Characterisation of Transverse Cracking in a Quasi-Isotropic GFRP Laminate under Flexural Loading

Transverse cracking behaviour in a quasi-isotropic glass/epoxy (GFRP) laminate loaded in flexure is studied experimentally and theoretically. A theory developed for cross-ply laminates is applied to a [0°/90°/–45°/45°] _S quasi-isotropic laminate. An equivalent laminate is introduced to derive the Young's modulus of a cracked transverse ply on the basis of a shear lag analysis. The model predicts the flexural stiffness, the neutral axis position and the residual curvature as a function of the transverse crack density and the in-situ ply stress at first ply failure. Experimental results are obtained with the use of the applied moment – strain data in four-point flexural tests and compared with predictions. Time-dependent behaviour of the residual curvature is also investigated.The theoretical predictions are in reasonably good agreement with the experimental results. It is found that the decrease in the residual curvature after unloading is mainly ascribed to viscoelasticity of the material.     

Energy-based prediction of failure in general symmetric laminates

This paper describes a new homogenisation technique for general symmetric laminates that enables progressive ply crack formation to be predicted in any number of plies having a variety of orientations. The approach involves (i) the analysis of non-uniformly spaced discrete ply cracks having a single orientation, (ii) a novel technique to homogenise the properties of the cracked ply so that discrete ply cracking can be analysed in plies having a different orientation, and (iii) the use of energy based methods to predict the progressive formation of ply cracks in any number of plies during loading. The analysis takes full account of the effects of thermally induced residual stresses. A key feature of the approach is the inclusion of a shear coupling term in the stress-strain relations for homogenised plies that ensures that the homogenised laminate has exactly the same effective properties as the laminate having a ply with discrete cracks in place of one of the homogenised plies. The model is applied to the prediction of the significant dependence of ply thickness and ply lay-up on laminate strength, and results for carbon fibre reinforced plastic laminates are compared favourably with published experimental results.     

Buckling analysis of composite laminates under end shortening by higher‐order shear deformable finite strips

A higher‐order shear deformable finite strip is developed and employed in the buckling analysis of laminated composite plates when subjected to uniform end shortening. This enables the transverse shear deformation to be accurately incorporated. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. Results with respect to the number of plies, thickness of laminate and ratios of E₁₁/E₂₂ are presented for unsymmetric cross‐ply and angle‐ply lay‐ups and for laminates with arbitrary lay‐up arrangements. Copyright © 2002 John Wiley & Sons, Ltd.     

Behaviour of unidirectional and crossply ceramic matrix composites under quasi-static tensile loading

Experimental results are presented for the quasi-static tensile behaviour of unidirectional, (0/90)_s, (0₂/90₄)_s and (0/90)_3s silicon carbide fibre (Nicalon) reinforced calcium aluminosilicate glass-ceramic matrix laminates. The stress-strain behaviour and associated damage development is described in detail for each laminate. The damage development is quantified by counts of crack density (in both the longitudinal and transverse plies) and stiffness reduction as functions of applied strain. The damage initiation and growth (and its effect on residual properties) are discussed with reference to the Aveston-Cooper-Kelly (ACK) theory for unidirectional ply cracking and crossply laminate shear-lag (originally developed for polymer matrix composites) to describe the transverse ply cracking behaviour.     

The Displacement Perspective During Ultimate Failure of Composite Laminates

This paper deals with the studies on the state of displacement of symmetric and anti-symmetric angle-ply and cross-ply laminated composite plates during its ultimate failure, subjected to transverse static load. First-order shear deformation theory (FSDT) is employed in conjunction with the finite element approach using eight-noded quadratic isoparametric element. The free vibration analyses of isotropic and laminated composite plates are carried out to ensure the overall validity of the present finite element formulation. The mid surface of the laminate is considered as the reference plane. The principal material directions in different laminae are oriented to produce a laminated structural element capable of resisting loads in several directions. The stiffness of a composite laminate is obtained from the properties of the constituent laminae. The affected stiffness of the failed lamina is discarded completely after the failure of weakest ply. The rigidity matrix of the laminate with remaining laminae is re-established. The re-evaluation process continues until the laminate fails completely. To investigate the displacement behaviour of laminates during the ultimate failure, parametric studies are carried out for different cases by varying the stacking sequences, fiber orientations, layer thicknesses, aspect ratios and the number of layers in the laminate. The comparison of results in terms of non-dimensional natural frequencies and ply-by-ply failure analyses obtained from the present investigation are made with those available in the reported literature.     

Computational homogenization of discrete fracture in fibre-epoxy systems

In the present paper the effective mesoscale failure response of a fibre-epoxy sample is computed from its complex microscale fracture behaviour. The mesoscale failure response is represented by a traction-separation curve derived from numerically homogenizing the fracture response of a periodic fibre-epoxy microstructure loaded under uniaxial tension. The traction-separation curve can be applied in material points of interface elements that are used for simulating mode I mesoscopic fracture in macroscopic laminate failure problems. The effect of the size of the microscopic fibre-epoxy sample on the mesoscale failure response is examined, as well as the effect of local imperfections at fibre- epoxy interfaces.     

