Form Of Matrix Cracking Research Articles

Electromechanical response of smart ultra-high-performance concrete under uniaxial load: Experimental investigation and electric field analysis

This study explores the electromechanical response of smart ultra-high-performance concrete (S-UHPC) under uniaxial tension and compression using both attached and embedded electrodes with direct current. Within the linear elastic region, the response of S-UHPC was influenced by the type of electrode due to the deformation of the silver paste used in the attached electrodes. Furthermore, although the electromechanical response of S-UHPC beyond the linear elastic region showed minimal variation between different electrode types, their self-sensing capabilities were significantly affected by the choice of electrode. Under uniaxial tension, the electrical resistivity of S-UHPC decreased marginally up to the limit of proportionality and then more substantially beyond it, primarily owing to the formation of matrix cracks. This reduction in electrical resistivity associated with crack formation was corroborated through electrical field analysis performed using COMSOL MultiphysicsⓇ. A key finding was that the decrease in electrical resistivity (from 0.1788 to 0.0286 kΩ·cm, -84.0 %) in the tensile strain-hardening region could be attributed to an increase in electrical current density within steel fibers; specifically, the current density increased from 0.2417 to 0.7047 A/mm2 as the number of matrix cracks increased from zero to seven.

Tensile Behavior of Parts Manufactured Using a Material Extrusion Process from a Filament with Short Carbon Fibers and PET Matrix

One of the latest tendencies in research related to material extrusion based on additive manufacturing is to determine the mechanical characteristics of parts taking into consideration the most influential manufacturing parameters. The main research objective is to describe how the manufacturing parameters, part orientation, layer thickness and infill density influence the tensile behavior of specimens made from PET with 15% short carbon fibers. The most advantageous result is obtained for a layer thickness of 0.15 mm, with 100% material infill, and material deposition on the longitudinal direction of the part. The obtained mean values are: 65.4 MPa tensile strength, 1.93% strain at rupture, and 9 GPa Young Modulus. For these values, the tensile behavior of specimens manufactured along transverse and thickness directions are presented. The least favorable results are obtained for manufacturing by thickness. The novelty of the discussed research consists in all these aspects together with an original mathematical model that was determined based on design of experiments with a correlation of the regression model of over 90%. By optical and electronic microscopy material gaps are visible in the filament and manufactured parts, and the failure occurs in most cases in form of matrix cracks and delamination.

Interface, thermal, and Fourier transform—infrared spectroscopy investigation on polylactic acid/polyhydroxyalkanoate composites with silane‐treated aluminum particles and intercalated montmorillonite inclusions for semiconductor devices

AbstractIn this investigation, the dielectric properties of silane‐influenced aluminum conductive particles in polylactic acid, polyhydroxyalkanoates, and intercalated montmorillonite (MMT) composite were assessed for enhancing the dielectric constant, dielectric loss, and AC conductivities. Eight different sets of samples were fabricated with untreated and silane‐treated batches of biopolymer composites where the highest recorded dielectric constant was 3.98 at relaxation frequency of 10 kHz. One of the notable observations in the dielectric loss was with PLA/PHA/iMMT/Al (10 wt%) (silane‐treated) composites exhibited the lowest losses past relaxation frequencies. Furthermore, FT‐IR spectra were conducted on the samples to identify stretching and bonds created by silane and aluminum particles. The IR spectra confirm the formation of the SiOAl bond when treated with 3‐glycidyloxypropyl‐trimethoxysilane (GPTMS) solution and confirm the bond of AlOH hydroxyl bonds in the untreated composite samples. Other IR spectra information that was gathered would include carbonyl group stretching at 1750 cm−1 and absorption bands of hydroxy acids, between 3511 and 3640 cm−1, respectively. Scanning electron microscopy was performed on the sample to observe the formation of matrix cracks and exfoliation. A rough surface can be seen on PLA/PHA blends and the crystallization of these polymer blends regions can be vividly seen from the micrographs. Lastly, thermogravimetry analysis on the composite samples shows a predominant mass loss at 300°C before complete degradation and the notable composite with the lowest mass loss would be PLA/PHA/iMMT/Al (10 wt%) (ST) composite samples and with the inclusion of a constant 5 wt% organoclay MMT fillers imposed a high‐onset degradation temperature, which was remarkable for composites that were fabricated through standard hot‐press compression molding and cooling procedures.

