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Residual strains and shape distortions in a polymer-based composite structure may depend on the cure schedule used for manufacture. Aiming to understand the cure history effects, the influence of the curing “path” (time [Formula: see text] and temperature [Formula: see text] path during curing) on viscoelastic (VE) response of a fully cured (FC) ([Formula: see text] = 0.992) epoxy was investigated. Five different “families” of the same epoxy were manufactured in constraint-free conditions using different sets of curing parameters. Then, tensile tests were performed at different temperatures (T = 30 to 110 °C), and the time–temperature superposition principle (TTSP) and Schapery’s type of linear viscoelastic (VE) model, accounting for physical aging of specimens tested at high temperature, were used. The results show that the VE properties of the studied epoxy are independent of the curing history provided that at the end all specimens are fully cured. Also, the physical aging rate at high temperatures of all “families” is the same and it can be described by a simple aging-temperature independent equation reported in Nunes et al.1 It is expected that curing history of unconstrained and fully cured epoxy has an insignificant effect on final viscoelastic behavior, a knowledge which could assist in developing more time and cost-efficient cure cycles.

Intralaminar cracking in relatively thick 90-plies of [[Formula: see text]]s laminates is analyzed using experimental data for two Glass fiber/Epoxy (GF/EP) material systems. Weibull parameters for transverse failure stress of the 90-ply are obtained from experimental intralaminar crack density versus applied strain data, showing that a reliable analysis requires sufficient amount of data in so called noninteractive crack density region. Monte Carlo simulations of cracking were performed using stress distribution between two cracks calculated using two models: Hashin’s model and a novel model that ensures that the average stress is exactly the same as in FEM solution. Due to its features, the Hashin’s model predicts too low intralaminar crack density (it predicts too strong interaction between cracks). The results emphasize the importance of having a proper stress distribution model when performing Monte Carlo simulations. Simulations were used not only to simulate intralaminar cracking in high and very low crack density regions but also for improving the procedure of Weibull parameter determination.

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.

The growth of fiber/matrix interface cracks (debonds) located on consecutive fibers along the through-the-thickness (vertical) direction is studied in glass fiber-epoxy UD composites. Debonds could appear, along the vertical direction, on the same or on opposite sides of their respective fibers. Determining which configuration is the most energetically favorable to debond growth is the objective of this paper. To this end, two different families of Representative Volume Elements (RVEs) are developed: the first implements the classic condition of coupling of the vertical displacements to model a unit cell repeating symmetrically along the vertical direction; the second uses a novel set of boundary conditions, proposed here by the authors, to represent a unit cell repeating anti-symmetrically along the vertical direction. The model is analyzed in the context of Linear Elastic Fracture Mechanics (LEFM) and the Mode I and Mode II Energy Release Rate are evaluated to investigate crack growth. The calculation is performed using the Virtual Crack Closure Technique (VCCT) in the framework of the Finite Element Method (FEM). It is found that Mode I dominated propagation is favored when debonds are located on the same sides of their respective fibers; while for larger (Mode II-dominated) debonds, Mode II ERR is higher when they lie on the opposite sides. No interaction effect is present when at least two fully bonded fibers are located between the partially debonded ones.

Reliable accelerated testing routines involving tests at enhanced temperatures are of paramount importance in developing viscoelastic models for polymers. The theoretical basis, the time-temperature superposition (TTS) principle, is used to construct master curves and temperature-dependent shift factor, which is the necessary information to simulate the material response in arbitrary temperature and strain regimes. The Dynamic Mechanical and Thermal Analysis (DMTA) TTS mode, being one of the most promising approaches in terms of time efficiency and maturity of the software, is compared in this paper with macrotests at enhanced temperatures in their ability to give reliable master curves. It is shown, comparing simulations with test data for a chosen epoxy polymer, that none of the three DMTA TTS mode-based attempts used (at different temperature steps during frequency scanning) was successful in predicting the epoxy behavior in tests. On the contrary, using one-hour macrotests at enhanced temperatures gives a viscoelastic model with a very good predicting accuracy. Simulations were performed using an incremental formulation of the previously published VisCoR model for linear viscoelastic materials.

