Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading

Finite element models are developed for the in-plane linear elastic constants of a family of honeycombs comprising arrays of cylinders connected by ligaments. Honeycombs having cylinders with 3, 4 and 6 ligaments attached to them are considered, with two possible configurations explored for each of the 3- (trichiral and anti-trichiral) and 4- (tetrachiral and anti-tetrachiral) connected systems. Honeycombs for each configuration have been manufactured using rapid prototyping and subsequently characterised for mechanical properties through in-plane uniaxial loading to verify the models. An interesting consequence of the family of ‘chiral’ honeycombs presented here is the ability to produce negative Poisson’s ratio (auxetic) response. The deformation mechanisms responsible for auxetic functionality in such honeycombs are discussed.     

The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs

Four novel cylinder-ligament honeycombs are described, where each cylinder has 3 tangentially-attached ligaments to form either a hexagonal or re-entrant hexagonal cellular network. The re-entrant cylinder-ligament honeycombs are reported for the first time. The in-plane linear elastic constants and out-of-plane bending response of these honeycombs are predicted using finite element (FE) modelling and comparison made with hexagonal and re-entrant hexagonal honeycombs without cylinders. A laser-crafted re-entrant cylinder-ligament honeycomb is manufactured and characterized to verify the FE model. The re-entrant honeycombs display negative Poisson’s ratios and synclastic curvature upon out-of-plane bending. The hexagonal and ‘trichiral’ honeycombs possess positive Poisson’s ratios and anticlastic curvature. The ‘anti-trichiral’ honeycomb (short ligament limit) displays negative Poisson’s ratios when loaded in the plane of the honeycomb, but positive Poisson’s ratio behaviour (anticlastic curvature) under out-of-plane bending. These responses are understood qualitatively through considering deformation occurs via direct ligament flexure and cylinder rotation-induced ligament flexure.     

Analysis of the stress distribution of crimped pultruded composite rods subjected to traction

The stress state of crimped pultruded composite rods subjected to traction has been investigated analytically using the linear theory of elasticity of anisotropic body and the superposition principle. The theoretical solution is able to reproduce the finite element analysis results and clarify the relation between the stress state and the boundary stresses. It can be appreciated from the theoretical solution that a longitudinal compressive stress at the edge of the crimping zone is generated by the boundary shear stress induced by the flow of metal end-fitting. Thus it can be deduced that the stress concentration at the edge of crimping zone could be mitigated through appropriately increasing the extent of the flow of the metal end-fitting away from the middle of the crimping zone. Our research shows that a radial tensile stress existing at the edge of the crimping zone is corresponding to the area of the rod that axial splitting is taken place. Comparison between analytical and numerical results shows the analytical results are in good agreement with the numerical ones except for stress distribution at the edge of the loading zone. The detailed study on stress state at the edge of the crimping zone provides better understanding of the failure mechanism, the improvement possibilities on the crimping technique and the monitoring of the structural health of the composite rod.     

Prediction of stiffness and stresses in z-fibre reinforced composite laminates

The mechanical properties of z-pinned composite laminates were examined numerically. Finite element calculations have been performed to understand how the through-thickness reinforcement modifies the engineering elastic constants and local stress distributions. Solutions were found for four basic laminate stacking sequences, all having two percent volume fraction of z-fibres. For the stiffness analysis, a micro-mechanical finite element model was employed that was based on the actual geometric configuration of a z-pinned composite unit cell. The numerical results agreed very well with some published solutions. It showed that by adding 2% volume fraction of z-fibres, the through-thickness Young's modulus was increased by 22–35%. The reductions in the in-plane moduli were contained within 7–10%. The stress analysis showed that interlaminar stress distributions near a laminate free edge were significantly affected when z-fibres were placed within a characteristic distance of one z-fibre diameter from the free edge. Local z-fibres carried significant amount of interlaminar normal and shear stresses.     