Vibro-acoustic modulation based measurements in CFRP laminates for damage detection in Open-Hole structures

The occurrence of matrix cracks, fibre failures and delaminations results in a critical degradation of the structural integrity of composites. A reliable early detection of these damages is mandatory for a safe operation. In this paper, the application of Vibro-Acoustic Modulation measurement in notched carbon fibre reinforced polymers (CFRP) for damage detection is demonstrated. A piezoceramic actuator introduces an ultrasonic signal into the specimen, which is modulated by a low-frequency vibration excited by a servo-hydraulic testing system. The specimens tested are open hole tensile specimens according to ASTM D5766, made from a quasi-isotropic CFRP layup. Degradation in the form of matrix cracks or delaminations localised along the drill hole significantly reduces the stiffness and can be detected as a modulation increase. Taking into account the extent of the crack size and the acoustic emission (AE), a magnitude estimate of the modulation increase is possible. In consequence, the presented method can be used for damage monitoring in CFRP.

Towards numerical simulation of fatigue damage detection in CFRP laminates by modelling of stochastic vibration response

Due to the widespread use of composites in aerospace applications, there is an increasing need for developing Structural Health Monitoring (SHM) systems for composite structures. In this process, simulation models can play a crucial role by contributing to the optimization of the experimental techniques and to understanding of the physical mechanisms. The objective of this work is to numerically simulate fatigue damage detection in laminated composites subjected to random vibration through a white gaussian noise. To this end, the ANSYS FE code has been used. The developed FE model represents an experimental set-up consisting of the composite specimen, the speakers producing the white noise and the measuring equipment. 24 specimens were modelled in total, a healthy one and 23 damaged ones. The white noise was modelled by introducing a normalized sequence of numbers adapted to the free vibration eigenfrequency range. Fatigue damage in the form of matrix cracking and delamination was modelled based on C-Scan images of fatigued specimens by degrading the appropriate elastic properties of the layers in specific groups of elements. Damage of different geometry, size, and type was modelled. The numerical results are in the form Power Spectral Density (PSD) diagrams, natural frequencies, eigenfrequencies and contour plots. The comparison between the numerical and experimental eigenfrequency values show a maximum deviation of 1.7%. The numerical results show a change in the vibration response even in the presence of a small damage, which is an indication of the sensitivity of the method. A significant decrease in natural frequencies of the specimen with the damage accumulation is observed. The present model comprises the first effort towards a fully validated digital twin which will be used for the virtual testing and the optimization of the vibration test.

Determination of the ballistic performance ramie-fiber-reinforced epoxy composite-sic ceramic in multilayered armor system

Multilayered Armor System (MAS) is being extensively studied around the world for its ability to retain ceramic fragmentation after a collision occurs. MAS consist of a ceramic layer placed at the front and supported by a composite layer of ramie-fiber-reinforced epoxy resin. Present study utilizes natural fibers of 50 % ramie fibers with epoxy resin as the matrix and Silicon Carbide (SiC) ceramic as the front panel. The ballistic testing in this study used 7.62×51 mm NATO Ball projectile with a firing distance of 15 m from the bullet panel. The velocity of projectile was detected using LIGHT SCREEN B471 type. The aim of the study is to conclude the optimal thickness of ramie fiber-epoxy and SiC ceramics MAS structure based on experiments which can withstand 7.62 NATO ball bullet penetration. To achieve this aim, the following objectives are accomplished: study the effect of SiC ceramic addition to ramie composite on BFS and study the effect of SiC ceramic addition to ramie composite on failure mode. Results show that the addition of the number of layers of SiC increases resistance of ballistic MAS marked by a decrease in the value of BFS clay. The 5SiC+10R is the optimal thickness in resisting the penetration of 7.62×51 mm bullets with 12 mm BFS clay. Failure phenomena found in this study were projectile fragments, matrix cracks, radial cracks, impact points, and ceramic fragments. Matrix crack formation appears on 5SiC+10R with mini deformation in rear side. Phenomenon of ceramic fragmentation in the shot causes the MAS structure to be damaged, so that the ramie fiber composite layer will face the bullet directly if it is subjected to a second shot. Ultra High Hardness Armor (UHHA) as first layer on the MAS structure is an attractive option for further research.