Experimental results are presented on the onset and propagation of local delaminations caused by the interaction between specimen edges and intralaminar cracks in fiber bundles of 90° layers in quasi-isotropic [–45/90/45/0]s CF/EP noncrimp fabric (NCF) laminates subjected to tension-tension fatigue loadings. It is confirmed that the first damage mode is intralaminar cracking in 90° layers, which consists of intrabundle cracks and cracks in the matrix between bundles (often beginning from stitches). This damage mode triggers cracking in off-axis layers and local delaminations in positions where the 90° layer crack meets an adjacent layer. The process of local delamination is significantly enhanced at specimen edges, where the out-of-plane edge stresses contribute to the local delamination. During cyclic loadings, delaminations grow and coalesce along the edge and propagate towards the specimen center. These processes are quantified experimentally at different levels of cyclic load. In a low-stress fatigue, a very high number of cycles is required to detect small edge delaminations, and they stay at the edge. In high-stress cyclic tests, delaminations grow faster inside the composite: about 20% of the interface in the central zone can be delaminated. It is found that the reduction in the axial modulus is proportional to the relative delaminated area, proving that delamination is the major stiffness reduction factor in these laminates.

Models of Representative Volume Elements of cross-ply laminates with different geometric configurations and damage states are studied. Debond growth is characterized by the estimation of the Mode I and Mode II Energy Release Rate using the Virtual Crack Closure Technique. It is found that the presence of the [Formula: see text] interface and the thickness of the [Formula: see text] layer has no effect, apart from laminates with ultra-thin [Formula: see text] plies where it is however modest. The present analysis supports the claim that debond growth is not affected by the ply-thickness effect.

Methodology for cracking evolution simulation in 90-plies during cyclic loading is suggested in this paper. It includes using low crack density (where the neighboring cracks do not interact with each other) data from quasi-static and cyclic testing (at one load) to determine parameters in Weibull transverse failure stress distribution generalized for fatigue. Then, Monte Carlo process is used to assign failure stress to elements in the 90-ply. In the model, the failure stress of the element degrades with number of cycles and a crack appears when the failure stress becomes equal to the stress in the element, calculated with computationally efficient analytical method. The model is successfully used to predict cracking in the whole crack density range. In this model, data from cyclic test at one load is sufficient to predict damage at different load. The results suggest that the dependence on stress is slightly underestimated and the shape parameter in fatigue may be higher than in quasi-static tests. Therefore, fatigue tests at least at two load levels are recommended for reliable predictions. Validerad;2022;Nivå 2;2022-06-01 (hanlid);Funder: Swedish Aeronautical Research Program, NFFP7 (2019-02777)

The concept of the “effective stiffness” for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson’s ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described.

The crack opening and crack sliding displacements of both faces of an intralaminar crack are the main parameters defining the significance of each crack in laminate stiffness degradation, according to the previously published GLOB-LOC approach for symmetric laminates with an arbitrary number of cracks in all plies. In the exact stiffness expressions of this approach, the crack density is always multiplied by crack opening displacement and crack sliding displacement. The dependence of crack opening displacement on geometrical and elastic parameters of adjacent plies was studied previously and described by simple fitting functions. The crack sliding displacement has been analyzed for low-crack densities only and the proposed finite element method-based fitting expressions are oversimplified not including the out-of-plane ply stiffness effects. Based on finite element method analysis, more accurate expressions for so-called non-interactive cracks are suggested in the presented article. For the first time the shear stress perturbations are analyzed and interaction functions are presented with the feature that they always lead to slightly conservative predictions. The presented simple fitting functions, when used in the GLOB-LOC model, give predictions that are in a good agreement with finite element method results and with experimental data for laminates with damaged off-axis plies in cases when crack face sliding is of importance. The significance of including crack sliding displacement in stiffness predictions is demonstrated.

In this paper, the propagation of radial matrix cracks and debond cracks at the coating/matrix interface in unidirectional carbon fiber structural micro-battery composite are studied numerically. The micro battery consists of a solid electrolyte-coated carbon fiber embedded in an electrochemically active polymer matrix. Stress analysis shows that high hoop stress in the matrix during charging may initiate radial matrix cracks at the coating/matrix interface. Several 2-D finite element models of the transverse plane with different arrangements of fibers and other matrix cracks were used to analyze the radial matrix crack growth from the coating/matrix interface of the central fiber in a composite with a square packing of fibers. Energy release rates of radial cracks along two potential propagation paths are calculated under pure electrochemical loading. The presence of a radial matrix crack imposes changes in the stress distribution along the coating/matrix interface, making debonding relevant for consideration. Results for energy release rates show that the debond crack growth is governed by mode II.

