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Mesh Size Optimization of Unidirectional Fiber-Reinforced Composite Model for Precisely Characterizing the Effective Elastic Property
Abstract
Structural representative volume unit (RVU) has been extensively used to characterize the real effective elastic properties (EEPs) of fiber-reinforced composites (FRCs). The focus of this study is to optimize the optimum mesh size of a multiscale unidirectional RVU (UD-RVU) model to precisely characterize the EEPs of unidirectional FRCs (UD-FRCs). First, a variety of mechanical properties test experiments are carried out to obtain the real EEPs of UD-FRCs for the preparation of the optimization analysis. Then, a microscopic structural UD-RVU is established according to the fiber distribution of the UD-FRCs, and the corresponding ABAQUS/Python code that is used to characterize the EEPs is developed based on asymptotic homogenization theory. Finally, a complete optimization analysis, which is used for balancing simulation time and characterization accuracy, is performed to obtain the optimum mesh size of the multiscale finite element model. The optimized results reveal that the global mesh size of approximately 0.7 μm is the most optimal mesh, which has high accuracy and high simulation efficiency for characterizing the EEPs of UD-FRCs. The maximum error is close to 4.23% compared with experiments, which has a higher precision than the conventional calculation model, and the characterization model is reported in the literature.
... Considering that the alternative arrangement is more similar to the randomness of fiber arrangement, and the rectangular staggered RVE model that is the simplest structure has been confirmed to more accurate than square model [18,19,[25][26][27], which is employed for analysis to improve calculation efficient in the macro FE drilling model. The entire research work of RVE [2,29,30], published by us, has been recognized by the Journal of Composite Structures, etc. ...
... In this study, a new damage evolution law for computing macroscopic damage variables is adopted for intralaminar progressive damage. The macroscopic damage variables are directly evaluated by the degraded elastic parameters of the microscopic constituents computed from RVE via the mixture rule [30,38], which is given as ...
... Based on the above established progressive failure theories of the span-scale model, the corresponding user-defined material subroutine VUMAT with solid elements was developed and implemented in the FE code ABAQUS/Explicit in the "FORTRAN" language. For RVE modeling, the periodical boundary conditions imposing and the SAFs extracting, etc. the entire ABAQUS-Python code script was developed to recognize automatic parametric analysis according to our previous research works [2,29,30]. Furthermore, a detailed algorithm flowchart of the logic in the implementation of VUMAT is shown in Fig. 5. The procedure of spanscale numerical implementation is mainly divided into three steps. ...
The focus of this study is exploring a scale-span modeling method to simulate the structural mechanical responses and dynamic progressive failure behaviors of carbon fiber reinforced plastics (CFRPs) in drilling. A dynamic progressive failure theory based on modified micromechanics of failure (MMF) criterion with new damage evolution laws was first introduced for intralaminar damage. The relationship between macroscopic stress and microscopic stress was established by the stress amplification factors (SAFs). Meanwhile, an auxiliary deleting element criterion was introduced to delete the serious distortion elements for the sake of preventing nonconvergence of the simulation model, and the bilinear cohesive model with mixed-mode failure criterion was employed to simulate the interlaminar delamination. Then, the drilling behaviors of T700S-12 K/YP-H26 CFRPs using a tapered drill-reamer (TDR) were simulated based on the established scale-span theory model which is implemented by user-defined material subroutine VUMAT built on ABAQUS/Explicit platform. Finally, a series of experiments were performed to validate correctness of the simulation results from the perspectives of hole-making quality evaluation index. Results show that the established scale-span simulation model is shown to agree reasonably well with the experiments, and different kinds of damage behavior of the prefabricated hole can be truly simulated in drilling CFRPs.
... Considering that the alternative arrangement is more similar to the randomness of fiber arrangement, and the rectangular staggered RVE model that is the simplest structure has been confirmed to more accurate than square model [18,19,[25][26][27], which is employed for analysis to improve calculation efficient in the macro FE drilling model. The entire research work of RVE [2,29,30], published by us, has been recognized by the Journal of Composite Structures, etc. ...
... In this study, a new damage evolution law for computing macroscopic damage variables is adopted for intralaminar progressive damage. The macroscopic damage variables are directly evaluated by the degraded elastic parameters of the microscopic constituents computed from RVE via the mixture rule [30,38], which is given as ...
