Two analogous methods for estimating the compressive strength of fibrous composites

In this paper, an analogy is made between the solution of micro-buckling of fibrous composites using a three-dimensional model and that of biaxial bending of reinforced concrete short columns. Two approaches are used; the first one uses a reciprocal formula and the second one uses a bilinear approximation to the non-dimensional stresses interaction equation, to estimate the compressive stress in a fibrous composite. The initial misalignment angles of composite fibers, which are the main parameters in the determination of the compressive strength of fibrous composites, are analogous to load eccentricities in concrete columns. The initial misalignment angles in both directions perpendicular to the axis of the fibers are defined by sinusoidal curves. The compressive strength of different fibrous composites, which also depends on the nonlinear shear stress–strain relationship of the matrix material, is estimated using the present approaches. The results obtained in this study agree well with experimental and analytical results available in the literature.     

Micro-mechanical modeling the densification behavior of titanium metal matrix composites

Vacuum hot pressing has been used for the development of Ti-MMCs using foil–fiber–foil method, and a unified micro-mechanical model has been presented to determine the densification behavior. The effects of processing conditions on the consolidation, together with microstructural evolutions of the materials have been investigated. The explicit representation of fiber array, which is coupled with deformation behavior of matrix materials, is modeled in finite element simulation to determine the effect of geometrical arrangements on densification process. The approach is then used to model the densification behavior of porous plastic materials using the parameters obtained, and comparisons are made with experimental data. As shown by the results, either increasing temperature or pressure leads to increasing densification rate but the conditions should be determined by the precisely controlled geometrical arrangements with processing conditions. Further experimental investigation of the densification behavior of SiC/Ti–6Al–4V composites using thermo-acoustic emission analysis has been performed, and the results obtained are compared with the model predictions. Good comparisons are achieved.     

Study of layup influences on the nonlinear behavior of composites by evaluation of ply stiffness reduction

The influence of the stacking sequence on the nonlinear response of composite laminates is investigated. It is shown that a layup dependency solely emerges from damage evolution mechanisms, whereas damage initiation and viscoelastic and viscoplastic strain accumulation are not affected by the layup. This is a result of a proposed procedure that enables the evaluation of the stiffness reduction on lamina level. The residual ply stiffness components can be determined at large deformations and for various laminates under in-plane loading conditions. A finite element study is utilized to characterize the properties of a ply containing discrete cracks. The relationship between transverse and shear stiffness reduction is derived from the FE results. This allows the combined determination of the residual lamina moduli from an axial laminate stiffness. The analysis approach is validated by angle-ply specimens with different layups.     

Effect of thermal residual stresses on the matrix failure under transverse compression at micromechanical level - A numerical and experimental study

The influence at micromechanical scale of thermal residual stresses, originating in the cooling down associated to the curing process of fibrous composites, on inter-fibre failure under transverse compression is studied. In particular, the effect of these stresses on the appearance of the first debonds is discussed analytically; later steps of the damage mechanism are analysed by means of a single fibre model, making use of the Boundary Element Method. The results are evaluated applying Interfacial Fracture Mechanics concepts. The conclusions obtained show, at least in the case of dilute fibre packing, the effect of thermal residual stresses on the appearance and initiation of growth to be negligible, and the morphology of the damage not to be significantly affected in comparison with the case in which these stresses are not considered. Experimental tests are carried out, the results agreeing with the conclusions derived from the numerical analysis.     

Computational micromechanics evaluation of the effect of fibre shape on the transverse strength of unidirectional composites: An approach to virtual materials design

Computational micromechanics of composites is an emerging tool required for virtual materials design (VMD) to address the effect of different variables involved before materials are manufactured. This strategy will avoid unnecessary costs, reducing trial-and-error campaigns leading to fast material developments for tailored properties. In this work, the effect of the fibre cross section on the transverse behaviour of unidirectional fibre composites has been evaluated by means of computational micromechanics. To this end, periodic representative volume elements containing uniform and random dispersions of 50% of parallel non-circular fibres with lobular, polygonal and elliptical shapes were generated. Fibre/matrix interface failure as well as matrix plasticity/damage were considered as the fundamental failure mechanisms operating at the microscale under transverse loading. Circular fibres showed the best averaged behaviour although lobular fibres exhibited superior performance in transverse compression mainly due to the higher tensile thermal residual stresses generated during cooling at the fibre/matrix interface.     