This paper presents systematic numerical study of stresses in the adhesive of a single-lap joint with the objective to improve understanding of the main material and geometrical parameters determining performance of adhesive joints. For this purpose a 3D model as well as 2D model, optimized with respect to the computational efficiency by use of novel displacement coupling conditions able to correctly represent monoclinic materials (off-axis layers of composite laminates), are employed. The model accounts for non-linearity of materials (adherend and adhesive) as well as geometrical non-linearity. The parameters of geometry of the joint are normalized with respect to the dimensions of adhesive (e.g. thickness) thus making analysis of results more general and applicable to wide range of different joints. Optimal geometry of the single-lap joint allowing to separate edge effect from end effects is selected based on results of the parametric analysis by using peel and shear stress distributions in the adhesive layer as a criterion. Three different types of single lap joint with similar and dissimilar (hybrid) materials are considered in this study: a) metal-metal; b) composite-composite; c) composite-metal. In case of composite laminates, four lay-ups are evaluated: uni-directional ([08]T and [908]T) and quasi-isotropic laminates ([0/45/90/-45]S and [90/45/0/-45]S). The influence of the abovementioned parameters on peel and shear stress distributions in the adhesive layer is examined carefully and mechanical parameters governing the stress concentrations in the joint have been identified, this dependence can be described by simple but accurate fitting function. The effect of the used material model (linear vs non-linear) on results is also demonstrated.

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Composites formed from wood fibers and man-made cellulosic fibers in PLA (polylactic acid) matrix, manufactured using sheet forming technique and hot pressing, are studied. The composites have very low density (due to high porosity) and rather good elastic modulus and tensile strength. As expected, these properties for the four types of wood fiber composites studied here improve with increasing weight fraction of fibers, even if porosity is also increasing. On the contrary, for man-made cellulosic fiber composites with circular fiber cross-section, the increasing fiber weight fraction (accompanied by increasing void content) has detrimental effect on stiffness and strength. The differences in behavior are discussed attributing them to fiber/ fiber interaction in wood fiber composites which does not happen in man-made fiber composites, and by rather weak fiber/matrix interface for man-made fibers leading to macro-crack formation in large porosity regions. peerReviewed

A simple model for predicting intralaminar cracking in laminates under cyclic loads is proposed and validated. The model is limited to low stresses and low crack density and is based on the assumption that the non-uniformity of the fiber distribution is the main reason for the observed large variation of cracking resistance along the transverse direction of the layer. Hence, the resistance variation in quasi-static and in cyclic loading can be described by the same parameter. At low crack density the failure resistance variation is more significant than the variation of the stress state in the specimen, the latter becoming dominant at high crack density. At low crack density the Weibull distribution for probability of intralaminar cracking is used for crack density growth simulation during cyclic loading. Assuming the non-uniformity of the fiber distribution as the cause for variation of cracking resistance, the Weibull shape parameter in cyclic loading is the same as in quasi-static loading case while the scale parameter is assumed to degrade with the applied number of cycles and this dependence is described by a power function. Thus, the determination of parameters is partially done using quasi-static tests and partially using cyclic tests, significantly reducing the necessary testing time. The predictions of dependency of the cracking on the stress and number of cycles are validated against experimental observations of cracking in the 90-plies of quasi-isotropic non-crimp fabric (NCF) laminates as well as in tape based cross-ply laminates.

The present contribution is toward the systematic characterization and development of a one-dimensional incremental viscoelastic (VE) model for thermo-rheologically complex materials (called “VisCoR”) for the prediction of residual stresses and shape distortions in composites. Traditionally, models that have been developed for this purpose within the composites industry are based on incremental linear elastic methods. While these methods are robust, they fall short in predicting exact behaviour of large composite parts and high temperature composites where relaxation effects also play a vital role in the final shape of the part. Moreover, these models also do not consider the dependency of stresses on temperature and degree of cure. Although viscoelastic models have been formulated, they are not in an incremental form (which is suitable for Finite Element (FE) simulations), hence requiring higher computational efforts. The presented model is an incremental form and requires lesser computational cost and characterization efforts and most importantly takes into account the effect of temperature and degree of cure. Preliminary studies indicate that the incremental 1D viscoelastic model can accurately model VE stress relaxation behaviour when compared to exact solutions.

