Transverse Matrix Cracking Research Articles

Synergistic Damage Mechanic Model for Stiffness Properties of Early Fatigue Damage in Composite Laminates

In the initial period of the life in the composite laminates, the principal types of damage are diffused ones, such as matrix crack, diffused fiber breaking and local delamination. On account of these diffused damages, a synergistic damage mechanic model was proposed for the stiffness properties. The model included the microcosmic responses of the physical damage and macroscopic performance of the material's stiffness. In micro-level, mesoscopic RVE(representative volume element) model was established to obtain crack opening displacement and crack sliding displacement, which were used to define the damage tensor. In macro- level, through homogenizing the material strain and the surface displacement of the damage, the relationship of the stiffness matrix of unidirectional laminate or laminates in damage statue and damage tense was set up. Due to restriction of NDT (non- destructive testing) technology development, only the constitutive relations of matrix cracks were constructed. The influences of the transverse matrix cracks on the stiffness properties of the laminates [0/±45]s was analyzed with the present model and showed that it is capable to predict the reduction of the stiffness properties resulted from the fatigue diffused damage in the laminates.

Electrical Resistance of SiC Fiber Reinforced SiC/Si Matrix Composites at Room Temperature during Tensile Testing

The implementation of Ceramic Matrix Composites necessitates the understanding of stress‐dependent damage evolution. Toward this goal, two liquid silicon infiltrated SiCf reinforced SiC composites were tensile tested with electrical resistance (ER) monitoring as well as acoustic emission to quantify matrix cracking. ER was modeled using a combination of resistors in series and parallel to model transverse matrix cracks and fiber/matrix segments between matrix cracks. It is shown that resistance change is sensitive to transverse matrix crack formation and stress‐dependent debonding length. The model appears to be accurate up to the stress for matrix crack saturation.

Fatigue analysis of piezoelectric microdevice based on a continuum damage model

The utilization of piezoelectric materials in MEMS devices under harsh environments has gained affordable appreciations due to its unique mechanical and electrical material properties. However, the reliability of MEMS devices triggered by fatigue damage remains elusive and needs to be further explored. Here, we present a continuum constitutive model for piezoelectric materials containing a substantive amount of randomly dispersed microcracks. The constitutive equation of the piezoelectric materials with microcracks is formulated via Helmholtz free energy by combining the Kachanvo damage evolution law and the Chaboche fatigue damage development to express the fatigue damage growth. A case of the fatigue damage analysis of the piezoelectric microplate with transverse matrix cracks in the status of plane stress is presented by adopting the von Karman’s plate theory. With numerical schemes employed, the effect of cyclic impulsive loadings and electrical loadings on the fatigue damage and fatigue life prediction of a piezoelectric microplate is investigated and discussed. The findings provide valuable insights into the fundamental mechanism of reliability in piezoelectric MEMS devices due to cyclic loadings, thereby offering new ways to exploit and fabricate the piezoelectric-based MEMS devices suitable for harsh conditions.

Modelling of Multi-Axial Ultimate Elastic Wall Stress (UEWS) Test for Glass Fibre Reinforced Epoxy (GRE) Composite Pipes

This paper describes the modeling of multiaxial ultimate elastic wall stress (UEWS) at room temperature for glass fibre reinforced epoxy (GRE) composite pipes. The model developed, predicts the stress-strain response caused by the combined, static and cyclic of UEWS loading taking into effects of transverse matrix cracking within the laminates. The procedure, although not a standard method, seems to provide a good alternative to the current raw materials' re-qualification procedure delineated in ISO 14692 through ASTM D2992. The effective transverse and shear modulus of the lamina due to increasing presence of transverse matrix cracking were estimated. Classical laminate analysis was then applied to compute the corresponding ply properties as a function of increasing stress and strain. The model shows a good agreement with the experimental results of multiaxial UEWS tests on ±55° filament wound glass-reinforced epoxy pipes.