Failure response of fiber-epoxy unidirectional laminate under transverse tensile/compressive loading using finite-volume micromechanics

The transverse damage initiation and extension of a unidirectional laminated composite under transverse tensile/compressive loading are evaluated by means of Representative Volume Element (RVE) presented in this paper based on an advanced homogenization model called finite-volume direct averaging micromechanics (FVDAM) theory. Fiber, fiber-matrix interface and matrix phases are considered within the RVE in determining fiber-matrix interface debonding and matrix cracking. The simulated fracture patterns are shown to be in good agreement with experimental observations.     

Effect of humidity during manufacturing on the interfacial strength of non-pre-dried flax fibre/unsaturated polyester composites

The influence of moisture content in the environment during manufacture of a novel cobalt-free UP matrix reinforced with flax fibres, on the fibre–matrix adhesion was studied. Flax surface energy was experimentally determined by measuring contact angles on technical fibres, using the Wilhelmy technique and the acid–base theory. The mechanical strength of the interface under different humidity conditions was characterized by the critical local value of interfacial shear stress, τ_d, at the moment of crack initiation, which was assessed by single-fibre pull-out tests. Differential scanning calorimetry and X-ray photoelectron spectroscopy analysis gave further insight into the topic. The results suggest that the effect of humidity during manufacturing on the composite interface might be limited. However, longitudinal composite strength decreased somewhat for composites produced in humid conditions, showing that there is some detrimental effect of high levels of moisture during cure on the fibre mechanical performance, likely caused by some fibre degradation.     

The role of carbon nanofibers on thermo-mechanical properties of polymer matrix composites and their effect on reduction of residual stresses

In this research, the effects of carbon nanofibers (CNFs) on thermo-elastic properties of carbon fiber (CF)/epoxy composite for the reduction of thermal residual stresses (TRS) using micromechanical relations were studied. In the first step, micromechanical models to calculate the coefficient of thermal expansion (CTE) and Young's modulus of CNF/epoxy and CNF/CF/epoxy nanocomposites were developed and compared with experimental results of the other researchers. The obtained results of the CTE and Young's modulus of modified Schapery and Halpin-Tsai theories have good agreement with the experimental results. In the second step, the classical lamination theory (CLT) was employed to determine the TRS for CNF/CF/epoxy laminated nanocomposites. Also, the theoretical results of the CLT were compared with experimental results. Finally, reduction of the TRS using the CLT for different lay-ups such as cross ply, angle ply, and quasi-isotropic laminates were obtained. The results demonstrated that the addition of 1% weight fraction of CNF can reduce the TRS that the most reduction occurred in the unsymmetric cross-ply laminate by up to 27%.     

Synergistic effect of hybrid graphene nanoplatelet and multi-walled carbon nanotube fillers on the thermal conductivity of polymer composites and theoretical modeling of the synergistic effect

We found that the thermal conductivity of polymer composites was synergistically improved by the simultaneous incorporation of graphene nanoplatelet (GNP) and multi-walled carbon nanotube (MWCNT) fillers into the polycarbonate matrix. The bulk thermal conductivity of composites with 20 wt% GNP filler was found to reach a maximum value of 1.13 W/m K and this thermal conductivity was synergistically enhanced to reach a maximum value of 1.39 W/m K as the relative proportion of MWCNT content was increased but the relative proportion of GNP content was decreased. The synergistic effect was theoretically estimated based on a modified micromechanics model where the different shapes of the nanofillers in the composite system could be taken into account. The waviness of the incorporated GNP and MWCNT fillers was found to be one of the most important physical factors determining the thermal conductivity of the composites and must be taken into consideration in theoretical calculations.     

