Fiber Volume Fraction Distribution Research Articles

Model error estimation in surrogate models of failure for composite materials

Failure theories in amorphous polymer utilize critical values of stress or strain invariants to determine the onset of damage. In polymer matrix fiber composite materials these theories have been extended to identify the location of failure. Some of these models use homogenization methods that render average values of stress and strain fields that do not represent the actual value of the fields neither in the fiber nor the matrix. The micromechanical enhancement method, MME, is able to approximate local values of strain fields to estimate failure location from homogenized strain fields by assuming a regular arrangement of fibers. In this work we study the error in the MME model in the determination of the critical strain invariants when compared to simulations that take explicitly into account non-regular fiber arrangements. Our results indicate the need to shift from deterministic simulations towards methods that quantify local variations of the microstructure such as fiber volume fraction distributions to determine the tails in the distribution of maximum strain invariant. Bayesian analysis shows that large variations in the fiber distribution have a negative impact in the MME model predictions.

Integrating qPLM and biomechanical test data with an anisotropic fiber distribution model and predictions of TGF- $$\upbeta $$ 1 and IGF-1 regulation of articular cartilage fiber modulus

A continuum mixture model with distinct collagen (COL) and glycosaminoglycan elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus ([Formula: see text] were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, [Formula: see text] was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted [Formula: see text] values were 175 and 422MPa for superficial (S) and middle (M) zone layers, respectively. TGF-[Formula: see text]1 treatment was predicted to increase and decrease [Formula: see text] values for the S and M layers to 281 and 309MPa, respectively. IGF-1 treatment was predicted to decrease [Formula: see text] values for the S and M layers to 22 and 26MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF-[Formula: see text]1 and IGF-1 treatments, with modulated values strongly dependent on treatment.

Effects of Z-Direction Flowing RTM Technology on Distribution of Composites Fiber Volume Fraction and Thermoplastic Toughener

In this paper, a novel Z-direction flowing RTM technology using an in-mold resin distributor has been applied to the “Ex-situ” composites and the process feasibility was evaluated. The effect of injection type on distribution of fiber volume fraction and thermoplastic toughener in the composite were investigated. The results showed that perfect internal quality composite panels could be fabricated via the novel RTM technology and the injection type has some effects on distribution of fiber volume fraction along the thickness direction of the panels. After the injection and curing cycle, the typical bicontinuous phase structures were mainly observed at the interlaminar and also slightly spreading into the fibre beam.

Experimental validation of post-filling flow in vacuum assisted resin transfer molding processes

In Liquid Composite Molding (LCM) processes with compliant tool, such as Vacuum Assisted Resin Transfer Molding Process (VARTM), resin flow continues even after the inlet is closed due to the preform deformation and pressure gradient developed during infusion. The resin flow and thickness changes continue until the resin pressure becomes uniform or the resin gels. This post-filling behavior is important as it will determine the final thickness and fiber volume fraction distribution in the cured composite. In this paper, a previously proposed one dimensional coupled flow and deformation process model has been compared with the experimental data in which the resin pressure and part thickness at various locations during the post-filling stage is recorded. Two different post-infusion scenarios are examined in order to determine their impact on the final part fiber volume fraction and thickness. The effects of different venting arrangements are demonstrated. The model predictions compare favorably with the experimental data, with the minor discrepancies arising due to the variability of material properties.

Studies of fiber volume fraction and geometry of variable cross-section tubular 3D five-direction braided fabric

The requirements for the size and performance of fabric 3D five-directional braided variable cross-sectional tube can be met by using the appropriate reducing-yarn technique. Compared with the fabric processed with invariable cross-sectional yarns, the theoretical model of geometric structure and properties of variable cross-sectional yarn fabric is more complex. Based on the constituting method of yarn and the variation law of fabric, fiber volume fraction has changed greatly. The fabric is divided into different zones according to the constituting method of yarn in its unit cell, and the unit geometry models corresponding to different zones are established. The fabric geometry size and fiber volume fraction distribution are predicted. Research result shows that the model can describe the characteristics of braided fabric accurately. Therefore, the model lays theoretical foundation for the fabric structure design of the variable cross-sectional tubular fabric braided in 3D five-directions.

A parametric study of fiber volume fraction distribution on the failure initiation location in open hole off-axis tensile specimen

We present a model to study the effect of the spatial distributions in fiber volume fraction on the failure initiation location in the open hole off-axis tensile. These variations are introduced with a micromechanical enhancement dehomogenization process. Good agreement is obtained between our predicted failure locations and experimental results by considering a failure criterion based on the effective shear strain in the matrix. The predicted failure angle distribution is in good agreement with the experimental results when the variability in the fiber volume fraction is included in the simulations.

