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Simulation of the Mechanical Response of Thin-Ply Composites: From Computational Micro-Mechanics to Structural Analysis
Abstract
This paper provides an overview of the current approaches to predict damage and failure of composite laminates at the micro-(constituent), meso-(ply), and macro-(structural) levels, and their application to understand the underlying physical phenomena that govern the mechanical response of thin-ply composites. In this context, computational micro-mechanics is used in the analysis of ply thickness effects, with focus on the prediction of in-situ strengths. At the mesoscale, to account for ply thickness effects, theoretical results are presented related with the implementation of failure criteria that account for the in-situ strengths. Finally, at the structural level, analytical and computational fracture approaches are proposed to predict the strength of composite structures made of thin plies. While computational mechanics models at the lower (micro- and meso-) length-scales already show a sufficient level of maturity, the strength prediction of thin-ply composite structures subjected to complex loading scenarios is still a challenge. The former (micro- and meso-models) provide already interesting bases for in-silico material design and virtual testing procedures, with most of current and future research focused on reducing the computational cost of such strategies. In the latter (structural level), analytical Finite Fracture Mechanics models—when closed-form solutions can be used, or the phase field approach to brittle fracture seem to be the most promising techniques to predict structural failure of thin-ply composite structures.
... There are also numerous analytical and numerical studies on mechanical behavior of thin-ply laminates in the literature, e.g., [9,[12][13][14][15][16]. The effect of ply thickness on the crack propagation mechanisms was investigated in [4] calculating the ERR of the intralaminar transverse crack by finite element analysis. ...
... In [14], a comprehensive review has been performed on the available analytical and numerical analysis models for predicting mechanical response and damage in thin-ply laminates. Numerical studies in [14][15][16] analyzed the influence of ply thickness on the so-called in-situ transverse strength and showed a significant improvement of transverse strength and delamination resistance for thin-ply laminates. ...
... In [14], a comprehensive review has been performed on the available analytical and numerical analysis models for predicting mechanical response and damage in thin-ply laminates. Numerical studies in [14][15][16] analyzed the influence of ply thickness on the so-called in-situ transverse strength and showed a significant improvement of transverse strength and delamination resistance for thin-ply laminates. The fracture mechanics based analytical models for transverse crack propagation proposed in [2,3] have been widely implemented in analysis of transverse cracking of thin-ply laminates [9,[12][13][14][15][16]. ...
... Under an increasing applied strain, debondings at the fibre-matrix interface are found at locations where neighbouring fibres are close to each other, and more-or-less aligned perpendicular to the main loading direction, as indicated by the dashed boxes in Fig. 1(c). This observation has been reported in several previous micromechanical simulations [23,[31][32][33][34][35][36][37][38][39][40] and is consistent with the direct experimental observations in [22]. For sufficiently thin plies, the subsequent matrix crack growth from the debondings is slow and stable, with the crack arresting at the end of every strain increment. ...
... (3D) solid elements (C3D8R) [53] for the matrix, fibres and homogenized outer layers. The average element size within the inner layer is set to be 0.35 μm, to generate a well-structured, high-quality mesh, as suggested in [37][38][39][40] based on a sensitivity analysis. The fibre-matrix interface and the interface between inner and outer layers are modelled using cohesive elements (COH3D8) [53] of zero thickness. ...
... Due to the stress concentration at the fibre-matrix interface, debonding occurs when the peak interfacial stresses (radial and tangential) exceed the interfacial strength. For typical CFRPs, this has been found to occur when the applied strain reaches 0.6 ~ 0.8 % [22,23,[37][38][39][40]. In the present study, the length of this initial crack, 2a 0 , is taken as 8 μm, or a 0 = 4 μm, corresponding to one carbon fibre debonding from the matrix. ...
A new analysis is proposed, and verified, to quantitively explain the recent experimental observations of a transition from unstable to slow, stable through-thickness crack growth in cross-ply laminates, as the ply thickness is decreased to 40 µm. The approach is prompted by the observed stable rise of crack opening under increasing applied strain in micromechanical model simulations. Estimates of the energy release rates associated with these crack opening profiles clearly indicate an increasing value of crack growth resistance with crack extension, i.e. an R-curve effect. To verify that the thickness dependence of the matrix crack growth behaviour can be attributed to an R-curve effect, the R-curves were independently determined by micromechanical modelling and employed to predict the progression of through-thickness cracking in constrained plies of various thicknesses. These predictions are shown to agree closely with the reported experimental observations. The benefit of this new approach is that only one simulation is required to generate the R-curve, instead of requiring separate simulations for each ply thickness, thus considerably reducing the computational burden. This is particularly valuable for parametric studies to investigate the dependence on various material properties. As an illustrative example, the effects of changing the fracture energy of the epoxy matrix and the volume fraction of fibres present in the composite were investigated, and simple linear relationships were identified for both the steady-state value of the crack-growth resistance and the crack extension required to reach the steady state. Such relationships can further reduce the computational cost of micromechanical modelling, especially when the relevant material properties may not be available from direct measurements but can be reasonably estimated, as for cryogenic applications.
... To allow the introduction of thin-ply fiber reinforced polymers in industrial design, the prediction of their elastic properties and their damage tolerance has engaged the interest of many researchers. Arteiro et al. [7] and Galos [8] provided a wide coverage of the existing research into the experimental results and the predictive solutions for an understanding and prediction of the mechanical response and the damage mechanisms of the thin-ply laminates. Arteiro et al. [7] stated that no significant influence of the ply thickness on the elastic and strength properties of the thin ply UD was observed, except for an increase of approximately 20% for longitudinal compression. ...
... Arteiro et al. [7] and Galos [8] provided a wide coverage of the existing research into the experimental results and the predictive solutions for an understanding and prediction of the mechanical response and the damage mechanisms of the thin-ply laminates. Arteiro et al. [7] stated that no significant influence of the ply thickness on the elastic and strength properties of the thin ply UD was observed, except for an increase of approximately 20% for longitudinal compression. The constraining effect is investigated by Saito et al. [9] who demonstrated that the stiffness of the adjacent plies influences the matrix cracking propagation that is faster in an embedded 90°-ply surrounded by 45°-plies than in a similar ply surrounded by 0°-ply. ...
... Previous studies [7,3] showed that the progressive damage behavior for the thin ply composites differs from that of the conventional composites, in the sense that the order in which they appear is affected by a variation in the layer thickness. The studies in [18,7] showed that, as the thickness of a layer oriented transversely to the load decreases, the strain to microcracks initiation increases. ...
Ultra-light composites are produced through the spread tow technology. The success of spread tow fabrics lies in their unique woven structure. By interlacing widespread thin flat tapes, instead of regular (and thicker) yarns, more straight fibers and thinner plies are obtained which leads to improvements in the mechanical performance in terms of both stiffness and strength. The available numerical studies on spread tow fabric composites are based on the approximation to equivalent thin ply laminates, where the key observations are dedicated to a delayed or suppressed microcracking. This paper helps to investigate the limitations of considering thin-ply spread tow composites as equivalent laminates, as well as to bring more understanding on how the tow thickness affect the sequence of failure mechanisms. As an aid to these investigations, a parameterized mesoscale model has been developed that preserves the complex geometry of the woven structure and can analyze the tow thickness effect down to 35 µm. By applying shifted periodic boundary conditions through the thickness, the effect of periodic layer shifting is also analyzed without having to discretize and model more than one layer of the composite.
... To overcome the hurdles encountered in experiments, computational simulations using multi-scale hybrid models [10][11][12][13][14][15][16][17][18][19] have become an effective method to investigate the in-situ effect [20][21][22][23][24][25][26]. Saito et al. [20] computationally investigated the mechanisms of damage suppression, matrix cracking in a thin-ply laminate. ...
... In theoretical analysis, the in-situ effect is typically taken into account by using the analytical fracture mechanics theories [23]. In the case of very thin mid-90°ply, Y T is is given by Eq. ...
... Failure envelopes of (a) σ 22 -τ 12 , (b) σ 22 -τ23 , and (c) σ 11 -τ 12 predicted from in-situ-strength-based failure criteria. A comprehensive schematic diagram of the variations of (d)Y T is =Y T , (e)Y C is =Y C , (f)S L is =S L , and (g) S T is =S T with changing b=d and Δθ d . ...
In this work, multi-scale finite element analyses based on three-dimensional (3D) hybrid macro/micro-scale computational models subjected to various loading conditions are carried out to examine the in-situ effect imposed by the neighboring plies on the failure initiation and propagation of cross-ply laminates. A detailed comparative study on crack suppression mechanisms due to the effect of embedded laminar thickness and adjacent ply orientation is presented. Furthermore, we compare the results of in-situ transverse failure strain and strength between the computational models and analytical predictions. Good agreements are generally observed, indicating the constructed computational models are highly accurate to quantify the in-situ effect. Subsequently, empirical formulas for calculating the in-situ strengths as a function of embedded ply thickness and different ply angle between embedded and adjacent plies are developed, during which several material parameters are obtained using a reverse fitting method. Finally, a new set of failure criteria for σ22-τ12, σ22-τ23, and σ11-τ12 accounting for the in-situ strengths are proposed to predict laminated composites failure under multi-axial stress states. This study demonstrates an effective and efficient computational technique towards the accurate prediction of the failure behaviors and strengths of cross-ply laminates by including the in-situ effects.
... Crack propagation was observed at the strain of 0.64% (Fig. 10 c), forming a through-thickness crack when the applied strain was increased to 0.70% (Fig. 10d). Many studies have reported that heat treatment (annealing) can improve the mechanical properties of 3D printed composites through reduced porosity by infiltration and diffusion among adjacent filaments and layers and interface strengthening [23,33,34]. Thus, the ply cracking strain of 3D printed composite was expected to increase because of the reduced void areas after heat treatment compared to that of the as-printed sample. ...