Effects of the quality of pre-consolidated materials on the mechanical properties and morphology of thermoplastic pultruded flat laminates

Pre-consolidated tapes in thermoplastic pultrusion solve the problem of impregnating a reinforcement with high-viscosity thermoplastic resins. Thermoplastic glass fiber/polypropylene flat laminates (75 mm × 3.5 mm) were fabricated using pre-consolidated tapes from different manufacturers: pre-consolidated tapes by the ApATeCh-Tape Company (Russia) and pre-consolidated sheets by the Zhongji Company (China). In spite of the equal reinforcement volume fraction (38%), the laminates fabricated from the pre-consolidated sheets exhibited higher compressive, tensile, and flexural strengths than those made from the pre-consolidated tapes, differing by 27.1%, 27.3%, and 19.8%, respectively. The observed difference between the strength characteristics of the studied flat laminates was explained by the presence of unimpregnated regions in the fiber bundles and by matrix cracks in the pre-consolidated tapes, absent in the pre-consolidated sheets, as revealed by the scanning electron microscopy analysis. Such defects cannot be corrected during the pultrusion process, resulting in the formation of matrix cracks and debonding, impairing the mechanical performance of the produced pultruded laminates. Pre-consolidated sheets enable pultrusion flat laminates with larger cross-sections, exhibiting better mechanical performance and surface roughness, compared with thermoplastic pultruded composites fabricated from pre-consolidated tapes described in the literature.

Effects of the Pre-Consolidated Materials Manufacturing Method on the Mechanical Properties of Pultruded Thermoplastic Composites

The choice of a manufacturing process, raw materials, and process parameters affects the quality of produced pre-consolidated tapes used in thermoplastic pultrusion. In this study, we used two types of pre-consolidated GF/PP tapes—commercially available (ApATeCh-Tape Company, Moscow, Russia) and inhouse-made tapes produced from commingled yarns (Jushi Holdings Inc., Boca Raton, FL, USA)—to produce pultruded thermoplastic Ø 6 mm bars and 75 mm × 3.5 mm flat laminates. Flat laminates produced from inhouse-made pre-consolidated tapes demonstrated higher flexural, tensile, and apparent interlaminar shear strength compared to laminates produced from commercial pre-consolidated tapes by as much as 106%, 6.4%, and 27.6%, respectively. Differences in pre-consolidated tape manufacturing methods determine the differences in glass fiber impregnation and, thus, differences in the mechanical properties of corresponding pultruded composites. The use of commingled yarns (consisting of matrix and glass fibers properly intermingled over the whole length of prepreg material) makes it possible to achieve a more uniform impregnation of inhouse-made pre-consolidated tapes and to prevent formation of un-impregnated regions and matrix cracks within the center portion of the fiber bundles, which were observed in the case of commercial pre-consolidated tapes. The proposed method of producing pre-consolidated tapes made it possible to obtain pultruded composite laminates with larger cross sections than their counterparts described in the literature, featuring better mechanical properties compared to those produced from commercial pre-consolidated tapes.

Experimental analysis of polymer matrix composite microstructures under transverse compression loading

Strengthening the fundamental understanding of micromechanical methods in continuity is a critical aspect in developing and designing future composite systems. Virtual testing has provided additional understanding of the behavior of materials on a microstructural scale. However, experiments must be executed to determine their validity. Modeling realistic microstructures under realistic loading conditions could help develop physically based micromechanical constitutive laws needed to predict their intrinsic failure. In this study, a micropillar with varying sizes was manufactured out of continuous fiber reinforced composites and transversely compressed to observe micromechanical phenomena. The fiber shape, size, and distribution were recorded as well as stress vs strain curves for each size of micropillar. The specimens were speckled to perform 2D digital image correlation (DIC) to analyze displacement and strain contours of the surface. The results from this study provides basic knowledge of microstructural instabilities, effects of nanovoids, interfacial debonded and matrix crack formation while under transverse compressive loading.

