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In-situ fatigue damage quantification in non-transparent thermoplastic composites is cumbersome, however, it provides vital information for developing reliable fatigue damage models. This study investigates the tension -tension fatigue behaviour of Glass/Polypropylene laminates. The mechanical response and damage progres-sion in [02/902]s , [902/02]s and [0/90]2s lay-ups are characterized over 500 000 cycles. Microscopic analyses and through-the-width sectioning are considered to compare detected edge cracks to the internal damage state. Effects of ply thickness and location as well as fabrication-induced morphology on fatigue response are inves-tigated. Normalized stiffness reduction and Poisson's ratio evolution in function of measured crack density are compared with numerical results showing good agreements.

Accurate prediction of stiffness degradation in the damaged plies (laminae) is a fundamental requirement for developing damage models for composite materials. In this study, a mesoscale analysis is proposed to predict all the effective thermo-elastic constants of damaged plies containing ply cracks and delaminations based on a numerical homogenization method. To do so, the in-plane and out-of-plane loading conditions are imposed on the three-dimensional representative volume elements (RVEs) using the periodic boundary conditions (PBCs). Considering the stress/strain fields obtained from the numerical simulations, the effective behavior of the damaged plies is evaluated. Moreover, the effects of various damage configurations, material properties, orientations of adjacent plies and ply thicknesses are studied to address the dependency of the effective elastic constants to those parameters. Numerical results reveal that the ply cracking and delaminations significantly reduce the in-plane and out-of-plane properties ([Formula: see text], [Formula: see text],[Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) of the damaged plies. Furthermore, to demonstrate the accuracy and capability of the developed homogenization method, the homogenized properties of the damaged plies are used in the intact laminates where the stiffness of such laminates are compared with direct FE simulation and available experimental data of the laminates containing ply cracks and local delamination.

Delamination induced by ply cracking is an important damage mechanism that results in stress redistribution and degrades both the in-plane and out-of-plane laminate properties. In this work, a novel variational model is first developed that accurately predicts stress and displacement fields in arbitrary symmetric laminates, containing uniformly spaced ply cracks in a single orientation with delaminations on the interfaces between the plies at the tips of ply cracks, subject to general triaxial loading and thermal residual stresses. The model is then used to predict the dependence of the in-plane and out-of-plane laminate thermo-elastic properties on ply crack density and delamination length. The results are extensively compared with those obtained from refined finite element methods and available experiments, showing excellent accordance.

Longitudinal tensile failure of unidirectional fibre-reinforced composites remains difficult to predict accurately. The key underlying mechanism is the tensile failure of individual fibres. This paper objectively measured the relevant input data and performed a detailed experimental validation of blind predictions of six state-of-the-art models using high-resolution in-situ synchrotron radiation computed tomography (SRCT) measurements on two carbon fibre/epoxy composites. Models without major conservative assumptions regarding stress redistributions around fibre breaks significantly overpredicted failure strains and strengths, but predictions of models with at least one such assumption were in better agreement for those properties. Moreover, all models failed to predict fibre break (and cluster) development accurately, suggesting that it is vital to improve experimental methods to characterise accurately the in-situ strength distribution of fibres within the composites. As a result of detailed measurements of all required input parameters and advanced SRCT experiments, this paper establishes a benchmark for future research on longitudinal tensile failure The research leading to these results has been conducted in the framework of the FiBreMoD project and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 722626. Compressive tests on the neat epoxy resin were performed at the mechanical lab of the Institute of Mechanics, Materials and Civil Engineering (IMMC), Université Catholique de Louvain (UCLouvain) with the kind support of J. Chevalier and T. Pardoen. M.J. Emerson from QIM, Technical University of Denmark (DTU) is thankfully acknowledged for the handson training sessions and support of the Insegt Fibre segmentation toolbox. Support of C. Schlepütz from TOMCAT beamline at Swiss Light Source for optimising the acquisition settings during the beamtimes under proposal IDs 20161157 and 20171494 is thankfully acknowledged. J.M. Guerrero would like to acknowledge the grant BES-2016-078270 from the ‘Subprograma Estatal de Formación del MICINN’ cofinanced by the European Social Fund, and all authors from the University of Girona acknowledge the funding from the Spanish project RTI2018-097880-B-I00. The work of M. Hajikazemi forms part of the research programme of DPI, project 812T17. S. Pimenta acknowledges the funding from the Royal Academy of Engineering in the scope of her Research Fellowship on “Multiscale discontinuous composites for high-volume and sustainable applications” (2015-2019). R.P. Tavares and P.P. Camanho would like to thank the financial support provided by FCT - Fundação para a Ciência e a Tecnologia through National Funds in the scope of project MITP-TB/PFM/0005/2013

