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The aim of this work is to develop a methodology to analyze the influence of the curing history on the viscoelastic storage modulus. Two different experimental approaches are presented exposing the material to various cure temperature and cure time sequences. The evolving viscoelastic properties are characterized using standard Dynamic Mechanical and Thermal Analysis (DMTA) equipment. Therefore, the present study is limited to infinitesimally small strains and linear viscoelasticity only. The methodology is demonstrated using the LY5052 epoxy resin system for its storage modulus E′ in the frequency domain. Results indicate that evolution of thermo-viscoelastic properties could be indeed assumed independent of the cure history for the investigated LY5052. We observe that the shift factor in the reduced time expression for the viscoelastic model examined in this paper is a product of two shift functions, namely the temperature and cure shift functions.

Simple approach based on Classical Laminate Theory (CLT) and effective stiffness of damaged layer is suggested for bending stiffness determination of laminate with intralaminar cracks in surface 90-layers and delaminations initiated from intralaminar cracks. The effective stiffness of a layer with damage is back-calculated comparing the in-plane stiffness of a symmetric reference cross-ply laminate with and without damage. The in-plane stiffness of the damaged reference cross-ply laminate was calculated in two ways: (1) using FEM model of representative volume element (RVE) and (2) using the analytical GLOB-LOC model. The obtained effective stiffness of a layer at varying crack density and delamination length was used to calculate the A, B and D matrices in the unsymmetrically damaged laminate. The applicability of the effective stiffness in CLT to solve bending problems was validated analyzing bending of the damaged laminate in 4-point bending test which was also simulated with 3-D FEM.

Analytical closed form solution is derived for energy release rate due to steady-state debond growth along a broken fiber in unidirectional composite. The problem is represented by a three concentric cylinder model, where the broken and partially debonded fiber is embedded in resin and this unit is surrounded by homogenized effective composite. Parametric analysis shows that parameters in the very simple quadratic expression for energy release rate dependence on temperature change and mechanical strain are rather insensitive with respect to changes in constituent elastic properties and fiber content. The importance to have a large outer radius of the effective composite phase in the concentric cylinder model is demonstrated.

A comprehensive stress analysis by means of Finite Element Method (FEM) for single-lap joint subjected to thermal and mechanical loads is presented in this paper. Simulation is used to predict the effect of residual thermal stresses (caused by difference of temperature of use and elevated temperature during the assembly of the joint) on stress distribution within adhesive layer. The residual thermal stresses are assigned to joint members as initial condition before the mechanical load is applied. The FEM model employs linear and nonlinear material model and accounts for geometrical nonlinearity. It is confirmed that the difference between the manufacturing and the ambient temperature results in high residual thermal stresses, especially in axial and lateral directions of the joint. The calculation of total stress as superposition of thermal and mechanical stresses works only for linear materials. Moreover, simultaneous application of temperature and mechanical load (applied strain in case of displacement controlled test) in FEM produces inaccurate results, since in real situation the strain is applied to already thermally loaded structure. It is also found that the residual thermal stresses may reduce the peel and shear stress concentration in the adhesive at the ends of overlap and the shear stress within the overlap.

In this paper propagation of matrix cracks and debonds at the coating/matrix interface in the 90°-layer of a cross-ply structural composite battery are studied numerically. The structural composite battery consists of micro-battery units, made of a solid electrolyte coated carbon fiber embedded in an electrochemically active polymer matrix. During charging the fiber swells and the matrix shrinks leading to high stresses on the fiber/matrix scale and to anisotropic free expansion of the composite ply. Two load cases are considered, pure electrochemical load (intercalation) and combined electrochemical and thermomechanical load. Energy release rates (ERR) of radial matrix cracks along two potential propagation paths are calculated using 2-D finite element models of the transverse plane in a cross-ply laminate with a square packing of fibers in the 90°-ply and using homogenized 0°-ply. Results show that the matrix crack growth towards the nearest fiber is unstable, and that the debond crack growth is in mixed mode. For a cross-ply structural battery composite the sequence of macro-scale crack forming events differs from a conventional cross-ply composite, as well as for a UD composite battery laminate. The most likely course of failure events in a cross-ply laminate are: 1) vertical radial matrix crack initiation and unstable growth; 2) debond is initiated at certain length of the matrix crack.