Impact damage detection in glass fibre reinforced polymers via electrical capacitance measurements on integrated carbon fibre bundles

Impact damages are critical for fibre reinforced polymers, as they can lead to large delaminations that strongly influence the structural integrity of the components. Therefore, reliable detection of impact damages through structural health monitoring is desired. This paper demonstrates a method for the detection and size estimation of impact damages in glass fibre reinforced polymers using capacitance measurements on integrated carbon fibre bundles. Therefore, individual rovings of glass fibre fabrics are replaced by carbon fibre rovings. After infusion of the laminate, the electrical capacitance is measured between the carbon fibre bundles. Damage in the form of matrix cracks or delaminations results in incorporated air that changes the permittivity of the material and, therefore, can be detected as a capacitance decrease. Considering the magnitude of capacitance decrease, a size estimation of the impacts is possible. Consequently, the presented method can be used for in-situ monitoring of damages in glass fibre reinforced polymers.

Optimization of laser cutting quality characteristics for basalt –glass hybrid composite using hybrid approach

In this research work, hybrid composite with combination of basalt fiber and glass fiber have been fabricated by the hand lay composite manufacturing technique. Moreover, its mechanical testing have been conducted. It has been perceived that fabricated hybrid composite has superior mechanical testing results. Precise machining of these composites is a tedious task. There are various limitations in conventional machining such as: fiber pullout, delamination, burr formation, crack formation in matrix etc., which can cause for poor machined surface and it also reduce mechanical performance of the hybrid composite. Laser machining can be one of the best alternative because of its non-contact nature with high production rate. In the present study, Artificial Neural Network (ANN) merged with genetic algorithm (GA) hybrid technique has been used to investigate the effects of machining parameters on responses.

Experimental Investigation on the Low Velocity Impact Response of Fibre Foam Metal Laminates.

The combination of fibre metal laminates (FML) and sandwich structures can significantly increase the performance under impact of FMLs. The goal of this work was to create a material that will combine the superior properties of FMLs and foam sandwich structures in terms of the impact resistance and simultaneously have lower density and fewer disadvantages related to the manufacturing. An extensive impact testing campaign has been done using conventional fibre metal laminates (carbon- and glass-based) and in the proposed fibre foam metal laminates to assess and compare their behaviour. The main difference was observed in the energy absorption mechanisms. The dominant failure mechanism for fibre foam laminates is the formation of delaminations and matrix cracks while in the conventional fibre metal laminate the main failure mode is fibre cracking due to high local stress concentrations. The reduction in the fibre cracking leads to a better after-impact resistance of this type of structure improving the safety of the structures manufactured with these materials.

Monitoring Damage in Nonoxide Composites at High Temperatures Using Carbon-Containing CVD SiC Monofilament Fibers as Embedded Electrical Resistance Sensors

Abstract Electrical resistance (ER) has become a technique of interest for monitoring SiC-based ceramic composites. The typical constituents of SiC fiber-reinforced SiC matrix composites, SiC, Si, and/or C, are semiconducive to some degree resulting in the fact that when damage occurs in the form of matrix cracking or fiber breakage, the resistance increases. For aero engine applications, SiC fiber reinforced SiC, sometimes Si-containing, matrix with a boron nitride (BN) interphase are often the main constituents. The resistivity of Si and SiC is highly temperature dependent. For high temperature tests, electrical lead attachment must be in a cold region which results in strong temperature effects on baseline measurements of resistance. This can be instructive as to test conditions; however, there is interest in focusing the resistance measurement in the hot section where damage monitoring is desired. The resistivity of C has a milder temperature dependence than that of Si or SiC. In addition, if the C is penetrated by damage, it would result in rapid oxidation of the C, presumably resulting in a change in resistance. One approach considered here is to insert carbon “rods” in the form of CVD SiC monofilaments with a C core to try and better sense change in resistance as it pertains to matrix crack growth in an elevated temperature test condition. The monofilaments were strategically placed in two nonoxide composite systems to understand the sensitivity of ER in damage detection at room temperature as well as elevated temperatures. Two material systems were considered for this study. The first composite system consisted of a Hi-Nicalon woven fibers, a BN interphase and a matrix processed via polymer infiltration and pyrolysis (PIP) which had SCS-6 monofilaments providing the C core. The second composite system was a melt-infiltrated (MI) prepreg laminate which contained Hi-Nicalon Type S fibers with BN interphases with SCS-ultramonofilaments providing the C core. The two composite matrix systems represent two extremes in resistance, the PIP matrix being orders of magnitude higher in resistance than the Si-containing prepreg MI matrix. Single notch tension–tension fatigue tests were performed at 815 °C to stimulate crack growth. Acoustic emission (AE) was used along with ER to monitor the damage initiation and progression during the test. Post-test microscopy was performed on the fracture specimen to understand the oxidation kinetics and carbon recession length in the monofilaments.