Predicting the nonlinear mechanical response of short fiber reinforced composites (SFRCs) is a crucial and challenging task. In this paper, a computationally efficient multi-scale strategy is proposed to predict the anisotropic elasto-plastic behavior of SFRCs using the intrinsic mechanical behavior of the pure polymer and fibers without the requirements for reverse engineering. In doing so, different simple unit cells are first examined to find the one that can adequately describe the nonlinear mechanical response of SFRCs' representative volume elements (RVE) with aligned fibers. Considering the effects of packing configuration, fiber aspect ratio, volume fraction and material properties, the performance of different unit cells is investigated. Then, the homogenized mechanical responses of unit cells are linked to Hill's anisotropic plasticity model to correlate the mechanical response of the suggested unit cell to the continuum domain. Using the pseudo-grain approach and a numerical orientation averaging framework, the effects of fiber misalignment are taken into account. A multi-step homogenization strategy is also employed to consider the variation of fiber orientation tensor and volume fraction through the thickness. Finally, the validity and robustness of the proposed multi-scale strategy are extensively investigated based on the RVE-generated results and the available experimental observations.

Short gauge length coupons of plain woven Carbon/Epoxy with layup [ # ( 0 / 90 ) ] 24 and [ # ( 45 / − 45 ) ] 24 are subjected to Compression-Compression and Tension-Compression fatigue loading at several stress levels. Inspection of the gauge length with Digital Image Correlation (DIC) allows measurement of the strain field. The hysteresis loops, axial and shear stiffness as a function of the number of cycles are obtained from the strain field and measured load. For most of the tests a general degradation of the specimen stiffness is observed. For the coupons subjected to uniaxial Compression-Compression with layup [ # ( 45 / − 45 ) ] 24 , however, a 17% stiffness increase is seen during the first 10 4 cycles. Post-mortem inspection revealed that the aluminium tabs of the coupons, to facilitate load introduction from the clamps, had partially debonded during testing. A 3D finite element analysis of the coupons including tabs is carried out to investigate the phenomena. The degradation of the tab-coupon bond is modelled using contact with debond capability. This confirmed that tab debonding is responsible for significantly altering the stress state in the (short) gauge section which results in an apparent stiffening of the sample during fatigue loading. Hereby, the authors offer a new explanation for stiffness increase of composite coupons in fatigue tests. For future tests it is shown that quantification of tab debonding is necessary to provide a decisive answer about the experimental boundary conditions in the gauge section of the coupon.

The practically important problem of the modification of laminate out-of-plane shear stiffness by ply cracks is hardly investigated in the literature. In this paper, out-of-plane shear stiffness reduction of laminates containing uniform and non-uniform distributions of ply cracks is studied. A novel variational model is developed to determine accurately stress transfer mechanisms and consequently out-of-plane shear stiffness reduction of general cracked laminates under applied out-of-plane shear loads. It is shown that the presence of ply cracks in a laminate under out-of-plane shear loads, perturbs the uniform distribution of shear stresses and induces high gradients of in-plane stresses leading to large shear stiffness reductions. The results are compared with those of the finite element method (FEM) implementing periodic boundary conditions. It is shown that there is excellent accordance between the results obtained from these approaches. The outcome of the paper provides necessary information for determination of damage-based constitutive laws for composites.

This article presents a finite element model to predict the thermo-mechanical behavior of ply-cracked composite laminates from their discrete structure at the ply level, i.e., the mesostructure, utilizing the second order homogenization method. With the assumption that the cracks are statistically regularly distributed within a composite laminate, the homogenization theory for periodic materials can be employed. Thus, instead of considering the whole laminate under thermo-mechanical loading, a significantly less computationally demanding analysis can be done on a repeated unit cell (RUC). Finite element analyses are performed to determine the accurate stress fields in the RUC under in-plane and flexural out-of-plane loading. During these analyses, the periodic boundary conditions are imposed on the surfaces of the RUC. The macroscopic thermoelastic properties are then derived from the stress/strain fields in the RUC by means of the numerical homogenization scheme. The physical fidelity of the proposed model is shown by good agreement between the predicted thermo-mechanical properties of the considered ply-cracked composite laminates and the corresponding data from experiments and analytical methods. In addition, insightful analyses of ply-cracked laminates with one or more off-axis plies are also conducted. Results from these analyses have been rarely reported in literature and can be utilized for benchmark solutions.

