Random Distribution Of Fibers Research Articles

Effect Mechanism and Simulation of Voids on Hygrothermal Performances of Composites.

Voids are comment defects generated during the manufacturing process and highly sensitive to moisture in the hygrothermal environment, which has deleterious effects on the mechanical performances. However, the combined impact of void content and water-absorbed content on mechanical properties is not clear. Based on the random sequential adsorption algorithm, a microscale unit cell with random distribution of fibers, interfaces and voids was established. The quantitative effects of voids content on strength and modulus under the loading of transverse tension, compression and shear were investigated by introducing a degradation factor dependent on water content into the constitutive model, and the different failure mechanisms before and after hygrothermal aging were revealed. Conclusively, before hygrothermal aging, voids induce the decrease in mechanical properties due to stress concentration, and every 1% increase in the void content results in a 6.4% decrease in transverse tensile strength. However, matrix degradation due to the absorbed water content after hygrothermal aging is the dominant factor, and the corresponding rate is 3.86%.

Experimental characterization and micro-modeling of transverse tension behavior for unidirectional glass fibre-reinforced composite

The mechanical behaviour of unidirectional fibre-reinforced polymer composites under transverse tension was studied using micromechanical computation and macroscopic experimentation. The representative volume element (RVE) of a composite with random fibre distribution was built by the proposed algorithm, which can effectively solve the jamming-limit problems for the hard-core-based model. The progressive damage process of the interface and matrix was simulated using the cohesive zone model and the extended Drucker–Prager model. The solutions of the mechanical loading case and the thermal mechanics loading case were compared to illustrate the effect of thermal residual stress. According to parametric studies, the failure models were mainly divided into two categories: interface-dominated and matrix-dominated damage, which rely on the interface strength, interface fracture energy, and matrix plastic deformation.

A mesomechanics-based analysis on the flexural behavior of ultra-high-performance concrete (UHPC) with different steel fiber lengths

This study investigates the flexural behavior of UHPC materials containing steel fibers of varying lengths. Mesomechanical analysis is performed according to the analytical pullout model, using actual measured fiber distributions. The flexural behavior of UHPC after cracking is simulated by superposing the fiber bridging and matrix softening curves. Subsequently, the evolution of stress–strain along the axial crack of UHPC is evaluated under different loading conditions. The obtained results indicate that longer steel fibers can efficiently improve the flexural behavior of UHPC. Moreover, the actual fiber orientation and pullout length distributions can be well fitted by two-parameter probability distribution (PDF) and Gaussian functions, respectively. Based on the micromechanical analysis, the fiber bridging behavior is overestimated under the assumption of 2D random fiber distribution, and it is underestimated under the assumption of 3D random fiber distribution. Interestingly, the length of the shear lag zone is independent of the fiber length, which is about 20.16 mm. The obtained results demonstrate that the compressive stress and strain at the top of the tested specimen gradually transform into tensile stress and strain at the opposite side. Interestingly, the stress of the specimens with fiber length of 20 mm are slightly higher than the specimens with fiber lengths of 6 and 13 mm, and the strain just lower than the specimens with fiber lengths of 6 and 13 mm in all crack propagation stages, respectively. This indicates that, in addition to the number of steel fibers, the stress/strain dispersion depends on fiber length.

Homogenized moduli and local stress fields of random fiber composites under homogeneous and periodic boundary conditions

We incorporate homogeneous traction and displacement boundary conditions into a recently proposed hybrid homogenization theory for unidirectional composites with random fiber distributions in order to investigate the convergence of homogenized moduli and local stress field statistics with representative volume element size. The hybrid approach combines elements of finite-volume and locally-exact elasticity approaches in the solution for the fiber and matrix displacement and stress fields within multi-inclusion representative volume elements that is extremely efficient and accurate, producing four-fold and greater reductions in execution times relative to the finite-volume micromechanics. Enabled by the extended approach, we then determine homogenized moduli and their standard deviations, as well as local stress field statistics, of domains containing increasing number of randomly spaced fibers under homogeneous and periodic boundary conditions for a large number of microstructural realizations. We show that fiber randomness and boundary condition type have substantially greater effects on the little investigated statistics of local stress fields than the homogenized moduli, and remain significant for domains with even 100 fibers. The choice of boundary conditions influences the location of plasticity and failure initiation at the fiber/matrix interfaces within a representative volume element, whose impact on the post-elastic homogenized response remains to be fully explored.