Intralaminar cracking in layers of multidirectional laminates lead to reduced ability of these layers to carry load which is the reason for damaged laminate thermo-elastic properties reduction. The average stress reduction in the damaged layer is uniquely linked with displacements of the crack faces and, therefore, the crack opening displacements (CODs) and the crack face sliding displacements (CSDs) are alternative descriptors in damaged laminate stiffness predictions. In this chapter, exact closed form relationships are established linking thermo-elastic constants of the damaged laminate with crack density in layers and local parameters of the crack (average normalized COD and CSD). These robust local parameters depend on surrounding and damaged layer stiffness and thickness ratio-relationship, which is investigated numerically and described by simple fitting functions. It is also shown that the energy release rate (ERR) for propagation of the intralaminar crack in steady-state conditions has simple expression through the COD and CSD, leading to simple predictive tool for thin ply laminates where the cracking is propagation controlled.

Three analytical models with increasing complexity, all based on minimization of complementary energy, are compared in their ability to predict shear modulus reduction of laminates with intralaminar cracks in 90-layer. The very elegant and simple (and the less accurate) model by Hashin assumes linear out-of-plane shear stress distribution across the ply in all layers. The second model assumes exponential shape of these stresses in the constraint layer keeping linear assumption in the cracked layer. The model developed in the present paper accounts for nonlinear out-of-plane shear stress thickness distribution in all layers described by shape functions determined in the procedure of minimization. Increasing the complexity of the model the predicted shear modulus of the damaged laminate increases approaching to value obtained using finite elements (FE). Results show that for laminates with relatively thick cracked layers the stress state description in the cracked layer should be refined whereas for laminates with constraint layer thicker than the cracked layer more accurate stress description in the constraint layer is necessary. More accurate solutions could be derived using the described methodology, but the involved complexity and the numerical routines required for their application diminish their value comparing with direct FE solution.

Many approximate analytical models have been developed to calculate stress state between intralaminar cracks with the aim to predict the degradation of certain elastic property (most often axial modulus or shear modulus) of cross-ply laminate. Often they are plane stress solutions and laminate constants like Poisson's ratios cannot be considered. On the other hand the so called GLOB-LOC approach, presented in WWFE III, allows calculation of any thermo-elastic property of a general symmetric laminate with an arbitrary number of cracks in each layer provided that two local parameters – average and normalized crack opening displacement (COD) and crack face sliding displacement (CSD) are known. In this paper relationships are derived expressing these two parameters (COD and CSD) with average value of transverse stress and in-plane shear stress perturbation between cracks. Expressions are exact and independent on the approximations in the stress model. As examples, average perturbation functions for two shear lag models and Hashin's variational model are used to calculate damaged laminate properties that would not be available in original formulation: Poisson's ratio and thermal expansion coefficients. Predictions are compared with test data for GF/EP laminates and with more accurate predictions based on FEM calculations.

Problems occurring, when nonlinear time-dependent material model with parameters identified in creep tests is applied to simulate high-strain response in strain-controlled tests, are described and analyzed. Reasons for discrepancies with experimental loading curves are revealed. Presented numerical/experimental examples deal with three bio-based composites showing highly nonlinear behavior due to damage, nonlinear viscoelasticity and viscoplasticity. Schapery's approach for viscoelasticity and Zapas' model for viscoplasticity are used. The model is generalized to include microdamage effect. It is shown that the main problem in simulations at high stresses is the reliability of data from creep test for model identification in this region because creep rupture limits the available data region and extrapolation to higher stresses is rather uncertain. Alternative solution is to employ relaxation tests at high strains to obtain the missing information. However, it would work only in absence of viscoplastic strains: viscoelastic relaxation functions cannot be determined by maintaining constant total strain if viscoplastic-strain is developing. Based on sensitivity analysis of composite response to variations of the elastic modulus, damage, viscoelastic and viscoplastic parameters, suggestions are made for improving (further “tuning”) the model in high stress region by using tensile stress–strain curves in quasi-static loading.

Gradients in lithium ion concentration distribution in carbon fiber are accompanied by non-uniform fiber swelling leading to development of mechanical stresses. During lithium deintercalation these stresses may lead to initiation and growth of radial cracks in the fiber. The subsequent cycle of intercalation may result in arc-shaped cracks deviating from the tip of the radial cracks. These phenomena decrease the mechanical properties of fibers if used in structural batteries and reduce the charging properties of the battery by decreased diffusivity of lithium ions and by exfoliating layers on the fiber surface. The crack propagation and possible damage evolution scenarios are analyzed using linear elastic fracture mechanics. The crack geometry dependent ion concentration distributions and the elastic stress distributions were found using finite element software ANSYS.

The effect of voids on quasi-isotropic carbon-fibre reinforced plastic laminates under quasi-static loading is compared with that under cyclic tension loading. Emphasis is placed on following damage development at the non-crimp fabric ply-level by investigating the influence of voids on damage accumulation, most notably transverse cracking and delamination. Details from experiments include micrographs of voids taken in both scanning-electron and light microscopy, measurements of void content and crack density using light microscopy, and stiffness plots from both quasi-static and cyclic tests. The stiffness results are compared with theoretical predictions accounting for transverse cracks. Voids have a significantly more detrimental effect on the mechanical properties in cyclic loading compared with quasi-static loading. Specifically, the stiffness reduction development, the underlying transverse cracking in layers and the number of cycles to failure are affected. Quality control by only quasi-static testing for void-containing composite materials to be used in components subjected to fatigue cannot therefore be recommended.