In this paper, a new constitutive model is proposed for the behavior of thermoplastic polymers under non-isothermal conditions. The model couples linear viscoelasticity, viscoplasticity and thermal effects. It is formulated within the framework of irreversible thermodynamics. The total strain is the sum of viscoelastic, viscoplastic and thermal strains. General hereditary integrals describe the thermo-viscoelastic response. The viscoplastic part accounts for both isotropic and kinematic hardenings. The stress-strain response and the material self-heating are predicted and compared to experimental data on Polyamide 66 (PA66) and Polypropylene (PP). Good agreement between the numerical simulations and experimental data was obtained for the two materials.

In this paper a calculation tool is mentioned for the design of simply supported single span GFRP pedestrian and bicycle bridges. The overall goal of this tool is to help users create an initial design based on a limited number of input parameters. In addition and to show the power of this calculation tool, a parametric study is presented, demonstrating the influence of different input parameters on the design outcomes. The cal-culation tool clearly demonstrates that the design of a typical GFRP pedestrian and bicycle bridge is not strength driven, but mainly depends on the deflection and the vibration criteria, i.e. on SLS requirements. Moreover, it is shown that the choice of the deflection requirement itself, which is in a sense arbitrary, has an important influence on the design and the total mass of the bridge. Further, a design graph giving the most 'economic' bridge for different lengths and slendernesses is drawn up and the effect of a comfort level based design is shown.

Many models for prediction of longitudinal tensile failure of unidirectional (UD) composites have been developed in the last decades. These models require significant assumptions and simplifications, but their consequences for the predictions are often not clearly understood. This paper therefore presents a blind benchmark of seven different models applied to two virtual materials. Reliably capturing the localisation of stress concentrations was vital in predicting the effect of matrix stiffness and strength on composite failure strain and strength as well as fibre break and cluster development. Although the models have different assumptions regarding stress redistributions around fibre breaks, the 2-plet (clusters of two fibre breaks) development was similar. Distance-based criteria were shown to be inadequate for monitoring cluster development. The discussions provide detailed insight into how the model assumptions are linked to the differences in the predictions. European Union’s Horizon 2020 research and innovation programme published

We performed in-situ tensile tests on two carbon fibre/epoxy composites with continuous scanning using synchrotron computed tomography (CT). Both composites were cross-ply laminates, and two specimens were tested for each compos- ite. The voxel size was sufficiently small to recognize individ- ual fibres and fibre breaks. For each test, 16-19 volumes were reconstructed, cropped down to the 0° plies and analysed to track fibre break and cluster development. This dataset provides the last CT volume before failure for each of the four specimens as well as the individual fibre break locations in all reconstructed volumes. These data are then plotted against predictions from six state-of-the-art strength models. The target is that these data become a benchmark for the development of new models, inspiring researchers to set up refined experiments and develop improved models. © 2021 Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. Such randomness in microstructure and in failure evolution generally leads to non-uniform distributions of ply cracks. Modeling this non-uniformity is a crucial factor in predicting the initiation and propagation of matrix cracks. Therefore, a novel stress-based variational model is developed to accurately predict stress transfer and stiffness reduction in general symmetric laminates containing non-uniformly spaced ply cracks. In contrast to available approaches for uniformly spaced ply cracks based on the unit cell, the analysis is carried out for the entire laminate. Results derived from the developed method for thermo-elastic properties of the cracked laminates show an excellent agreement with finite element results. Moreover, the accuracy of predictions based on an approximate approach is discussed using a comprehensive analysis of various laminates and crack patterns for both carbon and glass fibre systems.

In this work the modelling of wind turbine blades subjected to torsional loads is explored. Usually, wind turbine blades are modelled using Outer Mold Layer (OML) shell models, whose mid-surface does not coincide with the nodal plane, and have been shown not to capture their behaviour correctly in torsional loadings, highly underestimating the torsional stiffness of the blade. To better understand the differences between using OML shell models and solid element models, a cylinder tube first is analysed and the conclusions from this study are applied for the wind turbine models. It was observed that artificial deformation modes were responsible for the erroneous results when using offset shell elements. These results can be drastically improved by controlling the stiffness associated with the drilling Degree Of Freedom (DOF). Furthermore, a high fidelity definition of the geometry of the blade is crucial to accurately capture its behaviour in torsion. By carefully controlling these parameters, the stiffness difference between the offset shell and solid models was reduced from 35% to 5%.

A variational model is developed to exactly determine both stress and displacement fields at free edges of general symmetric composite laminate strips under thermomechanical loads. By partitioning the total stresses in a composite with free edges into unperturbed (without free edge) and perturbation stresses and using the minimum complementary energy principle, the optimal stress and displacement fields are derived that exactly satisfy equilibrium, compatibility, boundary and continuity conditions. The paper extends the theory of stress-based variational stress transfer so that the effects of both applied traction and displacement loads can be considered. It has been also shown how the displacement field can be determined for a stress-based variational approach. The results are compared to refined finite element results. The superiority of the developed method over finite element method, both in terms of accuracy and computational efficiency, is discussed. The method is also applicable to thin-ply laminates and is computationally efficient.

