Undamaged Laminate Research Articles

Repairing damaged composite laminates using carbon fiber reinforced bulk mold compound

This work used short carbon fibers (SCFs) of different lengths to manufacture epoxy bulk mold compound (BMC) composites. Drop-weight-impact tests were performed on the intact carbon-fiber-reinforced-polymers (CFRPs) laminates to generate artificial damage. The damaged CFRP laminates were then repaired using the SCF-BMC composites. Compression after impact (CAI) tests were conducted to measure the compressive strength of the repaired laminates. Tensile properties and compressive properties of the SCF-BMC composites were also measured. The results show that 48-mm carbon fibers result in the largest tensile modulus, tensile strength, and compressive strength, while 12-mm carbon fibers result in the largest compressive modulus. CAI test results show that the compressive strength of the repaired laminate can be restored to 80.3% of that of the undamaged laminate. Therefore, SCF-BMC composites significantly contribute to repairing damaged composite laminates.

Visualization and investigation of healing mechanism in carbon fiber reinforced Elium® composites

In this study, carbon fiber/Elium® composites are manufactured using the resin infusion manufacturing technique. Artificial cracks representing impact-induced delamination are incorporated during layup. The laminates are subsequently healed using several healing parameters. The bonding mechanisms are investigated through microscopic analyses and X-ray Computed Tomography (XCT). The mechanical performance of the healed composites is investigated through four-point bending tests. It is found that as the healing temperature is increased, the cracks are gradually healed by interdiffusion and macroscopic resin flow across each crack interface. The 3D models generated from XCT images show an increase in solid volume fraction from 48% to 70% at the optimum healing parameters. The flexural strength and flexural modulus of the undamaged composites subjected to optimized healing condition are significantly increased relative to the room temperature cured pristine samples. The residual flexural strength of the damaged samples healed at the optimum parameters is 96% of the reference condition. The SEM images confirm that delamination from the previously-healed crack interfaces is the most dominant failure mode in the healed samples, in contrast to fiber fracture and brittle failure in the undamaged reference composite samples. The results show that the damaged composite laminates can be effectively healed and repaired to as good as undamaged laminates using the interdiffusion mechanism.

Bending Stiffness of Damaged Cross-Ply Laminates

The bending stiffness of carbon/epoxy and glass/epoxy cross-ply laminates with intralaminar cracks in the surface 90° plies and local delaminations were studied experimentally using 4-point bending tests. The bending stiffness is defined as the slope of the relation between the applied bending moment and the corresponding midplane curvature. To measure the midplane curvature of laminates with different damage states, the digital image correlation system was used. The reduction in the bending stiffness with increasing density of transverse cracks and delamination length was also analyzed using a 3-D FEM model. The analysis and optical microscopy observations showed that, in the initial stage of damage evolution, local delaminations were small, but with increasing load, the delaminations grew rapidly from the tips of existing and newly created cracks, enhancing the bending stiffness degradation. As an alternative to the 3-D FEM modelling of the test, analytical approaches in conjunction with the classical laminate theory were suggested. The analytical approach was based on the concept of the “effective stiffness of damaged ply,” where the initial stiffness of the damaged ply was replaced by the effective stiffness depending on the damage state. In the present work, two routines were used to determinate the effective stiffness of the damaged ply: a) back-calculation from the difference in the stiffnesses of damaged and undamaged laminates employing the FEM model of the representative volume element; b) simple analytical fitting functions. It is shown that the analytical approach suggested is accurate and convenient for predicting the degradation of bending stiffness of a laminate with an evolving microdamage.

A FINITE ELEMENT ANALYSIS OF CRITICAL BUCKLING LOAD OF COMPOSITE PLATE AFTER LOW VELOCITY IMPACT

Composite is a material formed from two or more materials that macroscopically alloyed into one material. Nowadays, composite has been generally applied as lightweight structure of aircraft. This is due to the fact that composites having high strength-to-weight ratio. It means the composites have the capability to take on various loads, despite their lightweight property.Laminate composite is one type of composite that has been generally used in aircraft industries. This type of composite is susceptible to low-velocity impact induced damage. This type of damage can be happening in manufacture, operation, or even in maintenance. Low-velocity impact could cause delamination. Delamination happens when the plies of laminated composites separated at the interface of the plies. This type of damage is categorized as barely visible damage, means that the damage couldn’t be detected with visual inspection. Special method and tool would be needed to detect the damage. Delamination will decrease the strength of the laminated composite.Delamination can be predicted with numerical simulation analysis. With increasing capability of computer, it is possible to predict the delamination and buckling of laminated composite plate. This research presents the comparisons of buckling analysis results on laminated plate composite and damaged laminated plate composite. By the result of LVI simulation, it is shown that low velocity impact of 19.3 Joule causing 6398 mm2 C-Scan delamination area inside the laminated composite. The delamination causing structural instability that will affect buckling resistance of the plate. The result of analysis shows that the existence of delamination inside laminate composite will lower its critical buckling load up to 90% of undamaged laminate’s critical buckling load.Keywords : composite, laminate, delamination, buckling.