The first failure mode in tensile quasi-static and in tension-tension fatigue (cyclic) loading of composite laminates is intralaminar cracking in layers with off-axis fiber orientation. These tunnel-building cracks are result of combined action of in-plane transverse and shear stresses. We assume that due to non-uniform fiber distribution (clustering) which leads to local stress concentrations, different positions in the layer have different resistance to crack initiation (initiation strength). If so, the weakest position in quasi-static loading is also the weakest in fatigue and some of the distribution parameters for fatigue behavior can be obtained in quasi-static tests, thus significantly reducing the number of required fatigue tests. Methodology is suggested and validated for cases when the cracking is initiation governed-initiated crack almost instantly propagates along fibers. Distribution parameters are identified using data in low crack density region where stress perturbations from cracks do not interact. Monte-Carlo simulations are performed for cracking in layers under quasi-static and cyclic loading using novel approach for computationally efficient stress state calculation between existing cracks.

Methodology for development of a macro-scale model (with strain as an input) for Regenerated Cellulose fiber (RCF) composites with highly non-linear (viscoelastic (VE) and viscoplastic (VP)) constituents is presented and demonstrated. The VE is described by Schapery's models and Zapas' model is used for VP. For a purely VE constituent the model can be identified from stress relaxation in constant strain tests. In the presence of VP the constant strain test does not render VE stress relaxation functions, because part of the applied strain is VP and the VE strain is changing. As an alternative creep and strain recovery tests are suggested to find the plasticity law and also the nonlinear creep compliances to identify the VE model where stress is an input. The incremental form of this model is then inverted and used to simulate the VE relaxation tests and the simulated relaxation functions are used to identify the VE model with VE strain as an input. Models for constituents are used in micromechanics simulations of the composite behavior in arbitrary ramps including the composite VE relaxation test. Using the latter, a macro-model is developed and its validity and accuracy are demonstrated.

The energy release rate (ERR) of a fiber–matrix debond crack in a unidirectional composite subjected to transverse tension is studied numerically. The focus of the study is the effect of the proximity of the neighboring fibers on the ERR. For this, a hexagonal pattern of fibers in the composite cross-section is considered. Assuming one fiber to be debonded at certain initial debond arc-length, the effect of the closeness of the surrounding six fibers on the ERR of the crack is studied with the inter-fiber distance as a parameter. Using an embedded cell consisting of discrete fibers in a matrix surrounded by the homogenized composite, a finite element model and the virtual crack closure technique are used to calculate the ERR. Results show that the presence of the local fiber cluster accelerates the crack growth up to a certain initial crack angle, beyond which the opposite effect occurs. It is also found that the residual stress due to thermal cooldown reduces the ERR. However, the thermal cooldown is found to enhance the debond growth in plies within a cross-ply laminate.

Plausible mechanisms of transverse crack formation in unidirectional (UD) composites under applied tension normal to fibres are investigated numerically using a finite element model. Two initial scenarios are considered: Scenario 1 where a pre-existing single fibre/matrix debond crack kinks out into the matrix and induces fibre/matrix debonding at neighbouring fibres, and Scenario 2 where multiple pre-existing debond cracks link up by the debond growth and crack kink-out process. The 2-D finite element model consists of a circular region of matrix with a central fibre surrounded by six fibres in a hexagonal pattern. The region is embedded in a homogenized UD composite of rectangular outer boundary. Energy release rates (ERRs) of interface cracks and kinked-out cracks are calculated under applied tension normal to fibres. Results show that Scenario 2 is more likely to lead to formation of a transverse crack than Scenario 1. These results provide understanding of the roles of fibre clustering and fibre volume fraction on transverse crack formation in composites.