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.

Predicting residual stiffness of cracked composite laminates subjected to multi-axial inplane loading

This is a contribution to the exercise that aims to benchmark and validate the current continuum damage and fracture mechanics methodologies used for predicting the mechanical behaviour of fibre-reinforced plastic composites under complex loadings. The paper describes an analytical approach to predict the effect of intra- (matrix cracking and splitting) and inter-laminar (delamination) damage on the residual stiffness properties of the laminate, which can be used in the post-initial failure analysis, taking full account of damage mode interaction. The approach is based on a two-dimensional shear lag stress analysis and the equivalent constraint model of the damaged laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of a multidirectional laminate with multilayer intra- and inter-laminar damage is demonstrated for [Formula: see text] and [Formula: see text] cross-ply laminates made from a specific glass/epoxy system under in-plane uniaxial and biaxial loading damaged by transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delamination.

Effect of insulation layer for thermal shock in cryogenic composite laminates

AbstractThe structural weight of a cryogenic propellant tank for reusable launch vehicles (RLVs) can be effectively reduced by the use of advanced composite materials. However, microscopic damage such as transverse matrix cracks (TMC) and delaminations are prone to develop in composites well below the load levels that would result in mechanical failure. This microscopic damage leads to a leakage path for the fuel. The leakage is influenced by many factors including connectivity of the cracks, residual and service‐induced stresses, and composite stacking sequence. This article is concerned with the effect of thermal gradients due to sudden exposure to a cryogenic temperature with and without insulation layer. An investigation of the insulation layer for sudden exposure to cryogenic temperatures is conducted numerically. The exposure of the harsh environment could make the damages such as delaminations, TMC, and leakage path. The defects from manufacturing could be formed, and they are critical parts under sudden exposure to cryogenic temperature. Therefore, the qualitative analysis for insulation technique is needed. The results from this article are very important because the stress levels which cause damages can be predicted and also controlled using the insulating techniques. The insulation skill which can suppress the stress levels is newly introduced in this article for RLV cryogenic fuel tank. Moreover, the effect of lay‐ups is also investigated in this article. The thermal gradient can be controlled by using different lay‐ups. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers

A finite element analysis of impact damage in composite laminates

AbstractIn this work, stress-based and fracture mechanics criteria were developed to predict initiation and evolution, respectively, of intra- and inter-laminar cracking developed in composite laminates subjected to low velocity impact. The Soutis shear stress-strain semi-empirical model was used to describe the nonlinear shear behaviour of the composite. The damage model was implemented in the finite element (FE) code (Abaqus/Explicit) by a user-defined material subroutine (VUMAT). Delamination (or inter-laminar cracking) was modelled using interface cohesive elements and the splitting and transverse matrix cracks that appeared within individual plies were also simulated by inserting cohesive elements between neighbouring elements parallel to the fibre direction in each single layer. A good agreement was obtained when compared the numerically predicted results to experimentally obtained curves of impact force and absorbed energy versus time. A non-destructive technique (NDT), penetrant enhanced X-ray radiography, was used to observe the various damage mechanisms induced by impact. It has been shown that the proposed damage model can successfully capture the internal damage pattern and the extent to which it was developed in these carbon fibre/epoxy composite laminates.

Benchmark solution for degradation of elastic properties due to transverse matrix cracking in laminated composites

Degradation of laminate moduli and laminate coefficients of thermal expansion, as well as degradation of the cracked lamina moduli and lamina coefficients of thermal expansion, are predicted as a function of crack density for laminated composites with intralaminar matrix cracks. The methodology assumes linear elastic behavior and periodicity of the transverse cracks. The representative volume element is discretized into finite elements. Stress free conditions on the crack surfaces are enforced. Periodic boundary conditions are applied so that any state of applied far-field strain can be simulated. An averaging procedure is used to yield the average stress field. Three uniaxial states of strain and a null state of strain coupled with a unit increment of temperature are used to obtain the degraded stiffness and coefficients of thermal expansion. Results are presented for a number of laminates and materials systems that are customarily used in the literature for experimentation. The modeling approach and results can be used to assess the quality of approximate models. Comparisons are presented to the predictions of one such model and to experimental data. Also, comparisons are presented to classical lamination theory for asymptotic values of crack density.

