Unnotched Laminates Research Articles

Mesoscale Model for Composite Laminates: Verification and Validation on Scaled Un-Notched Laminates.

This paper presents a mesoscale damage model for composite materials and its validation at the coupon level by predicting scaling effects in un-notched carbon-fiber reinforced polymer (CFRP) laminates. The proposed material model presents a revised longitudinal damage law that accounts for the effect of complex 3D stress states in the prediction of onset and broadening of longitudinal compressive failure mechanisms. To predict transverse failure mechanisms of unidirectional CFRPs, this model was then combined with a 3D frictional smeared crack model. The complete mesoscale damage model was implemented in ABAQUS®/Explicit. Intralaminar damage onset and propagation were predicted using solid elements, and in-situ properties were included using different material cards according to the position and effective thickness of the plies. Delamination was captured using cohesive elements. To validate the implemented damage model, the analysis of size effects in quasi-isotropic un-notched coupons under tensile and compressive loading was compared with the test data available in the literature. Two types of scaling were addressed: sublaminate-level scaling, obtained by the repetition of the sublaminate stacking sequence, and ply-level scaling, realized by changing the effective thickness of each ply block. Validation was successfully completed as the obtained results were in agreement with the experimental findings, having an acceptable deviation from the mean experimental values.

Strength prediction of the notched composite laminates from equivalent un-notched laminates

In this paper, a theoretical failure model is proposed to predict ultimate strength of fiber-reinforced composite laminate with a circular hole. In the failure model, the laminate with a circular hole is modeled by an equivalent intact laminate which contains laminae with the same stacking sequence but with equivalent stiffness and strength derived by micromechanics and point stress formulation, respectively. The ultimate strength of this equivalent intact laminate is calculated by the improved Puck’s failure theory combined with stiffness degradation model. The failure model so formulated is applied to notched laminates with arbitrary stacking sequences. The capability is demonstrated by strength predictions of several multidirectional notched laminates, including [45∘/0∘/−45∘/90∘]2s AS4/3501-6 notched laminates, [45∘/90∘/−45∘/0∘]4s IM7/8552 notched laminates and [0∘/902∘/0∘]4s AS4/3502 cross-ply notched laminates, which are in good agreement with experimental results.

An interactive orthotropic non-local damage model for progressive failure analysis of composite laminates

In this study, the non-local continuum damage model is further developed for progressive failure analysis of laminated composites. Characterized by two internal length scales, an orthotropic non-local integral strategy is implemented to model the constrained matrix damage along fiber direction. The introduction of spatial averaging may avoid spurious strain localization and thus ensure the physically-meaningful energy dissipation during damage evolution process. Compared to standard damage descriptions, the pathological mesh sensitivity and mesh orientation bias are effectively alleviated, leading to objective and accurate solutions. Moreover, an interactive damage transfer scheme is proposed to capture the strong interaction between matrix cracking and interface delamination, so that faithful predictions on the complex failure mechanisms of composite laminates are guaranteed. Performance of the present model and its superiority over conventional methods are demonstrated through several numerical examples, including the typical tensile failure of notched and unnotched laminates.

Combined peridynamics and kinetic theory of fracture for fatigue failure of composites under constant and variable amplitude loading

This study presents a fatigue model for constant and variable amplitude cyclic loading by combining kinetic theory of fracture (KTF) with peridynamics (PD). The KTF is applicable to constant and variable amplitude loading, and cumulative damage is inherent in the assumptions. Also, it is extremely suitable for implementation in the PD model of laminates. The standard stress versus cycles to failure data for unnotched laminates provides the determination of necessary parameters for the KTF. Using the test data generated by the Air Force Research Laboratory under the Tech Scout Project, the fidelity of this model is established by simulating three different composite laminates with an open-hole under cyclic loads for stiffness reduction and failure progression. The PD predictions agree with the measured reduction in stiffness as a function of number of load cycles. Also, the progressive damage predictions capture the general characteristics of the experimentally observed damage patterns.

CFRP Thin-Ply Fibre Metal Laminates: Influences of Ply Thickness and Metal Layers on Open Hole Tension and Compression Properties.