Determination of the effective elastic properties of unidirectional short fiber reinforced composites (SFRCs) is a key fundamental requirement which is usually estimated by mean-field homogenization (MFH) methods. Available classical MFH methods only account for volume fraction and aspect ratio of the fibers and do not consider the physical cylindrical geometry of the fibers. Moreover, classical MFHs are not designed for predicting the effective properties of SFRCs with distinct packing configurations and order of fibers. In this work, new modified Eshelby tensors associated with an enhanced MFH are developed which resolve the mentioned limitations of the available MFH methods and preserve their computational efficiency. While classical Eshelby tensors used in MFHs depend only on the aspect ratio of the fictitious ellipsoidal inclusion and material properties of the matrix, the introduced modified Eshelby tensors additionally account for physical cylindrical geometry as well as interactions of the short fibers with different packing configurations. Moreover, non-uniform homogenizing eigenstrains required for accurate homogenization of the short fibers are also incorporated by the proposed analytical treatment. Predictions of the developed enhanced MFH for various packing configurations are compared with those obtained from Finite Element Method implementing periodic boundary conditions and very good agreements are observed. It is shown that packing configuration and geometrical specifications of short fibers can significantly affect the effective properties of the SFRC.

A general multiscale hierarchical framework is proposed to identify the material parameters of a mesoscale model using numerical simulations based on virtual micro-mechanical tests. The identification of the material parameters is usually done with several experiments on different laminates. These experiments are replaced by virtual tests on a microscale finite element model with the same load conditions than the real experiments. The microscale model represents the unidirectional ply geometry based on its constituents, fibers and matrix, with their corresponding properties and the damage behavior of the matrix and interface between them. Under the defined load conditions, the homogenized stress-strain behavior of the laminates is obtained and then, the constitutive model parameters of the ply damage mesomodel are identified. As an example, the proposed framework is applied to identify the material parameters of the elementary ply damage mesomodel developed at LMT-Cachan. It is shown that, when the materials, geometry and load conditions are correctly defined in the micromodel, the real experiments can be replaced by virtual tests. As a result, the amount of experiments can be reduced saving costs and time. In addition, further studies can use the proposed methodology based on virtual micro-mechanical tests to improve the current mesoscale models.

Tensioned fabric membrane structures, in which a coated fabric material is used as both cladding and supporting structure, are classified as unconventional structures and demand a dedicated design method. In this paper, we propose a method to combine different stages in design and analysis of these structures within the shape optimization framework. The proposed method facilitates the incorporation of various sources of nonlinearities in the analysis of tensioned membrane structures. Especially, the amount of fabric panels compensation when using simple material model for the coated fabric, i.e., linear orthotropic elasticity, as is widely used in practice, is presented. The novelty of the proposed method lies on the postulation of a stress-free 3-D intermediate configuration, which is built from flat fabric panels. The goal is to find an optimum shape of this 3-D intermediate configuration such that the stress distribution in the resulting structure, which is formed by deforming the 3-D intermediate configuration, remains at desired levels. A nonlinear finite element analysis is employed to identify these stress fields in the resulting structures. In this analysis, material and geometrical nonlinearities are taken into account. Moreover, the nonlinear kinematical interaction between the boundary cables and the membrane is also considered. Hence the stress fields on the resulting structures are expected to be reliable and close to the physical ones. In this work, different gradientless optimization algorithms, viz., genetic algorithm, pattern search, and Bayesian, are considered. The obtained results show that the stress levels in the resulting structures obtained from the proposed method are close to the desired ones, and the Bayesian optimization algorithm has the best performance among the considered algorithms.

A criterion is developed which predicts matrix fatigue crack initiation for Uni-Directional (UD) composite plies subjected to multiaxial fatigue load at all stress-ratio's: Tension-Tension, Compression-Compression and Tension-Compression. This research is based on physical observations of matrix damage types and their respective driving forces. Existing fatigue prediction formulations, that partly succeed in predicting fatigue life to initiation, are investigated for their key attributes which are subsequently combined in a coherent way. The framework requires 7 material parameters: 4 for Tension-Tension load, 2 for Compression-Compression load and 1 to take into account the accelerated occurrence of damage under Tension-Compression load. The material parameters can be calibrated from only 7 crack initiation S-N curves. 5 experimental datasets, a variety of the two most common reinforcing fibres and matrix (Carbon and Glass fibres combined with an epoxy or PEEK resin), are selected for a thorough verification and validation of the criterion. The agreement of the prediction with experiment is, remarkably, excellent for Glass/Epoxy, good for Carbon/Epoxy and reasonable for Carbon/PEEK. This new framework establishes a solid base for further developments to predict matrix crack initiation and the inclusion of other failure types such as fibre kinking.