Structural composites hybridized with epoxy compatible polymer/MWCNT nanofibrous interlayers

Surface reactive P(St-co-GMA) copolymer and P(St-co-GMA)/MWCNT fibrous mats are placed onto a conventional carbon fiber/epoxy prepreg as interlayer reinforcing material. Experimental observations are used to demonstrate excellent epoxy wetting and structural compatibility of the interlayers chemically tuned for the epoxy matrix. Comparisons of increase in mechanical performance by incorporating P(St-co-GMA) and P(St-co-GMA)/MWCNT interlayers also show the contribution of MWCNT presence in the copolymer nanofibers. Flexural strength and stiffness of (0/0/0) and (90/0/90) laminates increase up to 17% when the nanocomposite interlayers are integrated. Cross-sectional SEM analyses of the failure surfaces suggest reinforcing ability of interlayers both against transverse cracking and delamination. Further examination for the delamination resistance is presented by the End Notched Flexure (ENF) tests. An improvement up to 70% in mode II strain energy release rate (GIIc) is recorded for the laminates with nanocomposite interlayers. The resistance against transverse matrix cracking in the presence of interlayers is also elaborated. Charpy-impact and transverse-tension tests result in up to 20% and 27% increase in the impact energy absorbance and transverse tensile strength, respectively. Overall, the test results suggest that mechanical behavior of the laminates is enhanced by the nanofibrous interlayers chemically-tuned for epoxy crosslinking, with no weight penalty.

Modeling composite wing aeroelastic behavior with uncertain damage severity and material properties

The effect of uncertain material properties and severity of damage on the aeroelastic behavior of a finite element composite wing model are predicted by applying the Polynomial Chaos Expansion method (PCE). Different damage modes, including the transverse matrix cracking and broken fibers, are induced into pre-defined locations in the laminates and the aeroelastic stability and dynamic response of the wing due to “1-cosine” vertical gusts are evaluated. For this purpose, PCE models that predict the variation due to uncertainty of the flutter speed and an “Interesting Quantity” (root shear force) of the wing box are developed based upon a small sample of observations, exploiting the efficient Latin Hypercube sampling technique. The uncertainty propagation on the output responses, in the form of probability density functions, is evaluated at low computational cost, implementing the PCE models and verified successfully against the actual results.

Statistical modeling for the accumulation of transverse matrix cracking in cross‐ply laminates

AbstractA statistical model has been proposed to predict the evolution of matrix cracking in the transverse lamina of cross‐ply laminates subjected to longitudinal tensile loading. The analytical model is based on a fracture mechanics approach which considers that the critical fracture toughness Gc of the 90° layers is not a constant but follows a Weibull distribution. Monte‐Carlo simulation technique is applied to predict the initiation and propagation of transverse cracking in terms of applied stress versus crack density. The effects of the thickness of the 90° layers on progressive damage and failure are also discussed in this study. Good agreements are reached between simulation and experimental results. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers

Damage Analysis of CFRP under Impact Fatigue

In recent years carbon fibre reinforced polymers (CFRPs) have become some of the most important structural materials in the aerospace industry due to their excellent stiffness and strength to weight ratios. The real-life loading histories of aerospace composite components and structures involve the generation of transient loads that can propagate as cyclic impacts. This phenomenon is known as impact fatigue (IF). Such loads can cause various types of damage in composites, including fibre breakage, transverse matrix cracking, de-bonding between fibres and matrix and delamination, resulting in a reduction of residual stiffness and a loss of functionality.