... Based on the above established progressive failure theories of the span-scale model, the corresponding user-defined material subroutine VUMAT with solid elements was developed and implemented in the FE code ABAQUS/Explicit in the "FORTRAN" language. For RVE modeling, the periodical boundary conditions imposing and the SAFs extracting, etc. the entire ABAQUS-Python code script was developed to recognize automatic parametric analysis according to our previous research works [2,29,30]. Furthermore, a detailed algorithm flowchart of the logic in the implementation of VUMAT is shown in Fig. 5. The procedure of spanscale numerical implementation is mainly divided into three steps. ...
This paper reports a single-loop PLL that operates wide-bandwidth fractional- N mode(without any fractional spur reduction circuits) during transient and in a narrow-bandwidth integer- N mode in locked state. This hybrid operation executed via a simple reconfiguration of the single-loop attains both fast locking and design simplicity, a combination that has been previously difficult to achieve. The frequency division mode switching allows the loop bandwidth switching to be performed in a more digital fashion which increases the degree of design freedom for bandwidth switching. A 2.4GHz CMOS prototype synthesizer with a 1MHz resolution performing the hybrid operation has a 20mus lock time for a 64MHz frequency jump, which is 4 times faster than its fixed integer- N operation.
... The micromechanical RVE model was meshed using linear elastic 8-node hexahedral 3D solid reduced integration and hourglass control (C3D8R) elements. The element size of approximately 0.7 m is considered to be the optimum mesh size to accurately characterise the effective elastic constants of unidirectional FRCs [13]. Thus, it is adopted in this study. ...
In this paper, the effect of intra-yarn hybridisation on the macroscopic homogenised properties of natural fibre-based hybrid composites (NFHCs) was computationally investigated. Many researchers have experimentally investigated hybrid effects on their mechanical properties. Only a limited number of computational studies on NFHCs have been reported. Four hybrid plain weave laminates: jute-glass, hemp-glass, jute-carbon and hemp-carbon were studied using a two scale modelling approach. The approach is based on homogenisation in which micromechanical representative volume element (RVE) model and mesomechanical repeating unit cell (RUC) model are established separately. The results indicate that hemp-glass hybrid 2D woven composites may be more cost-effective than glass woven composites in structural applications.
The focus of this paper is to explore the effects of different failure criteria, including Tsai-Wu, Hashin, Chang-Chang and micromechanics of failure criterion, on the dynamic progressive failure properties of carbon fiber reinforced polymers (CFRPs) in drilling. First, a unified finite element (FE) formulation on the dynamic intra-laminar damage and inter-laminar delamination of laminates was developed. Then, the intra-laminar damage model using four failure criteria were implemented by the explicit FE subroutine ABAQUS/VUMAT. Meanwhile, the delamination is simulated by the developed bilinear cohesive elements (CEs) model with mixed-mode failure criterion. Finally, numerical analysis and experiments were performed on drilling T700S-12K/YP-H26 CFRPs laminates to compare the predicted thrust force, torque and the visualized damage phenomenon. Results show that the prediction accuracy of the thrust force and torque is significantly improved. The actual damage behaviors which appear the tearing at the entry, pits of hole-wall’s surface, burrs and interlayer delamination at the exit are simulated when adopts the scale-span modeling method. In contrast, it is required to take more slightly simulation time under the same condition. This research provides fundamental support for appropriate selection and use of different failure criteria to achieve high-efficiency and high-fidelity simulation in the drilling of composites.
A new finite element formulation was developed to simulate the prepreg resin impregnation effect in vacuum-assisted resin infusion/prepreg co-curing process. The numerical model combined the fiber compaction and resin flow model in prepreg part with resin impregnation front tracking model in dry fiber fabric. The influences of processing parameters, including various temperature and time, on the impregnation height in dry fiber fabric and change of fiber volume fraction in prepreg stack were analyzed by numerical model and micrographs in experiment. The accuracy of numerical model was validated by the good agreement between simulation and experimental results. These results are greatly helpful to optimize processing parameters and improve the manufacturing efficiency in co-cured vacuum-assisted resin infusion process.
