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Variation of maximum and minimum matrix stress invariants in regular arrays along the unit cell direction angle due to various loading (v f ¼ 0.6): (a) maximum von Mises stress; (b) maximum first invariant; (c) maximum von Mises stress; (d) minimum first invariant; (e) maximum von Mises stress and (f) unit cell and ply directions.
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Micromechanical approaches are employed to investigate the influence of different fiber arrangement on the mechanical behavior of unidirectional composites (UD) under various loading conditions. A micromechanical model with a random fiber array is generated and used in a finite element analysis together with two frequently used representative volum...
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Citations
... However, due to the diminishing effect of microscale randomness at higher length scales, microstructural variability is often ignored and micromechanics-based models assuming periodic boundary conditions, with an ordered array of fibers (either square or hexagonally packed fibers), are typically utilized. Researchers have investigated the effect of random or disordered microstructures on various composite response behaviors, assuming elastic and damage behavior [15][16][17][18][19][20][21]. In our previous work [22], the influence of ordered and disordered microstructures on the effective properties and fatigue life of graphite/epoxy polymer matrix composite (PMC) at low volume fractions was studied in the context of assessing the advantages/limitations of the micromechanics idealizations (GMCgeneralized method of cells or HFGMC -high fidelity generalized method of cells) available within the general, synergistic, multiscale-modeling framework for composites (developed by the NASA Glenn Research Center (GRC)) and known as MAC/GMC and FEAMAC [23] when considering microstructural arrangement. ...
The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses. Finally, to demonstrate the multiscale analysis framework, a CMC gas turbine engine vane structure is analyzed involving a progressive damage model.
... Varying morphology of fibre reinforced composites at microscale such as fibre clustering or matrix-rich regions may occur during the manufacturing process [11]. Studies show that the heterogeneity of the reinforcement at microscale affects stress distributions at the microstructural level [12], interface stress distribution [13], transverse crack formation [14], transverse creep behaviour [15] and effective elastic properties [16]. It is therefore essential to have a thorough understanding of the effect of the spatial distribution of fibres on the response of composite material in both linear and nonlinear regime. ...
Computational homogenization is commonly used to predict the responses of composite materials. However, it poses practical issues due to large computational cost especially in the material-by-design setting when various design parameters are to be examined. This paper presents the development of a parametric model order reduction strategy for the micromechanical analysis of composites when fibre distribution is the parameter of interest. The reduced order model is obtained by applying Galerkin projection in combination with proper orthogonal decomposition. The presented framework enables a significantly reduced computational load during parametric studies as the model dimension of the microscale analyses is significantly
smaller. The results show that the proposed approach can reproduce the homogenized properties of material and local stress
distributions in the microstructures very well.
... During the manufacturing process of composites, the cavitation stays inside the matrix in the form of voids. Ha and co-workers [70][71][72] conducted extensive analysis on the effects of fibre arrangement and interface properties on the failure prediction of composites based on unit cell modelling under different loading conditions. The mechanical performance of CFRP composite materials was conducted on a unit cell and a random model by Trias et al. [73,74]. ...
The recent decades have seen various attempts at the numerical modelling of fibre-reinforced polymer (FRP) composites in the aerospace, auto and marine sectors due to their excellent mechanical properties. However, it is still challenging to accurately predict the failure of the composites because of their anisotropic and inhomogeneous characteristics, multiple failure modes and their interaction, especially under multiaxial loading conditions. Micromechanics-based numerical models, such as representative volume elements (RVEs), were developed to understand the progressive failure mechanisms of composites, and assessing existing failure criteria. To this aim, this review paper summarises the development of micromechanics-based RVE modelling of unidirectional (UD) FRP composites reported in the literature, with a focus on those models developed using finite element (FE) and discrete element (DE) methods. The generation of fibre spatial distribution, constitutive models of material constituents as well as periodic boundary conditions are briefly introduced. The progressive failure mechanisms of UD FRP composites simulated by RVEs under various loadings are discussed and the comparison of failure envelopes predicted by numerical results and classical failure criteria are reviewed.
... In reality, the bundles of fibers constituting tows are distributed irregularly [59,60]. However, it is common to idealize the structure as straight cylinders with ellipsoidal cross-sections having hexagonal, square or random packings. ...