PROGRESSIVE FAILURE ANALYSIS OF HELICOPTER ROTOR BLADE UNDER AEROELASTIC LOADING

Unlike metal structure, composite structures don’t give any clue till the fatal final collapse. The problem is more complicated when applied load on the structure is aeroelastic in nature. Under such loading, composite laminate experiences stresses. The first layer failure happens when stresses in the weakest ply exceed the allowable strength of the laminate. This initial layer-based failure changes overall material characteristics. It is important now to degrade the composite laminate characteristics for the subsequent failure prediction. The constitutive relations are required to be updated by the reduction in stiffness. The rest of the undamaged laminates continue to take the load till the updated strength is reached. In the present work, layer wise progressive failure analysis under aeroelastic loading has been performed by the inclusion of different failure criteria which allow for the identification of the location of the failure. ANSYS APDL environment has been used to model geometry of helicopter rotor. Under the loading conditions, stresses are calculated in the blade. Using stress tensor and failure criteria, failure location and modes have been predicted. It has been found that failure starts at higher speeds and failure starts from the root chord and tend towards the tip chord.

Electromagnetic modeling of damaged fiber-reinforced laminates

As a prerequisite to nondestructive testing of damaged fibered laminates, the Green's function, corresponding with an undamaged structure, and the electromagnetic fields associated with the damaged one are investigated herein. For the undamaged fibered laminate, benefiting from the periodicity of the fibers within each layer, the field solution follows the scattering-matrix-based method using the Floquet theorem. Yet, the periodicity is destroyed by the analytical source (for the Green's function) or by damages, and the Floquet theorem cannot be directly applied to compute the associated scattering matrices. The array scanning method is introduced to that effect. Inserting fictitious sources to get a quasi-periodic source array, the modeling approach for undamaged laminates can be used to compute the field with the source array, the integration of which cancels the effects of the fictitious sources and yields the Green's function. With the multipole method, field disturbances by damages, which include missing, displaced, shrunk, and expanded fibers and circular inclusions inside fibers, are accurately modeled by setting equivalent sources inside sound fibers, and the array scanning method applies. Modeling accuracy and efficiency of the approaches are illustrated by numerical simulations.

Assessment of Residual Elastic Properties of a Damaged Composite Plate with Combined Damage Index and Finite Element Methods

In structural component applications the use of composite materials is increasing thanks to their optimal mechanical characteristics. However, the complexity of the damage evolution in composite materials significantly limits their widespread diffusion. Non-destructive tests are thus becoming ever more important. The detecting Damage Index ( D I d ) technique has been recently brought in the realm of the non-destructive characterization tests for components made of composite material. In contrast to other techniques, this methodology allows to quantitatively assess local residual properties. In this paper, the D I d technique is adopted in combination with the finite element method. The mechanical response of two composite plates (an 8-layer twill fabric carbon/epoxy) subjected to four-point bending test is firstly used to tune a finite element model of the laminate. Then, an undamaged laminate of the same composite material is progressively damaged through repeated four-point bending tests. Local residual elastic properties are mapped on the plate through the D I d technique. A continuous polynomial curve has been considered to account for the variation of the elastic modulus in the finite element model. The resulting force-displacement curve of the numerical analysis is compared to experimental data of damaged plate, resulting in very good agreement. The combination of the experimental activity and the numerical finite element analysis points out the accuracy of the D I d methodology in assessing local residual elastic properties of composite materials.

On quantifying damage severity in composite materials by an ultrasonic method

This work reports a study aimed at quantifying damage severity in composite materials by an in-field inspection technique known as Acousto-Ultrasonics (AU) where Lamb waves are transmitted through a damage zone by exciting a pulse onto the composite surface and capturing the received waves after their interactions with the damage. It builds on a previous study that proposed as quantitative descriptors of the received signal a set of stress wave factors (SWFs) extracted from the power spectral density (PSD) distribution of the AU signal. The SWFs were previously shown to detect the spatial extent of impact damage, but the severity of the damage within the impact damage zone was not quantified. The present study takes a step in the direction to achieve that goal. Lamb waves are transmitted through a cross ply laminate in which transverse ply cracks of increasing density (number of cracks per unit axial length) are induced. The PSD distribution is first analyzed for the case of an undamaged laminate and then the SWFs are correlated with the crack density. The implications of the correlations obtained and the future prospects of quantifying the damage severity by such correlations are discussed.