The current work focuses on evaluation of the effective elastic properties of cementitious materials through a voxel based finite element analysis (FEA) approach. Voxels are generated for a heterogeneous cementitious material (type-I cement) consisting of typical volume fractions of various constituent phases from digital microstructures. The microstructure is modeled as a microscale representative volume element (RVE) in ABAQUS® to generate cubes several tens of microns in dimension and subjected to various prescribed deformation modes to generate the effective elastic tensor of the material. The RVE-calculated elastic properties such as moduli and Poisson's ratio are validated through an asymptotic expansion homogenization (AEH) and compared with rule of mixtures. Both periodic (PBC) and kinematic boundary conditions (KBC) are investigated to determine if the elastic properties are invariant due to boundary conditions. In addition, the method of "Windowing" was used to assess the randomness of the constituents and to validate how the isotropic elastic properties were determined. The average elastic properties obtained from the displacement based FEA of various locally anisotropic microsize cubes extracted from an RVE of size 100 × 100 × 100 μm showed that the overall RVE response was fully isotropic. The effects of domain size, degree of hydration (DOH), kinematic and periodic boundary conditions, domain sampling techniques, local anisotropy, particle size distribution (PSD), and random microstructure on elastic properties are studied.
In this article, the carbon fiber/epoxy resin matrix composite laminates were fabricated using a co-curing process combining resin film infusion (RFI) process with prepreg-autoclave process, called co-resin film infusion. A kind of unidirectional prepreg and its corresponding resin film were adopted. The compaction and defects of laminates cured by different processing were studied. Mode I and mode II interlaminar fracture toughness were adopted to evaluate the co-cured interlaminar properties of the co-curing laminates and were compared with those of laminates processed by the prepreg-autoclave process and the resin film infusion process. Moreover, the effects of lay-up type of prepreg part and resin film infusion part, isothermal dwell and epoxy tackifier of fiber preform were also studied. The results show that these factors have important effects on the processing qualities of the laminates cured by co-curing process, including resin-rich regions and voids, resulting in different interlaminar fracture toughness at the co-cured interface. Affected by the prepreg part and the resin film infusion part in the co-resin film infusion laminates, the mode I and mode II initial interlaminar fracture toughness of co-cured laminate lie between those of the prepreg laminate and resin film infusion laminate, and GIC at crack propagation stage for co-resin film infusion laminate are higher due to fiber bridging and deflection of crack. These results have close relationships with the compacting structure of fibers in prepreg and resin film infusion parts and the interfacial bonding between the two kinds of fiber and the matrix.
In this paper, the strength of braided textile composites is predicted using a multi-scale approach bridging the mesoscale and microscale regimes. Mesoscale finite element models of representative unit cells of biaxial and triaxial braided composites are developed for predicting strength. The constituent stresses of tows inside the braided unit cell are calculated using micromechanics. Correlations between mesoscale stresses and microscale constituent stresses are established by using stress amplification factors. After calculating microscale stresses, a micromechanics-based progressive damage model is employed to determine the damage statuses of braided composites. A volume-averaging homogenization method is utilized to eliminate damage localization in the matrix of tows, and a parametric study is performed to evaluate the effects of damage homogenization. Subsequently, the ultimate strength is predicted for braided composites in which the braiding angle ranges from 15° to 75°. The prediction results are compared with the experimental values, and good agreement is observed.
A study on the flexural properties of E glass and TR50S carbon fiber reinforced hybrid composites is presented in this paper. Specimens were made by the hand lay-up process in an intra-ply configuration with varying degrees of glass fibers added to the surface of a carbon laminate. These specimens were then tested in the three-point bend configuration in accordance with ASTM D790-07 at three span-to-depth ratios: 16, 32, and 64. The failure modes were examined under an optical microscope. The flexural behavior was also simulated by finite element analysis, and the flexural modulus, flexural strength, and strain to failure were calculated. It is shown that although span-to-depth ratio shows an influence on the stress-strain relationship, it has no effect on the failure mode. The majority of specimens failed by either in-plane or out-of-plane local buckling followed by kinking and splitting at the compressive GFRP side and matrix cracking combined with fiber breakage at the CFRP tensile face. It is shown that positive hybrid effects exist for the flexural strengths of most of the hybrid configurations. The hybrid effect is noted to be more obvious when the hybrid ratio is small, which may be attributed to the relative position of the GFRP layer(s) with respect to the neutral plane. In contrast to this, flexural modulus seems to obey the rule of mixtures equation.
