Micromechanics characterization of sublaminate damage

A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.     

Analysis of a buffer strip laminate with fiber and matrix damage and interlaminar debonding

A shear lag solution for a hybrid buffer strip laminate containing initial damage in the form of a rectilinear notch, matrix splitting and interlaminar debonding is presented. The model is a unidirectional monolayer with two symmetric constraint layers that represent angle plies. The intent of the analysis is to estimate the remote strain required to propagate the initial damage and/or to fail the laminate catastrophically. The analytical solution has a set of integral equations in which material and geometric parameters appear explicitly. Some typical results are presented for a graphite/epoxy panel having either high strength and low modulus or low strength and low modulus buffer strips. Matrix damage, angle plies, and interlaminar debonding are shown to affect the damage tolerance capability of buffer strip laminates.     

Evaluation of different advanced finite element concepts for detailed stress analysis of laminated composite structures

Despite their high specific stiffness and strength, laminated composite materials, e.g. fibre-reinforced plastic plies stacked at different fibre orientations, are susceptible to damage. Damage can be divided into interalaminar damage and interlaminar damage. Delamination is a typical kind of interlaminar damage which occurs in laminated composite materials, often accompanied with intralaminar damage, and may lead to a catastrophic structural collapse. The first and most crucial step in the prediction of failure of Laminated Composite Structures (LCS) is to accurately determine the stresses, particularly the three transverse stress components, also called the interlaminar stresses. It is proposed in the present paper that the integration of a displacement based solid-shell formulation and partial-hybrid stress formulation will lead to an accurate and robust solid-shell element, suitable for the efficient and detailed interlaminar stress calculation.     

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

Acoustic structural health monitoring of composite materials : Damage identification and evaluation in cross ply laminates using acoustic emission and ultrasonics

The characterisation of the damage state of composite structures is often performed using the acoustic behaviour of the composite system. This behaviour is expected to change significantly as the damage is accumulating in the composite. It is indisputable that different damage mechanisms are activated within the composite laminate during loading scenario. These “damage entities” are acting in different space and time scales within the service life of the structure and may be interdependent. It has been argued that different damage mechanisms attribute distinct acoustic behaviour to the composite system. Loading of cross-ply laminates in particular leads to the accumulation of distinct damage mechanisms, such as matrix cracking, delamination between successive plies and fibre rupture at the final stage of loading. As highlighted in this work, the acoustic emission activity is directly linked to the structural health state of the laminate. At the same time, significant changes on the wave propagation characteristics are reported and correlated to damage accumulation in the composite laminate. In the case of cross ply laminates, experimental tests and numerical simulations indicate that, typical to the presence of transverse cracking and/or delamination, is the increase of the pulse velocity and the transmission efficiency of a propagated ultrasonic wave, an indication that the intact longitudinal plies act as wave guides, as the transverse ply deteriorates. Further to transverse cracking and delamination, the accumulation of longitudinal fibre breaks becomes dominant causing the catastrophic failure of the composite and is expected to be directly linked to the acoustic behaviour of the composite, as the stiffness loss results to the velocity decrease of the propagated wave. In view of the above, the scope of the current work is to assess the efficiency of acoustic emission and ultrasonic transmission as a combined methodology for the assessment of the introduced damage and furthermore as a structural health monitoring tool.     

Surface and bulk stress/strain measurements in composite laminates with a fibre-optic Raman probe

Fibre stress/strain measurements in unidirectional, as well as, multidirectional aramid/epoxy composites have been conducted with the use of a laser Raman microprobe. The composite was incrementally loaded in tension while Raman measurements were taken. Fibre-optic probes sandwiched between adjacent laminae were employed for channelling the laser excitation light to a specified location within the bulk of the composite. The direction of the fibre-optic was either perpendicular or parallel to the reinforcing fibres. For comparison purposes, the same fibre-optic probe was used to scan the surface of the laminates. The perpendicular configuration was found to reduce the tensile strength of the as-received composite coupon by 10% whereas the parallel second configuration had no effect. In the unidirectional coupons the stress or strain in the principal fibre direction could be measured prior to loading and at every increment of applied tensile load up to fracture. The take-up of fibre strain for both bulk and surface set of measurements was identical with that obtained from the attached electrical resistance strain gauges. In the case of multidirectional coupons the stress or strain in the principal direction could be measured within successive plies situated at angles θ to the loading direction. The results for the 0° plies were in good agreement with those obtained by conventional laminate analysis whereas small deviations from linearity were observed in the angle plies. The proposed methodology paves the way for simultaneous in-service stress/strain measurements on the reinforcing fibres situated on the surface or within the bulk of a composite laminate.     