... For the 3D printed CFRP composite at RT, the ply cracking strain was found to be 2.75%. By contrast, carbon fibre reinforced epoxy composites at RT were reported to feature a ply cracking strain ranging from 0.6% to 0.8% [9,[33][34][35][36]. The notably higher ply cracking strain of the 3D printed CFRP composite (2.75%) can be attributed to the superior fracture toughness of its nylon matrix, which boasts an estimated fracture toughness of 7 kJ/m 2 [37], particularly when compared to the epoxy's 0.12 kJ/m 2 [8,25] at RT. ...
Thermoplastic composites present considerable promise for the 3D printing of cryogenic fuel storage tanks, offering enhanced recyclability and repairability compared to thermoset composites. However, a significant knowledge gap remains regarding their ability to withstand cryogenic environments without suffering ply cracking. This study investigates the microcracking behaviour of continuous carbon fibre reinforced thermoplastic (CFRTP) composites fabricated through extrusion-based 3D printing. The experimental results reveal that CFRTP composites printed at room temperature exhibit a remarkable ability to withstand an applied strain of 0.60% without ply cracking at liquid nitrogen temperature. This performance surpasses that of conventional carbon fibre reinforced epoxy composites, which typically experience ply cracking even with any applied strain. Some of microcracks were traced back manufacturing defects. The defects were found to be fused by a post-heat treatment at 180℃ for 60 min. Unexpectedly, however, the treatment reduced the ply-cracking strain to 0.40% at the liquid nitrogen temperature. Computational micromechanical modelling revealed that this unexpected decline in ply-cracking resistance resulted from the increased thermal residual stresses induced by the heat treatment. The findings of this study suggest that 3D-printed thermoplastic composites exhibit robust resistance to microcracking at cryogenic temperatures, making them a promising solution in the quest for sustainable lightweight cryogenic fuel storage solutions.
... Arteiro et al. [10] have predicted failure of composite laminates at micro-, meso-and macrolevels. They analysed ply thickness effects and predicted in-situ strengths at microscale level. ...
... The test specimen has been cut from the tube through its whole thickness, so thickness of the test specimen is 8 mm. In the FE macromodel, material model of reinforcement layers is transversely isotropic, material properties of the composite layers have been calculated based on rules of mixture [10] and material properties of the components (from material data sheets). Material properties of reinforcement layers are as follows: modulus of elasticity of fibre is E f = 2961 MPa, Poisson's ratio of fibre is supposed to be υ f = 0.2, modulus of elasticity of rubber matrix is E m = E r = 6 MPa. ...
The aim of this study is to examine displacements, strains and stresses as well as to predict possible failure mechanisms arising at the yarn-matrix level of a test specimen of a railway composite cord-rubber air brake tube undergoing uniaxial tension by microscale modelling.Furthermore, this paper also aims to verify the material properties of the micromodel of the test specimen.The micromodel is based on macromodels (by matching the boundary conditions of the micromodels with displacements of the macromodels) created previously by authors of this article. The reinforcing yarns are described by an orthotropic, elastic material model, whereas the matrix has been described by a 2 parameter Mooney-Rivlin model, which all have been validated before by a uniaxial tensile test and a three-point bending test.Force-displacement curves of the micromodel and experimental results show a considerably good agreement.Yarns have a less dominant role in the load transfer mechanism of the reinforcement layers, because of the short-yarn reinforced nature of the specimen. Shear strains are high at free yarn ends marking the possible locations of failure initiation in debonding in the shear mechanism of the reinforcement layers. High shear strain values imply that the dominant mode of load transfer is shear in the matrix in the reinforcement layers.
... Hence, multiscale models have become an essential tool for composite design, Arteiro et al. [3]. Motivated by ...
... Basically, VSPK model uses the same equations as the classical rule of mixture for of the VSPK model can be accessed in Vignoli et al.[7].Once the elastic properties are obtained, in sequence, the strengths must be evaluated. Three lamina strengths are required to do the damage modeling of notched CFRP plates under tensile load: the experimental part, two different specimens were tested to be used by the proposed model, both made by single-layered CFRP [0](3) with a central circular hole, with thickness and width equals to 0.9mm and 50mm, ...
The estimation of the damage offset of notched composite plates is an important mechanical design objective, for industries, as the aeronautical ones. To achieve this objective, a novel multiscale procedure is proposed to estimate the damage onset of notched composite plates submitted to axial load, minimizing the amount of experimental test required. The micromechanical modeling combines Tsai’s modulus with VSPK model. The macromechanical modeling uses the finite element method and the Puck failure criterion. The thermographic results of experimental tensile tests, using notched composite plates specimens, were used to compare with FEM results. The capability to capture significative sudden heating events, that are related to the damage onset, turns the thermography technique quite useful to implement the proposed methodology.
... Several ply thicknesses and fiber/matrix systems were studied and broadly revealed significant improvements in thin-ply mechanical performance over std-ply laminates. Laminate-level improvements were reported to arise generally due to a shift in composite failure mode from a complex, multi-mechanism mode dominated by matrix failures, to a quasi-brittle mode dominated by fiber failure [51,78,79]. A major consequence of this failure mode shift can be higher design strength in thin-ply laminates, which presents structural design advantages, in addition to other design benefits including smoother ply drops and more optimal ply orientation sequences due to the increased ply quantity for a given laminate thickness, as well as enhanced laminate thickness control [21,61]. ...
... As exemplified in the high load step (90% UTS) tomograms shown in Fig. 3, all matrix damage mechanisms were colored according to their host-ply orientation: 0 • ply (blue), ±45 • ply (yellow), and 90 • ply (red). The dominant damage mechanisms revealed in the loaded state in Fig. 3 comprise intralaminar matrix cracking and fiber/matrix interfacial debonding, which typically interacted to collectively form a single connected damage instance (generally spanning the ply thickness), thus they were simply classified together as 'matrix damage' as in prior work [79,106]. Additionally, relatively few and relatively small, sub-critical interlaminar delaminations appeared near notch edges (localized exclusively in the outermost 0 • /90 • interfaces), as demonstrated in the 90% UTS tomograms in Fig. 3; however, such delaminations, which were considered likely to have nucleated as mesoscale defects along the notch edge, are observed to stop widthwise propagation within a distance on the order of ten fiber diameters measured from the notch edge. ...
In situ X-ray synchrotron radiation computed tomography (SRCT) of carbon fiber composite laminates reveals the first-ever qualitative and quantitative comparisons of 3D progressive damage effects introduced by two mechanical enhancement technologies: aligned nanoscale fiber interlaminar reinforcement and thin-ply layers. The technologies were studied individually and in combination, using aerospace-grade unidirectional prepreg standard-thickness prepreg (‘std-ply’) and thin-ply composite laminates. The relatively weak interlaminar regions of the laminates were reinforced with high densities of aligned carbon nanotubes (A-CNTs) in a hierarchical architecture termed ‘nanostitching’. Quasi-isotropic double edge-notched tension (DENT) laminates were tested and simultaneously 3D-imaged via SRCT at various load steps, revealing a progressive 3D network of damage micro-mechanisms that were segmented according to modality and extent. For load steps of 0%, 70%, 80%, and 90% of baseline ultimate tensile strength (UTS), intralaminar matrix cracking and fiber/matrix interfacial debonding are found to be the dominant damage mechanisms, common to all laminate types. For both std-ply and thin-ply, nanostitched laminates had qualitatively and quantitatively similar matrix damage modality and extent compared to the baseline laminates through 90% UTS, including relatively few delaminations, despite an ∼9% increase in std-ply nanostitched UTS over the std-ply baseline. Complementary finite element-based modeling of damage predicts greater delamination extent in std-ply vs. thin-ply laminates that manifests only between 90% and 100% UTS, offering an explanation for the observed positive nanostitch effect in the std-ply, which is known to be more susceptible to delamination formation and growth than the thin-ply laminates. Thin-ply, with and without nanostitch, intrinsically suppresses matrix damage, as expected from past work and evidenced here by 6.5X less overall matrix damage surface area vs. std-ply baseline laminates averaged over all load steps. These findings contribute new insights from high-resolution experimental mapping of composite damage states that can guide and inform mechanical enhancement approaches and improved damage models.
... In this work, a type V COPV model is developed using tape trajectories and thickness profiles resulting from an automated laying process of carbon fiber-reinforced polymer (CFRP) pre-preg tapes, following the geometric modeling details from [21,22] already used for type IV vessels to obtain a representative model of the as-manufactured vessel. A full 3D transversely isotropic elastic-plastic damage propagation model is used for the constitutive modelling of the CFRP [29][30][31]. Fiber tensile failure uses non-interacting criteria [32,33] and matrix failure-dominated modes, including fiber kinking, using the stress-invariant criteria from [34] that were recently implemented with the smeared crack damage propagation model in [35]. ...
Linerless composite pressure vessels, or type V pressure vessels, are gaining increased interest in the transportation industry because they offer improved storage volume and dry weight, especially for low-pressure cryogenic storage. Nevertheless, the design and manufacturing of this type of pressure vessel bring several challenges due to the inherent difficulties in the manufacturing process implementation, assembly, and related analysis of structural integrity due to the severe operating conditions at cryogenic temperatures that should be taken into consideration. In this work, a novel analysis procedure using a finite element model is developed to perform an end-to-end simulation of a linerless pressure vessel, including the relevant features associated with automated fiber placement manufacturing processes regarding thickness and tape profiles, followed by an analysis of the structural response under service conditions. The results show that residual stresses from manufacturing achieve values near 50% of the composite ply transverse strength, which reduces the effective ply transverse load carrying capacity for pressure loading. Transverse damage is triggered and propagated across the vessel thickness before fiber breakage, indicating potential failure by leakage, which was confirmed by hydrostatic tests in the physical prototype at 26 bar. The cryogenic condition analysis revealed that the thermal stresses trigger transverse damage before pressure loading, reducing the estimated leak pressure by 40%. These results highlight the importance of considering the residual stresses that arise from the manufacturing process and the thermal stresses generated during cooling to cryogenic conditions, demonstrating the relevance of the presented methodology for designing linerless cryogenic composite pressure vessels.