The paper reviews the past and recent modeling techniques (both analytical and numerical) pertaining to the mechanical behavior of textile-reinforced composites in general and woven fabric textile composites in particular published in the literature. The finite-element analysis of repeating unit cell geometry in association with the homogenization technique proves to be vital in predicting the properties. The purpose of this paper is not only to discuss the different modeling strategies and the mathematics involved, but also to provide the reader with an overview of the investigations conducted.
A micromechanics-based constituent progressive damage model was proposed in this study to predict macroscopic failure behavior of composite laminates under multi-axial mechanical loadings as well as thermal influences. For this purpose, a micromechanics-based failure theory, named the micromechanics of failure, has been further developed not only to account for the constituent failure but also to progress damage. We first modeled the unit cell of the microstructure of a UD lamina both to derive ply properties from constituent properties and to calculate micro stresses within fiber and matrix from macro-level ply stresses using stress amplification factors. Independent failure criteria dedicated to each constituent are employed to judge failure modes of fiber, matrix, and fiber-matrix interface. Good agreement between theoretical predictions and test data was achieved.
This study proposes an analytical and numerical model, for the prediction of mechanical properties of orthogonal 3D reinforcement composite materials, taking into account their structural parameters (mechanical properties of the components and geometrical architecture). This first step of this work requires the definition of the composite representative elementary volume (REV). Microscope studies made possible to visualize the architectural aspect of the internal structure. From these observations two types of REV, adapted to the types of modeling (analytical and by finite elements FE), were defined. The first one takes into account the whole of material in its thickness thus integrating the characteristics of the layers and the vertical reinforcements. The second one, strongly simplified in order to minimize the costs of calculations, is used in the FE approach. Moreover the analytical model is extended to the prediction of the ultimate properties by using the tonsorial criterion 3D of Tsai. The results obtaining from these modeling are compared with experimental results. This comparison highlights the interest and the limits of each approach according to the effect of the choice of the REV.
A micro-macro strategy suitable for modeling the mechanical response of heterogeneous materials at large deformations and
non-linear history dependent material behaviour is presented. When using this micro-macro approach within the context of finite
element implementation there is no need to specify the homogenized constitutive behaviour at the macroscopic integration points.
Instead, this behaviour is determined through the detailed modeling of the microstructure. The performance of the method is
illustrated by the simulation of pure bending of porous aluminum. The influence of the spatial distribution of heterogeneities
on the overall macroscopic behaviour is discussed by comparing the results of micro-macro modeling for regular and random
structures.
In this paper a new algorithm for the generation of periodic microstructures with regular, irregular and random morphology is presented. It is used for the analysis of anisotropy of unidirectional continuous fiber-reinforced composite material. The generator algorithm is based on pseudo-physical model resembling the description of the mutual motion of particles in magnetic, gravitational or electrostatic fields with generally random attraction or repulsion forces and collision checking. The level or degree of irregularity of the generated periodic cells having the same fiber volume content is described using a recently proposed dimensionless parameter. The effective elastic constants and the stress concentration effect of the generated structures are numerically investigated using a large number of FEA models. A dependency between the degree of irregularity and the lower and upper limits of the effective parameters is demonstrated.
Carbon fiber is the most common reinforcing phase in composite materials. However, it is difficult to obtain the performance parameters of the monofilament. In this study, the relationship between the property variables of the carbon fiber monofilament and the macroscopic parameters of the composites is established using a regression tree, a type of decision tree model, in machine learning. First, in order to obtain the data for machine learning, representative volume element (RVE) models of single-layer and multi-layer carbon fiber reinforced plastic (CFRP) are established by a cross-scale finite element method (FEM), and periodic boundary conditions are loaded. Then, a correlation model between the carbon fiber properties and CFRP and matrix properties is established. The non-GUI mode is called by Software Isight to generate the sample data. Second, in order to avoid overfitting, the L1 norm method is used for feature selection before model training. Finally, the four elastic properties of the carbon fiber are analyzed by a regression tree model. After a series of parameter adjustments and model selection, the model with a better generalization performance was obtained. The validity of the models was verified by the validating sample set.