Numerical analysis of bending and transverse shear properties of plain-weave fabric composite laminates considering intralaminar inhomogeneity

In this study, the bending and transverse shear properties of plain-weave fabric composite laminates are investigated by considering the intralaminar inhomogeneity through finite element analysis. Using homogenization procedures, the effective Reissner–Mindlin plate bending and transverse shear properties of composite laminates are calculated. Assuming the number of plies to be infinite, the effective three-dimensional (3D) continuum properties (elastic properties of the equivalent 3D bulk material) of the composite are also calculated. Then, the effect of the number of plies on the bending stiffness and transverse shear stiffness of the laminate, in other words, the effect of the intralaminar inhomogeneity on the laminate stiffness, is investigated. Through the numerical investigation, it is found that if the number of plies of the laminate is very small, the bending stiffness and transverse shear stiffness of the laminate are significantly lower than those evaluated using effective 3D continuum properties.     

Modelling of stable and unstable fracture of short beam shear specimens

Finite element analysis of interlaminar shear failure in unidirectional carbon fibre/epoxy is carried out. A short beam shear test with a large loading roller is modelled including the effects of large displacements and varying contact between the rollers and the specimen. The shear stress/deformation characteristics of the interfacial layers between plies are included by means of non-linear spring elements, and shown to determine whether the overall response of the specimen is stable or unstable. The span-to-thickness ratio also affects the stability of the response. The effect of specimen geometry on stability, which has also been observed experimentally, is difficult to explain by conventional analysis approaches. These results suggest that a good representation of the interface between plies is crucial for accurate modelling of overall structural response involving interlaminar shear failure.     

Piezoresistive effect of plain-weave CFRP fabric subjected to cyclic loading

The present study deals with electrical resistance changes in woven-fabric CFRP during loading. Four kinds of plain weave woven-fabric CFRP laminated specimens are prepared and subjected to cyclic tensile loading that does not cause any damages, and the electrical resistance changes of the specimens are measured experimentally by the four-probe method. As a result, the present study shows that the electrical resistance of a specimen comprised of six ±45° plies decreases remarkably with increasing number of loading cycles. The decrease is caused by shear plastic deformation of ±45° plies. The thickness shrinkage caused by shear plastic deformation increases the number of fiber contacts, and this decreases the interlaminar contact resistance between the plies. For a single ±45° ply, the same electrical resistance decrease caused by the shear plastic deformation is observed, and the magnitude of the decrease is smaller than that of the six-ply laminate tested. This is because the effect of interlaminar contact resistance decrease does not exist for a single ±45° ply. For the six 0°/90° plies, the present study shows that electrical resistance in the through-thickness direction is decreased by out-of-plane plastic deformation of carbon fiber and misalignment of the plies.     

Failure mechanisms of a notched CFRP laminate under multi-axial loading

A quasi-isotropic CFRP laminate, containing a notch or circular hole, is subjected to combined tension and shear, or compression. The measured failure strengths of the specimens are used to construct failure envelopes in stress space. Three competing failure mechanisms are observed, and for each mechanism splitting within the critical ply reduces the stress concentration from the hole or notch: (i) a tension-dominated mode, with laminate failure dictated by tensile failure of the 0° plies, (ii) a shear-dominated mode entailing microbuckling of the −45° plies, and (iii) microbuckling of the 0° plies under remote compression. The net section strength (for all stress states investigated) is greater for specimens with a notch than a circular hole, and this is associated with greater split development in the load-bearing plies. The paper contributes to the literature by reporting sub-critical damage modes and failure envelopes under multi-axial loading for two types of stress raiser.     

