One of the main drawbacks of wood fiber-based composite materials is their propensity to swell due to moisture uptake. Because the wood fibers are usually the main contributor to hygroexpansion, it is of interest to quantify the hygroexpansion coefficient of wood fibers, to compare and rank different types of fibers. This investigation outlines an inverse method to estimate the transverse hygroexpansion coefficient of wood fibers based on measurements of moisture induced thickness swelling of composite plates. The model is based on composite micromechanics and laminate theory. Thickness swelling has been measured on polylactide matrix composites with either bleached reference fibers or crosslinked fibers. The crosslinking modification reduced the transverse hygroexpansion of the composites and the transverse coefficient of hygroexpansion of the fibers was reduced from 0.28 strain per relative humidity for reference fibers to 0.12 for cross-linked fibers.
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.
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.
The objective of this work is to evaluate the effect of residual thermal stresses, arising after assembling a single-lap joint at elevated temperature, on the inelastic thermo-mechanical stress state in the adhesive layer. The numerical analysis (FEM) employing linear and non-linear material models, with geometrical nonlinearity accounted for, is carried out. Simulating the mechanical response, the calculated thermal stresses are assigned as initial conditions to polymeric, composite and metallic joint members to reflect the loading sequence where the mechanical strain is applied to cooled-down structure. It is shown that the sequence of application matters and simulations with simultaneous application of temperature and strain give different result. Two scenarios for adhesive joints with composites are studied: joining by adhesive curing of already cured composite parts (two-step process) and curing the adhesive and the composite simultaneously in one-step (co-curing). Results show that while in-plane stresses in the adhesive are higher, the peaks of out-of-plane shear stress and peel stress (most responsible for the joint failure) at the end of the overlap are reduced due to thermal effects. In joints containing composite parts, the one-step joining scenario is more favorable than the two-step. The ply stacking sequence in the composite has significant effect on stress concentrations as well as on the plateau value of the shear stress in the adhesive.
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.
This study presents comprehensive numerical stress analysis in the adhesive layer of a single-lap joint subjected to various loading scenarios (mechanical and thermal loading). For this purpose numerical model (finite element method) with novel displacement coupling conditions able to correctly represent monoclinic materials (off-axis layers of composite laminates) has been developed. This model includes nonlinear material model and geometrical nonlinearity is also accounted for. The effect of thermal residual stresses (in adhesive) is analysed for various methods of manufacturing of single lap joint. The sequences of application of thermal and mechanical loads for the analysis of the thermal residual stresses in joints are proposed. It is shown that the most common approach used in many studies of linear superposition of thermal and mechanical stresses works well only for linear materials and produces wrong results if material is non-linear. The present study demonstrates suitable method to apply combined thermal and mechanical loads to get accurate stress distributions. Based on the analysis of these stress distributions the conclusions concerning the effect of the thermal residual stresses on peel and shear stress concentrations are made. The comparison between effect of thermal stresses in case of the one-step and two-step joint manufacturing techniques is made.
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.
Abstract: The current investigation focuses on development and verification of a modelfor numerical simulation of performance of adhesive joints under tensile loading. Differentcombination of materials in joints is considered: metal-metal, composite-composite andcomposite-metal. The objective of this paper is to present simulation results of joints usingan accurate finite element model including non-linear behaviour and large deformation.Moreover, several loading scenarios are analysed, including simultaneous application oftemperature and mechanical load. Not only the effect of temperature on mechanicalperformance of materials (adhesive as well as adherents) is analysed but also built up ofresidual thermal stresses during the manufacturing of joints are taken into account. Thisapproach is demonstrated by simulation of tensile tests of joints at several temperatures.Two scenarios of application of temperature and mechanical load using large deformationtheory are considered: 1) the thermal and mechanical loads are applied simultaneously (theproperties of the materials are adjusted accordingly to their performance at differenttemperatures); 2) temperature is applied on specimen which is not macroscopicallyconstrained and the obtained stress distribution is used as initial state for the nextsimulation of mechanical loaded joint. The influence of edge effects (due to limited widthof the joint) on the stress distribution within the joint are studied. In order to eliminatethese effects the periodic boundary conditions (BC) are used in the numerical model.These BC are adjusted to optimize numerical model and obtain efficient calculation routinefor analysis of stresses within interior part of the structure. The validity of these BCs isevaluated and verified by analysing number of case studies. The comparison between full3D FEM model and simplified 2D model is carried out. The resulting stress distributions inthe overlap region of joints are presented for different joints (the parameters are: materialcombinations, material models, geometry of adhesive layer, constraints and BCs) withcomprehensive analysis and recommendations for optimal numerical model that can beused in joint design.