Numerical calculation of homogenized effective material properties of the single layer over arbitrary fiber distributions

The present work shows on the one hand the influence of symmetrical and random fiber distributions on the numerical determination of the effective homogenized material parameters of the unidirectional layer. On the other hand, the stress paths of symmetric and arbitrary RVE systems are analyzed and evaluated. In a fatigue-relevant consideration, the developed RVE systems map the damaging force paths between fiber and matrix. This numerical calculation of the stress on the matrix material is intended to simplify the fatigue strength assessment workflow of CFRP structures. The goal is to replace the currently required orthotropic Wöhler curves with a Wöhler curve for the matrix material. In investigations on pure resin samples it could be shown that the strength of these pure resin samples, corresponded to the matrix range of the numerical simulations of the RVE systems.

A study for effect of steel fibre on strength of conventional concrete

Discrete discontinuous fibre reinforced concrete (FRC) is a composite material made up of Portland cement, aggregate, and discrete discontinuous fibres used to construct bridges and other structural components. Why would we want to put such fibres in concrete in the first place, anyway? Plain, unreinforced concrete is discouraged because it is a fragile, low-tensile-strength, low-strain-capacity material that should be avoided if possible. A random distribution of discontinuous fibres was intended to bridge over fractures as they expanded, restoring the material's “ductility” after the cracks had developed. Fibre reinforced concrete (FRC) can endure considerable pressures with a reasonably high strain capacity at the post-cracking stage due to the strength and connection of the fibres to the concrete, provided the fibres are sufficiently strong and well-bonded to the concrete. There are, however, other (and more cost-effective) ways to increase the strength of concrete than the ones listed above. The fibres' most significant contribution is to enhance the toughness of the concrete, regardless of the kind of force applied to it. As a consequence, although the fibres have a tendency to increase strain at peak load, they also absorb a significant amount of energy throughout operation in the post-peak section of the load vs. deflection curve. Fiber reinforcement in the form of short, discrete fibres functions as stiff inclusions in the concrete matrix and is a very efficient means of reinforcing concrete. In terms of particle size and number, they are comparable to aggregate inclusions. It is believed that conventionally reinforced structural elements will be more resistant to cracking, deflection, and other issues that impact serviceability.

Fracture properties of steel fiber reinforced concrete: Size effect study via mesoscale modelling approach

Steel fiber reinforced concrete (SFRC) can exhibit superior performances of high strength and toughness due to the enhancing effect of discontinuous steel fibers randomly distributed in concrete matrix. For better understanding the size effect on the fracture properties of SFRC structural elements, we developed a three-dimensional (3D) two-phase mesoscale model considering the random distribution and orientation of steel fibers in concrete, to investigate the quasi-static flexural responses of the notched SFRC beams with different beam depths, i.e., 30 mm, 60 mm, 90 mm, 120 mm and 150 mm. A new coupling method was employed to describe the interfacial relationship between steel fibers and concrete matrix in the present simulations. The fracture behaviors of SFRC beam were numerically studied in terms of the load versus cracking mouth opening displacement curve, the evolution of fracture process zone, the nominal flexural strength and the fracture failure patterns. Through the analysis and comparison between the present numerical results and the available test data, it was found that there is negligible size effect on the fracture patterns of SFRC beam. The size effect on the nominal flexural strength of SFRC beam can be well characterized and analyzed using the Bažant’s size effect law. Further, the numerical results of SFRC beams showed a favorable agreement with the corresponding test results, demonstrating the great feasibility and potential of the developed mesoscale modelling approach in simulating and investigating the mechanical behaviors of SFRC.

Microstructure and mechanical properties of quasi-isotropic chopped fiber-reinforced PyC–SiC matrix composite prepared by novel nondamaging method

In this work, quasi-isotropic chopped carbon fiber-reinforced pyrolytic carbon and silicon carbide matrix (Cf/C–SiC) composites and chopped silicon carbide fiber-reinforced silicon carbide matrix (SiCf/SiC) composites were prepared via novel nondamaging method, namely airlaid process combined with chemical vapor infiltration. Both composites exhibit random fiber distribution and homogeneous pore size. Young's modulus of highly textured pyrolytic carbon (PyC) matrix is 23.01 ± 1.43 GPa, and that of SiC matrix composed of columnar crystals is 305.8 ± 9.49 GPa in Cf/C–SiC composites. Tensile strength and interlaminar shear strength of Cf/C–SiC composites are 52.56 ± 4.81 and 98.16 ± 24.62 MPa, respectively, which are both higher than those of SiCf/SiC composites because of appropriate interfacial shear strength and introduction of low-modulus and highly textured PyC matrix. Excellent mechanical properties of Cf/C–SiC composites, particularly regarding interlaminar shear strength, are due to their quasi-isotropic structure, interfacial debonding, interfacial sliding, and crack deflection. In addition to the occurrence of crack deflection at the fiber/matrix interface, crack deflection in Cf/C–SiC composites takes also place at the interface between PyC–SiC composite matrix and the interlamination of multilayered PyC matrix. Outstanding mechanical properties of as-prepared Cf/C–SiC composites render them potential candidates for application as thermal structure materials under complex stress conditions.