Damage Analysis of CFRP under Impact Fatigue

In recent years carbon fibre reinforced polymers (CFRPs) have become some of the most important structural materials in the aerospace industry due to their excellent stiffness and strength to weight ratios. The real-life loading histories of aerospace composite components and structures involve the generation of transient loads that can propagate as cyclic impacts. This phenomenon is known as impact fatigue (IF). Such loads can cause various types of damage in composites, including fibre breakage, transverse matrix cracking, de-bonding between fibres and matrix and delamination, resulting in a reduction of residual stiffness and a loss of functionality.The effects of IF are of major importance due its detrimental effect on the performance and reliability of components and structures after relatively few impacts and low force levels compared to those in a standard fatigue regime. This study employs a unique testing system with the capability of subjecting specimens to fully instrumented repetitive impact loading. The main aim of this paper is to provide results elucidating the effect of IF on the damage behaviour of CFRP specimens. A detailed damage analysis is implemented utilising an X-ray micro computed tomography (CT) system.

3D damage characterisation and the role of voids in the fatigue of wind turbine blade materials

The fatigue mechanisms of Glass Fibre Reinforced Polymer (GFRP) used in wind turbine blades were examined using computed tomography (CT). Prior to mechanical testing, as-manufactured [+45/−45/0] 3,s glass/epoxy specimens were CT scanned to provide 3-dimensional images of their internal microstructure, including voids. Voids were segmented and extracted, and individual characteristics and volumetric distributions were quantified. The coupons were then fatigue tested in uniaxial loading at R = −1% to 40% of the nominal tensile failure stress. Some tests were conducted to failure for correlation with the initial void analysis and to establish failure modes. Other tests were stopped at various life fractions and examined using CT to identify key damage mechanisms. These scans revealed transverse matrix cracking in the surface layer, occurring predominantly at free edges. These free-edge cracks then appeared to facilitate edge delamination at the 45/−45° interface. Propagation from sub-critical, surface ply damage to critical, inner ply damage was identified with either a −45/0° delamination, or a 0° fibre tow failure allowing a crack to propagate into the specimen bulk. Final failure occurred in compression and was characterised by total delamination between all the 45/−45° plies. A quantitative void analysis, taken from the pre-test CT scans, was also performed and compared against the specimens’ fatigue lives. This analysis, to the authors’ knowledge the first of its kind, measured and plotted approximately 10,000 voids within the gauge length of each specimen. The global void measurement parameters and distributions showed no correlation with fatigue life. A local ply-level investigation revealed a significant correlation between the largest void and fatigue life in the region of the laminate associated with the crack propagation from sub-critical to critical damage.

Fatigue tensile behavior of carbon/epoxy composite reinforced with non-crimp 3D orthogonal woven fabric

An experimental study of the in-plane tension–tension fatigue behavior of the carbon fiber/epoxy matrix composite reinforced with non-crimp 3D orthogonal woven fabric is presented. The results include pre-fatigue quasi-static test data, fatigue life diagrams, fatigue damage progression, and post-fatigue quasi-static test data for the warp- and fill-directional loading cases. It is revealed that the maximum cycle stress corresponding to at least 3 million cycles of fatigue life without failure, is in the range of 412–450 MPa for both loading directions. This stress range is well above the static damage initiation threshold and significantly above the first static damage threshold (determined by the onset of low energy acoustic emission). The second static damage threshold, determined by the onset of high energy acoustic emission and related to the appearance of local debonds and intensive transverse matrix cracking falls within this range. The established correlation between a 3000,000 cycle fatigue stress limit on one side and the second static damage threshold stress on the other is of a high practical importance, because it will significantly reduce the amount of future fatigue tests required for this class of composites. Surprisingly, for equal maximum cycle stress level, the fatigue life under fill-directional loading appears about three times shorter than that under warp-directional loading. The 100,000 cycle, 500,000 cycle and 1000,000 cycle fatigue loading with 450 MPa maximum cycle stress has resulted in so high variations of post-fatigue static modulus, strength and ultimate strain, that no consistent and statistically meaningful trends could have been established; further extensive experimental studies are required to reliably quantify this effect.