Reasons for nonlinear stress–strain curves in shear of unidirectional glass fibre composite are analysed. Laminate with stacking sequence [45/−45] s is used in tensile quasi-static as well as in tensile creep and strain recovery tests to study the development of viscoelastic and viscoplastic shear strains in local coordinates of the ply. It is shown that Zapa’s integral representation of viscoplasticity is applicable for this material and methodology for parameter determination is given. Schapery’s nonlinear viscoelastic material model was used for shear response characterisation and the nonlinearity parameters’ dependence on the shear stress was determined and described by fitting functions. Microdamage development is quantified by measuring axial modulus and Poisson’s ratio of the laminate. The obtained nonlinear viscoelastic, viscoplastic model with included effect of microdamage was successfully used to predict the nonlinear shear stress–strain curve in strain controlled tensile loading.

We present a statistical analysis based methodology for making assessment of the manufacturing quality of cross ply composite laminates as it relates to its effect on transverse cracking evolution. Assuming a two-parameter Weibull distribution of tensile strength of the transverse plies to represent randomly distributed manufacturing defects, multiple crack formation in the plies is simulated in the non-interactive and interactive regimes of cracking using the local stress fields calculated by a variational analysis. The statistical methodology is demonstrated on crack density evolution in cross ply laminates manufactured by four different processing routes and loaded in monotonic tension in the axial direction. The differences in the crack density evolution, supposedly due to different defect population induced by the four manufacturing conditions, could be described by the proposed statistical simulation method.

The first mode of damage in fiber reinforced composite laminates is usually intralaminar cracking in layers with off-axis orientation regarding the main loading direction. This papers analyzes the most typical methods used for the characterization of the damage state: edge replicas, optical microscopy, x-ray images, acoustic emission, speckle interferometry and Raman spectroscopy

A numerical study of the adhesivejoint made of similar and dissimilar adherends subjected to thermo-mechanical loading is presented. A comprehensive numerical model was used for this purpose with the novel displacement coupling conditions which are able to correctly represent monoclinic materials (off-axis layers of composite laminates). The geometrical nonlinearity as well as nonlinear material model are also taken into account. Three different types of single-lap and double-lap adhesive joints 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). This paper focuses on the parameters which have the majoreffect on the peel and shear stress distribution within adhesive layer at the overlap ends. The comparison of behaviour of single-and double-lap joints in relation to these parameters is made. The master curves for maximum stress (peel and shear) at the ends of the overlap with respect to the bending stiffness and axial modulus of the adherends are constructed by analysing stress distributions in the middle of the adhesive.The main conclusions of this paper are: the maximum peel stress value for SLJ is reduced with increase of the adherend bending stiffness and for DLJ,similar behaviour was observed at the end next to the inner plate corner, while, at the end next to the outer plate corner peel stress is reduced with increase of adherend axial modulus.

The potential of accurate modelling of the shear modulus reduction of laminates with cracked 90-layers using models based on the minimization of the complementary energy with improved stress description in the constraint layers is evaluated. This group of models refine Hashin’s model by introducing shape functions with unknown parameters to represent the out-of-plane shear stress distribution across the constraint layer thickness. The Hashin’s model becomes a particular case of the presented when the shape parameter approaches to zero. The most accurate shape parameters are found in the result of minimization. Three models are compared: the present variational model, Hashin’s model and the shear lag model introduced by Soutis which assumes linear out-of-plane shear stress distribution over an unknown part of the layer. It is shown in this paper that the size of this part may be determined by minimization of the complementary energy. The present model is the most accurate amongst the three, whereas Soutis’ model is more accurate than the Hashin’s model for laminates with constraint layer, thicker than the cracked layer. The comparison with finite element method results shows reasonable agreement. Agreement can be improved developing models with better description of the stress state in the cracked layer.

The change of thermoelastic properties of cross-ply and quasi-isotropic laminates with intralaminar cracks in layers is analysed. Predictions are performed using previously derived general expressions for stiffness of symmetric damaged laminates as dependent on crack density and crack face opening and sliding. It is shown that the average crack opening displacement can be linked with the average value of axial stress perturbation between two cracks. Using this relationship, analytical shear lag and Hashin’s models, developed for axial modulus, can be applied for calculating thermal expansion coefficients, in-plane moduli and Poisson’s ratios of damaged laminates. The approach is evaluated using finite element method and it is shown that the accuracy is rather similar to that in axial modulus calculation.