Micromechanical damage modeling of glass fiber-reinforced thermoplastic composites using homogenized volume elements

A simplified approach for micromechanical modeling of fiber-reinforced polymer composite is proposed. A hexagonal-type single unit cell was subjected to four loading conditions to predict the effective properties of the unit cell. The unit cell properties with different fiber fractions were distributed randomly across n × n homogenized unit cells, which was expected to represent the random fiber distribution in the actual composite lamina. It was proved that the proposed homogenized multi-cells model could predict the composite transverse tensile stiffness and strength with a good agreement against experimental results and required much less computational cost compared to the classical fiber/matrix micromechanics model.

Process modeling and characterization of thermoset composites for residual stress prediction

A computational process modeling framework is presented to predict performance-altering residual stress generation at the microscale. A comprehensive material characterization effort is carried out as a function of the resin temperature and curing state, resulting in a novel material database. For a prescribed cure cycle, in-situ elastic modulus evolution, chemical and thermal strains, and random fiber distribution are shown to significantly influence residual stress generation. The results also show that a full process modeling analysis that includes the complete cure cycle (instead of the standard approach of just considering post-processing cool-down) is necessary to accurately predict manufacturing-induced residual stresses.

Experimental and numerical investigation on flexural and fracture performance of steel fiber reinforced shotcrete

This paper presents an experimental and numerical study on the flexural behaviour and fracture performance of steel fiber reinforced shotcrete (SFRS). Firstly, a series of full-scale tests were carried out under four-point bending test procedure to investigate the ultimate strength and failure behaviour of SFRS. Then, parameter calibration was conducted against several lab tests to obtain the accurate meso-scale parameters which could be employed in the 3D discrete element model of SFRS. Finally, a 3D discrete element model for the SFRS specimen was established based on the bond size theory in the parallel bonding model. The numerical results obtained from the proposed 3D discrete element model of SFRS showed a good agreement with the experimental results in terms of the flexural behaviour and the failure performance. By analyzing the bond failure micrograph and contact force chain distribution diagram between particles, the flexural resistance characteristics of SFRS beams were revealed, and the results showed that the random distribution of steel fibers can be well simulated by using the random function. The proposed 3D particle discrete element model and the meso-parameters of bonded granules obtained from the parameter calibration could provide good results to investigate the flexural behaviour and failure characteristics of SFRS.

Progressive failure characteristics of unidirectional FRP with fiber clustering

For practical fiber reinforced plastic (FRP) structures, fibers are randomly packed in matrix, and some degree of clustering is often observed because of imperfect control of manufacturing process. In this work, a new method to generate random fiber distribution including fiber clustering is proposed according to fiber clustering characteristics of typical micro-image of FRP cross section. Irregularity and nearest neighbor fiber characteristics of random fiber distribution with fiber clustering are analyzed. Two-dimensional geometrically non-linear finite element (FE) modeling on representative volume element (RVE) is conducted to investigate transversely progressive tensile and compressive failure behavior of FRP. Extended linear Drucker-Prager model and cohesive zone model are employed to represent matrix deformation and interfacial debonding. Ultimate strength, fracture strain and crack characteristics of FRP with different degree of fiber clustering are derived and compared. It is shown that fiber clustering tends to result in significant decline and uncertainty of fracture strain and ultimate strength. The characteristics of fiber clustering can lead to two crack modes which affects the macro-scale mechanical properties of FRP.