... The effects of fiber packing arrangements (hexagonal, square and random) on the overall elastic properties, CTE and von Mises stress predictions for fiber volume fractions ranging from 10% to 60% are discussed in [59,63]. For the effective elastic properties, Huang et al. [59] showed that hexagonal and random packings are in a good agreement for the whole range of considered volume fractions while the square packing results in discrepancies that are growing progressively with the volume fractions, up to ∼ 20%, and results in a transverse anisotropy. ...
... The effects of fiber packing arrangements (hexagonal, square and random) on the overall elastic properties, CTE and von Mises stress predictions for fiber volume fractions ranging from 10% to 60% are discussed in [59,63]. For the effective elastic properties, Huang et al. [59] showed that hexagonal and random packings are in a good agreement for the whole range of considered volume fractions while the square packing results in discrepancies that are growing progressively with the volume fractions, up to ∼ 20%, and results in a transverse anisotropy. In the case of CTE, the predictions from all arrangements were found to be in an excellent agreement [59]. ...
... Based on the literature review, carbon fibres are considered to be rate-independent while glass and other polymer fibres are clearly rate sensitive. Carbon fibres are therefore modeled as a transversely isotropic and linearly elastic material [24,25] and glass fibres are assumed as a rate dependent elastic material [26]. A coupled viscoelastic -viscoplastic model is also developed for the aramid and polyester fibres for short loading times [27,28]. ...
... The isostress assumption is known to cause a significant underestimation of ⋆ 2 and ⋆ 12 for composites with unidirectional cylindrical fibres, as observed experimentally and by micromechanical finite element analysis [24]. The reason is that the fibres cause a nonuniform stress state in the matrix [24,25], which violates the isostress assumption. ...
... The isostress assumption is known to cause a significant underestimation of ⋆ 2 and ⋆ 12 for composites with unidirectional cylindrical fibres, as observed experimentally and by micromechanical finite element analysis [24]. The reason is that the fibres cause a nonuniform stress state in the matrix [24,25], which violates the isostress assumption. There is also an effect of the fibre distribution in the plane transverse to the fibres [24]. ...
Fibre reinforced polymeric composites are in high demand in automotive and aviation industries to improve fuel efficiency. However, the dynamic behaviour of composites is not very well understood. Furthermore, dynamic loading together with the anisotropic nature and complex nonlinear behaviour of polymer composites results in a complex failure behaviour. This behaviour is of significant importance to account for in automobile crash simulation and impact modeling of aircraft structures.
In this thesis, a micromechanics based constitutive model is developed to predict the nonlinear behaviour and failure of unidirectional fibre reinforced polymer composites subjected to compressive dynamic loading. The carbon fibres are assumed to be hyperelastic transversely isotropic. For the matrix, a viscoelastic-viscoplastic constitutive model with hardening enhanced by continuum damage is advocated. A three parameter Maxwell model is used for the linear viscoelastic behaviour of the matrix. The nonlinear viscoplastic behaviour is introduced by coupling a Perzyna-type Bingham/Norton model with an intralaminar matrix continuum damage model. The pressure dependence of the onset of plastic yielding in matrix shear dominated response under compressive loading is also considered. The proposed model is formulated in a geometrically nonlinear description that separates the fibre and the matrix contributions. The model draws from computational homogenization of the unidirectional ply level response, with the matrix and the fibres as subscale constituents. A major feature is that the subscale
constituents are coupled via isostrain and isostress assumptions parallel and transverse to the fibres, respectively. An improved isostress formulation is proposed to include in a better way longitudinal fibre shear response. The elastic response is improved by considering a non-uniform stress distribution in the matrix. For intralaminar damage growth, a continuum damage enhanced formulation of Lemaitre type is proposed. This model is combined with a surface based cohesive model that describes interlaminar delamination.
Based on the model, the shear induced failure behaviour in compression of the composite material is characterized. Finite element simulations are conducted to validate observed rate dependent properties of off-axis loaded unidirectional composites and angle-ply laminates. The predictions of the finite element simulations are compared to published experimental results of different material systems under compression loading at different strain rates. The results
obtained are in reasonable agreement with the experiments. Typical applications are carbon/epoxy composites, where unidirectional carbon fibres are embedded in a polymer matrix. In the future, the model is possible to extend to orthotropic plies and textile reinforced composites. The model is micromechanically motivated, hence it is also possible to extend for rate dependent fibres, e.g. glass fibres.
... for composites with unidirectional cylindrical fibres, as observed experimentally and by micromechanical finite element analysis [24]. The reason is that the fibres cause a nonuniform stress state in the matrix [24,25], which violates the isostress assumption. ...