In this chapter, a criterion for the prediction of fatigue crack initiation in UD composite plies for all R-ratios is proposed. First, a general background of the framework is given. This is followed by an overview of existing models for fatigue crack initiation prediction. The successful attributes of the discussed models are combined into one coherent criterion which succeeds in predicting crack initiation excellently for glass/epoxy, good for carbon/epoxy, and reasonable for carbon/PEEK. Lastly, several paths for future developments and expansion of the criterion are discussed.

A computational micromechanics based Finite Element (FE) analysis methodology is presented to predict the bi-axial failure envelope of a unidirectional (UD) carbon-epoxy composite ply. In order to estimate the effect of various microscale parameters that are influencing the macroscopic stress–strain behavior, under individual load cases, detailed numerical studies are conducted using a 3D RVE (Representative Volume Element) model. The constituent epoxy matrix plastic deformation in the RVE is captured using the linear Drucker-Prager plasticity model. The effect of the fiber–matrix interface damage, followed by frictional sliding of the constituent materials on the computed interface tractions is captured using the cohesive zone damage model combined with the Coulomb friction law, which is implemented into Abaqus using VUMAT. From the detailed FE analysis of the RVE under individual load cases, it is observed that the predicted macroscopic stress–strain behavior is sensitive to the fiber–matrix interface properties as well as the in-situ epoxy stress–strain behavior. Hence, using a coupled experimental-computational micromechanics approach the interface and the in-situ epoxy material properties are calibrated and validated. Using the calibrated interface and in-situ epoxy material properties, the bi-axial (transverse tension/transverse compression – in-plane shear) failure envelope of a UD composite ply is estimated. Comparing the predicted damage profiles and the failure envelope with the experimental results leads to good agreement and validates the proposed numerical methodology.

An enhanced two-stage inversion scheme for the determination of the viscoelastic properties of orthotropic plates (e.g. fiber reinforced polymers) based on the pulsed ultrasonic polar scan (P-UPS) is presented. A forward numerical model for the P-UPS is combined with an efficient optimizer routine (particle swarm optimizer, PSO) to inversely extract the complex orthotropic stiffness tensor, as well as the orientation of the main axes of orthotropy. The developed inversion technique is validated on synthetic data, yielding accurate results with small deviations: elasticity tensor [ 0 ] 8 carbon/epoxy laminate. The obtained inversion results yield complex stiffness parameters which are in close agreement to reported values in literature, and confirms the potential of the UPS technique and its inversion optimization routine as an enhanced NDT technique to quickly and accurately obtain characteristic material properties of composites.

The aim of this study is to deal with the simulation of intralaminar fatigue damage in unidirectional composite under multi-axial and variable amplitude loadings. The variable amplitude and multi-axial loading is accounted for by using the damage hysteresis operator based on Brokate method [6]. The proposed damage model for fatigue is based on stiffness degradation laws from Van Paepegem combined with the ‘damage’ cycle jump approach extended to deal with unidirectional carbon fibres. The parameter identification method is here presented and parameter sensitivities are discussed. The initial static damage of the material is accounted for by using the Ladevèze damage model and the permanent shear strain accumulation based on Van Paepegem’s formulation. This approach is implemented into commercial software (Siemens PLM). The validation case is run on a bending test coupon (with arbitrary stacking sequence and load level) in order to minimise the risk of inter-laminar damages. This intra-laminar fatigue damage model combined efficient methods with a low number of tests to identify the parameters of the stiffness degradation law, this overall procedure for fatigue life prediction is demonstrated to be cost efficient at industrial level. This work concludes on the next challenges to be addressed (validation tests, multiple-loadings validation, failure criteria, inter-laminar damages…).&nbsp

This work presents a numerical study that addresses the role of the interfacial fracture energy on the debonding process of a capsule embedded in an elastic matrix, which undergoes a uniaxial far-field stress. The motivation of this work is to analyze and to understand the effects of this energy in the framework of the so-called encapsulation-based self-healing cementitious materials, where glass capsules filled with a fluid healing agent are embedded in a cement-based matrix. A two-dimensional plane strain model based on a combination of the classical finite element method and cohesive surface techniques implemented in the commercial code Abaqus® has been used. It has been found that there exist three types of debonding regimes, ranging from a perfect brittle response up to a ductile-limited response, and whose range of validity is governed by a straightforward dimensionless number able to predict the type of debonding as a function of flexural properties of the capsule and the interface strength.