Measurement of the in situ transverse tensile strength of composite plies by means of the real time monitoring of microcracking

Failure of a ply due to transverse loading is one of the mechanisms that was taken into account in physically-based failure criteria, used in composites design. However, experimental data are scarce and the measurement techniques used in the past are time consuming and involve a lot of specimen handling during testing. While some physical information is currently well consolidated (such as the dependence of the strength on ply thickness, or in situ strength), there still remain relevant open questions. This work presents a methodology, which does not interfere with the tensile test, to detect transverse cracks by optical means. Four different configurations of CFRP are considered. The results show that the in situ strength depends on the thickness of the ply and the orientation of the adjacent layers. In the case of thick transverse plies, the strength is controlled by full-width transverse cracks whereas, in thin plies cracking parallel to the specimen’s mid-plane occurs before transverse matrix cracking.     

Thermal conductivity of polymer composites based on the length of multi-walled carbon nanotubes

The anisotropic development of thermal conductivity in polymer composites was evaluated by measuring the isotropic, in-plane and through-plane thermal conductivities of composites containing length-adjusted short and long multi-walled CNTs (MWCNTs). The thermal conductivities of the composites were relatively low irrespective of the MWCNT length due to their high contact resistance and high interfacial resistance to polymer resins, considering the high thermal conductivity of MWCNTs. The isotropic and in-plane thermal conductivities of long-MWCNT-based composites were higher than those of short-MWCNT-based ones and the trend can accurately be calculated using the modified Mori-Tanaka theory. The in-plane thermal conductivity of composites with 2 wt% long MWCNTs was increased to 1.27 W/m·K. The length of MWCNTs in polymer composites is an important physical factor in determining the anisotropic thermal conductivity and must be considered for theoretical simulations. The thermal conductivity of MWCNT polymer composites can be effectively controlled in the processing direction by adjusting the length of the MWCNT filler.     

Overall behavior and microstructural deformation of R-CNT/polymer composites

Carbon nanotubes (CNTs) are an excellent candidate for the reinforcement of composite materials owing to their distinctive mechanical and electrical properties. Reticulate carbon nanotubes (R-CNTs) with a 2D or 3D configuration have been manufactured in which nonwoven connected CNTs are homogeneously distributed and connected with each other. A composite reinforced by R-CNTs can be fabricated by infiltrating a polymer into the R-CNT structure, which overcomes the inherent disadvantages of the lack of weaving of the CNTs and the low strength of the interface between CNTs and the polymer. In this paper, a 2D plane strain model of a R-CNT composite is presented to investigate its micro-deformation and effective stiffness. Using the two-scale expansion method, the effective stiffness coefficients and Young’s modulus are determined. The influences of microstructural parameters on the micro-deformation and effective stiffness of the R-CNT composite are studied to aid the design of new composites with optimal properties. It is shown that R-CNT composites have a strong microstructure-dependence and better effective mechanical properties than other CNT composites.     

Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: A numerical and experimental analysis

In the present work the influence at micromechanical scale of thermal residual stresses, originated in the cooling down associated to the curing process of fibrous composites, on inter-fibre failure under transverse tension is studied. In particular, the effect of the presence of thermal residual stresses on the appearance of the first debonds is discussed analytically, whereas later steps of the mechanism of damage, i.e. the growth of interface cracks and their kinking towards the matrix, are analysed by means of a single fibre model and making use of the Boundary Element Method (BEM). The results are evaluated applying Interfacial Fracture Mechanics concepts. The conclusions obtained predict, at least in the case of dilute fibre packing, a protective effect of thermal residual stresses against failure initiation, the morphology of the damage not being significantly affected in comparison with the case in which these stresses are not considered. Experimental tests are carried out, the results agreeing with the conclusions of the numerical analysis.     

Enhanced strength analysis method for composite open-hole plates ensuring design office requirements

The use of unidirectional carbon fibre-reinforced composites in the design of primary structures, such as the centre wing box, has spread increasingly over the past few years. However, composite structures can be weakened by the introduction of geometrical singularities, such as holes or notches. The semi-empirical aspect of the current open-hole failure approaches requires the allowables to be systematically fitted against specific test results. This point constitutes a strong limitation for optimum design. A simplified strength analysis method for perforated plates is presented, ensuring design office requirements in terms of precision and computational time. The predictions of the proposed approach are compared successfully with a large experimental database, with different configurations of perforations, different stacking sequences and in different Carbon/Epoxy materials.     