... However, current high-fidelity techniques are still too computationally intensive and therefore not generally applied to large composite structures [5]. Since damage in composites occurs at multiple-scales, relevant details should be modelled and studied at each appropriate length scale [6][7][8]. In principle, concurrent adaptivity enables bridging between length scales in a single model, where only active damage mechanisms are explicitly modeled at the lower scale while inactive sites are represented by homogenized regions at the higher scale [9][10][11]. ...
The accurate prediction of failure of load-bearing fiber-reinforced structures remains a challenge due to the complex interacting failure modes at multiple length scales. In recent years however, there has been considerable progress, in part due to the increasing sophistication of advanced numerical modelling technology and computational power. Advanced discrete crack and cohesive zone models enable interrogation of failure modes and patterns at high resolution but also come with high computational cost, thus limiting their application to coupons or small-sized components. Adaptively combining high-fidelity with lower fidelity techniques such as smeared crack modelling has been shown to reduce computational costs without sacrificing accuracy. On the other hand, machine learning (ML) technology has also seen an increasing contribution towards failure prediction in composites. Leveraging on large sets of experimental and simulation training data, appropriate application of ML techniques could speed up the failure prediction in composites. While ML has seen many uses in composites, its use in progressive damage is still nascent. Existing use of ML for the progressive damage of composites can be classified into three categories: (i) generation of directly verifiable results, (ii) generation of material input parameters for accurate FE simulations and (iii) uncertainty quantification. Current limitations, challenges and further developments related to ML for progressive damage of composites are expounded on in the discussion section.
... Addressing this challenge, several concepts have been presented in the literature over the years to enhance the out-of-plane strength of composite laminates. Altering the stacking sequence and using multidirectional (MD) CFRP [10,11], strengthening individual components [12,13,] and employing thinplies [9,14] stand among various solutions proposed to deal with this issue. In the context of altering the stacking sequence, which aim to replicate forms, functions, and principles from the natural world, have led to the creation of lightweight, stronger composite materials capable of withstanding damage. ...
Biostructures found in nature exhibit remarkable strength, toughness, and damage resistance, achieved over millions of years. Observing nature closely might help develop laminates that resemble natural structures more closely, potentially improving strength and mimicking natural principles. Bio-inspired Carbon Fiber-Reinforced Polymers (CFRP) investigated thus far exhibit consistent pitch angles between layers, whereas natural structures display gradual variations in pitch angle rather than consistency. Therefore, this study explores helicoidal CFRP laminates, focusing on the Non-Linear Rotation Angle (NLRA) or gradual variation to enhance composite material performance. In addition, it compares the strength and failure mechanisms of the gradual configuration with conventional helicoidal and unidirectional (UD) laminates, serving as references while conducting transverse tensile tests (out-of-plane tensile). The findings highlight the potential of conventional and gradual helicoidal structures in reinforcing CFRP laminates, increasing the failure load compared to unidirectional CFRP laminate by about 5% and 17%, respectively. In addition, utilizing bio-inspired configurations has shown promising improvements in toughness compared to traditional unidirectional laminates, as evidenced by the increased displacement at failure. The numerical and experimental analyses revealed a shift in crack path when utilizing the bio-inspired helicoidal stacking sequence. Validated by experimental data, this alteration demonstrates longer and more intricate crack propagation, ultimately leading to increased transverse strength.
... Plastic deformation results from the mutual sliding of composite particles, and under external loading, the material primarily transmits and balances external forces through contact forces between particles and between particles and the binder. At the same time, the stress path and the material's initial anisotropy are related to the mechanical response of the material [2]. Therefore, it is a great challenge to construct a correlation model between material microstructure and material properties. ...
Establishing a mapping model between the microstructure and material properties of composite materials is crucial for material development. Scanning electron microscope (SEM) images are widely used for the prediction of material properties. However, the prediction from a single SEM image is independent and does not fully reflect the microstructure characteristics. To address this issue, this paper proposes a node graph construction strategy for SEM images and establishes a multi-graph-based graph attention network (GAT) material property prediction model to achieve the convergence of mutual complementation in microstructure features by using GAT. Firstly, multiple SEM images are constructed into node graphs by a microstructure feature encoder. Next, the microstructure features of multiple SEM images on the node graphs are mutually complemented and converged by using GAT. Finally, the prediction is carried out by using multiple SEM images. The experimental results show that the proposed method shows better performance than other methods.
... Predicting fracture is one of the major interests for efficient design and safety of structures. Computational fracture modeling using energetic approaches [2,3] helps in predicting crack initiation and propagation at different material length scales [4], which affect the mechanical and fracture response of any material. Phase field (PF) modeling is one of the most commonly used approaches for predicting diffused or smeared crack propagation, where the sharp/discrete crack is regularized to a smeared crack [5]. ...
The main aim of the current study is to explore direction-dependent fracture initiation and propagation within an arbitrary anisotropic solid. In particular, the specific objective is to develop an anisotropic cohesive phase-field (PF) fracture model. In this model, weak and strong anisotropy is considered both in the strain energy and fracture energy. This is achieved by considering contributions to strain energy of fiber and matrix as in the case of fiber-reinforced composites (FRC) together with introducing anisotropy in fracture energy through higher-order structural tensors. Motivated from earlier works of Van den Bosch et al. (Eng Fract Mech 73:1220–1234, 2006), the PF fracture model is integrated with a coupled exponential cohesive zone law which considers both normal and tangential components of separation. Such a cohesive PF description has a strong micromechanical basis for fracture, requiring interface fracture toughness and ultimate traction in normal and tangential directions. C0 and C1 approximations are used for modeling the weak and strong anisotropy. Several numerical examples are presented to demonstrate the usefulness of the model developed herein. The obtained numerical results are validated with the experimental results from the literature. The anisotropic fracture resulting in either intergranular or transgranular failure of polycrystalline material is analyzed by adopting a coupled anisotropic phase field and cohesive zone approach.
... The correlation of coefficients with the fibre volume fraction (variable)According to the derivation in Section 4.3.1, the relationships between D-index and DoRs under different fibre volume fractions can be calculated and expressed as the format of Eq. (6) and Eq.(7). Coefficients of the linear equations can be further calculated to be the function of the fibre volume fraction with the format of Cðv f Þ. ...
A new quantitative method, the D-index, is proposed to evaluate the departure of a given fibre arrangement from the completely spatial randomness (CSR) pattern. An explicit model which can effectively control the degree of randomness (DoR) is created to investigate the correlation between the D-index and DoR. The theory behind the correlation is analyzed followed by the derivation of first and higher order D-index with respect to the DoR under different fibre volume fractions. This may be the first time an accurate value of the departure from randomness is provided, which is considered important for accurate micro-mechanical analysis.
... Further, the nonlinear static and dynamic responses of shallow spherical shells or thin rectangular plates resting on Winkler-Pasternak elastic foundations are analyzed based on Donnell theory [141] and dynamic analogues Von Karman equations [142]. The damage and failure of thin-ply composite laminates at the micro-(constituent), meso-(ply), and macro-(structural) levels are studied can be used to comprehend the underlying physical phenomena that control the mechanical response of thinply composites [143,144]. To comprehensively examine the effects of source-uncertainty, Mukhopadhyay et al. provided machine learning-based probabilistic and nonprobabilistic (fuzzy) low-velocity impact assessments of composite laminates [145]. ...
This article reported a comprehensive review of computational modelling and analysis of fibre metal laminates (FMLs),
including the experimental techniques. The research is relevant to the metal (aluminium) stacked in the advanced fibres
(Glass/Carbon/Kevlar) reinforced with epoxy matrix, and composite behaviour is discussed in detail. The discussion also
includes damages like delamination on the bonds’ responses (frequency and static/dynamic deflections). The metal-bonded
composite has shown tremendous potential in the transportation industries without increasing the weight penalties in the
overall structure. This review focuses on recently devised technologies for making FML components, with brief overviews
of other working parameters. A complete outline of the historical background and contemporary advances of FMLs includes
the categories, sheet production procedures, benefits and drawbacks. Moreover, the forming technologies are discussed, indicating
their promising options for the large-volume manufacturing of intricate shape components of FML. The fracture and
flaws in the fabrications of FML, including the complexities available in the earlier studies, are surveyed comprehensively.
Finally, state-of-the-art research on the numerical methodologies of the FML structural modelling using different theoretical
approaches and experimental verifications is provided in detail.
... Tsai et al., 2005), with the resulting crack pattern having the form of a single fracture plane upon which any damage mechanisms that occur can be assumed lumped on. This simplifies the analysis and thus motivated, for this particular type of CFRPs, the use of methods tied to the fracture of quasi-brittle materials, in an equivalent single layer (ESL) approach (Arteiro et al., 2019;Reinoso et al., 2017). ...
... This effect could be used to inhibit transverse cracking with the use of the recently developed ultra-thin plies, see e.g. [36][37][38] or [39]. ...
... The need for structural design has also grown among structural engineers in the field of composites [8]. In all circumstances, the problem must be described in 3D, and the accuracy of the computed stress level relies on whether the problem is being examined at the micro, meso, or macro scale [9]. ...