Study of Thermal Stress of Iron-Boron Alloy Casing

The outer casing of heater made of iron-boron alloy is brittle fractured easily. It is a an effective way to add continuous fibers in brittleness material to improve the mechanical properties of composites. Temperature and thermal stress distribution of iron-boron alloy casing and the influence of thickness on the thermal stress of the casing is computed with finite element method, and the thermal stress distribution and influence of fiber volume fraction of continuous fiber-reinforced composites is studied. The result indicates that the external surface is in tensile stressed condition, and the internal surface is in compression stressed condition; the thermal stress increases with the thickness. The compression stress of the matrix decreases and the tensile stress increases with the increasing of the fiber volume fraction.

Automatic generation of random distribution of fibers in long-fiber-reinforced composites and mesomechanical simulation

An algorithm for the automatic generation of 2D representative volume element (RVE) of unidirectional long-fiber-reinforced composites (LFRCs) is presented in this paper. Both high fiber volume fraction and random fiber distribution are considered in the RVE. Two procedures which are named as global crisscrossing and local disturbing are included in this algorithm. Based on the model generated, mesomechanical analysis is carried out by using general finite element method (FEM) software ABAQUS. Firstly, the effect of the randomness of fiber distribution on the transverse modulus is investigated. Secondly, user subroutine to redefine field variables at a material point (USDFLD) in ABAQUS is used to simulate the damage behavior. A series of computational experiments are performed to evaluate the influence of mesh size on the ultimate load of the composites. The obtained results prove that the algorithm is capable of capturing the random distribution nature of these materials and the RVE produced could be used for predicting the damage onset and propagation of LFRCs.

Transverse Failure Behavior of Fiber-epoxy Systems

The transverse failure response of unidirectional fiber-epoxy systems is studied by means of finite element simulations. An interface damage model is used for modeling fiber debonding and epoxy cracking. The convergence of the numerical results upon mesh refinement is analyzed. It is found that the failure response depends on the relative strength and relative toughness of the fiber-epoxy interface and the epoxy matrix. The tensile failure response of epoxy systems containing multiple fibers is also analyzed. In addition, the simulations demonstrate the influence on the failure response by the relative strength of the fiber-epoxy interface and the epoxy matrix, and by the fiber volume fraction and fiber distribution. The simulated fracture patterns are shown to be in good agreement with experimental observations reported in the literature.

An Elastic-plastic Damage Model for Long-fiber Thermoplastics

This article proposes an elastic-plastic damage model that combines micromechanical modeling with continuum damage mechanics to predict the stress— strain response of injection-molded long-fiber thermoplastics. The model accounts for distributions of orientation and length of elastic fibers embedded in a thermoplastic matrix whose behavior is elastic-plastic and damageable. The elastic-plastic damage behavior of the matrix is described by the modified Ramberg—Osgood relation and the 3D damage model in deformation assuming isotropic hardening. Fiber/matrix debonding is accounted for using a parameter that governs the fiber/matrix interface compliance. A linear relationship between this parameter and the matrix damage variable is assumed. First, the elastic-plastic damage behavior of the reference aligned fiber composite containing the same fiber volume fraction and length distribution as the actual composite is computed using an incremental Eshelby—Mori—Tanaka mean field approach. The incremental response of the latter is then obtained from the solution for the aligned-fiber composite by averaging over all fiber orientations. The model is validated against the experimental stress—strain results obtained for long-glass-fiber/polypropylene specimens.

Analytical Modeling of Composite Molding by Resin Infusion with Flexible Tooling: VARI and RFI processes

We present analytical modeling and closed form solutions for composite resin infusion processes such as the vacuum assisted resin infusion (VARI) process and the resin film infusion (RFI) process. As a flexible bag is placed on the top of fabric stack, while a rigid tooling is still used on the other side, a fabric deformation takes place as the resin pressure changes during the resin infiltration process. Subsequently, it is important to take into account the reinforcement compaction as well as the resin flow in the analysis of resin infusion processes. We present a fully analytical modeling of resin pressure distribution, resin flow front position, fiber volume fraction distribution, and part height change during the resin infusion process. Parametric studies are provided to investigate the influences of process parameters on the process feasibility. The evaluation of bulk permeability in the RFI process implies that the fabric compaction should be taken into account to exactly characterize the through-thickness permeability of fibrous reinforcement.

Prediction of the Elastic—Plastic Stress/Strain Response for Injection-Molded Long-Fiber Thermoplastics

This article proposes a model to predict the elastic—plastic response of injection-molded long-fiber thermoplastics (LFTs). The model accounts for elastic fibers embedded in a thermoplastic resin that exhibits the elastic—plastic behavior obeying the Ramberg—Osgood relation and J-2 deformation theory of plasticity. It also accounts for fiber length and orientation distributions in the composite formed by the injection-molding process. Fiber orientation was predicted using an anisotropic rotary diffusion model recently developed for LFTs. An incremental procedure using Eshelby's equivalent inclusion method and the Mori—Tanaka assumption is applied to compute the overall stress increment resulting from an overall strain increment for an aligned-fiber composite that contains the same fiber volume fraction and length distribution as the actual composite. The incremental response of the latter is then obtained from the solution for the aligned-fiber composite by averaging over all fiber orientations. Failure during incremental loading is predicted using the Van Hattum—Bernado model that is adapted to the composite elastic—plastic behavior. The model is validated against the experimental stress—strain results obtained for long-glass-fiber/polypropylene specimens.