Probabilistic initial failure strength of hybrid and non-hybrid laminates

This paper deals with the initial failure of unidirectional hybrid laminates and [±θ/90]_s non-hybrid laminates. The initial failure strength or strain at the failure of low elongation layers is analysed by the statistical approach based upon the weakest link model. First ply failure is adopted as a criterion for the initial failure of the laminate. An expression for determining the first ply failure strength has been derived and this expression can be reduced to a volumetric relation as a special case. It is also shown that the initial failure strength or strain is greater in composites composed of low elongation and high elongation materials than in the pure low elongation composite. This is the result of the “size effect”, that is the failure probability is lower in the composite with the smaller size of low elongation material. A good agreement between the theoretical and experimental results is achieved. On leave from the Institute of Interdisciplinary Research, The University of Tokyo, Japan.     

Simulation of inelastic response of multidirectional laminates based on stress failure criteria

Abstract

The primary purpose of this paper is to simulate the non-linear stress–strain curve of a multidirectional laminate subjected to an arbitrary in plane load using constituent material data and laminate geometrical parameters. The simulation is performed at a ply level. The classical laminated plate theory is employed to determine the load shared by each lamina in the laminate, while internal stresses in the constituent fibre and matrix of the lamina are obtained using a recently developed bridging micromechanics model. Thus, various failure criteria can be incorporated to detect the failure of a lamina in the laminate, and a progressive failure process is assumed by stiffness discount. Another objective of this paper is to investigate the influence of three typical failure criteria, i.e. the maximum normal stress criterion, the Tsai–Wu criterion, and the Hashin–Rotem criterion, on the simulation. Prediction has been made for T300/5208 graphite–epoxy laminates of a number of layups subjected to uniaxial tension. For the considered laminates, the predicted curves agree well with available experimental data. It is found that the predic tions based on the maximum normal stress criterion are comparable with those based on the other two criteria. As the maximum normal stress criterion is the simplest in application, it is recommended as the first candidate for laminate non-linear and failure analysis.     

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.     

Tensile Behaviour of Multilayer Knitted Fabric Composites with Different Stacking Configuration

In this paper, multilayer plain weft knitted glass fabric reinforced epoxy composite laminates with different stacking configurations, i.e., [0°]₄, [0°/±45°/0°], [0°/90°/90°/0°] and [90°]₄, were investigated experimentally. The laminates were uniaxially tensile loaded until final fractures occurred. The experimental results show that with the change in layer stacking structure, a corresponding variation in composite strength and stiffness was achieved. The tensile strength and modulus rank as follows: [0°]₄ > [0°/±45°/0°] > [0°/90°/90°/0°] > [90°]₄, which implicates a potential desiguability of Knitted Fabric Composites (KFC) for engineering applications. Failure behaviours of the fractured laminate specimens were examined using a matrix digestion and layer peeling method, based on which the behaviour of each lamina in the laminate can be clearly shown. It was found that an angle-plied lamina in the laminate when subjected to a uniaxial tensile load has a different fracture mode from that of a single ply composite under an off-axial tensile load. This means that the lamina in the laminate is subjected to a more complicated load combination. By comparing the fractured mode of the latter lamina with that of the single ply composite, the load direction sustained by the lamina in the laminate can be identified, which provides a qualitative benchmark for verifying a theoretical simulation.     

Optimization of Composite Material System and Lay-up to Achieve Minimum Weight Pressure Vessel

The use of composite pressure vessels particularly in the aerospace industry is escalating rapidly because of their superiority in directional strength and colossal weight advantage. The present work elucidates the procedure to optimize the lay-up for composite pressure vessel using finite element analysis and calculate the relative weight saving compared with the reference metallic pressure vessel. The determination of proper fiber orientation and laminate thickness is very important to decrease manufacturing difficulties and increase structural efficiency. In the present work different lay-up sequences for laminates including, cross-ply [0 _m /90 _n ] _s , angle-ply [±θ] _ns , [90/±θ] _ns and [0/±θ] _ns , are analyzed. The lay-up sequence, orientation and laminate thickness (number of layers) are optimized for three candidate composite materials S-glass/epoxy, Kevlar/epoxy and Carbon/epoxy. Finite element analysis of composite pressure vessel is performed by using commercial finite element code ANSYS and utilizing the capabilities of ANSYS Parametric Design Language and Design Optimization module to automate the process of optimization. For verification, a code is developed in MATLAB based on classical lamination theory; incorporating Tsai–Wu failure criterion for first-ply failure (FPF). The results of the MATLAB code shows its effectiveness in theoretical prediction of first-ply failure strengths of laminated composite pressure vessels and close agreement with the FEA results. The optimization results shows that for all the composite material systems considered, the angle-ply [±θ] _ns is the optimum lay-up. For given fixed ply thickness the total thickness of laminate is obtained resulting in factor of safety slightly higher than two. Both Carbon/epoxy and Kevlar/Epoxy resulted in approximately same laminate thickness and considerable percentage of weight saving, but S-glass/epoxy resulted in weight increment.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

Stiffness and fracture analysis of laminated composites with off-axis ply matrix cracking