Thin-ply laminates exhibit a higher degree of freedom in design and altered failure behaviour, and therefore, an increased strength for unnotched laminates in comparison to thick-ply laminates. For notched laminates, the static strength is strongly decreased; this is caused by a lack of stress relaxation through damage, which leads to a higher stress concentration and premature, brittle failure. To overcome this behaviour and to use the advantage of thin-ply laminates in areas with high stress concentrations, we have investigated thin-ply hybrid laminates with different metal volume fractions. Open hole tensile (OHT) and open hole compression (OHC) tests were performed with quasi-isotropic carbon fibre reinforced plastic (CFRP) specimens. In the area of stress concentration, 90° layers were locally substituted by stainless steel layers of differing volume fractions, from 12.5% to 25%. The strain field on the specimen surface was evaluated in-situ using a digital image correlation (DIC) system. The embedding of stainless steel foils in thin-ply samples increases the OHT strength up to 60.44% compared to unmodified thin-ply laminates. The density specific OHT strength is increased by 33%. Thick-ply specimens achieve an OHC strength increase up to 45.7%, which corresponds to an increase in density specific strength of 32.4%.

Experimental and semianalytical investigation of X850 ± IM190 CFRP bolted joints

Considering the fact that the foundation data for a new X850 ± IM190 carbon/epoxy material system adopted in commercial aircraft industry are extremely scarce in the literature, an in-plane, static tensile experiment was carried out to investigate the bearing performance of double-lap, single-bolt joints in X850 ± IM190 carbon fiber-reinforced polymer (CFRP) composites. The effects of ply ratio, 0° layers’ combination percentage, bolt diameter, and curing method were considered. Then, special attention was paid to determine the design parameters of X850 ± IM190 CFRP bolted joints, such as tensile strength of un-notched laminate and stress concentration relief factor. Based on these design parameters, an efficient semianalytical approach was established to obtain the ultimate bearing strength of the joints. The failure prediction exhibited excellent agreement with the experimental data. These results will play an important role in design and strength evaluation of X850 ± IM190 CFRP bolted joints.

An orthotropic augmented finite element method (A-FEM) for high-fidelity progressive damage analyses of laminated composites

In this paper, we extended a recently developed augmented finite element method (A-FEM) to account for the complicated progressive damage processes in laminated composites, which are of orthotropic nature and typically develop multiple types of cracking systems including intra-ply matrix/fiber splitting, fiber rupture in tension and/or kinking in compression, and inter-ply delamination. The orthotropic A-FEM represents all of these major damage modes with improved nonlinear cohesive zone models (CZMs) that explicitly consider the asymmetric tension- and compression-responses. A rigorous verification and validation process demonstrates that the developed orthotropic A-FEM can adequately account for the initiation and propagation of various types of cracks and their coupled evolution under complex stress environments. A-FEM predictions to progressive damage processes in several multidirectional notched and un-notched laminates, including the initiation of multiple cracks and their nonlinearly coupled progression with delaminations all the way up to the final, catastrophic failure, are all in excellent agreement with experimental measurements and observations.

Temperature effect on the tensile behaviors of carbon/polyimide composite laminate

Experimental and numerical investigations were carried out to study the temperature effect on the stiffness, strength, and failure behaviors of carbon/polyimide composite laminates. Both unnotched laminates and open-hole laminates were tested under tension load at three temperatures (room temperature, 200 ℃, and 250 ℃). A three-dimensional finite element analysis was carried out to study the thermomechanical coupling behavior in the notched laminate. The model considers each layer and interface as a single element in the thickness direction so that in-plane stress and interlaminar stress could be analyzed in the model. The stresses around the open-hole changing characteristics with the temperature and tensile loading have been discussed in detail. Failure analysis was carried out to predict the residual strength of the notched laminates at different temperatures. Compared to the experimental data, the numerical results have an excellent agreement.