The finite element simulation of nesting phenomena in textile composites is challenging, because of the difficulties that come with creating a 3D finite element model of a stack of nested plies. This paper proposes a 2D modeling approach for prediction of crack initiation locations in nested textile composites. The model is built up based on high resolution microscopic images of the polished edge of a tensile specimen and routines have been developed to take the inhomogeneous intra-yarn fiber volume fractions into account. The locations of critical stresses are compared with high-resolution microscopic images during tensile loading of the nested textile composite, and correlated with the locations of crack initiation. The methodology is validated against tensile experiments on a steel fabric reinforced epoxy laminate. The steel fabric has a high tendency for layer nesting and a high inhomogeneity in intra-yarn volume fractions, and it shows very good contrast in micro-tomography and microscopic images.

During 3D printing by Selective Laser Melting (SLM) of the alloy Ti-6Al-4V, the phase transformation of BCC to HCP is associated with selection of particular crystallographic variants. In the present paper, the distribution of misorientation angle along grain boundaries was investigated by EBSd. It is revealed that the main misorientation pairs were located in the interval between 56° and 66°, which contains three theoretical misorientation angles, i.e. 60.00°, 60.83° and 63.26°. The observed misorientation axis/angle pairs were represented in the Rodrigues–Frank space with a certain tolerance angle, which illustrated clearly the distribution of the observed misorientations around the 5 theoretical values. The main peak of the misorientation pairs was observed for [ 10 5 5 3 ] / 63.26 ° with 43.8% frequency, followed by 1 2 0 ] / 60 ° with 21.8% population, whereas a distribution in the absence of variant selection would have produced values of 18.2% and 36.4%, respectively.

This article presents a fatigue model that can robustly capture the effect of high surface roughness on the fatigue crack initiation of additively manufactured Ti6Al4V (AM Ti64) alloys in the moderate cycle fatigue regime based on nonlinear finite element (FE) analyses and the theory of critical distances. We propose two methods to use surface measurements of AM components to create FE models, viz., surface topography of the component is explicitly represented in the FE models or a simplified geometrical model, which has only a single sinusoidal-shaped notch, is proposed to replace the surface topography in the FE models. The geometrical parameters of the simplified model are derived based on the MOTIF method (ISO 12085) and its parameters are determined by using the leave-one-out cross-validation method. In the moderate cycle fatigue regime, the stress applied to components is below the yield stress, but the high surface roughness acts as a stress raiser and causes local plasticity at surface valleys. Thus, a nonlinear hardening elasto-plasticity model is employed in the FE models to capture the cyclic mechanical behavior of AM Ti64 alloys. Afterward, the fatigue analyses are performed by employing our in-house C++ software within which fatigue indicator parameters (FIPs) are computed by post-processing the finite element results. In the present work, the Smith-Watson-Topper (SWT) parameter is used as an FIP and is computed at every element in the FE mesh, i.e., the local FIP. Subsequently, to account for the stress gradient effect in the proposed fatigue model, the SWT parameter is averaged over a so-called critical area to compute a nonlocal FIP. The physical fidelity of the proposed fatigue model is shown by a good agreement between the predicted fatigue life cycles based on the nonlocal FIP and the corresponding experimental data. Moreover, the predicted fatigue cycles obtained from the simplified geometrical model also yield good accordance to the experimental data, thus we can model the effect of the surface roughness on the fatigue properties of AM Ti64 in an efficient way.

Digital image correlation is utilized to detect automatically crack density in glass/epoxy laminates with different lay-ups under quasi-static and fatigue loading conditions. The DIC setups used in the present work are 2D-DIC and 3D-DIC which are considered to be at meso-scale and macro-scale, respectively. The main objective of this work is to study whether the DIC technique is reliable in automatic crack detection and functional in calculation of crack density. Therefore, an optimization analysis is implemented to evaluate the resolution and the standard uncertainty in strain and displacement measurements. An optimized compromise is attained between the resolution and the uncertainty of both measurements to decide about the final configuration of the DIC setup. The setup is executed by acquiring in-situ images under quasi-static and fatigue experiments so that the images are synchronized with the data acquired from the testing machine. The crack detection analysis is attained by DIC analysis using strain and displacement fields in order to obtain optimum results. Then a semi-automatic program is created to evaluate the crack density and weighted crack density from the edge and top of the specimen, respectively. Moreover, a comparison is established between both strain and displacement fields in crack characterization. Consequently, the displacement field has proved to deliver better and more accurate results than strain fields in crack density calculation and individual crack characterization. Accordingly, the results obtained from DIC analysis are compared and validated by microscopic images which are acquired after performing each test.