In situ fibre fracture measurement in carbon-epoxy laminates using high resolution computed tomography

High resolution Synchrotron Radiation Computed Tomography (SRCT) has been used to capture fibre damage progression in a carbon-epoxy notched [90/0]_s laminate loaded to failure. To the authors knowledge this provides the first direct in situ measurement of the accumulation of fibre fractures for a high performance material under structurally relevant load conditions (i.e. fractures within the bulk of an essentially conventional engineering laminate). A high level of confidence is placed in the measurements, as the failure processes are viewed internally at the relevant micromechanical length-scales, as opposed to previous indirect and/or surface-based methods. Whilst fibre breaks are the dominant composite damage mechanism considered in the present work, matrix damage, such as transverse ply cracks, 0° splits and delaminations, were also seen to occur in advance of extensive fibre breaks. At loads where fibre break density levels were significant, splitting and delamination were seen to separate the central 0° ply in the near notch region from the 90° plies. Fibre breaks were initially observed in isolated locations, consistent with the stochastic nature of fibre strengths. The formation of clusters of broken fibres was observed at higher loads. The largest clusters observed consisted of a group of eleven breaks and a group of fourteen breaks. The large clusters were observed at the highest load, at sites with no prior breaks, indicating they occurred within a relatively narrow load range. No strong correlation was found between the location of matrix damage and fibre breaks. The data achieved has been made available online at www.materialsdatacentre.com for ongoing model development and validation.     

Interlaminar shear fatigue of pultruded graphite fibre-polyester composites

The effect of cyclic loading on the interlaminar shear strength of pultruded graphite fibre-polyester was determined. Two fibre volume fractions, 0.5 and 0.33, were studied. The results indicate that the deterioration in the interlaminar shear strength with cycling is significantly greater than in flexural fatigue. The higher volume fraction material showed a greater drop in the interlaminar shear strength than the lower volume fraction material. Unlike the monotonic strengths, the effect of the fibre volume fraction on interlaminar shear fatigue strength at high cycles is small, indicating that there is little advantage in increasing the fibre volume fraction to improve the interlaminar shear strength in high cycle fatigue environments. A critical stress was determined above which interlaminar shear fatigue failure did not occur within 10⁷ cycles for the materials tested.     

Interface and impregnation relevant tests for continuous glass fibre-polypropylene composites

An experimental investigation was performed in order to compare the effect of the adhesive strength between fibres and matrix, contra the effect from the degree of impregnation on the mechanical properties of melt impregnated continuous glass fibre—polypropylene composites. Single fibre pull-out tests were performed in order to compare the interfacial bond strength. The degree of impregnation was measured using opacity and scattering from reflected light measurements of the prepregs. The testing included transverse tensile, ±45° tensile, double-notch shear, compression shear and double cantilever beam (DCB). These tests can to a certain degree be given interface relevance (InR) as well as impregnation relevance (ImR). With regard to InR sensitivity, the tests can be ranked in descending order according to prepreg transverse, laminate transverse, intralaminar, and interlaminar double-notch shear tests. With regard to ImR sensitivity, the tests can be ranked in descending order according to prepreg transverse, compressive interlaminar double-notch shear and laminate transverse tests. The measured shear and transverse modulus values showed limited relevance regarding the interface strength and degree of impregnation. The transverse and shear elastic modulus scored low regarding InR and ImR sensitivity. This was also true for the G_IC and G_ICPROP values.     

Nonlinear response in glass fibre non-crimp fabric reinforced vinylester composites

This paper addresses the nonlinear stress-strain response in glass fibre non-crimp fabric reinforced vinylester composite laminates subjected to in-plane tensile loading. The nonlinearity is shown to be a combination of brittle and plastic failure. It is argued that the shift from plastic to brittle behaviour in the vinylester is caused by the state of stress triaxiality caused by the interaction between fibre and vinylester. A model combining damage and plasticity is calibrated and evaluated using data from extensive experimental testing. The onset of damage is predicted using the Puck failure criterion, and the evolution of damage is calibrated from the observed softening in plies loaded in transverse tension. Shear loading beyond linear elastic response is observed to result in irreversible strains. A yield criterion is implemented for shear deformation. A strain hardening law is fitted to the stress-strain response observed in shear loaded plies. Experimental results from a selection of laminates with different layups are used to verify the numerical models. A complete set of model parameters for predicting elastic behaviour, strength and post failure softening is presented for glass fibre non-crimped fabric reinforced vinylester. The predicted behaviour from using these model parameters are shown to be in good agreement with experimental results.     

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.     