This paper presents a framework for multiphysics modeling of a novel type of multifunctional composite material, structured on microscale, with ability to function as battery cell in addition to carry mechanical load. The micro-battery consists of a single carbon fiber surrounded by very thin solid electrolyte coating and embedded in a matrix which is a porous material containing active particles able to intercalate lithium. During battery operation (discharging and charging) the structural battery constituents undergo volume changes, caused by lithium-ion movement. The presented mathematical model is solved numerically using COMSOL software and results are used to analyze the physical phenomena occurring in the structural battery material. Parametric analysis is performed to reveal the significance of geometrical parameters like fiber volume fraction in the battery and the porosity content in the matrix on the multifunctional performance of the composite unit including its swelling/shrinking during charging/discharging.

Effect of degree of cure on irreversible (viscoplastic) shear strain development in layers of glass fibre/ epoxy resin (LY5052 epoxy resin) [+45 °/−45 °]slaminate is studied performing a sequence of constant stress creep and viscoelastic strain recovery tests. For fixed values of degree of cure in range from 79.7% to 100%, the viscoplastic strains were measured as dependent on time and stress and Zapa's integral representation was used to characterize the observed behaviour. It is shown that at all degrees of cure the viscoplastic behaviour can be described by Zapa's model with parameters dependent on degree of cure. It is shown that for degree of cure lower than 80% the viscoplastic strains grow much faster and are much more sensitive to the increase of the applied shear stress. These irreversible strains developing in the final phase of the curing can significantly alter the residual stress state in the composite structure.

Structural composite materials that simultaneously carry mechanical loads, while storing electrical energy offers the potential of significantly reduced total component weight owing to the multifunctionality. In the suggested micro-battery, the carbon fiber is employed as a negative electrode of the battery and also as a composite reinforcement material. It is coated with a solid polymer electrolyte working as an ion conductor and separator while transferring mechanical loads. The coated fiber is surrounded by a conductive positive electrode material matrix. This paper demonstrates a computational methodology for addressing mechanical stresses arising in a conceptualized micro-battery and dimensional changes of the cell during electrochemical cycling, caused by time-dependent gradients in lithium ion concentration distribution.

An alternative to traditional fracture mechanics methodology to predict direction for crack propagation in the adhesive layer of bonded stiff materials is demonstrated. The approach is based on the analysis of the location of maximum of the hoop stress in relation to the existing crack tip. Such method is very convenient and fast as it does not require a lot of computational resources and is easy to implement compared to other known numerical methods dealing with similar problems (e.g. X-FEM). The method is validated by fracture mechanics approach using energy release rate to predict crack propagation direction. The verification is done by using bi-material DCB specimen with relatively thick adhesive layer as an example. After proving the applicability of the maximum hoop stress criterion the parametric study on factors affecting crack propagation in the adhesive layer is carried out. Such parameters as bending stiffness of beams, thickness of the adhesive layer, distance to the bond-line, length of the initial pre-crack are analyzed.

Fiber/matrix debonding in transverse tensile loading of a unidirectional composite is analyzed calculating energy release rate (ERR) for interface crack propagation. Non-uniform fiber distribution (local hexagonal fiber clustering) is assumed in the model. The matrix region containing the central fiber with the debond and the 6 surrounding fibers is embedded in a large block of homogenized composite which has the same fiber content as the region analyzed explicitly. Some of the fibers surrounding the central fiber may also have a debond. The effect of the local clustering and of the presence of other debonds on magnification of the ERR is analyzed.

In this work, we investigate the relationship between the rubbery modulus and the degree of cure for partially to fully cured LY5052 epoxy resin. In particular, this paper experimentally tests an existing model formulated for shear modulus by redefining for in the tensile storage modulus. Experiments to characterize viscoelastic behaviour were performed in a dynamic mechanical and thermal analysis (DMTA) instrument in the frequency domain. Master curves are then created from DMTA using general time–temperature–cure superposition. The master curves are then normalized using the model so that the master curve does not depend on the properties in the rubbery region. This results in a unique master curve that describes the viscoelastic behaviour of the LY5052 epoxy resin for the given conditions. Once the relationship between the rubbery modulus and the degree of cure has been established, the amount of experimental characterization can be reduced. This could lead to the development of simplified experimental...

