastic stability of functionally graded circular plates are investigated using finite element procedure. A three-noded shear flexible plate element based on the field-consistency principle is used. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are graded in the thickness direction according to simple power law distribution. For the numerical illustrations, aluminum/alumina is considered as functionally graded material. The variation in critical buckling load is highlighted considering gradient index, temperature, radius-to-thickness ratios, circumferential wave number and boundary condition of the plate.     

A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures

This paper presents the development of a highly efficient user-defined finite element for modelling the bolt-load distribution in large-scale composite structures. The method is a combined analytical/numerical approach and is capable of representing the full non-linear load-displacement behaviour of bolted composite joints both up to, and including, joint failure. In the elastic range, the method is generic and is a numerical extension of a closed-form method capable of modelling the load distribution in single-column joints. A semi-empirical approach is used to model failure initiation and energy absorption in the joint and this has been successfully applied in models of single-bolt, single-lap joints. In terms of large-scale applications, the method is validated against an experimental study of complex load distributions in multi-row, multi-column joints. The method is robust, accurate and highly efficient, thus demonstrating its potential as a time/cost saving design tool for the aerospace industry and indeed other industries utilising bolted composite structures.     

Numerical simulations of fracture-toughness improvement using short shaped head ductile fibers

Fibers can be shaped so as to anchor inside the matrix and resist pullout at a crack face, thus improving the fracture-toughness of the composites. This anchoring ability enables a greatly improved utilization of the plastic potential of ductile fibers, increasing fracture-toughness while maintaining stiffness. The purpose of this paper is to explore this property of shaped head fibers for composites with weak fiber–matrix bonding. Because of the difficulty in estimating the fracture-toughness contribution of shaped head fibers analytically or experimentally, we use a FEM based numerical scheme to investigate stress profiles induced during pullout of two chosen shaped head families. Annealed copper fiber with a large residual plastic potential and an elastic epoxy matrix have been used as representative materials. Using the computed strain energy distribution in the matrix as a measure of fracture-toughness contribution, we find that flat-head fibers out-perform ball-head fibers in minimizing failure potential. We have further discovered that within each shape family there exist optimal shapes. The optimal shape for the flat-head family is also computed for the example material system.     

Stress transfer analysis of unidirectional composites with randomly distributed fibers using finite element method

A three-dimensional representative volume element (RVE) of unidirectional composites with both randomly distributed fibers and periodic geometry was generated using DIGIMAT-FE software. Finite element analysis of the stress transfer mechanisms around a fiber break in the RVE was performed via ABAQUS/Standard. The influences of distance to the broken fiber, fiber/matrix stiffness ratio and fiber volume fraction on the stress transfer process of intact fibers were discussed for the case of perfect fiber/matrix adhesion. The study shows that the nearest fibers and the second nearest fibers share the stress released from the broken fiber. The stress transfer coefficient and the ineffective stress transfer length of the nearest fibers was found to increase with the increasing distance to the broken fiber and the stiffness ratio, while decrease with the increasing fiber volume fraction. However, the trends in the two stress transfer parameters of the second nearest fibers are slightly different from those of the nearest fibers due to the random distribution of other intact fibers.     

Numerical and analytical modeling of aligned short fiber composites including imperfect interfaces

Finite element calculations were used to bound the modulus of aligned, short-fiber composites with randomly arranged fibers, including high fiber to matrix modulus ratios and high fiber aspect ratios. The bounds were narrow for low modulus ratio, but far apart for high ratio. These numerical experiments were used to evaluate prior numerical and analytical methods for modeling short-fiber composites. Prior numerical methods based on periodic boundary conditions were revealed as acceptable for low modulus ratio, but degenerate to lower bound modulus at high ratio. Numerical experiments were also compared to an Eshelby analysis and to an new, enhanced shear lag model. Both models could predict modulus for low modulus ratio, but also degenerated to lower bound modulus at high ratio. The new shear lag model accounts for stress transfer on fiber ends and includes imperfect interface effects; it was confirmed as accurate by comparison to finite element calculations.     

Evaluation of interfacial strength in CF/epoxies using FEM and in-situ experiments

A combined experimental and numerical study has been carried out in order to study the mechanism of initial failure in transversely loaded CF/epoxy composites. Two composites with a high and a low temperature-curing matrix were investigated. Three point bending experiments on macroscopic composite specimen with special laminate lay-ups were carried out in a scanning electron microscope (SEM). The in-situ experiments allow observing the onset of microscopic composite failure under transverse loading and measurement of the macroscopic applied load at onset of failure. The experimental results show that interfacial failure was the dominating failure mechanism for both materials. For the same carbon fiber with the same treatment the interfacial failure was adhesive (weak interface) or cohesive (strong interface), depending on the matrix system. The interfacial stresses at initiation of failure were determined successfully by a non-linear micro/macro FE-analysis and compared with experimental results obtained from micro composite test. The results show that the interfacial normal strength (INS) governs failure under transverse loads.     

Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

Functionally graded material (FGM) bars in axial motion (hereafter called “FGM axial bars”) have great potential for applications in many engineering fields. Therefore, it is important to develop a reliable mathematical model that can provide very accurate dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. As an extension of our previous work, we present a spectral element model for a modified FGM axial bar model wherein nonuniform lateral contraction in the thickness direction is taken into account. We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the power law. The performance of the proposed spectral element model is validated through comparison with solutions from a conventional finite element model, and with the results from the previous FGM axial bar model. In addition, the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars are numerically investigated.     

Design of copper filled fibreglass moulds for manufacturing a customized product using linear programming optimization and finite element analysis

This paper presents a design procedure and cost analysis for a mould made of glass fibre reinforced polyester filled with copper particles (GRP/copper). It also describes their potential use in rotational moulding as an alternative to steel and aluminium moulds operating at high temperatures up to 250 °C. The thermal conductivity of glass reinforced polyester (GRP) was improved by incorporating copper particles acting as fillers in the composite. An optimum composite structure consisting of 25% glass fibres, 45% polyester, and 30% copper was achieved by linear programming search optimization methods. Then a finite element analysis (FEA) of a typical GRP/copper mould made of the optimized composite structure under thermal loading was conducted. The induced thermal stresses obtained from FEA were used to check the failure condition of the mould using the Tsai–Hill failure criterion. The FEA design procedure was also used to determine the mould thickness with a safety factor of at least four. Scheduling and cost analysis showed that 76% reduction in production time and 64% reduction in manufacturing costs have been achieved with the developed method.     

External CFRP tendon members: Secondary reactions and moment redistribution

The response of prestress secondary reactions in the post-elastic range has been a topic of much controversy. Due to the brittleness of FRP (fiber reinforced polymer) composites, external FRP tendon members may have different moment redistribution characteristics compared to conventional concrete members. This paper presents a numerical investigation into the secondary reactions and moment redistribution in prestressed concrete continuous members with external CFRP tendons. The investigation parameters include the initial prestress level and the pattern of loading. The secondary reactions are computed using a newly developed method based on the linear transformation concept combined with a nonlinear finite element analysis. The results indicate that the secondary reactions increase quicker after concrete cracking and nonprestressed steel yielding. As a consequence, the secondary moment should be included in the design moment. The moment redistribution behavior for symmetrical loading is shown to be quite different from that for unsymmetrical loading. The study also shows that the effect of initial prestress on the moment redistribution is rather important.     

Deformation gradient tensor decomposition for representing matrix cracks in fiber-reinforced materials

A new method is presented for the representation of matrix cracks in continuum damage mechanics (CDM) models for fiber-reinforced materials. The method is based on the additive decomposition of the deformation gradient tensor into ‘crack’ and ‘bulk material’ components, analogous to the additive strain decomposition of the smeared-crack approach. The potential improvements to the accuracy of CDM models that utilize the presented method are demonstrated for a single element subjected to simple shear deformation and for a unidirectional open-hole tension specimen. The presented method avoids load transfer across matrix cracks and eliminates the prediction of spurious secondary failure modes that occurs when conventional strain-based CDM models are used in geometrically nonlinear finite element analyses involving large shear deformations.     

A unit cell approach of finite element calculation of ballistic impact damage of 3-D orthogonal woven composite

This paper presents ballistic impact damages of 3-D orthogonal woven composite in finite element analysis (FEA) and experimental. A unit-cell model of the 3-D woven composite was developed to define the material behavior and failure evolution. A user-defined subroutine VUAMT was compiled and connected with commercial available FEA code ABAQUS/Explicit to calculate the ballistic penetration. Ballistic impact tests were conducted to investigate impact damage of 3-D kevlar/glass hybrid woven composite. Residual velocities of conically-cylindrical steel projectiles (Type 56 in China Military Standard) and impact damage of the composite targets after ballistic perforation were compared both in theoretical and experimental. The reasonable agreements between FEA results and experimental results prove the validity of the unit-cell model in ballistic limit prediction of the 3-D woven composite. We believe such an effort could be extended to bulletproof armor design with the 3-D woven composite.