Smart soft composite actuator with shape retention capability using embedded fusible alloy structures

This work presents a new kind of shape memory alloy (SMA) based composite actuators that can retain its shape in multiple configurations without continuous energy consumption by changing locally between a high-stiffness and a low-stiffness state. This was accomplished by embedding fusible alloy (FA) material, Ni-chrome (Ni–Cr) wires and SMA wires in a smart soft composite (SSC) structure. The soft morphing capability of SMA-based SSC structures allows the actuator to produce a smooth continuous deformation. The stiffness variation of the actuator was accomplished by melting the embedded FA structures using Ni–Cr wires embedded in the FA structure. First, the design and manufacturing method of the actuator are described. Then, the stiffness of the structure in the low and high-stiffness states of the actuator were measured for different applied currents and heating durations of the FA structure and results show that the highest stiffness of the actuator is more than eight times that of its lowest stiffness. The different shape retention capability of the actuator were tested using actuators with one or two segments and these were compared with a numerical model.     

Investigating the mechanical properties of single walled carbon nanotube reinforced epoxy composite through finite element modelling

Varying experimental results on the mechanical properties of carbon nanotube reinforced polymer composites (CNTRPs) have been reported due to the complexities associated with the characterization of material properties in nano-scale. Insight into the issues associated with CNTRPs may be brought through computational techniques time- and cost-effectively. In this study, finite element models are generated in which single walled carbon nanotube models are embedded into the epoxy resin. For modelling interface regions, two approaches named as non-bonded interactions and perfect bonding model are utilized and compared against each other. Representative volume finite element (RVE) models are built for a range of CNTRPs and employed for the evaluation of effects of diameter and chirality on the Young’s modulus and Poisson’s ratio of CNTRPs, for which there is a paucity in the literature. The outcomes of this study are in good agreement with those reported available in the literature earlier. The proposed modelling approach presents a valuable tool for determining other material properties of CNTRPs.     

Progressive damage analysis as a design tool for composite bonded joints

This paper discusses the application of progressive damage analysis (PDA) methods as a design tool. Two case studies are presented in which the effects of changing design features on the strength of bonded composite joints are evaluated. It is shown that the trends of parametric evaluations performed with full-featured PDA models can be unintuitive and the trends can be opposite to those obtained with traditional design criteria. The joint configurations that were tested exhibit multiple damage modes, requiring several different PDA tools to accurately predict the structural peak loads. For damage tolerant structures that exhibit complex sequences of multiple failure mechanisms, traditional failure prediction tools are insufficient. Parametric PDA models encompassing a bonded joint specimen's design space have the potential to reveal unintuitive and advantageous design changes.     

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.     

Micromechanical modeling and experimental characterization on viscoelastic behavior of 1–3 active composites

A study on the temperature-dependent viscoelastic behavior of (1–3 active composites) 1–3 piezocomposites and bulk piezoceramic subjected to electromechanical loading is carried out. The temperature-dependent effective properties are obtained experimentally using resonance based measurement technique. Experiments are also preformed for various fiber volume fractions of 1–3 piezocomposites subjected to constant compressive prestress and cyclic electric field at elevated temperature to understand the time-dependent behavior. Based on the measurements it is observed that the viscoelastic behavior has a significant influence on the electromechanical responses of 1–3 piezocomposites. Hence a viscoelastic based numerical model (unit cell approach) is proposed to predict the time-dependent effective properties of 1–3 piezocomposites. The evaluated effective properties are incorporated in a finite element based 3-D micromechanical model to predict the time-dependent thermo-electro-mechanical behavior of 1–3 piezocomposites and compared with the experimental observations.     

Numerical method for optimizing design variables of carbon-fiber-reinforced epoxy composite coil springs

To successfully reduce a vehicle's weight by replacing steel with composite materials, it is essential to optimize the material parameters and design variables of the structure. In this study, we investigated numerical and experimental methods for determining the ply angles and wire diameters of carbon fiber/epoxy composite coil springs to attain a spring rate equal to that of an equivalent steel component. First, the shear modulus ratio for two materials was calculated as a function of the ply angles and compared with the experimental results. Then, by using the equation of the spring rate with respect to the shear modulus and design variables, normalized spring rates were obtained for specific ply angles and wire diameters. Finally, a finite element model for an optimal composite coil spring was constructed and analyzed to obtain the static spring rate, which was then compared with the experimental results.     