A lignin composite reinforced with 30% flax fibers at two levels of relative humidity, 34 and 66%, was used in this study. The nonlinearity of the composite was analyzed by studying the degradation of its modulus and the development of viscoelastic and viscoplastic strains. The reduction in the modulus of lignin-based composites in tension starts before the maximum in the stress–strain curve is reached and can be as large as 50%. With increasing relative humidity, these effects are slightly magnified. The time-dependent phenomena in tension were examined in short-term creep and strain recovery tests, demonstrating a rather high viscoplastic strain in lignin composites. Both viscoelastic and viscoplastic strains are larger at a higher relative humidity.

The strain energy release rate related to debond crack growth along the fiber/matrix interface in a unidirectional composite with a broken and partially debonded fiber is analyzed. The focus of this article (Part II) in contrast to the self-similar crack growth analysis in Part I [1] is on the growth of short debonds near the fiber break. Since the self-similarity condition is not valid for interactive cracks, numerical FEM simulations were used to calculate magnification of previously described coefficients in the strain energy release rate expression. The findings from these studies are used in simulation of the debond growth in tension-tension fatigue using Paris law.

The strain energy release rate related to debond crack growth along the fiber/matrix interface in a unidirectional (UD) composite with a broken fiber is analyzed. The UD composite is represented by...

The fiber/matrix interface crack (debond) growth from fiber break in unidirectional composite subjected to high stress tension–tension cyclic loading is analyzed. The debond growth is simulated calculating the strain energy release rate GII by FEM in three-dimensional formulation and using power law with respect to the GII change to describe the debond growth rate. Two models were applied. In Model 1 the partially debonded fiber/matrix cylindrical unit with a fiber break is surrounded from all sides by an effective composite phase. In Model 2 the effective composite phase was used around the fiber/matrix unit except the region between the unit and the specimen surface, which contains neat matrix only. Calculations show that the average GII is slightly larger, when the analyzed fiber is closer to the specimen surface. The debond growth was simulated using interface fatigue parameters obtained from single fiber composite specimen tests in the literature. Simulation results show that debonds from fiber breaks close to the specimen surface grow faster than from fiber breaks inside the composite specimen.

The degradation of the elastic properties of composite laminates with intralaminar cracks is caused by reduced stress in the damaged layer which is mainly due to two parameters: the crack opening displacement (COD) and the crack sliding displacement (CSD). In this paper these parameters are measured experimentally, providing laminate stiffness reduction models with valuable information for validation of used assumptions and for defining limits of their application. In particular, the displacement field on the edges of a [0/ +704/ −704]s glass fiber/epoxy laminate specimens with multiple intralaminar cracks is studied, and the COD and CSD dependence on the applied mechanical load is measured. The specimen full-field displacement measurement is carried out using ESPI (electronic speckle pattern interferometry). By studying the displacement discontinuities, the crack face displacements were measured. A comparison between the COD and the CSD (for the same crack) is performed.

Fiber/matrix interface debond crack growth from a fiber break is defined as one of the key mechanisms of fatigue damage in unidirectional composites. Considering debond as an interface crack its growth in cyclic loading is analyzed utilizing a power law, where the debond growth rate is a power function of the change of the strain energy release rate in the cycle. To obtain values of two parameters in the power law cyclic loading of fragmented single fiber specimen is suggested. Measurements of the debond length increase with the number of load cycles in tension–tension fatigue are performed for glass fiber/epoxy single fiber composites. Analytical method in the steady-state growth region and FEM for short debonds are combined for calculating the strain energy release rate of the growing debond crack. Interface failure parameters in fatigue are determined by fitting the modeling and experimental results. The determined parameters for interface fatigue are validated at different stress levels.

This article is the author’s contribution to the third World-Wide Failure Exercise which aims at benchmarking current damage models for composites. Reduction of thermo-elastic constants of laminates and their nonlinear behaviour due to intralaminar cracking and nonlinear shear response of the composite are analysed using global–local approach. The macroscopic properties of damaged laminates are expressed in simple forms containing density of intralaminar cracks and their surface displacement features obtained from local solutions. The initiation and evolution of the intralaminar damage is analysed using strength-based approach for laminates with thick layers and fracture mechanics approach for thin layers. Due to a lack of information, certain characteristics, such as statistical failure properties distribution parameters and transition point (thickness) from strength to fracture mechanics applicability, were assumed. All calculations are based on analytical expressions, some of which were developed previously through numerical analysis. The present method was applied to solve 9 out of the 13 test cases of the third World-Wide Failure Exercise and that was sufficient to illustrate the capability of the damage model.