A numerical study of the adhesive joint 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 major effect 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.
Damage initiation and evolution in NCF composites leading to final failure includes a multitude of mechanisms and phenomena on several length scales. From an engineering point-of-view a computational scheme where all mechanisms would be explicitly addressed is too complex and time consuming. Hence, methods for macroscopic performance prediction of NCF composites, with limited input regarding micro- And mesoscale details, are requested. In this paper, multi-scale modelling approaches for in-plane transverse strength of NCF composites are outlined and discussed. In addition a simplistic method to predict transverse tensile and compressive strength for textile composites featuring low or no fibre waviness is presented
Models based on variational analysis are compared with respect to the elastic properties of cross-ply laminates with transverse cracks. All models use the principle of minimum complementary energy for calculation of the stress state in a laminate element between two cracks, as was the case with the original model by Hashin (1985). The models are based on assumptions of different degree of accuracy, where the most refined model was developed by the present authors. Experimental data for the longitudinal stiffness are compared with predictions for glass fiber/epoxy cross-ply laminates. The agreement between model predictions and data is good provided the initial assumptions of the stress state are sufficiently accurate
The effect of toughness on the onset of transverse cracking was studied in [0m/90n]s cross-ply laminates. Experimental observations indicated that carbon fiber composites based on tougher matrices show weaker constraint effect although their mechanical cracking strain improves in the low constraint region. From LEFM theory it was predicted that the total transverse cracking strain in a thick 90-deg layer of a cross-ply laminate is 1 . 58 times higher than the transverse failure strain of the unidirectional composite. This was verified by experimental data. The LEFM-based model by Isida was applied to the transverse cracking problem in order to predict the total transverse cracking strain for different cross-ply laminates. Model predictions showed good agreement with experimental data for the brittle matrix T300/934 carbon fiber composite. However, for carbon fiber composites the predictions did not describe the experimentally observed weakening of the constraint effect with increasing toughness.
[04/90n]s and [90n/04 ]s laminates were used to study 90°-layer failure mechanisms in HTA/6376 carbon fiber/toughened epoxy. The different stacking sequences were chosen to vary the stress states, since experimental results show differences in failure strains as well as in the local delamination behavior at the crack tip. Differences in the onset of transverse cracking and local delamination behavior between [04/90m]s and [90 n/04]s laminates was discussed using a model based on linear elastic fracture mechanics (LEFM). Although quantitative LEFM-predictions do not agree with data for the carbon fiber/toughened epoxy investigated, the general predictions for differences in and causes of local delamination behavior were confirmed by experimental data. The fact that the main features were correctly predicted, encourages the development of some modified LEFM-approach to describe toughened matrix composites.
A critical analysis of two simple and convenient analytical models for calculation of elastic properties of woven fabric composites is performed. Predictions of these models are compared with results obtained using the method of reiterated homogenization and with experimental data for plain weave glass fiber and carbon fiber polyester composites. Three different scales are identified in the analysis. The first scale predictions, which are the tow properties (obtained by applying Hashin's concentric cylinder model, the Halpin-Tsai expressions or mathematical homogenization technique), are the most critical because they form the input information for woven composite modeling. It appears that the uncertainty in this information causes larger differences in predictions than the deviations between models of different degree of accuracy. This fact sets limits on the required accuracy of the models. Model comparisons reveal that the woven compoiste model based on isostrain assumption in the compoiste plane and isostress assumption for out-of-plane components is in very good agreement with both experimental data and the reiterated homogenization method, whereas the modified mosaic parallel model fails to describe composites with large interlaced regions.
The Energy Release Rate (ERR) and the contact zone size for a fiber/matrix interface debond are studied for a thin-ply glass fiber/epoxy laminate. The main objective is to analyze the effect on the debonding process of the presence of a traction-free specimen surface or an adjacent material, in the form of a stiffer UD ply or by considering it as part of a thick 90° layer, at different levels of fiber content. To this end, a model of Representative Volume Element (RVE) subjected to different combinations of boundary conditions is proposed. It is found that the constraining effect of the adjacent ply favors at high fiber volume fractions the opening of small debonds (10 − 40°) for the same level of strain. The results agree well and provide a mechanical explanation to previous microscopic observations available in the literature [4].
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 support the claim that debond growth is not affected by the plythickness effect.
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.