... for composites with unidirectional cylindrical fibres, as observed experimentally and by micromechanical finite element analysis [24]. The reason is that the fibres cause a nonuniform stress state in the matrix [24,25], which violates the isostress assumption. There is also an effect of the fibre distribution in the plane transverse to the fibres [24]. ...
... The reason is that the fibres cause a nonuniform stress state in the matrix [24,25], which violates the isostress assumption. There is also an effect of the fibre distribution in the plane transverse to the fibres [24]. Square and hexagonal fibre arrays result in relatively similar values of E 2 or G 12 . ...
Strain-rate effects in a unidirectional non-crimp fabric carbon/epoxy composite are addressed. To allow for kink-band formation including strain-rate effects and damage in such composites, the paper advances a recent model focused on compression loading at small off-axis angles. The model is based on computational homogenization with a subscale represented by matrix and fibre constituents at finite deformation. The fibre constituent is assumed to be elastic transversely isotropic and the matrix is viscoelastic-viscoplastic with damage degradation. Novel model improvements of special importance to small off-axis loading relate to the isostress formulation of the homogenized response in transverse shear. In this context, an enhanced homogenized elastic response is proposed based on Halpin–Tsai corrections to account for the nonuniform stress distribution on the microscale. The model captures the strongly rate sensitive kink-band formation due to localized matrix shearing and fibre rotation, confirming the experimentally observed increase in compressive strength for high strain rates.
... While performing the micro-mechanical analysis researchers have applied two kind of approaches. Many of them have considered the representative unit cell (RUC) approach [9] [20]. RUC assumes that the fibers are arranged in periodic manner either in square array or in hexagonal array. ...
... Melro et al. [8] has proposed new algorithm which includes three step procedure: a) Hard core model, b) Stirring the fibers and c) fibers in the outskirts. Up to 500 fibers were able to be arranged without overlapping with this algorithm for volume fraction of 65%.Huang et al. [20] has studied the effects of fiber arrangements on mechanical behaviour while analysing the RVE generated by self-developed algorithm. Chateau et al. [3] used the algorithm which follows the model proposed by He et al. [6]. ...
Stress concentration due to flaws in any material are very dangerous. Its understanding is thus very important before practical application of the material. As Fiber Reinforced Composite (FRC) is gaining wide range of application it is necessary to analyze it for stress concentration as one of the parameter. Literature survey reveals that the failure of FRC due to breakage of fiber is a cumulative process. If a fiber breaks stress concentration develops near the failure which leads to failure of other fibers in its vicinity. This process continues until the whole FRC gets failed. This phenomenon is quantified by a parameter called Stress Transfer Coefficient (STC). To analyze FRC generally it is practiced to analyze Representative Volume Element (RVE) which is a representation of the complete FRC. Another important aspect which is considered while analyzing FRC is the distribution of the fiber. Ideally the distribution of fibers should be uniform but no manufacturing process guarantees uniform distribution. Thus while analyzing FRC it is a good practice to generate RVE with randomly distributed fibers. In this paper an attempt is made to attain the relationship between volume fraction and STC. FRC with unidirectional fiber orientation is considered. RVEs with different volume fraction are analyzed. A new method is implemented to generate RVE with randomly distributed fibers. RVEs are so generated that it contains a broken fiber at its geometrical center and other fibers surrounding it. The RVE is loaded along the fiber direction.
... Given that analytical solution can only be derived for a few simple composite structures, semi-analytical techniques combing AHM with FEM may be required for analyzing more complex microstructures [25,26]. Besides, the micromechanics-based FE-RVE approach has been used for decades as powerful tools for the same purpose [27][28][29][30][31][32]. In general, the FE-RVE homogenization approach takes full advantage of powerful functions in commercial FE packages such as ANSYS and ABAQUS, which would facilitate interaction between academia and industry. ...
... We began by calculating the effective properties for elastic RVE by treating both matrix and fiber as linear elastic materials. Although analytical and numerical approaches have been wellestablished in the literature [27,29] to evaluate the effective elastic properties of unidirectional composites made of elastic matrix and fibers using RVE analysis, here we reproduce the benchmark case to validate the effectiveness of Viscoelastic RVE Calculator plug-in and reveal the effect of fiber arrangement on the predictions of effective elastic properties. In this case, the fiber and matrix properties are taken from Ref. [29], in which the authors developed a micromechanical FE-RVE model with a random fiber array. ...