Condition Monitoring of Wind Turbine Blades Using Active and Passive Thermography

The failure of wind turbine blades is a major concern in the wind power industry due to the resulting high cost. It is, therefore, crucial to develop methods to monitor the integrity of wind turbine blades. Different methods are available to detect subsurface damage but most require close proximity between the sensor and the blade. Thermography, as a non-contact method, may avoid this problem. Both passive and active pulsed and step heating and cooling thermography techniques were investigated for different purposes. A section of a severely damaged blade and a small “plate” cut from the undamaged laminate section of the blade with holes of varying diameter and depth drilled from the rear to provide “known” defects were monitored. The raw thermal images captured by both active and passive thermography demonstrated that image processing was required to improve the quality of the thermal data. Different image processing algorithms were used to increase the thermal contrasts of subsurface defects in thermal images obtained by active thermography. A method called “Step Phase and Amplitude Thermography”, which applies a transform-based algorithm to step heating and cooling data was used. This method was also applied, for the first time, to the passive thermography results. The outcomes of the image processing on both active and passive thermography indicated that the techniques employed could considerably increase the quality of the images and the visibility of internal defects. The signal-to-noise ratio of raw and processed images was calculated to quantitatively show that image processing methods considerably improve the ratios.

A study of tensile residual strength of composite laminates under different patch-repaired series

The tensile behavior of composite laminate structures repaired by bonding external patches was studied in the paper. Two different types of patches including wedge patches and inverted wedge patches were used and failure mechanisms, failure load and strength predictions were studied. A convenient and fast method of building 2-D finite element modeling (FEM) of laminate structure repaired was proposed and the strength of repaired laminate structures was calculated by FEM. The results showed that more than 80% tensile strength of the undamaged laminate could be recovered by bonding patch repairs. Moreover, the results indicated that the strength of inverted wedge patches repair were higher than that of wedge patches repair. FEM simulation results indicated that high stress concentration was found along the edges of invert patches and the most weakness part located in the adhesive bondline. FEM analysis results showed that the strength predicted matched well with the test strength.

Stress distributions and mechanical properties of laminates [θm/90n]S with closed and open cracks in shear loading

The classical elastic theory of laminates states that the transverse normal stresses in the local axis of the 90° layer of an undamaged laminate [θm/90n]S are positive due to in-plane shear force, the transverse normal stresses will be negative when the shear load is inthe oppositedirection. For the laminate [θm/90n]S with transverse matrix cracks, the cracks in the 90°-layer should be open for the tensile stress and closed for the compressive stress. Therefore, two cases of the transverse cracks in the unbalanced laminates subjected to shear loading are studied such that the cracks are open for one case and the cracks are closed for another case. A stress-based variational model is developed to study the effective in-plane compliance and the stress distribution in symmetrical laminates with two different types of transverse matrix cracks in 90°-ply under an in-plane shear loading. The inter-laminar shear stresses are assumed to be in the form of general functions. A partition coefficient λ is introduced into the normal stresses σx for the closed cracks. The expressions of the stress components for the closed and the open cracks are obtained from the equilibrium equations and the boundary conditions, respectively. The governing equations for the two types of cracks are also derived using a variational approach with the principle of minimum complementary energy. In addition, analysis of strain energy and analysis of deformation on surface are used to estimate the effective in-plane shear properties of the laminates. The coupling coefficients and the shear elements in the compliance matrix are investigated for the two types of cracks. The distributions of the in-planar and the inter-laminar stresses are also presented. Limits of the compliance elements and the stress distributions at the infinite crack density are compared to the results of the classical theory of laminates.