This study examines a new approach to facilitate the convergence of upcoming user-subroutines UMAT when the secant material matrix is applied rather than the conventional tangent (also known as Jacobian) material matrix. This algorithm makes use of the viscous regularization technique to stabilize the numerical solution of softening material models. The Newton–Raphson algorithm predictor-corrector of ABAQUS then applies this type of viscous regularization to a UMAT using only the secant matrix. When the time step is smaller than the viscosity parameter, this type of regularization may be unsuitable for a predictor-corrector with the secant matrix because its implicit convergence is incorrect, transforming the algorithm into an undesirable explicit version that may cause convergence problems. A novel 3D orthotropic damage model with residual stresses is proposed for this study, and it is analyzed using a new algorithm. The method’s convergence is tested using the proposed implicit-to-explicit secant matrix as well as the traditional implicit and explicit secant matrices. Furthermore, all numerical models are compared to experimental data. It was concluded that both the new 3D orthotropic damage model and the new proposed time step algorithm were stable and robust.
... Here, testing is the most time-consuming part of novel FRP product development for the composite industry. Thus, durability prediction methods are seen helpful in reducing the involved costs [7,22,26]. Accelerated testing methodology (sometimes termed ''accelerated degradation tests'') are testing programs that are designed to accelerate the property degradation of materials such as polymers and FRPs by subjecting them to conditions outside their normal service range [27,28]. In such methodologies, the degradation is controlled, providing a reliability estimation combined with modeling while reducing the experimental testing time [29,30]. ...
Epoxies and epoxy-based fiber reinforced polymers (FRP) are significantly affected by environmental impacts during their service life. Exposures to water, humidity, temperature and UV radiation are known to substantially influence the (thermo-) mechanical properties and durability of the materials. Design-relevant characteristics like strength, stiffness, or the glass transition temperature change with time. Therefore, expensive test campaigns are often necessary in advance of a structural design. Prediction models based on physical relations or phenomenological observations are typically required to reduce costs and increase reliability. Consequently, a combined methodology for fast prediction of long-term properties and accelerated aging purposes is presented in this work for a common DGEBA-based epoxy. Therefore, master curves are obtained by creep and constant-strain-rate tests under temperature and moisture impact. A combined time–temperature-water superposition and the Larson-Miller parametrization demonstrate that time-saving CSR tests and modeling can replace long-lasting creep testing. Resulting, the presented methodology allows to determine a polymer’s entire (environmental) failure envelope in a relatively short time and with low testing effort.
... A numerical framework is built for unstable crack propagation modelling, making use of the size effect method [18], having the advantages of: limiting the detailed region to a small embedded cell (EC) around the pre-crack tip; generating small virtual specimen geometries which are hard or even impossible to manufacture experimentally; and avoiding the necessity to track the position of the crack tip throughout the numerical simulations. The predictive capability of computational mechanics for heterogeneous materials largely depends on the scale at which damage is explicitly modelled [30,31]. In particular, micromechanics can be used as a reliable tool for analysis and derivation of upscaled material properties in composite materials [32][33][34][35][36][37]. ...
A three-dimensional micromechanics framework is developed to estimate the mode I through-thickness intralaminar crack resistance curve of unidirectional carbon fibre-reinforced polymers. Finite element models of geometrically-scaled single edge notch tension specimens were generated. These were modelled following a combined micro-/meso-scale approach, where the region at the vicinity of the crack tip describes the microstructure of the material, while the regions far from the crack tip represent the mesoscopic linear-elastic behaviour of the composite. This work presents a novel methodology to estimate fracture properties of composite materials by combining computational micromechanics with the size effect method. The size effect law of the material, and consequently the crack resistance curve, are estimated through the numerically calculated peak stresses. In-depth parametric analyses, which are hard to conduct empirically, are undertaken, allowing for quantitative and qualitative comparisons to be successfully made with experimental and numerical observations taken from literature.
... Similarly to the WLF and Arrhenius equations for TTSP, the choice of the most applicable model for the stress shift function, Equation (16) or (17), depends on the material state and application. Based on their fundamental origin, Equation (16) is the most suitable when considering polymers in a rubbery state (T > T g ), while Equation (17) is valid for glassy polymers (T < T g ). ...
Polymers and polymer composites are negatively impacted by environmental ageing, reducing their service lifetimes. The uncertainty of the material interaction with the environment compromises their superior strength and stiffness. Validation of new composite materials and structures often involves lengthy and expensive testing programs. Therefore, modelling is an affordable alternative that can partly replace extensive testing and thus reduce validation costs. Durability prediction models are often subject to conflicting requirements of versatility and minimum experimental efforts required for their validation. Based on physical observations of composite macro-properties, engineering and phenomenological models provide manageable representations of complex mechanistic models. This review offers a systematised overview of the state-of-the-art models and accelerated testing methodologies for predicting the long-term mechanical performance of polymers and polymer composites. Accelerated testing methods for predicting static, creep, and fatigue lifetime of various polymers and polymer composites under environmental factors’ single or coupled influence are overviewed. Service lifetimes are predicted by means of degradation rate models, superposition principles, and parametrisation techniques. This review is a continuation of the authors’ work on modelling environmental ageing of polymer composites: the first part of the review covered multiscale and modular modelling methods of environmental degradation. The present work is focused on modelling engineering mechanical properties.
... For these reasons, alternative approaches at the macro-scale, i.e. laminate level, must be considered in the numerical failure predictions [10,11]. ...
This paper presents the extension and validation of omni-failure envelopes for first-ply failure (FPF) and last-ply failure (LPF) analysis of advanced composite materials under general three-dimensional (3D) stress states. Phenomenological failure criteria based on invariant structural tensors are implemented to address failure events in multidirectional laminates using the “omni strain failure envelope” concept. This concept enables the generation of safe predictions of FPF and LPF of composite laminates, providing reliable and fast laminate failure indications that can be particularly useful as a design tool for conceptual and preliminary design of composite structures. The proposed extended omni strain failure envelopes allow not only identification of the controlling plies for FPF and LPF, but also of the controlling failure modes. FPF/LPF surfaces for general 3D stress states can be obtained using only the material properties extracted from the unidirectional (UD) material, and can predict membrane FPF or LPF of any laminate independently of lay-up, while considering the effect of out-of-plane stresses. The predictions of the LPF envelopes and surfaces are compared with experimental data on multidirectional laminates from the first and second World-Wide Failure Exercise (WWFE), showing a satisfactory agreement and validating the conservative character of omni-failure envelopes also in the presence of high levels of triaxiality.
... In contrast, the effect of ply thickness on the open-hole specimen strength is not evident for compression-shear loading. The in-situ effect on the transverse compressive strength is smaller than on the transverse tensile strength [176], resulting in similar crack initiation stresses for the 'thin' and 'thick' ply laminates loaded in the compressive loading regimes. Furthermore, the load- , Laminate 2 sustains on average 10% higher stresses than Laminate 3. ...
In this study, the last ply failure (LPF) load of composite laminates with VO-notches under pure mode I and mixed mode I/II was investigated experimentally, analytically, and numerically. The efficiency of the virtual isotropic material concept (VIMC) in combination with a new combined failure criterion was also evaluated. The J-integral and average strain energy density failure criteria were combined with VIMC. Using analytical expressions for the J-integral and the average strain energy density (ASED), the prediction of the fracture load of notched components was simplified and expedited. The experimental fracture loads of notched specimens were determined for quasi-isotropic and cross-ply laminates under mode I and mixed mode I/II. The fracture loads were predicted using analytical expressions for the J-integral and ASED, combined with VIMC. The VIMC-ASED and VIMC-J-integral failure criteria demonstrated good accuracy in predicting the LPF, with the highest accuracy for mode I, slightly reduced accuracy for mixed mode I/II. VIMC, in combination with energy-based failure criteria, effectively predicts the fracture load. The use of analytical expressions further simplified and expedited the prediction process without losing accuracy, making it a practical approach for engineering applications. Additionally, this approach significantly reduces the time and cost associated with extensive experimental testing.
After conducting a comprehensive historical review of presently established methods for computational modeling of multilayered bending plates, the present work introduces a novel 2D multiscale strategy, termed the 2D+ approach. The proposed approach is based on the computational homogenization formalism and is envisaged to serve as an appealing alternative to current methodologies for modeling multilayered plates in bending-dominated situations. Such structural elements involve modern and relevant materials, such as laminated composites characterized by the heterogeneous distribution of low-aspect-ratio layers showing substantial non-linear mechanical behavior across their thickness.
Within this proposed approach, the 2D plate mid-plane constitutes the macroscopic scale, while a 1D filament-like Representative Volume Element (RVE), orthogonal to the plate mid-plane and spanning the plate thickness, represents the mesoscopic scale. Such RVE, in turn, is capturing the non-linear mechanical behavior throughout the plate thickness at each integration point of the 2D plate-midplane finite element mesh. The chosen kinematics and discretization at the considered scales are particularly selected to (1) effectively capture relevant aspects of non-linear mechanical behavior in multilayered plates under bending-dominated scenarios, (2) achieve affordable computational times (computational efficiency), and (3) provide accurate stress distributions compared to the corresponding high-fidelity 3D simulations (computational accuracy).
The proposed strategy aligns with the standard, first-order, hierarchical multiscale setting, involving the linearization of the macro-scale displacement field along the thickness. It employs an additional fluctuating displacement field in the RVE to capture higher-order behavior, which is computed through a local 1D finite element solution of a Boundary Value Problem (BVP) at the RVE. A notable feature of the presented 2D+ approach is the application of the Hill–Mandel principle, grounded in the well-established physical assumption imposing mechanical energy equivalence in the macro and meso scales. This links the 2D macroscopic plate and the set of 1D mesoscopic filaments, in a weakly-coupled manner, and yields remarkable computational savings in comparison with standard 3D modeling. Additionally, solving the resulting RVE problem in terms of the fluctuating displacement field allows the enforcement of an additional condition: fulfillment of linear momentum balance (equilibrium equations). This results in a physically meaningful 2D-like computational setting, in the considered structural object (multilayered plates in bending-dominated situations), which provides accurate stress distributions, typical of full 3D models, at the computational cost of 2D models.