Microdamage in the layers of CF Thornel® T650 8-harness satin-weave composites with a thermosetting NEXIMID® MHT-R polyimide resin, designed for high service temperatures, is analyzed. After cooling down to room temperature (RT), a multiple intrabundle cracking due to tensile transverse thermal stresses was observed in the [(+45/–45)/(90/0)]2s laminates studied. Then, the composite was subjected to two ramps of thermal cycling quantifying the increase in crack density in its layers. A comparison of two ramps with the same lowest temperature showed that the highest temperature in the cycle where thermal stresses were low had a significant detrimental effect on the thermal fatigue resistance of the composite. The effect of holding it at 288°C for 40 days was also studied: many new cracks formed in it after cooling down to RT. During the time at the high temperature, the mechanical properties degraded with time, and the crack density versus aging time was measured at RT. Then, both aged and nonaged specimens were tested in uniaxial quasi-static tension quantifying the damage development in layers of different orientation. Cracking in the layers was analyzed using fracture mechanics arguments and probabilistic approaches: a) a simple one, not considering crack interaction; b) Monte Carlo simulations. It is shown that cracking in the off-axis layers which are not in contact with the damaged 90°-layer can be predicted based on the Weibull analysis of the 90°-layer, whereas in the off-axis layer contacting the 90°-layer, the crack density is much higher due to the local stress concentrations caused by cracks in the 90°-layer. The thermal treatment degraded the cracking resistance in the surface and adjacent layer, whereas the composite close to the midplane was not changed.

Carbon fibre T650 8-harness satin weave fabric composites with thermosetting polyimide resin designed for high service temperatures are solidified at 340 °C. High thermal stresses develop after cooling down to room temperature, which lead to multiple cracking in bundles of the studied quasi-isotropic composite. The composites are subjected to two thermal cycling ramps and the increase of crack density in each bundle is quantified. Comparison of two ramps with the same lowest temperature shows that the highest temperature in the cycle has a significant effect on thermal fatigue resistance. During thermal aging tests at 288 °C the mechanical properties are degrading with time and the crack density after certain aging time is measured. Aging and fatigue effects are separately analysed showing that part of the cracking in thermal cycling tests is related to material aging during the high temperature part of the cycle. Numerical edge stress analysis and fracture mechanics are used to explain observations. The 3-D finite element edge stress analysis reveals that there is large edge effect that induces a large difference in the damage state between the different layers on the edge. The linear elastic fracture mechanics explains the higher initiated and propagated crack density in the surface layers comparing to the inner layers.

Curvature of unsymmetrical [0/90] specimens caused by thermal stresses changes if the specimen is subjected to large axial strains introducing intralaminar cracks in the 90-layer. It is shown that the large curvature reduction can not be explained by cracking related stress release only. The large irreversible viscoplastic strains introduced during the axial tensile loading (with 5 min holding at high strain for crack counting) give the main contribution to the curvature change. The effect of transient viscoelasticity (VE) was found to be of minor significance. Simple approach based on effective damaged layer stiffness and constant irreversible strain is used in the framework of laminate theory to extract the viscoplastic and VE strains from experimental curvature data. The obtained fitting expressions for viscoplastic- and VE-strain development are successfully used to describe curvature change in [0/902] laminate subjected to the same test procedure. It is suggested that the used curved beam tests could be efficient to characterize the viscoplastic strain development in the thin 90-layers.

A novel variational model is developed that can predict the stress transfer between plies in cracked general cross-ply laminates subject to general in-plane (Nxx, Nyy, Nxy) and out-of-plane bending (Mxx, Myy, Mxy) loading. The effects of thermal residual stresses are taken into account. Admissible stress systems, which satisfy equilibrium and all boundary and interface conditions, are constructed and the principle of minimum complementary energy is employed to find the optimal solution. The approach yields rigorous lower bounds for stiffness matrices. A methodology based on Levin's theorem is developed to evaluate the effective thermal expansion coefficients of non-symmetric cracked laminates. A ply-refinement technique is used in order that through-thickness variations of the stress components can be precisely taken into account. It is found that the developed method, when used in conjunction with ply refinement technique, results in stress fields and thermo-mechanical properties comparable in accuracy to refined finite and boundary element solutions.

The effects of crack shielding, finite thickness of the composite and fiber content on fiber/matrix debond growth in thin unidirectional composites are investigated analyzing Representative Volume ...