Microstructure effects on transverse cracking in composite laminae by DEM

A particle discrete element method (DEM) was employed to simulate transverse cracking in laminated fiber reinforced composites. The microstructure of the laminates was modeled by a DEM model using different mechanical constitutive laws and materials parameters for different constituents, i.e. fiber, matrix and fiber/matrix interface. Rectangular, hexagonal and random fiber distributions were simulated to study the effect of fiber distribution on the transverse cracking. The initiation and dynamic propagation of transverse cracking and interfacial debonding were all captured by the DEM simulation, which showed similar patterns to those observed from experiments. The effect of fiber volume fraction was also studied for laminae with randomly distributed fibers. It was found that the distribution and volume fraction of fibers affected not only the transverse cracking path, but also the behavior of matrix plastic deformation and fiber/matrix interface yielding in the material.     

Evaluation of long-term durability in high temperature resistant CFRP laminates under thermal fatigue loading

Thermal fatigue tests were conducted on high temperature resistant carbon fiber reinforced plastics cross-ply laminates to evaluate microscopic damage progress which affects macroscopic mechanical behavior of the laminates. Materials system used were thermoplastic polyetheretherketone based, AS4/PEEK and thermoset bismaleimide based, G40-800/5260. Several types of laminate configuration were used to clarify the effect of ply thickness on microscopic damage progress. Microscopic damages were observed using optical microscopy and soft X-ray radiography. Energy release rate associated with transverse cracking was calculated using variational analysis. The modified Paris law was used to predict transverse cracking. From comparison to mechanical fatigue test results, it is clarified that transverse crack accumulation rate was larger under thermal fatigue loading at same energy release rate range due to the dependence of the fracture toughness on temperature.     

On modelling of damage evolution in textile composites on meso-level via property degradation approach

The continuous damage mechanics (CDM) approach is a popular tool for modelling of damage evolution in textile composites on the meso-level. It is based on the assumption that a material with defects can be replaced by a fictitious material with no defects but with degraded elastic constants. In such way the presence of defects is only reflected in the material elastic properties and damage evolution is recorded through the loss of these properties. The CDM approach incorporated into finite element analysis often predicts unphysically wide damage zones and in some cases failure across yarns – findings that are not supported by experimental data. The current work is geared toward identifying the source of inconsistencies between experiment and modelling by revisiting basic assumptions of CDM. A test problem is proposed to illustrate a break down of the CDM approach where a single crack-like defect in a yarn is modelled as an inhomogeneity with elastic constants reduced according to Murakami–Ohno model. It is shown that CDM in combination with local stress analysis of failure may predict a different direction of damage evolution as well as an incorrect failure mode in comparison with the crack problem. We also investigate whether the Murakami–Ohno model adopted for calculation of properties of a fictitious inhomogeneity contributes to the unphysical results. For this we compare contributions of a crack and an inhomogeneity into material elastic response. A new property degradation procedure is suggested (referred here as an effective elastic response model) where the size of an inhomogeneity and properties of the surrounding material are taken into account.     

The effect of pin reinforcement upon the through-thickness compressive strength of foam-cored sandwich panels

Titanium and carbon fibre pins have been inserted into the polymethacrylimide foam core of a sandwich panel (with carbon fibre face sheets) in order to increase the through-thickness strength. The elevation in compressive strength has been measured both quasi-statically and dynamically using a direct Kolsky bar, and the sensitivity of strength to the relative density and thickness of foam have been determined. An X-ray CAT scan machine was used to examine the deformed shape of the pins during interrupted compression testing of the sandwich specimens. It was found that the foam core stabilises the pins against elastic buckling, and the pin-reinforced core has a strength and energy absorption capacity in excess of the individual contributions from the foam and unsupported pins. It is shown that the compressive strength is governed by elastic buckling of the pins, with the foam core behaving as an elastic Winkler foundation in supporting the pins. The peak strength of the pin-reinforced core is increased by a factor of about four when the speed of loading is increased from the quasi-static rate of about 10⁻⁶ ms⁻¹ to the dynamic value of 10 ms⁻¹; it is concluded that the micro-inertia of the pins stabilises them against elastic buckling and leads to the observed elevation in strength.