Microdamage in layers of CF Thornel® T650 8-harness satin woven composite with thermosetting polyimide NEXIMID® MHT-R resin was analysed. After cooling to room temperature multiple intra-bundle cracking due to tensile transverse thermal stresses was observed in the studied [(+45/-45)/(90/0)]2s composite. The composite was subjected to thermal cycling quantifying the increase of crack density in layers. Comparison of two ramps with the same lowest temperature shows that the highest temperature in the cycle has a significant detrimental effect. Exposure for 40 days to 288°C caused many new cracks after cooling down to room temperature. Both aged and not aged specimens were tested in uniaxial quasi-static tension. Cracking was analysed using fracture mechanics and probabilistic approaches. Cracking in off-axis layers was predicted based on Weibull analysis of the 90- layer. The thermal treatment degraded the cracking resistance of the surface layer and of the next layer.

The propagation of fiber–matrix interfacial debonding under axial loading is analyzed, using the single-fiber fragmentation test as a reference, in order to determine fiber–matrix failure properties. A data reduction technique is presented in which the fiber–matrix Mode II interfacial fracture toughness is obtained from the measurements of the average debond crack growth. A set of boundary element models are employed to evaluate the energy release rate associated with interfacial crack propagation. The interfacial friction coefficient is parametrically varied until a constant value of the energy release rate (which is then equal to the fiber–matrix Mode II interfacial fracture toughness) is obtained. The applicability of the properties evaluated is demonstrated using a set of finite element models with cohesive elements.

The present contribution is toward systematic characterisation of the thermo-viscoelastic properties of a curing epoxy resin system. Characterising the viscoelastic solid behaviour is performed using a dynamic mechanical analyser. The aim of this work is to investigate the dependence of the viscoelastic response on time, temperature and degree of cure and to derive a model that covers the dependency of the relaxation modulus on all three factors and also to investigate how various factors would influence each other in the overall evolution of the relaxation modulus. In particular, we investigate the linearity between the three factors above. To summarize, the results indicate that these three parameters indeed obey a linear relationship.

The effect of intralaminar cracking in layers of laminates on laminate macroscopic thermoelastic constants is the subject of this chapter. General expressions are derived for arbitrary symmetric laminates with any number of cracks in different layers. In addition to layer properties and laminate lay-up, the expressions contain two local parameters characterizing the presence of the crack: its average values of crack opening displacement (COD) and crack sliding displacement (CSD) corresponding to a unit stress in the layer. It is shown that these two parameters are proportional to the corresponding average perturbations of the axial and shear stresses due to cracks. This allows using any of the simple analytical stress solutions (shear lag models, variational models, etc.) to calculate all thermoelastic constants. As an alternative, which is more accurate but less mechanism based, COD and CSD are obtained by fitting simple functions to the finite-element method-based parametric analysis results. Predictions are compared with experimental data for cross-ply laminates.

Intralaminar matrix cracking is recognized as the primary mode of damage appearing in laminates. Local Raman strain measurements in neighboring layers show that the distribution shape in the vicinity of the crack tip is smoothened with increasing magnitude of the applied strain. This behavior is attributed to secondary damage development in the neighboring supporting plies close to the transverse crack tip. In this article, an approximate analytical variational model, based on the principle of minimum complementary energy, is proposed for the investigation of the stress state in a glass/ epoxy cross-ply laminate with cracks in 90°layer and with homogenized damage (reduced elastic properties) in part of the 0° layer. The extent of damage (fiber breaks) is estimated combining modeling with measured local strain distributions. The model is applied in order to examine the effect of ply thickness on the magnitude of the secondary damage at the transverse crack tip.

Stiffness reduction simulation in laminates with intralaminar cracks is usually performed assuming that cracks are equidistant and crack density is the only parameter needed. However, the crack distribution in the damaged layer is very non-uniform, especially in the initial stage of multiple cracking. In this article, the earlier developed model for general symmetric laminates is generalized to account for non-uniform crack distribution. This model, in which the normalized average crack-opening and crack-sliding displacements are the main characteristics of the crack, is used to calculate the axial modulus of cross-ply laminates with cracks in internal and surface layers. In parametric analysis, the crack-opening displacement and crack-sliding displacement are calculated using finite element method, considering the smallest versus the average crack spacing ratio as non-uniformity parameter. It is shown that assuming uniform distribution, we obtain lower bond to elastic modulus. A ‘double-periodic’ approach presented to calculate the crack-opening displacement of a crack in a non-uniform case as the average of two solutions for periodic crack systems is very accurate for cracks in internal layers of cross-ply laminates, whereas for high crack density in surface layers, it underestimates the modulus reduction. Validerad; 2013; 20120323 (andbra)