An attempt was made to map the distribution of stress in fibrous composites with imperfect bonding. Two analytical micro-mechanics models were developed. In the first model, the composite was subjected to axial tensile loading, parallel to the fiber direction, and the assumption of iso-strain was employed to derive the control equations. In the second model, the composite was loaded in the direction transverse to the fiber. An iso-stress condition was employed, and Airy stress function was utilized to articulate the stress and displacement equations. An assumption of how the stress is transferred between the matrix and the fiber was introduced in both models. To investigate and validate the models, specimens were fabricated using a carbon plain weave fabric and a geopolymer matrix. Single fiber pullout and three-point bending tests were carried out. The maximum average tensile stress obtained from the three-point bending tests, as well as the mechanical properties of the fiber and geopolymer, served as input for the models. Results indicate that the effect of the level of bonding is very high in the transverse direction while almost negligible in the axial direction. The difference in the maximum value of the axial tensile stress at the fiber-matrix interface was used to calculate the numerical value of the interfacial shear strength, and the numerical result matched the data obtained from the single fiber pullout test.
The degree of randomness of fibre arrangements within the resin area is of great importance to the composites’ micro-distribution of stress and strain. A new algorithm, hard-core model & random shaking model, is developed to generate the unidirectional continuous fibre-reinforced composites. Another two algorithms, the random sequential expansion model and the initially periodic shaking model are presented and improved to generate the representative volume element microstructures. Statistical analyses are performed to compare these representative
volume element microstructures generated by different algorithms at different fibre volume fractions. A quantitative approach is first applied to provide the exact degree of randomness of both virtual and real microstructures. Results of qualitative and quantitative analyses show that the novel algorithm is capable of generating statistically equivalent fibre distributions to real continuous fibre-reinforced composites.
This article reported a comprehensive review of computational modelling and analysis of fibre metal laminates (FMLs),
including the experimental techniques. The research is relevant to the metal (aluminium) stacked in the advanced fibres
(Glass/Carbon/Kevlar) reinforced with epoxy matrix, and composite behaviour is discussed in detail. The discussion also
includes damages like delamination on the bonds’ responses (frequency and static/dynamic deflections). The metal-bonded
composite has shown tremendous potential in the transportation industries without increasing the weight penalties in the
overall structure. This review focuses on recently devised technologies for making FML components, with brief overviews
of other working parameters. A complete outline of the historical background and contemporary advances of FMLs includes
the categories, sheet production procedures, benefits and drawbacks. Moreover, the forming technologies are discussed, indicating
their promising options for the large-volume manufacturing of intricate shape components of FML. The fracture and
flaws in the fabrications of FML, including the complexities available in the earlier studies, are surveyed comprehensively.
Finally, state-of-the-art research on the numerical methodologies of the FML structural modelling using different theoretical
Approaches and experimental verifications is provided in detail.
The prerequisite to equip structures with in situ electrical health monitoring systems in a meaningful manner is to estimate potential damage locations. In this context, an analytical approach to model the spatial and temporal evolution of transverse inter-fibre fractures (IFF) is exemplified for [Formula: see text] cross-ply laminates under three-point bending. The model is based on the tensile load in the bottom 90°-layer. The effective stress is computed directly from the specimen displacement, whereas the strength is considered to be periodically distributed due to material inhomogeneities along the specimen. The continuous comparison between the sinusoidal strength function and the effective stress allows modelling progressive damage in form of IFF. A modified Hann window is used to consider their effect to the bottom 90°-layer. Experiments with the same configuration are performed and the observed IFF evolution is used to tune the model parameters in an optimisation procedure, e.g., the peak separation of the sinusoid and the length of the Hann window. The comparison between model and experiment shows a high level of agreement. The model is thus capable to reproduce experiments with minimal computational effort. This makes it highly suitable as input for electrical monitoring models that rely on the continuous damage evolution of the investigated structure. In its current form, the model is limited to the specified configuration. However, the simple analytical approach allows it to be easily adapted. It is furthermore shown that progressive composite damage in terms of spatial and temporal evolution can be accurately described using an analytical approach.
The 6th BCCM was attended by over 300 participants from 14 countries. More than 100 articles have been published and presented orally, with authors from more than 60 research, teaching and technology institutions. The 6th BCCM was held from 14th to 18th August 2022, in Tiradentes, a charming and warm-hearted historical city famous for its gastronomy and architecture. Tiradentes was founded in 1718, named after Joaquim José da Silva Xavier, the “Tiradentes”, patron of the Brazilian Republic. Since its first edition in 2012, the Conference congregates Brazilian and worldwide students, professors, and researchers from academia and industry to promote the recent developments and discuss the challenges in composite materials in Brazil and abroad. The range of topics is comprehensive, including Damage and Fracture; Simulation in Composites; Adaptive Composites; Durability and Ageing; Mechanical and Physicochemical Properties of composites; Nanocomposites; Recycling and reuse of composite materials; Experimental Techniques; Lignocellulosic Composites; Processing and Manufacturing of composites; Health Monitoring in composite structures; Multi-Scale Modelling; Industrial Applications.
Design of notched laminates is a challenge issue due to the large number of variables involved in this process. This investigation aims to improve the physical understanding of damage onset and its propagation, up to final failure. A multiscale procedure is proposed, where the micromechanical analytical models are used to estimate the effective properties for finite element macromechanical simulation. Additionally, experimental results from monitoring tensile tests with thermographic camera are also discussed. The multiscale procedure estimations and experimental results are very close, indicating matrix dominating damage. Thermography showed to be able to capture damage onset and its propagation, indicating that this experimental technique can become a useful tool for damage tolerance studies. A parametric study is carried out, indicating that damage onset load is approximately 20% of the rupture load for fibers parallel to the load, independently of plate geometrical dimensions. Multiscale procedure compared with experimental results. Damage onset forces, rupture forces and theirs ratio have similar results from theoretical and experimental approaches.
The in situ effect on cross-ply laminates under out-of-plane shear loading is firstly studied with a two-dimensional RVE-based computational micromechanics method. High fidelity simulations of the interface de-bounding and crack propagation in laminates are performed, which shows good consistency with experimental observation. The matrix cracking behaviors and micro-mechanical response demonstrate that an in situ effect exists in cross-ply composites under out-of-plane shearing. Specifically, thinner ply laminates provide higher shear strength and stronger damage resistance due to the delay effect of transverse cracking and delamination. The analytical predictions on interlaminar shear strength of cross-ply laminates agree well with the existing theoretical criteria. A parametric study is performed to explore the possibility of acquiring stronger fiber-reinforced composites. The coupled load analysis sheds useful insights on the failure mechanism and optimization design of multi-layer composites.
Stress concentrations induced by notches is an engineering problem, presented in most real structural failures. Due to the importance of this topic and considering the large amount of variables related to composite design, a novel multiscale procedure is proposed to evaluate damage onset and propagation in notched composite plates, minimizing the amount of experimental test required. The micromechanical modeling combines Tsai's modulus with VSPK model, while the macromechanical modeling uses the finite element method and the Puck failure criterion. Experimentally, tensile tests of notched plates are carried out monitored by thermographic camera. The thermography technique is a fundamental part of the proposed methodology, due to its capability to capture damage onset related to significative heating events. Just 3 experimental tests are necessary: 1 unnotched specimen for tensile test and 2 notched specimens monitored with thermography. 3 constituents’ properties from supplier datasheet are necessary to obtain others 15 properties: 8 lamina properties, 2 matrix properties and 5 fiber properties. Comparing the experimental results with the numerical-analytical methodology, a mean square error of 1.42% is obtained.
View Video Presentation: https://doi.org/10.2514/6.2022-0375.vid In this study, the effects on 3D strengthening and toughening mechanisms of interlaminar nanoreinforcement (termed ‘nanostitch’ here, achieved by embedding highly dense forests of vertically aligned carbon nanotubes in polymer-rich ply/ply interfaces) are studied qualitatively and quantitatively via 4D progressive damage in carbon (micro) fiber reinforced plastic/polymer (CFRP) composite laminates by implementing in situ synchrotron radiation computed tomography (SRCT) of delamination-prone cross-ply double edge-notched tension (DENT) configurations (scaled-down specimen geometry) via semi-automatic (human-driven) damage segmentation. A 20°-canted loading rig fixture was also designed, fabricated, and employed here to enable clear imaging of features that are typically blurred due to their alignment with the X-ray beam (e.g., 90° lamina-based features). SRCT here was performed at beamline 47XU (BL47XU) of the Super Photon ring-8 GeV (SPring-8) facility in Japan. Intermediate-thickness-ply laminates (2× thicker ply vs. thin-ply, similar to conventional aerospace-grade unidirectional plies) exhibit no change in DENT ultimate tensile strength for baseline vs. nanostitched configurations, explained mechanistically by an observed progressive damage mode transition from notch-blunting inter- and intra-laminar matrix damage-dominated (typical of thicker-ply laminates in literature) to brittle fiber breakage- and diffuse matrix damage-dominated (typical of thinner-ply laminates in literature). Thin-ply and thick-ply laminates have been tested similarly, showing significant strength increase in the nanostitched thick-ply (3× thicker ply vs. thin-ply) configuration, which will be the subject of future work. These findings contribute new CFRP failure insights, which can guide and inform mechanical enhancement approaches fundamental to eliciting synergistic latency in hybrid/hierarchical laminates, as well as advance currently limited modeling.