Homogenization of braided fabric composite for reliable large deformation analysis of reinforced rubber hose

High pressure rubber hose is in the lamination structure composed of pure rubbers and braided fabric composite layers to have the sufficient strength against the excessive radial expansion and the large deformation, in which the braided fabric layer is woven with wrap and fill tows inclined to each other with the predefined helix angle in the complex periodic pattern. The consideration of detailed geometry of braided fabric layer in the numerical analysis leads to a huge number of finite elements so that the braided fabric layer has been traditionally simplified as an isotropic cylindrical one with the homogeneous isotropic material properties of braid spun tread. However, this simple model leads to the numerical prediction and design with the questionable reliability. In this context, this paper addresses the development of an in-house module, which is able to be interfaced with commercial FEM code, for the reliable large deformation analysis of the reinforced rubber hose with the element number at the level of the traditional simple model. The in-house module is able to not only automatically generate 3-D unit cell (or RVE) model of the braided fabric layer but evaluate the homogenized orthotropic material properties by automatically performing a serious of unit cell finite element analyses based on the superposition method. The validity of the in-house module and the reliability of the homogenization method are verified through the illustrative numerical experiments.     

Cryogenic through-thickness tensile characterization of plain woven glass/epoxy composite laminates using cross specimens: Experimental test and finite element analysis

This paper investigates the through-thickness tensile behavior of woven glass fiber reinforced polymer (GFRP) composite laminates at cryogenic temperatures. Tensile tests were carried out with cross specimens at room temperature and liquid nitrogen temperature (77 K), and the through-thickness elastic and strength properties of the woven GFRP laminates were evaluated. The failure characteristics of the woven GFRP laminates were also studied by optical and laser scanning microscopy observations. A three-dimensional finite element analysis was performed to calculate the stress distributions in the cross specimens, and the failure conditions of the specimens were examined. It is found that the cross specimen is suitable for the cryogenic through-thickness tensile characterization of laminated composite materials. In addition, the through-thickness Young's modulus of the woven GFRP composite laminates is dominated by the properties of the matrix polymer in the given temperature, while the tensile strength is characterized by both, the fiber to matrix interface energy and the cohesion energy of the matrix polymer.     

Assessment of the fibre orientation factor in SFRC slabs

The design of steel fibre reinforced concrete (SFRC) structures is evolving towards a new approach that uses correction factors to consider differences between the small-scale characterisation specimens and the real-scale elements. Recently, the Model Code 2010 proposed an orientation factor (K) that accounts for the effects of the orientation in the structural response of elements. The present study focuses on the identification of this factor in SFRC slabs with different dimensions. For that, flexural tests on real-scale slabs were conducted and the fibre orientation was assessed with an inductive method. A finite element analysis showed the differences between the experimental curves and the prediction of the Model Code without considering K. Based on the results obtained, a range of values is proposed for K and validated. This study sheds light on possible modifications that this philosophy of design might require to better reproduce the behaviour of slabs.     

On the tensile behavior of hetero-junction carbon nanotubes

Several straight hetero-junctions carbon nanotubes (CNTs) are constructed and their tensile behavior are investigated. It is pointed that the Young's modulus of hetero-junctions is lower than the values of their fundamental homogeneous CNTs due to the existence of pentagon–heptagon pair defects. In addition, it is revealed that the Young's modulus of homogeneous zigzag CNTs increases by increasing the chiral number of these nano-structures. Finally, it is concluded that as the connecting length of the hetero-junctions increases the Young's modulus of these particular CNTs decreases. Therefore, the tensile strength of hetero-junctions depends on the presence of pentagon–heptagon pair defects.     