Flexural Behavior of Steel Fiber Reinforced Concrete Beams: Probabilistic Numerical Modeling and Sensitivity Analysis

One of the principle issues concerning the practical application of steel fiber reinforced concrete (SFRC) is the uncertainty related to its structural behavior, primarily caused by the partially random distribution and orientation of steel fibers in SFRC structural elements. This paper aims to provide a better understanding of how the variance of material properties of the SFRC affects the flexural behavior of SFRC beams. First, a distributed plasticity fiber finite element model of beam flexural behavior is proposed and validated. Then, probability distributions of selected material properties are defined based on existing probabilistic models and experimental results from the literature. Finally, a variance-based sensitivity analysis is performed using Sobol’ indices to identify uncertainties in material properties that contribute most to the uncertainties related to three characteristic points of a beam’s flexural behavior: first crack, yield, and collapse point. Sensitivity analysis is performed by surrogating the numerical model using polynomial chaos expansion. The variance in residual tensile strength is identified as the main contributor to the variance in the flexural behavior of an SFRC beam used in the case study.

Microscopic stresses of discontinuous carbon fiber reinforced thermoplastics under thermal loading: two-fiber interactions

Discontinuous carbon fiber reinforced thermoplastics have a random fiber distribution, leading to complicated microscopic stresses under thermal loading. This complex condition can be simplified as an interaction between two individual fibers. The thermally induced microscopic stresses within 20 different representative volume elements were simulated in this study by leveraging a finite element modeling strategy involving the shear lag and Saint Venant's principles. It was found that the normal stress perpendicular to two short fibers at the cross point increased with the inter-fiber spacing and decreased with the orientation angle. The inter-fiber spacing and orientation angle to the residual von Mises stress at the cross point fits a newly proposed binary function. The results support the understanding of thermally induced microscopic stresses in discontinuous carbon fiber reinforced thermoplastics.

Finite element modeling of glass particle reinforced epoxy composites under uniaxial compression and sliding wear

Abstract In this study, the failure mechanism of glass particle epoxy composites was investigated under compression and sliding wear. Random fiber distribution with minimum interfiber distance was modeled by representative volume elements (RVEs). Spherical and platelet type glass particles were used for the reinforcements. A numerical simulation of the elastic properties of composites was performed for a perfectly bonded interface, and the results were compared using the Mori Tanaka mean field approach. The elastic stiffness results indicated that the platelet reinforced composites bore more load than spherical ones because of the aspect ratio effects. The separation distance based cohesive zone model was applied to modeling the failure zone at the particle matrix interfaces to establish sliding wear. The effect of the perfectly bonded interface and the cohesive zone interface on overall stiffness and elasto-plastic behavior were discussed. The cohesive zone interface was found to be effective at the interface in terms of the strength and debonding characteristics of the composites. The results were compared with the sliding wear test results of glass particle reinforced composites. The numerical and sliding wear experimental results indicated that matrix yield stress, plastic strain, particle penetration at the contact interface and particle stress are found to be effective parameters for the debonding mechanism.

Transverse mechanical properties of unidirectional FRP including resin-rich areas

Fiber reinforced plastic (FRP) is known to possess advantages of high strength and low density, and it is extensively used in engineering structures. However, most FRP have a certain level of microstructural uncertainty, and resin-rich areas in FRP can exist as inter-lamina resin layers or intra-lamina resin pockets. This work proposes a new algorithm to generate non-uniform random fiber distribution which contains resin-rich areas. The transverse tensile and compressive mechanical behavior of unidirectional FRP including resin-rich areas are studied using numerical simulation. The representative volume element (RVE) of the FRP with resin-rich areas is constructed. Matrix plastic deformation and interfacial debonding are described by extended Drucker-Prager model and cohesive zone model. Detrimental effect of resin-rich areas on the mean values and uncertainty of transversely ultimate strength and fracture strain is quantified. A new observation is that the resin-rich areas would result in large uncertainty on the ultimate strength of FRP, while its influence on the mean values of ultimate strength and fracture strain is limited. The large uncertainty on the tensile strength is attributed to that different morphology of resin-rich areas would lead to different cracks. The size of the resin-rich areas is also found to have an effect on transverse tensile and compressive mechanical properties.

Modelling method of fibre distribution in steel fibre reinforced concrete based on X-ray image recognition

The accurate and efficient simulation of steel fibre reinforced concrete (SFRC) is of great significance for its further application in civil engineering. Problems of existing modelling methods can be recognized as two points; (1) the integral model only simplified fibre contribution into the unified post-peak ductility in concrete element but cannot reflect the material variation caused by real fibre distribution, and (2) the separate model built the concrete matrix and fibre inclusions respectively, but the directly random fibre distributions still need to be refined based on the actual material. In this paper, based on the X-ray image recognition results from real SFRC material, a mathematical model of fibre distribution and orientation is proposed for SFRC simulation, and the detailed value distributions of geometrical parameters are optimized for convenience and accuracy of material modelling. In the geometrical extraction of near 4000 fibres from X-ray images, the whole comprehensive procedure of image processing, enhancement and recognition is presented with technologies like pixel semantic classification and Hough transform. With the proposed geometrical mathematical model, the modelling method that consists of multiple refined sampling is illustrated with mechanical applications. After the model verification by experimental comparison, the detailed contribution of steel fibre and the effect of fibre distribution refinement are discussed as well.