The mechanical behaviour of polylactic acid/flax fibre composite in tension was investigated by analysing elastic properties and loading curves. The observed non-linearity was attributed to microdamage, viscoelastic and viscoplastic response, suggesting Schapery’s type of model for viscoelasticilty and Zapas’ model for viscoplasticity. It was found that after loading at stress levels below the maximum possible, the elastic modulus is not affected, and therefore, damage does not need to be included in the material model. Viscoplastic and viscoelastic strain development was analysed in creep and strain recovery tests at several high stress levels. The identified and validated material model is non-linear viscoelastic and viscoplastic with slight non-linearity even in the elastic strain term. It appears that there is no region of linear viscoelasticity for this material. Non-linear elasticity, viscoelasticity and viscoplasticity are equally responsible for the observed non-linearity in the tensile tests.

Full-field displacement measurements between intralaminar cracks in cross-ply laminates were performed to evaluate the accuracy of shear lag models and Hashin’s model. The dependence of the average crack opening displacement on the crack density was measured and compared with model predictions. It was found that Hashin’s model overestimates the average COD by at least 25%. The value of the shear lag parameter was back-calculated by fitting. With the same goal the strain in the middle between two cracks was measured rendering shear lag parameter which was only 1% different. The found value does not agree with any of the used shear lag models. Measurement shows nonzero intralaminar shear zones in both layers covering a part of the ply thickness.

The effect of temperature ( T = 22°C, 30°C and 35°C) and relative humidity (RH = 34% and 66%) on mechanical behavior of natural fiber reinforced bio-based matrix composites subjected to tensile loading was investigated. Three composites were studied (a) polylactic acid (PLA) composite with 10% weight fraction of flax fibers; (b) PLA composite containing 5% viscose fibers (filaments of regenerated cellulose); (c) lignin-based composite with 30% of flax fibers. Elastic modulus, the nonlinear tensile stress–strain curves and failure were analyzed showing that all materials are temperature sensitive. The nonlinearity was analyzed studying modulus degradation as well as development of viscoelastic and viscoplastic strains. The modulus reduction in PLA-based composites starts after reaching the stress maximum and is not significant, whereas the modulus reduction in lignin-based composites starts before the maximum and it can reach 50%. With increasing RH these effects are slightly larger. The time-dependent phenomena were analyzed in short-term creep and strain recovery tests demonstrating significantly higher viscoplastic strain in lignin composites. Both viscoelastic and viscoplastic strains are larger at higher RH.

The time-dependent mechanical response of flax fiber-reinforced thermoplastic starch matrix composite and neat starch is analyzed. It is demonstrated that the response is highly sensitive to the relative humidity (with specific saturation moisture content in the composite) and special effort has to be made to keep it constant. It was found that the accumulation of micro-damage and the resulting reduction of the elastic modulus in this type of composite is limited. The highly nonlinear behavior of composites is related to the nonlinear viscoelasticity and viscoplasticity. These phenomena are accounted for by simple material models, as suggested in this study. The stress-dependent nonlinearity descriptors in these models are determined in creep and strain recovery tests at low as well as by high stresses.

Methodology is suggested for calculation of effective elastic constants of layer containing intralaminar cracks. Trends are presented for layers with low and medium high crack densities, where the interaction between cracks can be neglected. The effective properties of the damaged layer are determined by back- calculation using previously developed GLOB-LOC model for thermo-mechanical properties of damaged laminate [1]. It is shown that the effective transverse modulus and shear modulus of a layer decrease linearly with increasing crack density, whereas longitudinal modulus and major Poisson’s ratio do not change at all. Experimental data for multiple cracking are analyzed showing that linear approximation of crack density versus applied strain may have sufficient accuracy. These two linear trends are used to calculate the effective elastic properties of a layer as a function of strain.

The non-linear and time-dependent stress—strain response of NCF [±45]s laminates in tension is studied. Testing methodology is suggested to separate and quantify the effect of damage development, non-linear viscoelastic effects, and viscoplasticity on the inelastic response. This is achieved by decomposition of viscoelastic and viscoplastic response, both of them being affected by microdamage accumulated during the service life. Material model based on Schapery’s work on viscoelasticity and Zapas viscoplastic function with added damage terms is presented and used. Simulation is performed and validated with constant stress rate tensile tests, identifying the non-linear viscoelasticity and viscoplasticity as the major sources of the non-linear response.

Inelastic mechanical behavior in tension of a recycled polypropylene (rPP and a rPP with addition of 10% of maleic anhydride grafted polypropylene (rPP + MAPP) was characterized and compared. The time-dependent response was decomposed into nonlinear viscoelastic and viscoplastic parts and each of them quantified. It was found that the elastic properties did not degrade during loading. The addition of MAPP did not change the mechanical properties of the rPP. A nonlinear material model was developed and the involved parameters (stress-dependent functions) were identified. The model was then validated in a stress controlled test at a constant stress rate.