Transverse crack onset and growth in cross-ply [formula omitted] laminates under tension. Application of a coupled stress and energy criterion

Crack initiation in the inner ply of symmetric [0/90]s laminates under tension is studied applying the coupled stress and energy criterion proposed by Leguillon (Eur. J. Mech. A/Solids 21, 2002) in the framework of the finite fracture mechanics. This criterion assumes that a crack of a finite extension appears abruptly when the stress criterion is fulfilled and this crack onset is energetically admissible.The stress state is calculated by applying the laminate theory to the undamaged laminate which provides explicit expressions to be used in the stress criterion. Assuming generalised plane strain, the magnitude involved in the (incremental) energy criterion is evaluated numerically by means of a boundary element code and a dimensional analysis. The two criteria lead to a theoretical model providing explicit expressions of the critical parameters for the crack onset, which depend only on the computational results through a scalar value.This model predicts that the crack grows unstably after the onset in the inner ply and is arrested close to the interface between the plies for a length larger than a certain threshold length independent of the fracture and strength properties. This threshold length depends only on the elastic and geometric properties of the laminate. The model also predicts the existence of a size effect which agrees with the experimental results found in the literature. In addition, the model provides a physical interpretation of this size effect.

Derivations of energy-based modelling for ply cracking in general symmetric laminates

Recently, as a part of the third World-Wide Failure Exercise (WWFE-III), the author provided a modelling capability, entitled ‘Energy methods for modelling damage in laminates’, published in this special issue (2013, Vol 20–21, pages 2613–2640). This paper describes full details and the mathematical basis of the author’s methods used to predict the properties of undamaged laminates and the development of damage in laminates, based on an energy balance methodology.

Single Transducer Pair Lamb Wave Time Reversal for Damage Detection in Composite Laminates

This paper investigates the potential of single transducer pair guided waves time reversal to detect damage in composite laminates. According to dynamic reciprocity of Lamb waves propagation in linear media, the time reversal process should reconstruct the original signal. The similarity of original and reconstructed time signals is calculated for different damage types using numerical and experimental studies with the aim to investigate, if the interaction of the wave pulse with inhomogeneities introduces any nonlinearity that time reversibility breaks down and single transducer pair time reversal could be used as damage diagnostics tool. 3D explicit finite element analysis is used for the numerical simulation and laser Doppler vibrometry is used to capture out-of-plane displacement time histories excited by an adhesively bonded piezoceramic transducer disc in the experimental time reversal process. In the case of an undamaged composite laminate the similarity index used to quantify the similarity of the original and reconstructed wave pulses is better than 95%. The similarity index is smaller for laminates with artificial damages including embedded fluoro polymer films to simulate delamination damage, through holes and bonded mass inhomogeneities. Although numerical and experimental similarity indices are smaller at higher frequencies, there is no clear evidence that single transducer pair time reversibility breaks down and represents a reliable damage diagnostics tool.

Compression after impact strength of thin laminates with various percentage of 0° plies

Conventional wisdom dictates that adding more 0° plies in the load-bearing direction of a laminate will increase its stiffness and strength. While this is true for undamaged laminates, the compression strength of laminates with impact damage may not be as straightforward. In this study, compression after impact strengths of relatively thin laminates with 25%, 33% or 50% of plies aligned in the 0° load-bearing direction were measured for three different damage severity levels. Results show that the increase in compression strength of the laminates with a higher percentage of plies in the 0° direction is lessened as impact damage severity increases indicating that a laminate that is stronger in compression when undamaged may not be stronger in compression when impact damage is accounted for.

Energy-based delamination theory for biaxial loading in the presence of thermal stresses

Abstract This paper addresses the issue of using energy balance methods and crack closure concepts to predict the growth of delaminations associated with ply cracks during the progressive loading of cross-ply laminates subject to a combination of in-plane biaxial stresses and thermal residual stresses. When the effective applied stresses and the temperature are held fixed during delamination growth, and there is negligible interaction of the delamination tips with the ply cracks, very simple analytical formulae for the energy release rate can be derived for unconstrained and generalised plane strain conditions, which are exact when the ply crack separation tends to infinity. In some practical applications, such as for wide plates, delamination growth is constrained transversely by surrounding undamaged laminate and this has an effect on energy release rates. An analytical method is described that determines the energy release rate for delamination growth under such constrained conditions. This result is also exact in the limit of ply crack separations tending to infinity. The boundary element method (BEM) has been used to investigate energy release rates for constrained conditions for a range of ply crack densities, both in the presence and absence of thermal residual stresses, for a special case where the delamination tips are mid-way between neighbouring ply cracks. BEM results show a slight dependence of the energy release rate on ply crack separation, and predictions for the maximum ply crack separation considered are within 1.6% of the exact limiting analytical predictions valid for infinite separation. This agreement indicates the validity of both the analytical methods used, and the numerical analysis based on the BEM.