Initiation and propagation of fiber/matrix interface cracks are analyzed in Representative Volume Elements (RVEs) of UD and cross-ply laminates. By studying the distribution of stresses at the fiber/matrix interface in the undamaged case, an estimate of the initial flaw size is derived. By adopting a 2-parameters energy-based criterion for propagation [1], we then proceed to the estimation of the expected debond size in different microstructural arrangements. Finally, the results are compared with microscopic observations available in the literature [2].
The growth of fiber/matrix interface cracks (debonds) locatedon consecutive fibers along the through-the-thickness (vertical)direction is studied in glass fiber-epoxy UD composites. Debonds couldappear, along the vertical direction, on the same or on opposite sides oftheir respective fibers. Determining which configuration is the mostenergetically 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 ofcoupling of the vertical displacements to model a unit cell repeating symmetrically along the vertical direction; the second uses a novel setof boundary conditions, proposed here by the authors, to represent a unitcell repeating anti-symmetrically along the vertical direction. The modelis analyzed in the context of Linear Elastic Fracture Mechanics (LEFM)and the Mode I and Mode II Energy Release Rate are evaluated toinvestigate crack growth. The calculation is performed using the VirtualCrack Closure Technique (VCCT) in the framework of the Finite ElementMethod (FEM). It is found that Mode I dominated propagation is favoredwhen debonds are located on the same sides of their respective fibers;while for larger (Mode II-dominated) debonds, Mode II ERR is higher whenthey lie on the opposite sides. No interaction effect is present when atleast two fully bonded fibers are located between the partially debonded ones.
Non-crimp fabric (NCF) composites, manufactured by resin infusion techniques are one of the most promising next generation composite materials. They offer large potential for application in primary structures as they give excellent performance at low production costs. However, before NCF composites will be efficiently used in design, detailed understanding of governing micro mechanisms must be accumulated and described by predictive models. In the present study, NCF cross-ply laminates have been tested in tension. Intralaminar cracks caused in the 90° fibre bundle layers and their effect on laminate mechanical properties have been monitored. Occurrence of ‘novel' type of cracks propagating in the load direction (longitudinal cracks) is explained by a thorough FE analysis using an Representative Volume Element (RVE) approach, revealing stress concentrations caused by 0° fibre bundle waviness. Effects of damage on mechanical properties are modelled using modified micro mechanical models developed for analysis of conventional laminated composites. The analysis reveals mechanical degradation to be ruled by the crack opening displacement (COD). However, unlike traditional composites, transverse cracks do not generally extend through the entire thickness of the 90° layer, but are rather contained in single fibre bundles, limiting the COD
Assuming that Paris law is applicable for individual debond crack propagation along the fiber/matrix interface, the related strain energy release rate in a unidirectional composite is analysed using FEM and also using simple analytical considerations based on self-similar debond crack propagation. Model with axial symmetry consisting of three concentric cylinders is used: partially debonded broken fiber in the middle is surrounded by matrix cylinder which is embedded in a large block of effective composite with properties calculated using rule of mixtures and Halpin-Tsai expressions. It is shown for pure mechanical loading that the fiber elastic properties have a huge effect on the released energy, whereas fiber content in the composite in the considered realistic range has effect only for short debonds. The interaction between debonds approaching from both fiber fragment ends is investigated and related to material properties and geometrical parameters. It is shown that the self-similar debond propagation model gives slightly overestimated values of the strain energy release rate which may be related to interaction effects not included in the analytical model.
The main objectives of this study are to visualize the displacement field on the edge of a [0, 554, -554]s GF/EP laminate specimen with multiple transverse cracks and to analyze the crack opening displacement dependence on the applied mechanical load. The specimen full-field displacement measurement was carried out using ESPI (Electronic Speckle Pattern Interferometry) and phase-shifting. ESPI is an optical technique that provides the displacement for every point on a surface. The measurement resolution is roughly 20 nm. The displacement measurement is along the tensile axis and takes place on the specimen edge. Using the displacement map, it is possible to obtain the displacement profiles along the tensile-axis. The different profiles were drawn along the specimen edge at several distances from the mid-plane corresponding to the different plies. Studies of the displacement discontinuities make it possible to carry out a measurement of the crack opening displacements corresponding to the cracks in the measurement field. The experimental results are in a good agreement with idealized straight crack model in low stress region and much larger in the high stress region, which is attributed to development of local inter-ply delaminations.
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.