... Although analytical and numerical approaches have been wellestablished in the literature [27,29] to evaluate the effective elastic properties of unidirectional composites made of elastic matrix and fibers using RVE analysis, here we reproduce the benchmark case to validate the effectiveness of Viscoelastic RVE Calculator plug-in and reveal the effect of fiber arrangement on the predictions of effective elastic properties. In this case, the fiber and matrix properties are taken from Ref. [29], in which the authors developed a micromechanical FE-RVE model with a random fiber array. The matrix was modeled as a linear isotropic elastic material with A variety of elastic RVEs with three different fiber arrangements, i.e., square array, diamond array and hexagonal array, were generated by setting and varying fiber volume fraction V f from 0.1 to 0.6 using the Viscoelastic RVE Calculator and the effective material properties are calculated and compared to that of elastic FE-RVE with random fiber distribution taken from [29] in Fig. 5. ...
Due to the inherent viscoelasticity of constituent matrix and the possibility of long-term storage, space deployable structures made of composites are likely to exhibit relaxation in the stored strain energy, which may degrade their deployment performance. This paper presents a bottom-up finite element based multiscale computational strategy that bridges the experimentally measurable properties of constituent fibers and matrix to numerical predictions of viscoelastic behavior of composite laminates and general shell structures. A user-friendly RVE analysis plug-in tool is developed in Abaqus/CAE to rapidly estimate the effective orthotropic viscoelastic properties of unidirectional composites by taking as input the microstructure geometry as well as the known properties of fibers and matrix. Some benchmark problems were solved, and the accuracy and efficiency of the proposed plug-in tool were verified. Next, the strategy is shown to be applicable to model the viscoelastic behavior of macroscale composite laminates and deployable shell structures, by utilizing built-in functions in Abaqus to define the stacking sequence and accordingly update the material properties. In particular, the proposed multiscale strategy was employed to simulate the influence of modulus relaxation on the deployment dynamics of a composite tape-spring hinge, and good agreement was achieved as compared to reported experimental results.
... Especially the transverse strengths of a fiber reinforced composite (FRP) are strongly influenced by the polymer matrix. Even with simple transverse loads on the composite, a complicated multiaxial stress state occurs locally in the matrix [4][5][6][7]. Such local effects were investigated within the framework of numerical micromechanical models [8][9][10]. ...
... It was shown that the standard paraboloid criterion significantly overestimates the hydrostatic tensile strength of epoxy resin. Even for simple transverse loads on a composite, multiaxial stress states occur locally in the matrix [4][5][6][7]. Such triaxial stress states inside the matrix material reduce the transverse tensile strength of an FRP [12,13]. ...
For use in micromechanical simulations of continuous fiber reinforced polymers, a more general form of the paraboloid failure criterion by Stassi‐D'Alia for matrix failure was developed with explicit consideration of the hydrostatic tension strength. Regarding polymers, limits for hydrostatic tensile strength based on isotropic linear elasticity could be derived. The comparison of the newly developed extended paraboloid criterion with experimental data for yielding as well as for material separation (fracture) shows good agreement.
... For the polymer composites, effects of different microstructure characteristics on the elastic and strength properties have been revealed including the fiber distribution, fiber shape, void distribution, void shape and so on. The effects of fiber distribution patterns on the elastic and inelastic properties of polymer composites have been revealed with the FEM method [1][2][3][4]. It has been found that the results predicted from the fiber random distribution model are more close to the experimental results. ...
To evaluate the effects of microstructure characteristics on the properties of SiC/SiC composites (Silicon Carbide Fiber/Silicon Carbide Matrix), models with different fiber and void shapes are analyzed with the FFT-based method. Especially for the voids, a newly developed method is presented for the random void generation. The FFT-based method is validated through comparing the predicted results with those from the FEM method and published literature. For the circular shaped fiber models, it is found that the damage initiates in the matrix around the fibers and with the increase of loading, the damages are joint. After considering the voids, the failure strength decreases and the random voids contribute to the largest decrease degree. The gear shaped fiber models have larger equivalent transverse modulus and strength compared with the circular shaped fiber models. The predicted failure strength also decreases due to the voids. However, the failure strength is less sensitive to the void shape than that of the circular shaped fiber model, as the interphase damage induced by the gear teeth plays an important role for the damage initiation.