Unification of strength scaling between unidirectional, quasi-isotropic, and notched carbon/epoxy laminates

An investigation into size effects and notch sensitivity in quasi-isotropic carbon/epoxy laminates was carried out. The purpose is to draw a complete picture of the strength scaling in unidirectional, quasi-isotropic, and notched carbon/epoxy laminates. A link was established between the strength scaling of the unidirectional and quasi-isotropic laminates. Efforts were made to understand the relationship between unnotched and open-hole strengths. For very small holes, the notched strengths approach the unnotched strength limit. A scaling law based on Weibull statistics was used to predict the unnotched laminate strengths. For very large holes, the same scaling law in conjunction with a detailed 3D ply-by-ply FE analysis with matrix cracks in the 90° plies and delamination cohesive interface elements was used to predict the large notched strengths. A good agreement between the modelling and experimental results was achieved. The effects of 90° matrix cracks on unnotched and notched strengths were also studied.

Influence of matrix nature on the post-fire mechanical behaviour of notched polymer-based composite structures for high temperature applications

Abstract This study aims to investigate the influence of matrix nature (thermosetting – epoxy 914; and thermoplastic – Polyphenylene Sulfide PPS) on the tensile thermo-mechanical behaviour of both notched and unnotched laminates. Depending on variable prior fire-exposures, the purpose was to compare the changes on the residual tensile mechanical properties of carbon fibre reinforced epoxy 914- and PPS-based laminates subjected to stress concentration for aeronautical purposes (e.g., at service temperatures higher than glass transition temperature, Tg). With respect to the unnotched laminates, the area of the hole is an open access through the thickness for the heat flux causing more or less thermal degradation (depending on matrix nature) and resulting in variably decreasing the laminate tensile properties. Surprisingly, a low heat flux leads to virtually no decrease in the residual tensile strength of PPS-based laminates; however, in epoxy 914-based composites, the exposure to a low heat flux is more detrimental as exposure time is long. Fractography analyses were performed to investigate damage mechanisms in perforated laminates. The influence of fire-induced damages, the subsequent degradation of the mechanical properties due to fire exposure, combined with the overstresses near the hole all contribute to significantly decrease both stiffness and strength of C/epoxy notched laminates. In notched C/PPS laminates, the fire-induced degradation, resulting from the redistribution of melted PPS matrix within the fibre network, may compete with a relaxation effect in the overstressed 0° carbon fibres in the vicinity of the hole. These competing mechanisms are expected to reduce the influence of fire-exposure on the residual tensile strength of notched C/PPS laminates.

Multiscale static analysis of notched and unnotched laminates using the generalized method of cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites with and without notches subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/−45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (1) Layup 1: [0,45,90,−45]2S, (2) layup 2: [60,0,-60]3S, (3) layup 3: [30,60,90,−30,−60]2S) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within NASA's multiscale framework (FEAMAC). Both MMCDM and plasticity models incorporate brittle strain and stress based failure criteria for the fiber. Upon satisfaction of this criterion, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber/matrix) is characterized using a combination of vendor data and the axial, transverse and shear response of unnotched laminates. Then, the capability of the multiscale methodology is assessed, by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e. stress–strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

Static strength prediction in laminated composites by using discrete damage modeling

Discrete Damage Modeling of complex local failure patterns in laminated composites including matrix cracking, delamination, and fiber failure was performed. Discrete Damage Modeling uses the Regularized eXtended Finite Element Method for the simulation of matrix cracking at initially unknown locations and directions independent of the mesh orientation. Cohesive interface model is used both for Mesh Independent Cracking as well as delamination propagation. The fiber failure mode is modeled by two different methods in tension and compression. Tensile failure is predicted by Critical Failure Volume criterion, which takes into account volumetric scaling of tensile strength. Compression fiber failure is simulated with a single parameter continuum damage mechanics model with non-compressibility condition in the failed region. Ply level characterization input data were used for prediction of notched and unnotched laminate strength. All input data required for model application is directly measured by ASTM tests except tensile fiber scaling parameter and compression fiber failure fracture toughness, which were taken from literature sources. The model contains no internal calibration parameters. Tensile and compressive strength of unnotched and open hole composite laminates IM7/977-3 has been predicted and compared with experimental data. Three different layups, [0/45/90/−45]2S, [30/60/90/−60/−30]2S, and the [60/0/−60]3S, were modeled and tested and showed good agreement with experiment in the case of tensile loading, whereas the compressive strength was generally under predicted for unnotched laminates and overpredicted for open hole laminates.