Through-thickness reinforcement repair of delaminated carbon–epoxy panels

This paper outlines a through-thickness reinforcement repair (TTRR) technique for delaminated polymer matrix composite (PMC) laminates. This involves drilling holes through the delaminated region and bonding pins into these holes. An experimental study was conducted to assess the effectiveness of the technique to restore the compression strength of laminates with a hole that were deliberately delaminated by controlled lateral loading. The TTRR technique was found to be highly effective, with eight pins bonded in a ring at the mid-span of the circular delamination restoring the compression strength to 93% that of the undamaged laminate. A further increase in pin density was found to provide no additional improvement in the repair efficacy.

Stiffness Degradation in Hygrothermal Aged Cross-Ply Laminate with Transverse Cracks

Stiffness degradation resulting from 90-deg ply cracking in hygrothermal aged cross-ply laminates is analyzed. First, the material properties of the composite are affected by the variation of temperature and moisture and are based on a micromechanical model of laminates. Consequently, the hygrothermal conditions degrade the stiffness of the laminate. On the other hand, when this latter is subjected to tensile mechanical loading, the early stage of damage is dominated by matrix cracking in the transverse plies; its presence causes stiffness reduction and can be detrimental to the strength of the laminate. In this investigation, a modified shear-lag analysis, taking into account the hygrothermal effect on the material properties of the laminate, is employed to evaluate the effect of transverse cracks on the stiffness reduction in the hygrothermal aged cross-ply laminated composites. The results represent well the dependence of the degradation of elastic properties on the crack density and hygrothermal conditions. Nomenclature E f =Y oung’s modulus of the fiber E L = longitudinal Young’s modulus Em =Y oung’s modulus of the matrix ET = transverse Young’s modulus Ex =Y oung’s modulus of the damaged laminate Ex0 =Y oung’s modulus of the undamaged laminate G f = shear modulus of the fiber GLT = longitudinal shear modulus of ply Gm = shear modulus of the matrix GTT’ = transverse shear modulus h0 = ply thickness l0 = half-crack spacing Nx = applied load R = stress perturbation function S ij = compliance matrix of the unidirectional ply t0 = thickness of the 0-deg layer

The Integrity of Polymer Composites during and after Fire

This paper reports on changes to the mechanical properties of woven glass laminates with polyester, vinyl ester and phenolic resins during fire exposure. Two sets of experiments were carried out. First, unstressed laminates were exposed to a constant one-sided heat flux (50 kW m 2) for various times, and the residual post-fire strength at room temperature was reported. In a second series of experiments, laminates were tested under load. The times corresponding to a given loss of properties were 2-3 times shorter than in the previous case. It was found in both cases that modes of loading involving compressive stress were more adversely affected by fire exposure than those involving tension. A simple ‘two-layer’ model is proposed, in which the laminate is assumed to comprise (i) an unaffected layer with virgin properties and (ii) a heat-affected layer with zero properties. For residual properties after fire, the ‘effective’ thickness of undamaged laminate was calculated using this model and compared with measured values. A thermal model was employed to predict the temperature and the residual resin profile through the laminate versus time. Comparing the model predictions with the measured values of effective laminate thickness enabled simple criteria to be developed for determining the position of the ‘boundary’ between heat-affected and undamaged material. For post-fire integrity of unloaded laminates, this boundary corresponds to a Residual Resin Content (RRC) of 80%, a criterion that applies to all the resin types tested. For polyester laminate under load in fire, the boundary in compressive loading (buckling failure) appears to correspond to the point where the resin reaches 170 C. In tensile loading, significant strength is retained, because of the residual strength of the glass reinforcement. The model was used to produce predictions for ‘generic’ composite laminates in fire.

Modelling residual mechanical properties of polymer composites after fire

A thermomechanical modelling approach is proposed for estimating the residual properties of fibre reinforced polymer composites damaged by fire. The modelling was carried out in two parts: (i) prediction of the extent of thermal decomposition (or charring) using a thermal model; and (ii) prediction of the post-fire behaviour using a two layer model that combines the properties of the undamaged laminate and the residual char. Fire experiments were performed on glass-polyester, vinyl ester, and phenolic laminates using a cone calorimeter operated at heat fluxes in the range 25-100 kW m 2, for times up to 30 min. After cooling to room temperature the thickness of the thermal damage layer was determined, along with values of the residual tensile, compressive and flexural properties. For the 'two layer' model it was found that the effective boundary between char material and undamaged laminate corresponded to the point where the residual resin content (RRC) of the laminate was 80%. Surprisingly, this value was found to hold for all three resin types tested. Using this RRC value, excellent agreement was found between the measured and predicted post-fire char thickness and the residual mechanical properties. The approach presented is the first reliable method for accurately predicting the residual properties of composites after fire.