In-situ investigation of dynamic failure in [05/903]s CFRP beams under quasi-static and low-velocity impact loadings

In this paper, experimental work to investigate the failure sequence in cross-ply CFRP beams under quasi-static and low-velocity impact (LVI) loadings is presented. [05/903]s CFRP beams with thick clustered plies are investigated for clear observation of damage mechanisms. A non-standard LVI test setup is designed and built in order to conduct line impact experiments and to allow in-situ observation of damage evolution using a high-speed camera. Full-field strain measurement on the visible edge prior to initial failure is performed with digital image correlation (DIC) analysis. In both static and dynamic loading cases, failure sequence is demonstrated to initiate in the middle 90° plies as a diagonal matrix crack leading to delaminations at the upper and lower 0/90 interfaces. Major diagonal matrix crack formation is shown to occur consistently at a local transverse shear strain peak in conjunction with a tensile transverse normal strain. Two additional distinct types of matrix damage, namely hairline cracks and micro-matrix cracks, are discovered in post-mortem examination. Delamination propagation in a composite beam subjected to line loading is monitored using high-speed photography at half-a-million frames-per-second for the first time. It is observed that, in both static and impact cases, delaminations are not only dynamic, but they also reach the same speed plateau of 850 – 900 m/s. We suggest that the experimental crack tip speed data can be used as a benchmark to fine-tune interlaminar damage models.

Failure assessment of fiber metal laminates based on metal layer dispersion under dynamic loading scenario

In this study, tensile behavior of Glass Fiber Reinforced Polymer (GFRP) sandwiched with different thickness aluminium alloy layers were investigated at strain rates of the order 400–480 /s. The loading was induced through Spilt Hopkinson Tensile Bar (SHTB) setup and specimen size and shape were determined through Finite Element (FE) analysis by ensuring all damage modes should evolve inside the gauge region of the specimen. Three GLAss fiber REinforced (GLARE) aluminium laminates with top/bottom metal layers apart from the inside layer(s) were investigated. The idea is to observe the dynamic response of these laminates when they are sandwiched with no metal layer, one metal layer and two metal layers inside their lay-up configuration. They were named as 2/1–0.6, 3/2–0.4 and 4/3–0.2(O) laminates respectively. The FE analysis is used to observe the damages occurred within these laminates which are later compared with the experimental results. However, FE analysis results were able to investigate in-depth damage and failure occurring in these laminates unlike in experiments. Johnson-Cook (J-C) damage model was used as a material model for metal layer modeling while for GFRP a strain rate dependent 3D Hashin damage user-defined model is incorporated via VUMAT to observe the failure occur in these laminates. The interface delamination between the laminas were invoked through cohesive surface methodology. The GLARE laminates with metal layer(s) inside the configuration i.e. 3/2–0.4 and 4/3–0.2(O) laminates, was found to have comparable strength with GLARE having no metal layer inside the layup i.e. 2/1–0.6 laminate. From FE analysis it was noticed that the initiation of delamination due to the formation of matrix cracks in quasi-static loading was delayed in high strain rate loading as the strength in the matrix failure mode was higher due to rate sensitivity. However, the sequence of failure events occurring in these laminates like metal yielding, matrix failure, fiber failure accompanied with delamination remains same as in quasi-static loading.

Predicting the matrix cracking formation in symmetric composite laminates subjected to bending loads

The present study investigates analytically the effects of matrix crack formation on the properties of composite laminates subjected to bending loads, using a crack density-based model. For this purpose, by assuming that the plies prone for matrix cracking are sufficiently thin, the relationships of the stiffness reduction due to matrix cracking formation is applied. Then, by considering the equivalent damaged lamina and using the relationships of classical laminates theory (CLT), the variation of mechanical properties of symmetric laminates in the presence of matrix crack is calculated. In addition, a method is proposed to estimate the fracture toughness caused by the matrix crack in composite laminates by using the concept of finite fracture mechanics and calculating the energy release rate due to a matrix crack in a laminate under bending loading. Finally, the progressive growth of matrix crack in the cross-ply symmetric composite laminates is studied by applying the developed relationships into the nonlinear finite element code. The credibility of the proposed method is verified by comparing the obtained results with those achieved numerically and experimentally.