An experimental and finite element study of the transverse bending behaviour of CFRP composite T-joints in vehicle structures

The behaviour of a woven fabric carbon/epoxy composite T-joint (representing a simplified version the T-joint located at the connection between the B-pillar and the longitudinal rocker in a car body structure) is investigated using experimental and numerical methods. Details of the manufacturing process and experimental design factors are considered to understand their influence on the performance of the T-joint structure. The experimental results reveal the influence of manufacturing process and experimental setup on the load-carrying capacity and failure mode of the T-joint. Numerical simulation accurately predicts the stress distribution and load-carrying capacity of the T-joint obtained from experimental tests. The FEM model, which includes the adhesive interface layers at the edges, convincingly represents the experimentally found stiffness: the error is less than 3%. According to Hashin matrix tension criteria, the first ply failure occurs at 3.746 kN when the Hashin failure index (R) becomes equal to 1. Whereas, in the case of experimental tests, the first ply failure occurs around 3.4 kN, at which force the first load drop is observed.     

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.     

A micromechanics-based incremental damage model for carbon black filled rubbers

This paper is to develop a simple micromechanics-based model taking account of progressive damaging for carbon black (CB) filled rubbers. The present model constitutes of the instantaneous Young's modulus and Poisson's ratio characterizing rubber-like material, a double-inclusion (DI) configuration considering the absorption of rubber chains onto CB particles, and the incremental Mori-Tanaka formula to compute the effective stress–strain relations. The progressive damage in filled rubbers is described by the DI cracking, which is represented by the remaining load–carrying capacity. The present predictions are capable of embodying the well-known S-shaped response of filled rubbers, and also verified by the comparison with the experimental and analytical results. Moreover, strain localization effect is clearly demonstrated by finite element method (FEM) simulations, and reaches a decisive interpretation to the complicated synergic micro-mechanisms between hard fillers and soft phase in such flexible composites.     

Measurement and prediction of embedded copper foil fatigue crack growth in multifunctional composite structure

Copper strips embedded in glass/epoxy composite compose a discrete-path multifunctional load-bearing configuration which can conduct electricity. This combination of materials permits efficient packaging of increasingly large numbers of electrical systems being installed in aircraft and vehicle systems. It also allows systems such as large aperture antennas to be embedded within an aircraft’s load-bearing structural skin. The fatigue fracture of the embedded metal foil is of interest since composite materials tend to be more fatigue resistant. Copper embedded glass/epoxy coupons were manufactured and fatigue tested at 35% and 50% of the composite ultimate tensile strength. Nondestructive evaluation was used to measure copper crack growth and debonding at the copper-to-composite interface. The debonding plays a key role controlling the crack growth. A combined experimental-analytical methodology is defined for establishing relationships between crack tip opening angle (CTOA), crack size, and crack growth rate of the embedded copper via a combined experimental-analysis approach.     

Composite structure composed of overlapped fibre bundles,thermoplastic resin and metal plate for secondary forming process

A simple shape of a composite is preferable in mass production, while a curved or stretched shape is sometimes preferable for final products. High formability would enable the composite to deform into a preferable shape by secondary forming. In this paper, a structure for a composite is proposed to enhance formability. The composite is composed of reinforcing fibre bundles, thermoplastic resin as the matrix and metal plates. The reinforcing fibre bundles are discontinuous, and are intentionally overlapped in the longitudinal direction. The resin including fibre bundles is sandwiched between the metal plates. As the thermoplastic resin is melted at an adequate temperature, heating would enhance the mobility of thermoplastic resin resulting in high formability at the secondary forming. If the overlapped length is adequately designed, the composite would still maintain high strength after the secondary formation. The validity of the concept was checked by finite element analyses and experiments.     

A rate-dependent non-orthogonal constitutive model for describing shear behaviour of woven reinforced thermoplastic composites

A rate dependent constitutive model for woven reinforced thermoplastic matrix composites at forming temperatures is proposed in this work. The model is formulated using a stress objective derivative based on the fibre rotation. Nonlinear shear behaviour is modelled as a polynomial function and the rate dependence is described using a Cowper–Symonds overstress law formulated in terms of shear angle rate. The model parameters are determined by means of bias extension tests. The applicability of the material model is validated through a forming experiment.