The effects of crack shielding, finite thickness of the composite and fiber content on fiber/matrix debond growth in thin unidirectional composites are investigated analyzing Representative Volume Elements (RVEs) of different ordered microstructures. Debond growth is characterized by estimation of the Energy Release Rates (ERRs) in Mode I and Mode II using the Virtual Crack Closure Technique (VCCT) and the J-integral. It is found that increasing fiber content, a larger distance between debonds in the loading direction and the presence of a free surface close to the debond have all a strong enhancing effect on the ERR. The presence of fully bonded fibers in the composite thickness direction has instead a constraining effect, and it is shown to be very localized. An explanation of these observations is proposed based on mechanical considerations.

International audience; A novel testing methodology for the characterization of viscoplastic (VP) deformation of unidirectional (UD) composites under transverse tensile loading is described. The law of transverse VP deformation, which, due to specimen failure, is almost impossible to obtain using UD specimens, is identified from curvature changes of an unsymmetrical CF/EP [0/90] specimen. An initially thermally curved specimen is loaded in the axial direction to different high levels of tensile strain, with a specified holding time. After unloading and waiting for recovery of the viscoelastic strains, the curvature of the specimen had changed due to the irreversible transverse VP strain and microdamage had developed in the 90° ply. The damage effect is incorporated into the model by introducing the“effective stiffness” of the damaged layer, which is a function of the crack density and the local delamination length. A model based on the classical laminate theory is used to construct a relationship between the measured curvature after a loading step and the accumulated VP strain, temperature, and the effective stiffness. The back-calculated VP strains are analyzed, and their functional dependence on the stress and time in the viscoplasticity law is obtained. The model and the methodology are validated by comparing calculation results with test data for [902/0] laminates subjected to a similar loading. The methodology suggested could be very accurate on using a laminate with ultrathin plies in the test. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Stress relaxation and strain recovery phenomena during curing and changed thermal conditions are analyzed using a viscoelastic model developed for thermorheologically complex materials (VisCoR). By making several simplifying assumptions regarding the material behavior, the incremental form of the VisCoR model is reformulated to a version describing thermorheologically simple material and presented in one-dimension for simplicity. The model (called VisCoR-simple) is used to analyze material behavior under various conditions, including stress relaxation behavior at varying temperatures and time scales; tensile loading and unloading tests at high temperatures; stress build up and “frozen-in” strains during curing and following cool-down and strain recovery during the next step of heating. Furthermore, the differences between the so-called “path-dependent” model, which is a linear elastic model with different elastic properties in glassy and rubbery regions, and the presented viscoelastic model are studied. The path-dependent model is an extreme case of the viscoelastic model presented. The importance of considering viscoelasticity when considering temperature and curing effects on polymers and the shortcomings of the path-dependent model are revealed and discussed. © The Author Finansiär: Clean Sky 2 Joint Undertaking, European Union (EU), Horizon 2020, ProTHiC, 821019Finansiär 2: Vinnova, HiSim

Models of Representative Volume Elements (RVEs) of cross-ply laminates with different geometric configurations and damage states are studied. Debond growth is characterized by the estimation of the Mode I and Mode II Energy Release Rate (ERR) using the Virtual Crack Closure Technique (VCCT). It is found that the presence of the 0° /90° interface and the thickness of the 0° layer have no effect, apart from laminates with ultra-thin 90° plies where it is however modest. The present analysis supports the claim that debond growth is not affected by the ply-thickness effect.

A numerical study for the double-lap adhesive joint made of similar adherends subjected to tensile and thermal loads is presented. A novel displacement coupling conditions which are able to correctly represent monoclinic materials (off-axis layers of composite laminates) are used to build a comprehensive numerical model. Two types of double-lap joints are considered in this study: metal–metal and composite-composite. In case of composite laminates, four lay-ups are evaluated: unidirectional ([08]T and [908]T) and quasi-isotropic laminates ([0/45/90/−45]S and [90/45/0/−45]S). The effect of different parameters (adherend stiffness, ply stacking sequence, adherend thickness, one-step or two-step manufacturing of the joint) on peel and shear stress distribution in the middle of the adhesive is studied. The comparison of the behaviour of single-lap and double-lap joint in relation to these parameters is made. The maximum peel and shear stress at the ends of the overlap with respect to the axial modulus of the adherends are presented in a form of the master curves. The analyses of results show that: the maximum peel and shear stress concentration at the overlap ends is reduced with the increase of the axial modulus of the adherend; the stress distribution in the adhesive layer can be improved (lower stress concentrations and level-out the curve) by changing the fibre orientation (which affect the stiffness) in plies connected to the adhesive layer.