Four-dimensional quantitative characterization of heterogeneous materials using in situ synchrotron radiation computed tomography can reveal 3D sub-micron features, particularly damage, evolving under load, leading to improved materials. However, dataset size and complexity increasingly require time-intensive and subjective semi-automatic segmentations. Here, we present the first deep learning (DL) convolutional neural network (CNN) segmentation of multiclass microscale damage in heterogeneous bulk materials, teaching on advanced aerospace-grade composite damage using ∼65,000 (trained) human-segmented tomograms. The trained CNN machine segments complex and sparse (<<1% of volume) composite damage classes to ∼99.99% agreement, unlocking both objectivity and efficiency, with nearly 100% of the human time eliminated, which traditional rule-based algorithms do not approach. The trained machine is found to perform as well or better than the human due to “machine-discovered” human segmentation error, with machine improvements manifesting primarily as new damage discovery and segmentation augmentation/extension in artifact-rich tomograms. Interrogating a high-level network hyperparametric space on two material configurations, we find DL to be a disruptive approach to quantitative structure-property characterization, enabling high-throughput knowledge creation (accelerated by 2 orders of magnitude) via generalizable, ultra-high-resolution feature segmentation.
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This study presents a novel method to describe the microscale phenomenon of cracks initiation based on sensitivity analysis in laminate fiber-reinforced composites. The failure of fiber-reinforced composite laminates often roots in the microscale phenomenon of fiber/matrix interfacial debonding. The micro-cracking and interfacial debonding in composites are difficult to detect both experimentally and numerically. This paper shows that the sensitivity of the stress response in a transverse ply with respect to individual fiber/matrix interface cohesive properties follows a normal distribution before cracks initiate. The distribution of the sensitivities rapidly deviates from a normal distribution from crack initiation to the formation. Several realistic microstructural representations of a fiber-reinforced composite laminate are simulated to validate the proposed method of detecting crack initiation. This proposed prediction method of crack initiation can be used as a failure risk indicator to increase the reliability of laminates’ designs.
Compressive strength and elastic modulus of unidirectional carbon fiber reinforced polymer (UD-CFRP) have been enhanced experimentally by using soft micro-length Aramid pulp (AP) micro/nano-fiber interlays. This study presents a micro-mechanics model to prove theoretically such enhancements in the compressive strength and elastic modulus of UD-CFRP are possible. The micro-mechanics model recognizes the importance of in-situ formed graded interfacial region between carbon fiber plies generated from the random distribution and out-of-plane movements of micro-length AP micro/nano-fibers. The micro-mechanics model shows that even an areal density of only ∼4 g/m² of AP micro/nano-fibers (with the interlay thickness < 30 μm) is sufficient to generate the enhancements in both compressive strength and elastic modulus along the carbon fiber direction of UD-CFRP. The new micro-buckling or shear failure mechanism has been identified to be responsible for the compressive strength enhancement, instead of local delamination in plain UD-CFRP. The theoretical and experimental findings show interfacial microstructural designs at the carbon fiber ply interface can be critical to the bulk properties of CFRP.
We present here the development and evaluation of a deep learning (artificial intelligence)-based computer vision machine to automate segmentation of multiclass progressive matrix damage across micro and mesoscales in aerospace-grade advanced composite laminates visualized in 4D via nondestructive in situ mechanical testing coupled with synchrotron radiation computed tomography (SRCT). Leveraging tens of thousands of manually-/human-annotated SRCT tomograms (i.e., 2D virtual cross-sectional slices) encompassing two different aerospace-grade advanced composite laminate systems (standard-thickness-ply and thin-ply) that were SRCT-scanned while under progressive tensile loading, we teach a fully convolutional neural network machine to segment complex polymer matrix damage mechanisms according to their host ply, replacing ~10 hours of trained human labor per scan segmentation (~2000 tomograms per scan) with negligible time to configure the trained machine data-processing pipeline. Evaluating qualitatively and quantitatively the segmented tomograms independently in 2D, as well as collectively in 3D scans, we demonstrate good agreement between the state-of-the-art human-based region growing (semi-manual) method and machine-based segmentation results, summarized by test set macro-averages of the following common classification/segmentation performance metrics: 79% for F1 score (harmonic mean of precision and recall) and 67% for intersection over union (IoU) score. Moreover, 2D inspection of segmented damage within tomograms reveals that F1 and IoU scores actually underrate machine performance due to a nontrivial degree of human (used as ground truth) segmentation error, as the machine is found to regularly exceed the human (resulting in F1 and IoU score penalties) by discovering new damage instances, augmenting existing diffuse segmentations, and extending segmentations to image artifact-prone specimen edges. Consequently, we discover that deep learning-based segmentation successfully and efficiently characterizes sparse (<<1% of scan volume), extremely complex 3D damage states within SRCT datasets, resolving an intractable computer vision challenge (as viewed through the lens of traditionally programmed automation) and establishing these high-throughput tools as promising candidates to accelerate understanding of basic structure-property relationships in traditional and next-generation advanced composite materials.
This work presents a novel computational framework to simulate fracture events in brittle anisotropic polycrystalline materials at the microscopical level, with application to solar-grade polycrystalline Silicon. Quasi-static failure is modeled by combining the phase field approach of brittle fracture (for transgranular fracture) with the cohesive zone model for the grain boundaries (for intergranular fracture) through the generalization of the recent FE-based technique published in [M. Paggi, J. Reinoso, Comput. Methods Appl. Mech. Engrg., 31 (2017) 145–172] to deal with anisotropic polycrystalline microstructures. The proposed model, which accounts for any anisotropic constitutive tensor for the grains depending on their preferential orientation, as well as an orientation-dependent fracture toughness, allows to simulate intergranular and transgranular crack growths in an efficient manner, with or without initial defects. One of the advantages of the current variational method is the fact that complex crack patterns in such materials are triggered without any user-intervention, being possible to account for the competition between both dissipative phenomena. In addition, further aspects with regard to the model parameters identification are discussed in reference to solar cells images obtained from transmitted light source. A series of representative numerical simulations is carried out to highlight the interplay between the different types of fracture occurring in solar-grade polycrystalline Silicon, and to assess the role of anisotropy on the crack path and on the apparent tensile strength of the material.
The competition between crack penetration in the layers and cohesive delamination along interfaces is herein investigated in reference to laminate ceramics, with special attention to the occurrence of crack deflection and crack branching. These phenomena are simulated according to a recent variational approach coupling the phase field model for brittle fracture in the laminae and the cohesive zone model for quasi-brittle interfaces. It is shown that the proposed variational approach is particularly suitable for the prediction of complex crack paths involving crack branching, crack deflection and cohesive delamination. The effect of different interface properties on the predicted crack path tortuosity is investigated and the ability of the method to simulate fracture in layered ceramics is proven in relation to experimental data taken from the literature.
One of the goals of the Journal of Elasticity: The Physical and Ma- ematical Science of Solids is to identify and to bring to the attention of the research community in the physical and mathematical sciences extensive expositions which contain creative ideas, new approaches and currentdevelopmentsinmodellingthebehaviourofmaterials. Fracture has enjoyed a long and fruitful evolution in engineering, but only in - cent years has this area been considered seriously by the mathematical science community. In particular, while the age-old Gri?th criterion is inherently energy based, treating fracture strictly from the point of view of variational calculus using ideas of minimization and accounting for the singular nature of the fracture ?elds and the various ways that fracture can initiate, is relatively new and fresh. The variational theory of fracture is now in its formative stages of development and is far from complete, but several fundamental and important advances have been made. The energy-based approach described herein establishes a consistent groundwork setting in both theory and computation. While itisphysicallybased,thedevelopmentismathematicalinnatureandit carefully exposes the special considerations that logically arise rega- ing the very de?nition of a crack and the assignment of energy to its existence. The fundamental idea of brittle fracture due to Gri?th plays a major role in this development, as does the additional dissipative feature of cohesiveness at crack surfaces, as introduced by Barenblatt. Thefollowinginvited,expositoryarticlebyB. Bourdin,G. Francfort and J. -J. Marigo represents a masterful and extensive glimpse into the fundamentalvariationalstructureoffracture.
An efficient computational model to simulate tensile failure of both hybrid and non-hybrid composite materials is proposed. This model is based on the spring element model, which is extended to a random 2D fibre packing. The proposed model is used to study the local stress fields around a broken fibre as well as the failure process in composite materials. The influence of fibre strength distributions and matrix properties on this process is also analysed. A detailed analysis of the fracture process and cluster development is performed and the results are compared with experimental results from the literature.
A reliable virtual tool for the numerical simulation of the low-velocity impact damage on composite laminates is proposed. A continuum material model for the simulation of intraply damage phenomena is implemented in a numerical scheme as a user subroutine of the commercially available Abaqus finite element package. Delaminations are simulated by making use of cohesive surfaces. The use of structured meshes, aligned with fibre directions allows the accurate capturing of matrix cracks, and their interaction with the development of delaminations. Element erosion and the application of friction allow the simulation of fibre splits and their entanglement which results in the permanent indentation of the impacted specimen.
Phase-field models, sometimes referred to as gradient damage or smeared crack models, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith' criterion. For a one-dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter be identified with the material's internal or characteristic length. In this article, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.Our main claim, supported by validation and verification in a broad range of materials and geometries, is that crack nucleation can be accurately predicted by minimization of a nonlinear energy in variational phase field models, and does not require the introduction of ad-hoc criteria.
In this study, a new 3D finite element formulation which enables simulating the interaction between brittle crack propagation and interface delamination in heterogeneous materials is presented. The Phase Field (PF) model for brittle fracture has been coupled with the Cohesive Zone Model (CZM) within the framework of the large deformation analysis. These numerical techniques have been implemented within a 8-node locking-free solid shell element, relying on the enhanced assumed strain concept, and a 8-node interface finite element, respectively. The predictive capabilities of the proposed formulation have been assessed through the simulation of cracking in flat and curved geometries under in-plane and out-of-plane loading conditions. The results show the ability of the model to predict complex crack paths where intralayer crack propagation and delamination occur simultaneously and interact. The proposed formulation provides a powerful modeling tool for the simulation of fracture phenomena in heterogeneous materials and laminate structures, which are characterized by the existence of numerous interfaces, such as in photovoltaic laminates.