Damage evolution in open-hole laminated composite plates subjected to in-plane loads

Damage evolution of notched composite laminates is analysed in this work using a discrete damage model, which estimates matrix damage evolution and fibre failure. The fibre damage is regularised with a Weibull distribution, and a Regula Falsi method has been used to improve numerical convergence. The model is compared and validated with several experimental results taken from the scientific literature, which consider different materials, laminate stacking sequences and specimen geometries. A good correlation has been found for the failure strength and the stress–strain curve of notched and un-notched laminates subjected to in plane loads. The influence of the Weibull modulus on the matrix and fibre damage evolution, and the failure strength, is analysed.

Influence of matrix ductility on the high-temperature fatigue behaviour of notched and unnotched thermoplastic and thermoset laminates

An experimental study has been conducted on notched and unnotched carbon woven-ply PolyPhenylene Sulfide (PPS) and Epoxy laminates subjected to fatigue loadings at a test temperature T such as [Formula: see text]. Depending on matrix nature, the obtained results confirm that matrix ductility is prominent to rule the fatigue response of notched woven-ply laminates at high temperature. In C/PPS laminates whose behaviour is very ductile at T > Tg, the presence of a stress concentrator improves their fatigue life, whereas it reduces the fatigue life in C/Epoxy laminates. During cycling loadings, the dissipated energy is about four times as high in C/PPS laminates as in C/Epoxy laminates. The overstresses relieving known to be primarily due to diffuse damage around the hole in C/Epoxy is not efficient at high frequency, contrary to the overstresses accommodation due to the fibres rotation and to the plastic deformation along the ±45° oriented fibres in C/PPS, resulting in a longer fatigue life with respect to unnotched laminates.

Fatigue damage accumulation in notched woven-ply thermoplastic and thermoset laminates at high-temperature: Influence of matrix ductility and fatigue life prediction

This work was aimed at investigating the influence of matrix ductility on the high-temperature tensile fatigue behaviour in notched and unnotched C/PPS (thermoplastic) and C/Epoxy (thermoset) laminates. Damage mechanisms and overstress accommodation near the hole have been discussed by means of X-rays observations and fractography analysis. In order to quantitatively evaluate the fatigue damage within notched and unnotched laminates as a function of the cycles, a damage variable based on a mean strain calculated on each cycle from the experimental stress–strain loops has been used. Finally, a simple analytical model was applied to test its predictive capabilities to evaluate the fatigue damage accumulation in both materials. This model proved to be relevant to predict the evolution of fatigue damage in notched C/PPS composites but not in C/Epoxy laminates.

Damage monitoring and analysis of composite laminates with an open hole and adhesively bonded repairs using digital image correlation

High performance composite materials, such as Carbon–Fibre Reinforced Plastic (CFRP) composites, are being increasingly used in aerospace industry, such as fuselage primary structures in Boeing 787 or Airbus 350, where high strength and stiffness are required at minimum weight [1]. The design of composite structures frequently includes discontinuities such as cut-outs for access and fastener holes for joining and they become critical regions under thermo-mechanical loading. Understanding of notched specimen behaviour is necessary for the design of complex structures where parts are mostly connected with bolts and rivets [2]. The effect of these discontinuities on the behaviour of composite materials is an important topic because it causes a relatively large reduction in strength compared to the unnotched laminate [3]. In the first part of the current work, the assessment of the damage process taking place in notched (open-hole) specimens under uniaxial tensile loading was studied. Two-dimensional (2D) and three-dimensional (3D) Digital Image Correlation (DIC) techniques were employed to obtain full-field surface strain measurements in carbon–fibre/epoxy M21/T700 composite plates with different stacking sequences in the presence of an open circular hole. Penetrant enhanced X-ray radiographs were taken to identify damage location and extent after loading around the hole. DIC strain fields were compared to numerical predictions. In the second part of the study, DIC techniques were used to characterise damage and performance of adhesively bonded patch repairs in composite panels under tensile loading. This part of work relates to strength/stiffness restoration of damaged composite aircraft that becomes more important as composites are used more extensively in the construction of modern jet airliners. In the current work, external bonded patches have been studied. Adhesively bonded repairs are the most common type of repair carried out with composite materials [1,4]. The behaviour of bonded patches under loading was monitored using DIC full-field strain measurements. Location and extent of damage identified by X-ray radiography correlates well with DIC strain results giving confidence to the technique for structural health monitoring of bonded patches.