The excellent mechanical properties of Carbon Fiber Reinforced Plastics (CFRP) have great influence on the deformation and failure of the components. The accurate prediction of the mechanical properties of CFRP is always a necessary but tough task, especially the transverse elastic modulus and shear modulus. This paper proposed an approach to predict the mechanical properties of CFRP based on cross-scale simulation. Firstly, the structural representative volume element (RVE) of unidirectional CFRP (UD-CFRP) is established in ABAQUS software at microscopic level considering periodic boundary conditions. The macroscopic mechanical properties of UD-CFRP are predicted by applying the different loading conditions for RVE in each direction. Secondly, based on the homogenization theory, the mesoscopic simplified RVE of multidirectional CFRP (MD-CFRP) is established according to the dimension of structural RVE. The mechanical properties of CFRP with the change of the angle and the different stacking sequence of UD-CFRP are also predicted through the mesoscopic simplified RVE. Finally, a series of experiments have been carried out, which showed that the results of the prediction approach and the experiments are in good agreements.
Carbon fiber reinforced polymer (CFRP) has gained popularity in civil engineering applications due to its high tensile strength, light weight, corrosion resistance, and fatigue resistance. However, the anchorage of CFRP tendons has been a challenge due to the relative low transverse shear strength of CFRP. To study the mechanical properties of bond-type anchor for CFRP tendons, straight-type, inner-cone-type, and composite-type anchors were developed in this study. The bond-slip behavior of CFRP tendons inside anchors and multiaxial stresses of the steel sleeve were experimentally tested. The effects of anchor type and length on the anchorage performance of CFRP tendons were studied with the focus on the anchoring mechanism. Test results demonstrate that the composite-type anchor exhibits the most reliable load-transfer mode and can eliminate the notch effect occurred in the inner-cone-type anchor. The peak bond stress initially occurs at the loading end of the anchor and gradually moves to the free end of the anchor as the load increases. This is related to the gradual failure of chemical adhesive between the CFRP tendon and the colloid. Besides, bond-slip relationship of CFRP tendon inside anchor is nonlinear. The slippages of CFRP tendons are initially small but increase quickly with increasing load. When approaching failure, the slippages increased significantly. In addition, the slippage of the anchor with scattered-end tendon is smaller than that with non-scattered-end tendon, indicating that the anchor with scattered-end tendon has superior bonding property.
The most common materials used for electromagnetic interference shielding are metals and their alloys. However, those materials are heavy and highly reflective. In order to eliminate or reduce the intensity of wave radiation in their working environment, lightweight materials that have interference shielding properties are needed. In this paper, nickel wire mesh yarns (warps) were woven into carbon fibers-reinforced plastic yarns (wefts) to produce metal–carbon textile composite materials. The plain weave and 2/2 twill weave techniques were used, and the woven fabrics were laminated to manufacture experimental test samples. The nickel, which has high magnetic permeability and good electric conductivity, and carbon fibers, which have good electrical, thermal and mechanical properties, were used together to achieve the desired properties. The shielding effectiveness of each sample was investigated using a network analyzer connected with coaxial transmission line test in accordance with ASTM 4935-99 standard, with the frequencies ranging from 500 MHz to 1.5 GHz. Here, the plain weave structure showed higher shielding effectiveness than twill weave. The absorption losses for both materials were relatively greater than reflection losses. In reference to the orientation of wire mesh yarns about the loading axis, the tensile strengths in the transversal direction were 19.04 and 16.34% higher than the tensile strengths in longitudinal direction for plain weave and twill weave, respectively. The fractography analysis with SEM showed a ductile fracture of wire mesh and brittle fracture of epoxy matrix and carbon fibers.
Representative volume element (RVE) has commonly been used to predict the stiffness of undamaged composite materials using finite element analysis (FEA). However, never has been an independently measured true microstructural damage quantity used in FEA to predict composite stiffness. Hence, in this work, measured fiber crack density in unidirectional fiber composite (generated using controlled fatigue loading) was used to predict reduction in stiffness using a RVE. It was found that the stiffness changes with change in depth of the volume element along the fiber direction and asymptotically reaches a constant value beyond a critical length called representative depth. It was argued that this representative depth should be more than the minimum of two characteristic length scales, twice of ineffective length and average length of broken fibers. Effective stiffness obtained from FEA of the optimum-sized RVE was in excellent agreement with the experimental results for given microstructural damage state.