Thin ply laminates are a new class of composite materials with great potential for application in the design of thinner and highly optimized components, resulting in potential weight savings and improved mechanical performance. These new composites can stir the development of lighter structures, overcoming current design limitations as well as notably reducing the onset and development of matrix cracking and delamination events. This paper presents the application of two recent modeling methods for the failure analysis and strength prediction of open-hole thin ply laminates under tensile loading, which exhibit a brittle response upon failure: (i) the analytical coupled energy-stress Finite Fracture Mechanics (FFMs) technique, and (ii) the FE-based Phase Field (PF) approach for fracture that is incorporated into an enhanced assumed solid shell element. The predictions obtained using both strategies are compared with experimental data. These correlations exhibit a very satisfactory level of agreement, proving the robustness and reliability of both methods under consideration.
This paper presents a consistent anisotropic damage model for laminated fiber-reinforced composites relying on the 3D-version of the Puck failure criterion. The current model is based on ply failure mechanisms (fiber and inter-fiber failures) incorporating energetic considerations into the progressive damage evolution. The proposed formulation is implemented into the implicit FE commercial package ABAQUS using the user-defined capability UMAT. Additionally, the current damage model is combined with a locking-free solid shell formulation via the user-defined subroutine UEL in order to account for geometrical nonlinear effects in thin-walled applications. The reliability of the current formulation is first examined by means of several benchmark applications, and subsequently, the obtained numerical predictions are compared with experimental data corresponding to an open hole tension test. These applications show the practicability and accuracy of the proposed methodology for triggering damage in composite laminates, providing a robust modeling framework suitable for general specimens and loading conditions.
Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.
The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In this investigation, this problem is revisited in view of the recent progresses on the phase field approach to brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model, implemented within the finite element method framework using a monolithic fully implicit solution strategy, is applied to provide a further insight into the understanding of the role of model parameters on the above competition. In particular, in this study, the role of the fracture toughness ratio between the interface and the adjoining bulks and the characteristic fracture-length scales of the dissipative models are analyzed. In the case of a brittle interface, the asymptotic predictions based on linear elastic fracture mechanics criteria for crack penetration, single deflection or double deflection are fully captured by the present method. Moreover, by increasing the size of the process zone along the interface, or by varying the internal length scale of the phase field model, new complex phenomena are emerging, such as simultaneous crack penetration and deflection and the transition from single crack penetration to deflection and penetration with subsequent branching into the bulk.
Constitutive assumptions involved in phase field models of fracture in order to capture the behavior of cracks on the (smeared) continuum level are critically reviewed and several improvements are suggested. While some of the deficiencies of existing models are connected to the variational structure of respective phase field approaches, non-variational approaches are shown to allow for greater flexibility towards constitutive assumptions needed for a realistic representation of cracks. Benefits of the latter are illustrated by numerical examples.
This paper presents the modelling of tensile failure of composites using novel enriched elements defined based on the floating node method. An enriched ply element is developed, such that a matrix crack can be modelled explicitly within its domain. An enriched cohesive element is developed to incorporate the boundaries of matrix cracks on the interface, such that the local stress concentrations on the interface can be captured. The edge status variable approach allows the automatic propagation of a large number of matrix cracks in the mesh. A laminate element is formed, such that a fixed, planar mesh can be used for laminates of arbitrary layups. The application examples demonstrate that the proposed method is capable of predicting several challenging scenarios of composites tensile failure, such as the large number matrix cracks, grip-to-grip longitudinal splits, widespread delamination, explosive splitting and distributed fibre breaking in the 0 plies, etc. The complete failure process of ply-blocked composite laminates, up to the final breaking of the loosened 0° strips, are here firstly reproduced by modelling.
The phase field method is a versatile simulation framework for studying initiation and propagation of complex crack networks without dependence to the finite element mesh. In this paper, we discuss the influence of parameters in the method and provide experimental validations of crack initiation and propagation in plaster specimens. More specifically, we show by theoretical and experimental analyses that the regularization length should be interpreted as a material parameter, and identified experimentally as it. Qualitative and quantitative comparisons between numerical predictions and experimental data are provided. We show that the phase field method can predict accurately crack initiation and propagation in plaster specimens in compression with respect to experiments, when the material parameters, including the characteristic length are identified by other simple experimental tests.
The failure strain of fibre-reinforced composites can be increased by fibre hybridisation. A recently developed model for unidirectional composites was extended to hybrid composites to analyse this synergetic effect, called the hybrid effect. The model predicts individual fibre breaks and interactions among clusters of fibre breaks. Three key parameters were studied to understand how they can maximise the hybrid effect, namely low elongation fibre strength scatter and hybridisation fibre stiffness and failure strain. Larger strength scatter of the low elongation fibres leads to larger hybrid effects, as the scatter spreads out the cluster development over a larger strain interval. The failure strain ratio of the two fibre types should be above 2 for the properties used here, but a higher ratio did not yield any additional benefits. Increasing the stiffness of the hybridisation fibre reduces the stress concentrations on the low elongation fibre and may also enlarge the hybrid effect. These conclusions provide guidelines for designing optimal hybrid composites.
Three different models with increased complexity to study the effects of hybridization on the tensile failure of hybrid composites are proposed. The first model is a model for dry bundles of fibres based on the statistics of fibre strength. The second is a model for composite materials based on the multiple fragmentation phenomenon. Lastly, a micromechanical numerical model is developed that considers a random distribution of fibres and takes into account the stochastic nature of fibre strength. This study aims to understand the controlling factors that lead to pseudo-ductility, as well as establish the sequence of failure mechanisms in hybrid composites under tensile loadings.
An air-assisted fibre tow spreader was used to produce continuous commingled glass and carbon fibre tows. Hybrid carbon and glass fibre (CF/GF) reinforced epoxy composites were manufactured from these commingled fibre tows by resin film infusion. The degree of hybridisation of the hybrid CF/GF tow was defined and characterised. Compared with the corresponding continuous CF/epoxy composite, the hybrid composite with a degree of hybridisation of 32.45% exhibits a more gradual tensile failure. The final tensile failure strain increased by 14% as compared to that of the carbon fibre epoxy composite.
A novel invariant-based approach to describe elastic properties and failure of composite plies and laminates has been recently proposed in the literature. An omni strain failure envelope has been defined as the minimum inner failure envelope in strain space, which describes the failure of a given composite material for all ply orientations. In this work, a unit circle is proposed as a strain normalized failure envelope for any carbon fiber reinforced polymer laminate. Based on this unit circle, a failure envelope can be generated from the longitudinal tensile and compressive strains-to-failure of a unidirectional ply. The calculated failure envelope was found in good agreement with experimental data published in the well-known World Wide Failure Exercise.
An algorithm to create random distributions of uniform spherical or circular particles is proposed here with the aim of generating RVE-based micro-mechanical models for composites reinforced with long fibres or spherical particles. The algorithm is fast, able to represent the randomness of the material and to generate RVEs with any volume fraction, from 0 to its highest theoretical value, i.e. and for spheres and circles, respectively. Several statistical spatial descriptors were used to evaluate the goodness of the generated particles’ distributions. It was concluded that the proposed algorithm can be used to generate statistically representative distributions of uniform particles.
Thin ply laminates have shown much promise in recent times in terms of their exciting damage suppression characteristics. Utilisation of this damage suppression in carbon–epoxy angle-ply laminates has been shown experimentally to yield a highly non-linear stress–strain response. This paper presents an analytical modelling method that incorporates matrix plasticity and reorientation of the fibres into a classical laminate analysis for the prediction of the in-plane response of thin ply angle-ply laminates. It is shown that the method can successfully predict the non-linear behaviour of laminates with values of between 15° and 45°. The main characteristics of the stress–strain curve, such as the initial largely linear region, yield point and stiffening before final failure, are all well captured. The modelling has allowed straightforward identification of a particular fibre angle that exhibits strength in excess of 900 MPa, strain to failure of more than 3.5% and a promising pseudo-ductile strain of 1.2%.
Composite materials have grown rapidly both in their applications and their economic importance, and they will no doubt continue to do so. With this growth has come increased attention in engineering curricula, but most coursework tends to focus on laminate theory and the analysis of composites, not on the practical design aspects most important to engineers. Composite Materials: Design and Applications fills that gap. Updated and translated from the successful French text Materiaux Composites, it offers comprehensive coverage of composites and their use in a broad range of applications. Part I provides a detailed introduction to composite materials, including fabrication processes, properties, design concepts, assembly, and applications. This section could also be used by itself in a course on advanced materials. Part II discusses elastic anisotopic properties, the directional dependence of different properties, and the mechanical properties of thin laminates. Alone, this section is suitable for a course on the mechanics of composite materials. Part III addresses the orthotropic coefficients needed for design activities, the Hill-Tsai failure criterion, the bending and torsion of composite beams, and the bending of thick composite plates. While somewhat more theoretical than the preceding chapters, it helps students better understand the behavior of composite parts. Part IV contains 41 detailed, numerical examples illustrating the design and use of composites. These are presented on three levels and cover the mechanical properties of composite structures in different forms, thermoelastic properties and failure analysis and the bonding of cylinders, sandwich beam buckling and flexure shear, and vibrations in composite plates. Clearly written and filled with more than 500 illustrations, Composite Materials: Design and Applications forms an outstanding textbook for senior undergraduate and beginning graduate-level course work-one that can make a significant contribution to the training of future engineers.