A model is developed to analyze the growth of a fiber/matrix debond along a broken fiber interface in a single-fiber composite subjected to tension-tension fatigue. The Paris law expressed in terms of debond growth and strain energy release rates is used. An analytical solution for the Mode II energy release rate G II is obtained for long debonds, where the interface crack growth is self-similar. For short debonds, the interface crack interacts with the fiber break, and therefore a FEM modeling in combination with the virtual crack closure technique was performed to calculate the increase in G II . Finally, the calculated G II dependences are summarized in simple expressions that are used to simulate the debond growth in fatigue. A parametric study of the effect of Paris law parameters on the debond growth is performed.

Single fiber fragmentation test is extensively employed to characterize the fiber-matrix interface in composites. A novel technique for evaluating fracture toughness and friction coefficient at the fiber-matrix interface in an epoxy sample containing a single glass fiber is proposed. Using experimental measurements of the average fragment and debond lengths, Boundary Element (BE) models of the portion of sample corresponding to the average fiber fragment are created for increasing values of the applied strain. From the solution of the BE models, energy release rate (ERR) during crack propagation is evaluated using a Fracture Mechanics based approach which accounts for fiber-matrix interfacial friction. The calculated evolution of the ERR has a reasonably linear dependency on the applied strain, with a decreasing slope for increasing values of the interfacial friction coefficient. Since debond growth is stable, ERR should equal the interfacial fracture toughness during debond propagation. Consequently, interfacial friction coefficient and fracture toughness can be simultaneously determined by parametrically varying the friction coefficient until a null slope is obtained in the linear fit of the numerical solution of the ERR as a function of the applied strain. The applicability of the proposed technique is demonstrated with experimental results taken from the literature. Junta de Andalucía P08-TEP-04051

The effect of temperature and moisture on mechanical behavior of flax fiber/starch based composites was investigated experimentally. Elastic modulus, the nonlinear tensile loading curves, and failure strain were analyzed. Neat matrix and composites with 20 and 40% weight content of fibers were tested. It was found, performing tests with different amplitudes, that microdamage development with stress is rather limited and the related elastic modulus reduction in this type of composites is not significant. It was shown that the composite elastic modulus and failure stress are linearly related to the maximum tensile stress in resin. The sensitivity of the maximum stress of the resin with respect to temperature and moisture is the source of composites sensitivity to these parameters. Constant interface stress shear lag model for stress transfer assuming matrix yielding at the fiber/matrix interface has been successfully used to explain the tensile test data. It indicates that the sensitivity of the used composite with respect to the matrix properties change could be significantly reduced by increasing the average fiber length from 0.9 mm to 1.5 mm. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers

A composite made of recycled carbon fibres in recycled polypropylene matrix is studied experimentally to describe the features of the elastic and time dependent nonlinear mechanical behaviour. The properties of the developed material have a large variability to be addressed and understood. It was found that the stress-strain curves in tension are rather nonlinear at low strain rate and the strength is sensitive to strain rate. The elastic properties’ reduction for this composite after loading to high strains is rather limited. More important is that even in the “elastic region” due to viscoelastic effects the slope of loading–unloading curve is not the same and that at higher stress large viscoplastic strains develop and creep rupture is typical. The time and stress dependence of viscoplastic strains was analysed and described theoretically. The viscoelastic response of the composite was analysed using creep compliance, which was found to be slightly nonlinear.

The aim of this paper is to analyse fibre/matrix debond crack growth during high stress cyclic tension–tension loading of unidirectional composites. The debond crack evolution analysis is based on fracture mechanics concepts that mode II energy release rate calculations are performed analytically for long debonds, where crack growth is self-similar, and numerically for short debonds by finite element method in combination with virtual crack closure technique. From the calculation results simple expressions are derived for an arbitrary mechanical and thermal loading case. Finally, the obtained expressions are applied in Paris law for debond growth simulations in cyclic tension–tension loading.

Using Electronic Speckle Pattern Interferometry (ESPI), full-field displacement measurement was performed on the edge of a cracked cross-ply graphite/epoxy laminate subjected to a tensile loading. The displacement jumps corresponding to cracks are clearly visible and can be used to determine the crack opening displacement (COD) values along the cracks. The main objective of this study is to determine if the application of successive loads of increasing magnitude may have modified the existing cracks and thereby changed the COD dependence on the applied stress. Moreover, we have tested the applicability of the assumed linear elastic COD behavior in the presence of very high stress concentration at the crack tips. The profile of the opening along the crack was also studied.