This paper formulates an analytical model based on intrinsic material properties to predict ply cracking initiation and propagation in multiple plies and its impact on laminate strength in general symmetric laminates (possibly made of thin-plies) under combined triaxial normal loads and in-plane and out-of-plane shear loads while the effect of thermal residual stresses and statistical distribution of fracture energies are considered. To do so, a novel complete homogenization technique combined with recently developed accurate stress transfer models is implemented in conjunction with multi-axial energy-based failure criteria, Monte Carlo type of simulation and a strain-based fiber failure criterion. The model predictions show very good agreement with experimental results.

The aim of this study is to develop a novel model for predicting homogenized properties of a cracked ply in a symmetric laminate using the crack density and thickness of the ply. In doing so, the periodic boundary conditions are applied to the RVEs in a three-dimensional finite element model to calculate the thermo-elastic constants of symmetric laminates containing uniformly and non-uniformly spaced cracks under in-plane and out-of-plane loading conditions. On the other hand, homogenized material properties of the cracked ply are explicitly determined by averaging procedures for both stress and strain components. Using computed results and nonlinear least square fitting, an analytical formula is proposed to describe the mechanical properties of the cracked ply, which takes into account the effect of ply thickness, material properties and crack density. Different cracked laminates are tested to indicate the potential of the developed method in analyzing complex crack geometries in multiple orientations. Moreover, the applicability and accuracy of the suggested model are verified by comparing the results with those of experiments, variational approach and finite element method.

A robust variational approach is first developed for predicting stress/displacement fields and effective thermo-elastic constants in a laminate with arbitrary lay-up, containing uniformly spaced ply cracks, subject to general triaxial and bending loads when the effects of thermal residual stresses are also considered. The methodology extends some previously developed variational approaches so that general non-symmetric lay-ups (not only cross-ply) under through-thickness loading conditions can be analyzed. Secondly, an approximate methodology is introduced which enables the approach to predict all effective thermo-elastic constants of laminates having non-uniformly spaced ply cracks, including new types of constant required to account for out-of-plane loading. Thirdly, some novel inter-relationships among effective thermo-elastic constants of cracked and uncracked general laminates are obtained showing that just three macroscopic parameters define the dependence of all relevant laminate constants (thirty five) on the state of cracking. The results are compared with those obtained from finite element methods, experiments and other high accuracy models.

In this article, we propose a model that can account for the effect of porosity and high surface roughness on the fatigue crack initiation of AM Ti6Al4V alloys in moderate and high cycle fatigue regimes. Within these fatigue regimes, the applied force to the component is below the yield stress, however, defective features, viz., porosity and high surface roughness, can act as stress raisers. As a consequence, local plasticity can occur. To capture this phenomenon, a nonlinear isotropic kinematic hardening elasto-plasticity model is employed in our finite element (FE) model. For creating the geometry of the FE models, inputs from fractography analyses and surface roughness measurements are needed. From fractography analyses, the shape of pores formed by gas bubbles during manufacture appears quite regular. Thus, these pores are modeled as circles in FE models. The size of these pores and their distance to a free surface of the tested specimens are extracted from Scanning Electron Microscope images. Moreover, it has been mentioned in the literature that statistical parameters of surface roughness cannot fully describe the detrimental effect of this type of defect to the fatigue life of the associated component. Thus, in our FE model, the surface topography, which was measured using stylus-based profilometer, is explicitly modeled. The finite element results are then post-processed by our in-house software to extract the Smith–Watson–Topper (SWT) fatigue indicator parameter (FIP). The SWT parameter is calculated at each element centroid of the FE mesh, i.e., the local indicator. Afterward, an average value of the SWT parameter over a so-called critical area whose center is located at the considered centroid is also calculated, i.e., the average indicator. The results show that the local SWT indicator is too conservative in predicting the fatigue life of the AM Ti64 alloys while the average SWT one can provide good results.

The behavior of composite materials under out-of-plane loads is strongly affected by the presence of transverse ply cracks. The cracks perturb the distribution of stresses leading to large out-of-plane shear stiffness reductions. It is crucial to include these effects in the damage material models to improve their accuracy. Therefore, the stress transfer and stiffness reduction in cracked laminates have been studied with a mesoscale finite element model (FEM) under general in-plane, out-of-plane normal and shear loads. A symmetric laminate containing ply cracks in a single orientation has been considered under the hypothesis of periodicity using a novel relaxed three-dimensional formulation of Periodic Boundary Conditions (PBCs). The local stresses have been verified versus different analytical and numerical methods. In addition, the degraded effective thermo-elastic constants involving out-of-plane properties have been calculated as a function of crack density. Both uniform and non-uniform distributions of cracks have been considered for different lay-ups including angle-ply and unbalanced laminates. The effect of contact between the crack surfaces has been studied for specific loading conditions. It is shown that a single formulation based on three-dimensional periodic boundary conditions is sufficient to determine the interfacial stresses and the complete thermo-elastic constants under in-plane and out-of-plane loads accurately.