A microscopy study of impact damage of epoxy-matrix carbon-fibre composites

The damage associated with the impact of quasi-isotropic epoxy-matrix carbon-fibre composites was studied by sectioning through the impact area and photographing the polished sections. Composites with a state-of-the-art low fracture-energy matrix resin (Hercules 3501-6) and a new high fracture-energy resin (Hercules X8551) were compared. Damage in the lowtoughness matrix laminate was characterized by a network of interlaminar and transverse cracking that extended some distance beyond the centre of impact. A similar network of transverse and interlaminar cracking developed in the impacted tough-matrix laminate but was largely confined to a region immediately below the impact centre. This difference in the volume of impact damage could be easily attributed to the high interlaminar fracture energy of the X8551 resin compared to the 3501-6 resin. The type and distribution of impact damage are discussed in terms of energy-dissipative mechanisms and the stress patterns that develop during impact due to mechanical deflection and stress-wave interaction. Also, the results of the sectioning study are compared with damage assessment by ultrasonic backscattering.     

Querrißbildung in 0/90/0 CFK-Laminaten

Cross-ply Cracking in 0/90/0 CFRP Laminates Cross-ply cracking in carbon fibre reinforced plastics (CFRP) with thermoset as well as thermoplastic matrix systems was investigated on 0/90/0 laminates with varying 90°-ply thickness. Since in an angle ply laminate the 90°-ply fails first, the higher strength of the other plies cannot be taken advantage of. For this reason efforts have to be done to increase the transverse strength (strain) of fibre reinforced plastics. In the first place thus it is necessary to investigate the influence of the different parameters which contribute to the transverse strength. In this work the influence of matrix (fracture strain), fibre/matrix interface, voids and constraining effect of neighbouring plies is investigated. With the aid of two-parameter Weibull distributions of the 90°-ply fracture strain, which describe the phenomenon of multiple cracking in a specimen, it was found that the constraining effect due to neighbouring plies, improved fibre/matrix interface and matrix ductilty increase, whereas voids decrease the transverse fracture strain.     

Influence of titanium carbide on the interlaminar shear strength of carbon fibre laminate composites

The potential use of carbon fibre laminate composites is limited by the weak out-of-plane properties, especially delamination resistance. The effect of incorporating titanium carbide to the mesophase pitch matrix precursor of carbon fibre laminate composites on interlaminar shear strength is studied both on carbonised and graphitised composites. The presence of titanium carbide modifies the optical texture of the matrix from domains to mosaics in those parts with higher concentrations and it contributes to an increase of fibre/matrix bonding. This fact produces an increase of the interlaminar shear strength of the material and changes the fracture mode.     

C<Superscript>0</Superscript>-type global–local theory with non-zero normal strain for the analysis of thick multilayer composite plates

In this paper, an accurate and efficient C⁰-type third-order global–local model incorporating effects of the transverse normal strain is proposed to study the thermal/mechanical behaviors of thick multilayer cross-ply plates. Transverse displacement is assumed to be a linear distribution through the thickness direction, for which the normal strain could be readily computed. Based on the interlaminar continuity conditions of in-plane displacement and transverse shear stresses, layer-dependent variables could be reduced. Employing shear stress free condition at the upper and the lower surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C⁰ interpolation functions are only required for the finite element implementation. As a result, the number of variables is independent of the number of layers of the laminate. To assess the proposed model, the classical quadratic eight-node isoparametric element is used for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Comparing with various existing composite plate models, it is found that simple C⁰ finite elements with non-zero normal strain could produce accurate deformations and stresses of thick multilayer composite plates subjected to thermal and mechanical loads.     

铺层方向和裂纹混合比对复合材料层压板混合型断裂韧性影响的试验研究

试验研究了复合材料层压板的铺层方向以及裂纹混合比对层间裂纹分层扩展的影响规律。试验结果显示: 在非0°单向板的 Ⅰ 型层间裂纹分层扩展过程中, 会出现层间裂纹穿过分层开裂面的铺层而偏离到相邻铺层间扩展的现象, 而0°铺层具有阻止该裂纹偏离扩展的作用; 在不同裂纹混合比的层压板分层开裂试验中, 相应的0°单向板的断裂韧性均可以作为下限值而偏安全; 混合断裂韧性( Ⅰ 型断裂韧性+ Ⅱ 型断裂韧性)随着裂纹混合比的变化呈现类似正弦曲线的变化规律。