The role of matrix cracks and fibre/matrix debonding on the stress transfer between fibre and matrix in a single fibre fragmentation test

The single fibre fragmentation test is commonly used to characterise the fibre/matrix interface. During fragmentation, the stored energy is released resulting in matrix cracking and/or fibre/matrix debonding. Axisymmetric finite element models were formulated to study the impact of matrix cracks and fibre/matrix debonding on the effective stress transfer efficiency (EST) and stress transfer length (STL). At high strains, plastic deformation in the matrix dominated the stress transfer mechanism. The combination of matrix cracking and plasticity reduced the EST and increased STL. For experimental validation, three resins were formulated and the fragmentation of an unsized and uncoupled E-glass fibre examined as a function of matrix properties. Fibre failure was always accompanied by matrix cracking and debonding. With the stiff resin, debonding, transverse matrix cracking and conical crack initiation were observed. With a lower modulus and lower yield strength resin the transverse matrix crack length decreased while that of the conical crack increased.

Analysis of Stresses for Cross-Ply Laminates with Multiple Matrix Cracks under Bending

On the basis of the shear-lag theory, a layered shear-lag model was established to study the stress redistributions of cross-ply laminates with multiple transverse matrix cracks in the 90º ply under bending. The present results are in a good agreement with variational solutions and finite element results and show that approximate solutions of stress distributions for cross-ply laminates with transverse cracks under bending can be obtained by using a shear-lag method. The present paper therefore affords a new way or method for studying the stress redistributions and failure mechanism for cross-ply laminates with flaws under bending.

Damage assessment in CFRP laminates exposed to impact fatigue loading

Demand for advanced engineering composites in the aerospace industry is increasing continuously. Lately, carbon fibre reinforced polymers (CFRPs) became one of the most important structural materials in the industry due to a combination of characteristics such as: excellent stiffness, high strength-to-weight ratio, and ease of manufacture according to application. In service, aerospace composite components and structures are exposed to various transient loads, some of which can propagate in them as cyclic impacts. A typical example is an effect of the wind gusts during flight.This type of loading is known as impact fatigue (IF); it is a repetition of low-energy impacts. Such loads can cause various types of damage in composites: fibre breaking, transverse matrix cracking, de-bonding between fibres and matrix and delamination resulting in reduction of residual stiffness and loss of functionality. Furthermore, this damage is often sub-surface, which reinforces the need for more regular inspection.The effects of IF are of major importance due its detrimental effect on the structural integrity of components that can be generated after relatively few impacts at low force levels compared to those in a standard fatigue regime. This study utilises an innovative testing system with the capability of subjecting specimens to a series of repetitive impacts. The primary subject of this paper is to assess the damaging effect of IF on the behaviour of drilled CFRP specimens, exposed to such loading. A detailed damage analysis is implemented utilising an X-ray micro computed tomography system. The main findings suggested that at early stages of life damage is governed by o degree splits along the length of the specimens resulting in a 20% reduction of stiffness. The final failure damage scenario indicated that transverse crasks in the 90 degree plies are the main reason for complete delamination which can be translated to a 50% stiffness reduction.

Analysis of Stresses for Cross-Ply Laminates with a Matrix Crack under Bending

On the basis of the shear-lag theory, an analysis was presented for stress redistributions of cross-ply laminates with a transverse matrix crack in the 90º ply under bending by establishing a layered shear-lag model. The present results show that approximate solutions of displacement and stress distributions for cross-ply laminates with a transverse crack under bending can be obtained by using a shear-lag method. The present paper therefore affords a new approach for studying the stress redistributions and failure mechanism for cross-ply laminates with flaw under bending.