In this work, the aerodynamic loads acting on a large horizontal axis wind turbine are analysed in off-design conditions by means of computational fluid dynamics (CFD) simulations. The turbulent wind flow is solved using an unsteady RANS approach and choosing the \(k-\epsilon \) model. Appropriate boundary conditions are used in combination with modified wall functions in order to preserve the atmoshperic boundary layer (ABL) profiles throughout the entire domain. An overset technique is used to handle the rotation of the blades throughout the simulated time. Changing both the pitch angle of the blades and the tip-speed ratio (TSR) of the turbine, several operating points are investigated. The performance and the loads are highly affected by the ABL, whose effect is highlighted. The performance of the wind turbine in each simulated operating point is compared to the nominal operating point (NOP). The aerodynamic loads are monitored, analysed and mutually compared throughout the motion of the rotor, in order to identify the most critical conditions for the blade structures.

A dynamic load and stress analysis of a wind turbine is carried out using transient fluid-structure interaction simulations. On the structural side, the three 50 m long commercial glass-fiber epoxy blades are modelled using shell elements, accurately including the properties of the composite materials. On the fluid side, a hexahedral mesh is obtained for every blade and for the hub of the machine. These meshes are then overlaid to a structured background mesh through an overset technique. The displacements prescribed by the structural solver are imposed on top of the rigid rotation of the turbine. The atmospheric boundary layer (ABL) is included using the k-epsilon turbulence model. The computational fluid dynamics (CFD) and computational solid mechanics (CSM) solvers are strongly coupled using an in-house code. The transient evolution of loads, stresses and displacements on each blade is monitored throughout the simulated time. The ABL induces oscillating axial displacements in the outboard region of the blade. Furthermore, the influence of gravity on the structure is accounted for and investigated, showing that it largely affects the tangential displacement of the blade. The oscillating deformations lead to sensible differences in the torque provided by each blade during its rotation.

In this work the possibility to reverse engineer the transverse isotropic carbon fibre properties from the 3D homogenized elastic tensor of the UD ply for the prediction of woven ply properties is explored. Ultrasonic insonification is used to measure the propagation velocity of both the longitudinally and transversally polarized bulk waves at various symmetry planes of a unidirectional (UD) Carbon/Epoxy laminate. These velocities and the samples' dimensions and density are combined to obtain the full 3D orthotropic stiffness tensor of the ply. The properties are subsequently used to reverse engineer the stiffness tensor, assumed to be transversely isotropic, of the carbon fibres. To this end, four micro-scale homogenization methods are explored: 2 analytical models (Mori-Tanaka and Mori-Tanaka-Lielens), 1 semi-empirical (Chamis) and 1 finite-element (FE) homogenization (randomly distributed fibres in a Representative Volume Element). Next, the identified fibre properties are used to predict the elastic parameters of UD plies with multiple fibre volume fractions. These are then used to model the fibre bundles (yarns) in a meso-scale FE model of a plain woven carbon/epoxy material. Finally, the predicted elastic response of the woven carbon/epoxy is compared to the experimentally obtained elastic stiffness tensor. The predicted and measured properties are in good agreement. Some discrepancy exists between the ultrasonically measured value of the Poisson's ratio and the predicted value. Nonetheless, it is shown that virtual identification and prediction of mechanical properties for woven plies is feasible.

The simulation of the fatigue damage of laminated composites under multi-axial and variable amplitude loadings has to deal with several new challenges and several methods of damage modelling. In this paper we present how to account for the complex loading by using the damage hysteresis operator approach for fatigue. It is applied to a fatigue model for intra-laminar damage based on stiffness degradation laws from Van Paepegem and has been extended to deal with unidirectional carbon fibres. The parameter identification method is presented here and parameter sensitivities are discussed. The initial static damage of the material is accounted for by using the Ladeveze damage model and the permanent shear strain accumulation based on Van Paepegem’s formulation. This approach has been implemented into commercial software. The intra-laminar fatigue damage model combines efficient methods with a low number of tests to identify the parameters of the stiffness degradation law, this overall procedure for fatigue life prediction is demonstrated to be cost efficient at industrial level.