Carbon fiber reinforced polymer (CFRP) composites are increasingly used in civil, naval, aerospace, and wind energy applications, where they can be frequently exposed to harsh temperature conditions and under static and dynamic loads. The extreme temperature conditions and dynamic loading are critical for CFRP composites structural design as the constituent polymer properties are highly sensitive to temperature and strain rate. This work experimentally investigates the effect of temperature, ranging from −100 °C to 100 °C, on the mechanical properties of CFRP composites under static and dynamic three-point bending tests. The results reveal that CFRP composites provide enhanced flexural strength, maximum deflection, and energy absorption at lower temperatures (−60 °C, −100 °C) while relatively poor performance at a higher temperature (100 °C). Experimental images from the post-mortem photographs, scanning electron microscopy, and high speed videos are implemented to observe various failure behaviors including microbuckling, kinking, and fiber breakage at different temperatures. Analytical modeling is further applied to reveal the underlying mechanisms responsible for these temperature dependent mechanical behaviors. The findings reported here provide insights into the study of the temperature effect on the mechanical response of CFRP composites, which expands the way to design stiffer, stronger and tougher CFRP composites.
A depth dynamic-resolution thermal-wave radar imaging (TWRI) was used to detect fiber lay-up orientations in the unidirectional CFRP laminate composite. A phase characteristic of thermal wave radar (TWR) signal was proposed and calculated by discrete fractional Fourier transform (DFrFT). The DFrFT phase distribution contour line was approximated as an ellipse and fitted by a non-standard elliptic equation. The ellipse ration angle dependent on the DFrFT phase (defined as Ellipse Angle Curve, EAC) was found to be sensitive to the fiber lay-up orientations of CFRP composite. An inverse methodology was developed to quantitatively characterize the fiber lay-up orientation angle through reconstructing DFrFT phase distribution. A cost function that minimized the square of DFrFT phase difference between TWRI inspection and numerical calculations was constructed, and a hybrid algorithm that combined the simulation annealing (SA) with Nelder–Mead simplex research (NM) method was employed to solve the cost function and find the global optimal solution of the fiber layer-up orientation angle. Experimental investigation of a 7-layer CFRP laminates [0°/45°/90°/0°]s validated the feasibility of estimating carbon fiber layer-up orientations by TWRI.
Tufted and plain unidirectional carbon fabric-reinforced epoxy composite laminates were fabricated by vacuum-enhanced resin infusion technology and subjected to in-plane tensile tests with a view to study the changes in mechanical properties and failure responses.
Owing to the presence of tufts in the laminates, both the tensile strength and modulus decrease by ~38 and ~20%, respectively, vis-à-vis the values recorded for plain composites. The fracture features point to the fact that though both the composites fail in brittle manner, they, however, exhibit differing fiber pull out lengths. Further, it was noticed that for the tufted ones, crack originates in the vicinity of tuft thread, spreads through the composite in a brittle manner, and results in a display of shorter fiber pull out lengths. These observations and other results are discussed in this paper.
Thermal buckling of CFRP-Al honeycomb sandwich composites is numerically studied by performing linear eigenproblem analysis. The analysis focuses on the thermal buckling of the hexagonal faces of sandwich composites. Calculation of stress stiffness utilizes stresses responses obtained by homogenization-localization analysis employing twelve unit-cell models. In this regard, the homogenization-localization analysis is carried out by relieving periodicity in the thickness direction. The buckling analysis employs two modeling techniques, i.e. face modeling and face-core modeling, whereby the critical eigenvalues are found to be sensitive to the selected technique. In order to better understand the influence of out-of-plane periodicity, the results of standard analysis with three-dimensional periodicity are also presented. It is found that relieving periodicity in the thickness direction affects the calculation of stress responses as well as critical buckling eigenvalue, particularly for unidirectional laminate faces. Parametric studies of the critical buckling eigenvalue are also performed to investigate the effect of geometrical and material configuration, and obtain reasonable results.