Energy release rate (ERR) for fiber/matrix debonding in composite with local fiber clustering, subjected to axial tension, has been investigated numerically by a 3-D finite element (FE) model. In t ...

Final failure in composite structures often occurs from fiber failures in a local region. This paper aims to study the formation of a critical fracture plane that simulates the local failure region in a unidirectional composite. The nucleation site for the critical plane is assumed to be a broken fiber. An axisymmetric finite element model is constructed to study the progression of failure from the broken fiber placed at the center and surrounded by intact fibers. Two scenarios are considered: one, where the broken fiber results from a manufacturing process, and two, where a fiber fails at a weak point under loading. In the first case, a matrix crack is found to initiate from the broken fiber end and grow normal to the fiber axis, while in the second case, a matrix crack kinks out of an (assumed) short fiber/matrix debond crack and grows out towards the neighboring fibers. The consequent stress enhancement in the neighboring fibers is analyzed to determine their probability of failure. The influence of the initial debond length on the formation of the critical fracture plane is also studied.

Microdamage, viscoplastic and viscoelastic strain development in 90-layers of cross-ply laminates subjected to tensile loading is studied on unsymmetrical GF/EP laminates measuring the thermal curvature change. All three phenomena partially compensate for the effect of the thermal mismatch reducing the residual stress (specimen curvature). The viscoplastic strain contribution to curvature change is the largest whereas the effect of transient viscoelasticity is the smallest. Damage is included in the analysis through its effect on the effective transverse modulus of the 90-layer.

Steady-state energy release rate (ERR) for fiber/matrix interface debond growth originated from fiber break in unidirectional composite is calculated using 3-D FEM models with hexagonal fiber arrangement. In the model the debonded fiber is central in the hexagonal unit which is surrounded by effective composite. The effect of neighboring fibers focusing on local fiber clustering on the ERR is analyzed by varying the distance between fibers in the unit. The steady-state ERR is calculated from potential energy difference between a unit in the bonded region far ahead of the debond front and a unit in the debonded region far behind the debond front. The ERR for different modes of crack propagation is obtained from a FEM model containing a long debond by analyzing the stress at the debond front. Results show that in mechanical axial tensile loading fracture Mode II is dominating, it has strong angular dependence (effect of closest fibers) but the average ERR is not sensitive to the local fiber clustering. In thermal loading the Mode III is dominating and the average ERR is highly dependent on the distance to neighboring fibers. However, for realistic loads the thermal ERR is much smaller than the mechanical.

The old concept of the effective stiffness of a 90-layer with intralaminar cracks is revisited performing 3-D FEM parametric analysis of symmetric and balanced laminates. It is shown, focusing on the effective transverse modulus, that the expected dependence of this property on composite elastic properties and laminate lay-up is very weak and follows very simple rules. Calculations show that the effective longitudinal modulus and Poisson’s ratio of the layer are not affected at all by intralaminar cracking. Simple fitting curve for effective transverse modulus change with normalized crack density is obtained from analysis of GF/EP cross-ply laminate. It is shown, comparing with FEM results and experimental data, that this expression can be used as a ‘master curve’ in laminate theory to predict macroscopic elastic property change with crack density in laminates with very different lay-ups and made of different unidirectional composites.

Schapery’s nonlinear viscoelastic model is written in incremental form, and three different approximations of nonlinearity functions in the time increment are systematically analysed with respect to the convergence rate. It is shown that secant slope is the best approximation of the time shift factor, leading to significantly higher convergence rate. This incremental form of the viscoelastic model, Zapas’ model for viscoplasticity, supplemented with terms accounting for damage effect is used to predict inelastic behaviour of material in stress controlled tests. Then the incremental formulation is inverted to simulate stress development in ramps where strain is the input parameter. A comparison with tests shows good ability of the model in inverted form to predict stress–strain response as long as the applied strain is increasing. However, in strain controlled ramps with unloading, the inverted model shows unrealistic hysteresis loops. This is believed to be a proof of the theoretically known incompatibility of the stress and strain controlled formulations for nonlinear materials. It also shows limitations of material models identified in stress controlled tests for use in strain controlled tests.