Evaluation of Tensile Strength of Woven Carbon/Epoxy Composite Laminates at Cryogenic Temperatures Using the Open Hole Specimens

Abstract We propose a combined numerical-experimental method for the evaluation of the tensile strength properties of woven carbon fiber reinforced polymer (CFRP) composite laminates at cryogenic temperatures using the open hole specimens. Cryogenic tensile tests were conducted on the open hole specimens of quasi-isotropic woven CFRP laminates, and the length of the hole edge damage zone corresponding to the specimen failure was determined by the microscopic examinations of failed specimens. A finite element based method was developed for estimating the cryogenic tensile strength of the unnotched woven laminates using the experimentally determined failure load and damage zone length. In the damage zone, the material was assumed to carry a uniform normal stress equal to the tensile strength. The results demonstrate that the present method is an efficient approach to measuring the tensile strength of high-strength advanced composites at cryogenic temperatures.

About the influence of temperature and matrix ductility on the behavior of carbon woven-ply PPS or epoxy laminates: Notched and unnotched laminates

Could thermoplastic-based composites be used to replace thermosetting-based composites in high-temperature secondary aircraft structures? The purpose of this work is to establish the ability of a material system to be used in aircraft engine nacelles when subjected to static loadings, with a key upper temperature of 120 °C. In order to provide answers to this question, the thermo-mechanical behaviors of carbon fiber fabric reinforced PPS or epoxy laminates have been compared specifically within the temperature change with 120 °C at the upper bound. The temperature-dependent ductile behavior of laminates is more or less exacerbated, depending on polymers glass transition temperature, and laminates stacking sequence. For both materials, the degree of retention of tensile mechanical properties is quite high in notched and unnotched quasi-isotropic laminates. A Digital Image Correlation technique has been used in order to understand the influence of temperature and matrix ductility on the mechanisms of overstresses accommodation near the hole. In fabric reinforced laminates, the high-temperature results suggest a competition between the mechanisms of damage, and the mechanism of plasticization, enhanced in angle–ply lay-ups. Thus, the highly ductile behavior of TP-based laminates, at temperatures higher than their T g, is very effective to accommodate the overstresses near the hole.

Scaling effects in notched carbon fibre/epoxy composites loaded in compression

The aim of the work was to develop an understanding of the failure mechanisms controlling the strength of composites of different dimensions and hence to be able to predict size effects in composite structures without resorting to empirical laws. Adequate models do not currently exist, and extensive testing is necessary, which is very costly. The ability to predict the effect of size on strength would be a major step forward, which would reduce costs and encourage the more widespread usage of these materials in the aerospace and other industries. In this article the effects of scaling (specimen size) on the strength of notched laminates are presented. The most important variables have been identified as hole (notch) size, ply and laminate thickness. Manufacturing defects and specimen design can also lead to premature failures, especially in unnotched laminates, but in laminates with an open hole are of less significance, since the notch dominates the fracture. The compressive strength results are compared to data obtained for the same composite system and laminate stacking sequences loaded in uniaxial tension.

A STUDY OF 954-2A/IM7 COMPOSITE LAMINATES CONTAINING A CENTRAL HOLE

Predicting microcracking properties of the composite laminates in nonuniform stress conditions was the subject in this paper. The uniform stress field meant the stresses were independent of the width direction. The material was the 954-2A/IM7 laminates containing a central hole. Microcracks initiated at the edge of the hole and propagated into the laminate. Because the tensile stress concentration decreased with distance, the microcracks were arrested before the edge of the laminate. Because carbon fiber composites were opaque, a x-ray method was used to detect the length of the propagating microcracks. The microcracking at the near edge of the hole could be reasonably predicted by considering the local laminate stresses and the microcracking toughness measured in unnotched laminates. However, the data away from the hole did not agree with the predictions. The local microcrack density was always much higher than that predicted by the local laminate stress.