In this paper unidirectional fiber composites with imperfect interface conditions between the reinforcement and the filler are considered. The microstructure is periodic and the phases have isotropic properties. The periodicity of the microstructure is characterized by a parallelogram. Using the concept of a representative volume element (RVE) a finite element model is developed, in which the distribution of fibers and imperfect contact conditions between interfaces of phases can vary. Applying appropriate periodic boundary conditions to the chosen RVE effective material properties are derived, where those are related to a predefined coordinate system. The homogenization technique is validated by comparing results to literature as far as possible.
Maxwell’s concept of an equivalent inhomogeneity is employed for evaluating the effective elastic properties of tetragonal, fiber-reinforced, unidirectional composites with isotropic phases. The microstructure induced anisotropic effective elastic properties of the material are obtained by comparing the far-field solutions for the problem of a finite cluster of isotropic, circular cylindrical fibers embedded in an infinite isotropic matrix with that for the problem of a single, tetragonal, circular cylindrical equivalent inhomogeneity embedded in the same isotropic matrix. The former solutions precisely account for the interactions between all fibers in the cluster and for their geometrical arrangement. The solutions to several example problems that involve periodic (square arrays) composites demonstrate that the approach adequately captures microstructure induced anisotropy of the materials and provides reasonably accurate estimates of their effective elastic properties.
Macro/micromulti-scale analysis based on the efficient implementation of the Generalized Method of Cells coupled with classical lamination theory was conducted to predict failure of composite laminates, applying failure criteria at the constituent level, including fiber, matrix and interface. Representative unit cells with different fiber arrays were constructed in order to study the effect of reinforcement architecture and failure criteria on strength prediction of composite laminates. In order to compare the micromechanics model’s accuracy with commonly-used macroscopic failure theories, the experimental data obtained from the Worldwide Failure Exercise (WWFE) was utilized, and a quantitative assessment method for failure envelopes was developed to evaluate the model’s performance. Finally, the types of representative unit cell architectures and failure theories which are applicable for different layups were identified. The results indicate that the predictive performance of the employed micromechanics-based model is closest to the three leading macroscopic failure criteria of Puck, Cuntze and Tsai–Wu, and better than all other microscopic-based failure criteria (Chamis, Mayes, Huang), employed in the WWFE study.
In the present study, a new higher order shear deformable laminated composite plate theory is proposed. It is constructed from 3-D elasticity bending solutions by using an inverse method. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. It was observed that this theory gives most accurate results with respect to 3-D elasticity solutions for bending and stress analysis when compared with existing five degree of freedom shear deformation theories [Reddy JN. A simple higher-order theory for laminated composite plates. J Appl Mech 1984;51:745–52; Touratier M. An efficient standard plate theory. Int J Eng Sci 1991;29(8):901–16; Karama M, Afaq KS, Mistou S. Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity. Int J Solids Struct 2003;40:1525–46]. All shear deformation theories predict the vibration and buckling results with reasonable accuracy, generally within %2 for investigated problems. Previous exponential shear deformation theory of Karama et al. (2003) can be found as a special case.
Most micro-mechanical analyses for composites are based on repeated unit cell models (RUCs) by assuming a periodical distribution of the reinforcing phase. In this paper, the uniqueness of solution by applying unified displacement-difference periodic boundary conditions on the RUCs has been proved. Further it is deduced that (1) selection of the RUCs for a fixed periodic array may not be unique, however, the solution is independent on the choice of the different RUCs; (2) boundary traction continuity conditions can be guaranteed by the application of the proposed unified displacement-difference periodic boundary conditions. Illustrative examples are presented and advantages of applying this type of unified periodic boundary conditions are discussed.
A new virtual experimental approach to estimate the effective transverse properties of fiber-reinforced composite (FRC) is introduced. An explicit finite element method (FEM) is used to perform the composite progressive damage analysis, which successfully overcomes the numerical convergence problem that is encountered during continuous stiffness degradation. The virtual experiment includes four steps: first, generating a real microstructure; second, determining the composite constituent properties; third, progressive damage analysis; and fourth, comparing the results with those from an actual macro experiment. After completing these four steps, an accurate stress–strain curve under a transverse load is obtained. Then, we use this virtual experimental method to analyze the influence of micro parameters, such as interphase strength and residual thermal stress, on FRC macro performance. This virtual experiment method can be used for any composites and can provide more detailed material information than actual experiments as well as a direct reference for composite optimum design.