Using Electronic Speckle Pattern Interferometry (ESPI), the full-field displacement measurement was obtained on the edge of a cracked 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 high load may have modified the existing cracks and consequently changed the COD dependence on the applied stress. The profile of the opening was also studied.
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.
Usually, the viscoelastic (VE) response of polymers for applications in composites is obtained in uniaxial strainor stress-controlled tests. However, analyzing multimaterial structures by the Finite Element Method (FEM) or by other numerical or analytical tools, a material model in terms of a complete set of compliance functions and/or relaxation functions is required. In this paper, a methodology and exact analytical expressions for calculating the whole set of VE functions is presented based on the relaxation modulus E(t)and Poisson’s ratio v (t) determined in strain-controlled tests. The method is based on Laplace transforms, where an exact inversion is possible if a linear VE model with functions in Prony series is used. Results of the analytical model are compared with the FEM simulation, where specific boundary conditions to determine each particular VE function are used. Finally, the applicability of the so-called quasi-elastic method is investigated, where the expressions of elasticity theory are used to calculate a given viscoelastic function at an instant of time tk using the instant values of E(tk) and v(tk). For isotropic materials, the three approaches render almost coinciding results.
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.
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
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 characterization 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.
The effect that different curing time/temperature conditions bring to the final properties of a polymeric resin, along with measurements of their chemical shrinkage have been investigated in the present study.
Exposing a laminate structure to thermal cycles and to temperatures close to the curing temperature, followed by mechanical fatigue, cause interlaminar and intralaminar cracks leading to degradation of the mechanical properties. The effect of thermal and mechanical fatigue, as well as thermal aging, on carbon fiber composite laminate structures is under study in the present paper.
The most common damage mode and the one examined in this work is the formation of intralaminar cracks in layers of laminates. These cracks can occur when the composite structure is subjected to mechanical and/or thermal loading and eventually lead to degradation of thermo-elastic properties. In the present work, the shear modulus reduction due to cracking is studied. Mathematical models exist in literature for the simple case of cross-ply laminates. The in-plane shear modulus of a damaged laminate is only considered in a few studies. In the current work, the shear modulus reduction in cross-plies will be analysed based on the principle of minimization of complementary energy. Hashin investigated the in-plane shear modulus reduction of cross-ply laminates with cracks in inside 90-layer using this variational approach and assuming that the in-plane shear stress in layers does not depend on the thickness coordinate. In the present study, a more detailed and accurate approach for stress estimation is followed using shape functions for this dependence with parameters obtained by minimization. The results for complementary energy are then compared with the respective from literature and finally an expression for shear modulus degradation is derived.
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.
As polymeric resins are used as matrix in reinforced composites, understanding of their viscoelastic-viscoplastic response is critical for long-term performance design. However, during service life, thermosets are not in a thermodynamic equilibrium state, resulting in physical aging, which affects failure and viscoelastic (VE) properties, becoming a concern for industries. In this paper, an alternative methodology for testing and parameter determination for aging polymer, at different temperatures (TA) and times (tA), is proposed. The experimental data analysis was performed using a Schapery's type thermo-aging-rheologically simple VE model with constant coefficients in Prony series and the effect of temperature and aging included by two shift factors (aT, aA). Results showed that the shift factor can be presented as the product of shifts aT and aA. Furthermore, for short tA the change rate of the aA with tA does not depend on TA, whereas for long tA at high TA the rate increases.
At service temperatures, ultra-high molecular weight polyethylene (UHMWPE) is a highly viscoelastic (VE) material due to its low glass transition temperature (≈-113 °C). Since the mechanical response changes over time, the ability to predict and improve its performance over lifetime is an engineering concern. Adding short carbon fibers (SCF) as reinforcement (10 wt%) is expected to improve the material instant and long-term properties. VE relaxation functions for UHMWPE and composite at different temperatures (25-100 °C) are obtained from experimental data used to find parameters in a Schapery's type linear VE model. Then, relaxation functions of the SCF (randomly distributed) composite are predicted using the quasi-elastic approach. The results show that fibers affect positively the VE properties of UHMWPE and that the temperature- and time-dependent matrix behavior affects the stress transfer to fibers However, due to uncertainty regarding the input parameters, limiting the applicability of the chosen quasi-elastic approach, the quantitative agreement is not perfect.
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.
Numerical analysis was performed with the aid of the Boundary Element Method (BEM). Contact conditions were taken into account using a weak formulation of the equilibrium compatibility equations along the interface of the solids. Comparison of the different kinds of failure was made in terms of the energy release rate
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 analyze 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.