Generation of random fiber distributions in fiber reinforced composites based on Delaunay triangulation

This paper presents a new method for generating the random fiber distributions of carbon fiber reinforced plastic with high volume fraction. The novelty is that an adaptive fiber shaking module is developed on the basis of Delaunay triangulation and combined with the proposed algorithm. The adaptability is to realize coordination between the parameters of fiber volume fraction and fiber spacing, in order to overcome the jamming limit and eliminate the unreasonable resin-rich zone that may appear at the boundary of the microstructures. The maximum fiber volume fraction reached is 67.43%. Statistical analysis is conducted on the generated microstructures, and there is a good agreement by comparing it with the statistical results of random sequential expansion algorithm and completely spatial random pattern. Finite element analysis is also performed to predict the elastic properties of the generated microstructures. It shows that a maximum absolute error is only 7.354% in elastic property by comparing with the experimental and simulation results in literatures. The proposed algorithm contributes to the further researches on the strength and micro-damage evolution of carbon fiber reinforced plastic.

A new hybrid homogenization theory for periodic composites with random fiber distributions

A new homogenization theory is constructed for unidirectional composites with periodic domains containing random fiber distributions. Periodic domains are partitioned into subdomains comprised of single fibers embedded in matrix phase. The subdomain displacement field solutions combine finite-volume and locally-exact elasticity approaches. Inclusions are regarded as meshfree components whose displacement fields are represented by discrete Fourier transforms that satisfy exactly Navier’s equations. In contrast, the matrix is discretized into subvolumes and handled within the finite-volume micromechanics framework. Novel use of traction and displacement continuity conditions at the inclusion/matrix interface seamlessly connect inclusion and matrix phases. Subdomains’ assembly enforces traction, displacement continuity and periodicity conditions in a surface-average sense. Quadratic convergence of stress fields with decreasing matrix discretization relative to exact elasticity solution is obtained, yielding accurate homogenized moduli with relatively coarse matrix meshes. Fourfold and greater reductions in execution times relative to the finite-volume micromechanics justify the new theory’s construction. The proposed theory facilitates accurate and efficient studies of the rarely reported effect of random fiber distributions on homogenized moduli and local stress fields as a function of inclusion content and number of microstructural realizations. We illustrate this by computing probability distributions of homogenized moduli for up to 60,000 microstructural realizations of multi-inclusion periodic domains that may be used in machine-learning algorithms.

Longitudinal compression failure of 3D printed continuous carbon fiber reinforced composites: An experimental and computational study

Fused filament fabrication (FFF) with continuous carbon fiber filaments has proven to be a promising manufacturing technique in engineering applications. To provide guidance in the design of 3D printed carbon fiber reinforced polymer (CFPR) components, the longitudinal compression failure of continuous CFPR composites using the FFF technique is investigated systematically. First, longitudinal compression tests are performed for 3D printed continuous CFRP composites with and without designed waved filaments. The degradation of the failure strength is remarkable when the waved filaments are introduced. Nevertheless, further degradation is limited when more waved filaments are adopted. Next, the fracture morphologies are analyzed, and in-plane and out-of-plane kink-bands are observed in the microscopic images. For the specimens with waved filaments, fracture occurs at the cross-section with the contact region of the waved and regular filaments, as well as the cross-section with the maximum misalignment angle. Correspondingly, a computational framework for 3D printed continuous CFPR composites is established to explore the longitudinal compression failure mechanisms. The meso-scale computational models are reconstructed according to the geometric features of the deposited continuous CFRP filaments and the actual void volume fraction. The elastic properties of the filament are calculated by a micro-scale representative volume element (RVE) model, which is based on the fiber random distribution algorithm. The plastic deformation and failure is described by a filament constitutive model which is established by the Liu-Huang-Stout yield criterion and a simplified Tsai-Wu failure criterion. The experimental validation demonstrates the feasibility of the computational models to predict the stress-strain curves of 3D printed materials, and also capture the realistic longitudinal compression failure behavior.