Effective transverse elastic moduli for fiber-reinforced composites are calculated here by a numerical homogenization approach. The effects of fiber placement (staggering) and of weak-fiber and strong-matrix composites on the effective moduli, both of which are not very effectively treated by classical methods, are specifically investigated. Comparisons with classical, analytical approaches are included.
In present work, the compression strength and tensile strength of phosphate graphite sand with compositional and technological
parameters (phosphoric acid, Al2O3, drying temperature, and drying time) were experimentally investigated. An L9 (34) orthogonal array was employed to analyze the effect of these four parameters on the compression strength and tensile strength,
respectively. In addition, the radial basis function artificial neural network (RBFANN) was used to establish the models for
compression strength and tensile strength, respectively. Moreover, the simulation and prediction results by the RBFANN and
linear and non-linear regressions are compared. The results are as follows: the optimum scheme for phosphate graphite sand
designed by us is phosphoric acid 24%, Al2O3 30%, drying temperature 400°C, and drying time 60min. The ascending sequence of the effect of four factors on both compression
strength and tensile strength of phosphate graphite sand is drying time, drying temperature, Al2O3, and phosphoric acid. In addition, the prediction and simulation results show that RBFANN outperforms Taguchi approach for
modeling.
Image analysis was used to characterize the microstructure of a unidirectional glass/epoxy composite which was found to be transversely randomly packed. Starting from a measured distribution of fiber diameter, a Monte Carlo procedure was employed to generate periodic computer models with unit cells comprising of random dispersion of a hundred non-overlapping parallel fibers of different diameter. The morphology generated in this way showed excellent agreement with that of the actual composite studied. An ultrasonic velocity method was used to measure a complete set of composite elastic constants and those of the epoxy matrix. On the basis of periodic three-dimensional meshes, the composite elastic constants of the Monte Carlo models were calculated numerically. Numerical and measured elastic constants were in good agreement. It was shown numerically that the randomness of the composite microstructure had a significant influence on the transverse composite elastic constants while the effect of fiber diameter distribution was small and unimportant. The predictive potential of the Halpin-Tsai and some other models commonly employed for predicting the elastic behavior of unidirectional composites was also assessed.
Representative volume elements (RVEs) have been extensively used to estimate the elastic properties of fibre-reinforced composites. Most of them rely on the assumption of a periodic distribution of fibres which is not realistic. In order to reproduce damage phenomena, such as matrix cracking, it is necessary for volume element to represent properly the random distribution of fibres (distance to first neighbors, occurrence of clusters of fibres, etc.). Therefore, a statistical RVE (SRVE) should satisfy both mechanical and point pattern criteria. The present work establishes the size of a SRVE for a typical carbon fibre reinforced polymer. It is concluded that the minimum size is δ = L/R = 50 (L the side of the element and R the fibre radius).
A vigorous mechanics foundation is established for using a representative volume element (RVE) to predict the mechanical properties of unidirectional fiber composites. The effective elastic moduli of the composite are determined by finite element analysis of the RVE. It is paramount in such analyses that the correct boundary conditions be imposed such that they simulate the actual deformation within the composite; this has not always been done previously. In the present analysis, the appropriate boundary conditions on the RVE for various loading conditions are determined by judicious use of symmetry and periodicity conditions. The non-homogeneous stress and strain fields within the RVE are related to the average stresses and strains by using Gauss theorem and strain energy equivalence principles. The elastic constants predicted by the finite element analysis agree well with existing theoretical predictions and available experimental data.
Modelling for Predicting the Mechanical Properties of Textile Composites-A Review
- A Krauss
A. Krauss, Modelling for Predicting the Mechanical Properties of
Textile Composites-A Review, Compos. A Appl. Sci. Manuf., 1997,
28(28), p 903-922
Fibre-Reinforced Plastic Composites: Determination of the In-plane Shear Stress/Shear Strain Response, Including the In-Plane Shear Modulus and Strength, By the Plus or Minus 45 Degree Tension Test 2718
''Fibre-Reinforced Plastic Composites: Determination of the In-plane
Shear Stress/Shear Strain Response, Including the In-Plane Shear
Modulus and Strength, By the Plus or Minus 45 Degree Tension Test
2718-Volume 29(4) April 2020
Journal of Materials Engineering and Performance
Method,'' 14129, International Organization for Standardization.
Geneva (1997), p 14