A numerical analysis, using the Boundary Element Method, of the stress state within the specimen in the single fibre fragmentation test is presented first. Thermal residual stresses and fibre–matrix interfacial friction along the debonding crack faces have been considered in the study. Special attention has been paid to the axial stresses along the fibre and the interfacial tractions and relative displacements in the neighbourhood closest to the debonding crack tips. In order to analyse the debond propagation, the associated Energy Release Rate has been evaluated from the near-tip elastic solution. Numerical results show that both the effects of thermal residual stresses and of fibre–matrix interfacial friction are opposed to the debond propagation. Additionally, the effect of the debond propagation on the load transfer through the interface has been studied, showing that fibre–matrix interfacial friction has a weak influence on the distance needed to re-establish the nominal axial load within the fragment.

The previously developed closed form expressions for thermo-elastic properties of laminates with intralaminar cracks (Lundmark and Varna, 2005) contain crack surface opening and sliding as main local parameters. The dependence of these parameters on various material and geometrical characteristics was in (Lundmark and Varna, 2005) described by power functions valid only for noninteractive cracks in a given layer (low crack density). In this article the 90-layer crack interaction in terms of its effect on the crack opening displacement (COD) is discussed. The effect on COD is described by the introduced ‘interaction function’ which is determined fitting results of finite element (FE) analysis for cross-ply laminates. To simplify the application in stiffness predictions, the numerically found weak dependence of the interaction on geometrical and material parameters is neglected and the interaction function is presented as a function of crack density only. Using the interaction function to determine the COD, the previously developed calculation scheme (Lundmark and Varna, 2005) has been used to predict stiffness reduction in the entire crack density region. The results are validated comparing with tests and FE simulations.

The effect of the helical wood fiber structure on in-plane composite properties has been analyzed. The used analytical concentric cylinder model is valid for an arbitrary number of phases with monoclinic material properties in a global coordinate system. The wood fiber was modeled as a three concentric cylinder assembly with lumen in the middle followed by the S3, S2 and S1 layers. Due to its helical structure the fiber tends to rotate upon loading in axial direction. In most studies on the mechanical behavior of wood fiber composites this extension-twist coupling is overlooked since it is assumed that the fiber will be restricted from rotation within the composite. Therefore, two extreme cases, first modeling fiber then modeling composite were examined: (i) free rotation and (ii) no rotation of the cylinder assembly. It was found that longitudinal fiber modulus depending on the microfibril angle in S2 layer is very sensitive with respect to restrictions for fiber rotation. In-plane Poisson’s ratio was also shown to be greatly influenced. The results were compared to a model representing the fiber by its cell wall and using classical laminate theory to model the fiber. It was found that longitudinal fiber modulus correlates quite well with results obtained with the concentric cylinder model, whereas Poisson’s ratio gave unsatisfactory matching. Finally using typical thermoset resin properties the longitudinal modulus and Poisson’s ratio of an aligned softwood fiber composite with varying fiber content were calculated for various microfibril angles in the S2 layer.

A concentric cylinder model for an N-phase composite with orthotropic properties of constituents was previously presented by the authors. With only minor modifications the model allows for including also free hygroexpansion terms in the elastic stress–strain relationship in order to deal with orthotropic phase swelling. Thus the effect of wood fibre ultrastructure and cell wall hygroelastic properties on wood fibre composite hygroexpansion may be analysed.Multiscale modelling was performed to calculate the hygroexpansion coefficients of both the fibre cell wall and the aligned wood fibre composite.Furthermore, the fibre's helical structure leads to an extension–twist coupling and thus a free fibre will deform axially and also rotate upon loading in longitudinal fibre direction. Within the composite, however, the fibre rotation will be restricted. Therefore, the decision was to compare the composite performance in the two extreme cases(i) free rotation(ii) no rotation of the fibre in the composite.

The energy dissipated in cross-ply laminates during loading–unloading loops is obtained from stress–strain curves for cross-ply laminates and used in an energy based approach to predict the development of matrix cracking. The dissipated energy is correlated to the crack density growth data recorded for a reference laminate. The critical strain energy release rate, Gc obtained in this way is increasing with the applied strain. This phenomenon reflects the statistical nature of Gc distribution in the 90-layer: the first cracks (lower strain) develop in positions with lower fracture toughness. The obtained Gc data are in a good agreement with fracture toughness data obtained using LEFM based “compliance calibration” model in which the stiffness change with increasing strain is used. Finally, the matrix cracking development is successfully simulated using in the LEFM model, the data for critical strain energy release rate and an earlier derived stiffness–crack density relationship. It has been demonstrated that knowing the laminates geometry and measuring the laminate stiffness reduction with strain or (alternatively measuring the dissipated energy) the damage evolution may be simulated, thus reducing the necessity for optical observations to validation only.