Adaptive cycle jump and limits of degradation in micromechanical fatigue simulations of fibre-reinforced plastics

This research investigates the influence of numerical parameters of micromechanical fatigue damage models on the obtained progressive damage behaviour of fibre-reinforced plastics at transverse tensile fatigue loads. The simulated damage behaviour is evaluated using experimentally observed crack patters published in the literature. The investigated numerical model parameters are (1) whether or not the model considers static failure within a simulated load cycle, (2) the degree of material property degradation after sudden failure and (3) the size of the cycle jump. The results reveal a significant influence of the degree of material degradation and of the cycle jump on the simulated matrix crack formation at both higher and lower fatigue loads. Static failure within a simulated load cycle primarily affects the damage behaviour at higher fatigue loads. The paper gives recommendations of the parameter choice for plausible progressive fatigue damage simulation results. Regarding the cycle jump, an adaptive algorithm is proposed and implemented. This approach leads to plausible fatigue damage results paired with a significant reduction of computation time comparing to a cycle-by-cycle analysis.

Low Velocity Impact Behavior of 3D Hollow Core Sandwich Composites Produced with Flat-Knitted Spacer Fabrics

Impact failure of newly-designed textile composites from three-dimensional integrated weft-knitted spacer fabrics (3D-IWK-SF) was aimed to be investigated under drop weight loading. Using a computerized flat knitting machine, three different 3D-IWK-SF as the composite reinforcements varied in their cross-sectional shapes, were produced from E-glass yarns. The produced fabrics were then impregnated with unsaturated polyester resin via the vacuum assisted resin transfer molding (VARTM) which eventually results in 3D integrated spacer weft-knitted sandwich composites (3D-IWK-SC). For comparing the results, an additional core/sheet sandwich composite composed of the same sheet and the polyurethane foam core was also fabricated. From the resulted values of contact force, it was concluded that 3D-IWK-SC of V-shaped crosssection had the highest resistance against low velocity impact load. On the other hand, the evaluated damaged area of both Vshaped 3D-IWK-SC and the foam core sandwich composites were lower than the other samples. Moreover, it was observed that matrix crack-formation in face-sheets of all samples as well as transversely propagated cracks at the connecting layers of 3D-IWK-SCs were of dominant failure modes under drop weight impact test, while no sign of face-core de-bonding were observed for all type of 3D-IWK-SCs.

Effects of flexural fatigue cycles on the internal friction behavior of SiCnws-C/C composites

After loaded for different cycles at stress level of fatigue limit, the internal friction behavior of SiC nanowires reinforced carbon/carbon (SiCnws-C/C) composites was investigated. Experimental results indicate that the fatigue limit of SiCnws-C/C composites is 70% of the static flexural strength. Influence of temperature on internal friction is correlated with the synergistic effect of SiC nanowires, pyrolytic carbon, as well as defects induced by fatigue load. For SiCnws-C/C composites, internal friction increases with the increasing fatigue cycles. The reason is attributed to the increasing interfacial sliding and friction induced by the formation of matrix cracks, interfacial debonding and interlayer delamination. Despite the matrix internal friction decreases a bit due to the increasing Van der Waals force between carbon layers, this partial reduction is smaller compared with the increased internal friction caused by interfacial sliding. Thus, the post-fatigued SiCnws-C/C composites still exhibit increased internal friction.

On the validity of LEFM methods to investigate the fracture behavior of angle-ply laminates

In this research, an experimental characterization of the interlaminar fracture behavior of unidirectional and multidirectional glass/epoxy laminates is presented under pure mode I loading. The delamination growth resistance curves are obtained by means of two different data reduction methods based on the LEFM and the J-integral approaches. The J-integral approach has great advantages over the standard LEFM approach. It removes the need for measurement of the delamination length. Moreover, it is not subjected to the strictly limited scope of LEFM, the validity of which is not guaranteed in the presence of damage mechanisms. This might be a great concern for multidirectional laminates where distributed damage in the form of matrix cracking is usually anticipated. The current standards do not provide any validity criteria for LEFM assumptions in multidirectional laminates. Any way, these data are often reduced with common standard methods. In this study it has been shown that the LEFM method provides comparable results with the J-based one for unidirectional laminates. However, it may grossly underestimate the fracture resistance of multidirectional laminates.