The enhanced mechanical performance of thin-ply laminates results from their ability to delay the onset of damage typically observed in composite materials. However, in notched structures, subcritical damage growth causes beneficial stress redistributions in the vicinity of the notch, blunting the stress concentration. Precluding these damage mechanisms, as in thin-ply laminates, may potentially lead to inferior notched responses. To obviate this limitation of thin-ply laminates, a strategy based on the combination of standard grade 0° plies and thin transverse and off-axis plies is analysed in this paper. A detailed study of the effect of 0° ply blocking is carried out, with particular emphasis on the blunting mechanisms and notched response. Tests on scaled notched panels loaded in tension, with notch sizes between 6 mm and 30 mm, show that the combination of standard grade 0° ply blocks with thin transverse and off-axis plies promotes localised fibre-matrix splitting, which acts as an important notch blunting mechanism, while preventing matrix cracking and delamination. This results in an improved notched response and superior large damage capability. It is also shown that thicker 0° ply blocks provide higher stability in composite bolted joints, while the thin transverse and off-axis plies contribute for matrix-dominated damage suppression, resulting in an improved bolt-bearing response. The improvements of the large damage capability and bolt-bearing performance are obtained without compromising the superior unnotched tensile and compressive strengths intrinsic to thin-ply laminates.
A micromechanics framework for modelling the mode II interlaminar crack onset and propagation in
fibre-reinforced composites is presented with the aim of i) modelling the micro-scale failure mechanisms
that underlie interlaminar crack propagation, and ii) determining the effect of the through-thickness
pressure on mode II fracture toughness. An algorithm for the generation of the fibre distribution is
proposed for the generation of three-dimensional Representative Volume Elements (RVEs). Appropriate
constitutive models are used to model the different dissipative effects that occur at crack propagation.
Numerical predictions are compared with experiments obtained in previous investigations: it is
concluded that the proposed micromechanical model is able to simulate conveniently the interlaminar
crack propagation and to take into account the effect of the through-thickness pressure on mode II
interlaminar fracture toughness.
Three-dimensional fatigue failure criteria for unidirectional fiber composites under states of cyclic stress are established in terms of quadratic stress polynomials which are expressed in terms of the transversely isotropic invariants of the cyclic stress. Two distinct fatigue failure modes, fiber mode, and matrix mode, are modeled separately. Material information needed for the failure criteria are the S-N curves for single stress components. A preliminary approach to incorporate scatter into the failure criteria is presented.
The effect of ply thickness on the onset of intralaminar and interlaminar damage is extremely important for the structural response of laminated composite structures. This subject has gained particular interest in recent years due to the introduction in the market of spread-tow, ultra-thin carbon-fibre reinforcements with different configurations. In the present paper, an experimental test campaign was carried out to study the structural response of aerospace-grade plain weave spread-tow fabrics (STFs) of different areal weights. The results showed that, in spite of an apparent superior longitudinal tensile strength of the thick STF, the multidirectional thin-STF laminate exhibited an improved tensile unnotched strength over the thick-STF laminate, attributed to its damage suppression capability. However, damage suppression was also responsible for similar tensile notched strengths. In compression, the thin-STF laminate performed substantially better than the thick-STF laminate in both unnotched and notched configurations. Finally, a similar bearing response was obtained in both STF laminates, in spite of a slightly higher resistance of the thin-STF laminate to the propagation of subcritical damage mechanisms.
Advanced non-linear Finite Element models for the strength prediction of composite laminates normally result in long computing times that are not suitable for preliminary sizing and optimisation of structural details. Macro-mechanical analytical models, in spite of providing quick predictions, are based on properties determined from tests performed at the laminate level, making preliminary design and optimisation of composite structures still too costly in terms of testing requirements. To overcome these disadvantages, an analytical framework is proposed to predict the notched response of balanced carbon fibre-reinforced polymer laminates using only three ply properties as inputs: the longitudinal Young’s modulus, the longitudinal strength, and the -curve of the 0° plies. This framework is based on invariant-based approaches to predict the stiffness and the strength of general laminates, and an analytical model to estimate the -curve of balanced laminates. These laminate properties are then used in a Finite Fracture Mechanics model to predict size effects. The predictions for open-hole tension and compression tests are compared with experimental results obtained from the literature for five different material systems. Good agreement is observed considering that only three ply properties are used as inputs for the analytical framework.
Advanced non-linear Finite Element models for the strength prediction of composite laminates normally result in long computing times that are not suitable for preliminary sizing and optimisation of structural details. Macro-mechanical analytical models, in spite of providing quick predictions, are based on properties determined from tests performed at the laminate level, making preliminary design and optimisation of composite structures still too costly in terms of testing requirements. To overcome these disadvantages, an analytical framework is proposed to predict the notched response of balanced carbon fibre-reinforced polymer laminates using only three ply properties as inputs: the longitudinal Young’s modulus, the longitudinal strength, and the -curve of the 0° plies. This framework is based on invariant-based approaches to predict the stiffness and the strength of general laminates, and an analytical model to estimate the -curve of balanced laminates. These laminate properties are then used in a Finite Fracture Mechanics model to predict size effects. The predictions for open-hole tension and compression tests are compared with experimental results obtained from the literature for five different material systems. Good agreement is observed considering that only three ply properties are used as inputs for the analytical framework.
This chapter presents the analysis models, developed at different length scales, for the prediction of inelastic deformation and fracture of polymer composite materials reinforced by unidirectional fibers. Three different length scales are covered. Micro-mechanical models are used to understand in detail the effects of the constituents on the response of the composite material, and to support the development of analysis models based on homogenized representations of composite materials. Meso-mechanical models are used to predict the strength of composite structural components under general loading conditions. Finally, macro-mechanical models based on Finite Fracture Mechanics, which enable fast strength predictions of simple structural details, are discussed.
This study uses a recently developed phase-field approach to model fracture of arterial walls with an emphasis on aortic tissues. We start by deriving the regularized crack surface to overcome complexities inherent in sharp crack discontinuities, thereby relaxing the acute crack surface topology into a diffusive one. In fact, the regularized crack surface possesses the property of Gamma-Convergence, i.e. the sharp crack topology is restored with a vanishing length-scale parameter. Next, we deal with the continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler-Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the crack phase-field and the balance of linear momentum. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive model which is additively decomposed into an isotropic part for the ground matrix and an exponential anisotropic part for the two families of collagen fibers embedded in the ground matrix. In addition we propose a novel energy-based anisotropic failure criterion which regulates the evolution of the crack phase-field. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step (solved for the frozen crack phase-field parameter) and a crack evolution step (solved for the frozen deformation map); a history field governed by the failure criterion is successively updated. Subsequently, a conventional Galerkin procedure leads to the weak forms of the governing differential equations for the physical problem. Accordingly, we provide the discrete residual vectors and a corresponding linearization yields the element matrices for the two sub-problems. Finally, we demonstrate the numerical performance of the crack phase-field model by simulating uniaxial extension and simple shear fracture tests performed on specimens obtained from a human aneurysmatic thoracic aorta. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results agree favorably with the experimental findings.
This work presents an experimental study on the effect of ply-level hybridisation on the tensile unnotched and notched response of composite laminates. In a first assessment, notched tests were performed on laminates with nominal ply thicknesses between 0.03 mm and 0.30 mm. From the understanding of the effect of ply thickness on the damage mechanisms that govern the notched response of laminates, the concept of ply-level hybridisation is introduced, which consists in combining plies of different grades. A uniform combination of thin and conventional plies resulted in a hybrid laminate with intermediate notched response. Selective hybridisation, where thin off-axis plies are combined with thicker 0° plies, resulted in a globally enhanced notched behaviour without compromising the unnotched and fatigue responses. This work clearly shows how ply-level hybridisation, when designed to trigger specific damage mechanisms, can be used to improve the notched response of composite laminates.
Delaminations at the free-edges of a laminated composite under tension can be triggered by transverse cracks or by high interlaminar stresses. The capability for predicting these phenomena when the ply thickness is reduced (thin-ply laminates) is particularly challenging because damage mechanisms are delayed or even suppressed. In this work, an existing energy-based failure criterion and a simplified finite element model with cohesive elements are combined to develop a computationally inexpensive predictive tool. Its comparison with experimental data demonstrates that this approach captures the trends of the critical strain for delamination with respect to ply thickness and ply location and the quantitative agreement with the predictions is satisfactory.
A new fiber spreading technology (FUKUI method) to obtain the continuously wide and thin reinforcing fiber tow was developed. Thin prepreg sheet less than 0.05 mm in thickness can be prepared by using this method. In the previous study, the tensile tests were conducted on the Carbon/Epoxy quasi-isotropic laminates which were composed of stacking these prepreg sheets. As a result, the thin-ply effect was found, that is, the initial failure stress increases with decreasing ply thickness. This effect was previously predicted by Kageyama et al. In this work, the thin-ply effects on the compressive properties have been studied. As a result, the thin-ply effect was found not only in tensile tests but also in compression tests. This result implies that the design strength of composites can be improved by the use of thin prepreg sheets. In other words, this result means that the weight saving and reliability can be achieved using thin prepreg sheets as a composite materials.
It is common in many branches of continuum mechanics to treat material as though it is incompressible. Although no material is truly incompressible, there are many materials in which the ability to resist volume changes greatly exceeds the ability to resist shearing deformations; examples are liquids with low viscosity, like water, and some natural and artificial rubbers. For such materials, the assumption of incompressibility is a good approximation in many circumstances, and often greatly simplifies the solution of specific problems. It should be noted, though, that there are occasions when even a small degree of compressibility may produce a major effect; an example is the propagation of sound waves in water.
This paper presents the extension of the 7-parameter shell element for the analysis of layered CFRP composite structures assuming the Equivalent Single Layer (ESL) approach, and addresses some aspects of its numerical implementation into the package ABAQUS. The theoretical formulation of this element relies on the shell model proposed in Büchter and Ramm (1992) [15], which allows the use of unmodified three-dimensional constitutive laws. In order to remedy locking pathologies of the corresponding finite element implementation, the Enhanced Assumed Strain (EAS) and the Assumed Natural Strain (ANS) methods are simultaneously employed. A series of benchmark problems assess the applicability of this element for isotropic materials and layered composites. Finally, this element is also used for the analysis of a composite stiffened panel in postbuckling regime subjected to uniform pressure loading. The numerical results are corroborated with experimental data, obtaining a satisfactory agreement along the loading procedure.