Matrix cracks parallel to the fibres in the off-axis plies is the first intralaminar damage mode observed in laminated composites subjected to static or fatigue in-plane tensile loading. They reduce laminate stiffness and strength and trigger development of other damage modes, such as delaminations. This paper is concerned with theoretical modelling of unbalanced symmetric laminates with off-axis ply cracks. Closed-form analytical expressions are derived for Mode I, Mode II and the total strain energy release rates associated with off-axis ply cracking in [0/θ]_s laminates. Stiffness reduction due to matrix cracking is also predicted analytically using the Equivalent Constraint Model (ECM) of the damaged laminate. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

The response of a multi-directional composite laminate to through-thickness loading

The through-thickness mechanical response of a carbon fibre/epoxy laminated composite of lay-up [0/45/−45]_ns is measured at low rates of strain. Uniaxial tension and compression experiments are carried out on dogbone specimens cut from a thick laminate along different directions, and failure mechanisms are observed via optical and electron microscopy. The effect of direct and shear stresses at the ply interfaces on the onset of failure is measured, and a failure envelope is constructed. The compressive response of specimens of different shape is investigated. Composite beams of different volume and aspect ratios are tested to failure in three-point bending and these tests reveal a strong dependence of the apparent out-of-plane tensile strength of the composite on the beam volume; this effect is modelled by Weibull theory.     

Investigation of thermally induced bistable behaviour for tow-steered laminates

Traditionally, bistable laminates have been developed from prepreg plies stacked up together to achieve a layup which is either constant or discretely varying over the planform of the laminate. Laminates with discrete variation in layup are, in particular, of interest as they offer the prospect of easier blending. Moreover, such laminates can be manufactured to have Variable Angle Tows (VATs) in a ply using a tow-steering technique, doing so, ensures fibre-continuity and may impart additional structural strength. This paper presents an approach to develop finite element (FE) models which can accurately predict the cured shape(s) of tow-steered laminates that are designed to be bistable. Manufactured laminates are characterised using microscopy and resin burn-off tests to identify resin-rich layers, ply-thicknesses and fibre volume fractions (V_f) – which are then translated into FE models. Presented data highlights the influence of the manufacturing process in the thermally induced bistable behaviour of tow-steered laminates.     

Effect of off-axis ply orientation on 0°-fibre microbuckling

The aim of the present work is to study both experimentally and theoretically the compression failure mechanisms in multi-directional composite laminates, and especially the effect of the off-axis ply orientation on fibre microbuckling in the 0°-plies. The critical mechanism in the compressive fracture of unidirectional polymer matrix composites is plastic microbuckling/kinking. In multi-directional composites with internal 0°-plies, catastrophic failure also initiates by kinking of 0°-plies at the free-edges or manufacturing defects, followed by delamination. When 0°-plies are located at the outside, or in the case of cross-ply laminates, failure rather tends to occur by out-of-plane buckling of the 0°-plies. T800/924C carbon-fibre–epoxy laminates with a [(±θ/0₂)₂]_s lay-up are used here to study the effect of the supporting ply angle θ on the stress initiation of 0°-fibre microbuckling. Experimental data on the compressive strength of laminates with θ equal to 30, 45, 60 or 75° are compared to theoretical predictions obtained from a fibre kinking model that incorporates interlaminar shear stresses developed at the free edges at (0/θ) interfaces. Initial misalignment of the fibres and non-linear shear behaviour of the matrix are also included in the analysis.     

A computational continuum damage mechanics model for predicting transverse cracking and splitting evolution in open hole cross‐ply composite laminates

The present study focuses on a computational constitutive model which predicts the matrix cracking evolution and fibre breakage in cross‐ply composite laminates with open hole under in‐plane loading. To consider the effects of matrix cracking on the nonlinear response of laminates, a simplified crack density based model is applied which evaluates the representative damage parameters of matrix cracking. Furthermore, a developed subroutine based on continuum damage mechanics concepts is applied in ANSYS code which is capable to consider the transverse cracking/splitting evolution and predict the final failure load of mentioned laminate under monotonic loading in a progressive damage analyses. It is shown that the obtained stress–strain behaviours and the damage evaluation of considered laminates are in good agreement with the available experimental results.     

Quantification of flexural fatigue life and 3D damage in carbon fibre reinforced polymer laminates

Carbon fibre reinforced polymer (CFRP) laminated composites have become attractive in the application of wind turbine blade structures. The cyclic load in the blades necessitates the investigation on the flexural fatigue behaviour of CFRP laminates. In this study, the flexural fatigue life of the [+45/−45/0]_2s CFRP laminates was determined and then analysed statistically. X-ray microtomography was conducted to quantitatively characterise the 3D fatigue damage. It was found that the fatigue life data can be well represented by the two-parameter Weibull distribution; the life can be reliably predicted as a function of applied deflections by the combined Weibull and Sigmodal models. The delamination at the interfaces in the 1st ply group is the major failure mode for the flexural fatigue damage in the CFRP laminate. The calculated delamination area is larger at the interfaces adjacent to the 0 ply. The delamination propagation mechanism is primarily matrix/fibre debonding and secondarily matrix cracking.