Numerical investigation on flow through porous media in the post‐infusion process

AbstractDuring the vacuum‐assisted resin transfer molding (VARTM) processing, the post‐infusion behavior after complete wet‐out and before gelation of the resin is critical for the development of the thickness and fiber volume fraction distribution in the cured composite part. The pressure gradient developed during infusion results in a thickness gradient due to the flexible nature of the bagging approach. After full infusion, the resin typically bleeds into a vacuum trap, allowing redistribution of pressure and preform thickness. In this study, a non‐rigid control volume is used to formulate a set of governing equations for analysis of the post‐infusion process. The model is used to investigate the effects of processing parameters and different processing scenarios on resin flow, resin pressure, and thickness variation of the composite laminate. This work provides a tool for optimization of the VARTM process to reduce final part variability. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers

Numerical simulation of two‐dimensional flow and compaction during the consolidation of laminated composites

AbstractA new special finite element formulation and code are developed to simulate the two‐dimensional flow and compaction process during the autoclave processing of complex fiber‐reinforced thermosetting composite laminates. The numerical model is based on the Biot's consolidation principle, the fluid continuity equation, and Darcy's law. The simulation is performed for Hercules AS4/3501‐6 laminates and the predicted results are in good agreement with the results available in the literature. The laminate thickness and fiber volume fraction distribution of cured laminates are investigated from both the experiments and the simulations for T700S/5228 laminates. The simulations and experimental results are in good agreement for all the studied cases. A significantly uneven degree of consolidation along the laminate thickness direction is observed, and it is necessary to optimize the cure cycle to get uniformly compact and good quality laminates. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers

Characterization of microstructure in stitched unidirectional composite laminates

The internal geometry of stitched uniaxial multiply carbon-fiber preforms is investigated experimentally. The microstructure is parameterized by such four introduced parameters as distortion length, distortion width, minor axis and major axis. The quantificational measurements are performed for these parameters under different stitch densities and different stitch threads. A theoretical model, called fiber distortion model, is developed to describe the spatial distribution of in-plane fiber misalignment angle and inhomogeneous fiber volume fraction induced by stitching.

Numerical Simulation of Flow and Compaction During the Cure of Laminated Composites

The finite element formulation is developed to solve the flow and compaction problems to simulate the resin flow and laminate compaction during the hot-pressing process of fiber-reinforced composite laminates. The numerical flow-compaction model is based on the effective stress formulation, the continuity equations, and Darcy’s flow theory. Two methods are used to calculate the variation of the laminate thickness, the simulated results validate the relationship of fiber motion and resin flow velocity. Together with the post-processor software, the visual laminate deforming process is realized through the node moving. The comparison between the predicted and experimental data shows that the program is reliable to predict the laminate thickness and the final fiber volume fraction distribution in the thickness direction.

Numerical Simulation and Experimental Study on Consolidation of Toughened Epoxy Resin Composite Laminates

Toughened epoxy resin is one of the most important matrices in composite structural materials. In this article a one-dimensional resin flow/fiber compaction model was used for analysis of the consolidation of a toughened epoxy resin 5228/T700S carbon fiber laminates. The laminate thickness and the fiber volume fraction distribution of cured laminates under different cure cycles were investigated both from the experimental measurements and from the numerical simulation. The calculated and experimental results are in good agreement for all the studied cases. A significantly uneven degree of consolidation along the laminate thickness direction is observed, and it is difficult to improve by altering cure cycle. These results are valuable for the study of the performance of composite parts, provided that uneven distribution of fibers does affect some properties of composite materials.

Mathematical Analysis of Resin Flow through Fibrous Porous Media

Resin flow through fiber preforms was analyzed mathematically. Closed form solutions for fiber volume fraction distribution and pressure field during resin infusion into fiber preforms were suggested, and a new effective permeability was defined. The effect of preform compressibility on the fiber volume fraction and pressure distributions in resin-saturated region was investigated analytically. The findings show that the compaction behavior of preforms has significant impact on the resin infusion process. The solutions derived analytically in this study can provide insight into a liquid composites molding (LCM) process.

Digital-element simulation of textile processes

This paper establishes the concept of a digital-element. A digital-element model was developed to simulate textile processes and determine the micro-geometry of textile fabrics. It models yarns by a pin-connected digital-rod-element chain. As the element length approaches zero, the chain becomes fully flexible, imitating the physicality of yarns. Contacts between yarns are modeled by contact elements. If the distance between two nodes on different yarns approaches the yarn diameter, contact occurs between them. Yarn micro-structure inside the preform is determined by process mechanics, such as yarn tension and inter-yarn friction and compression. The textile process is modeled as a non-linear solid mechanics problem with boundary displacement (or motion) conditions. First, a simple twisting process is simulated, validating the digital-element model. Then, the yarn geometry of a 3-D, four-step braided preform is analyzed. These numerical results reveal the details of yarn paths within the preform. Such results can only be arduously and expensively obtained when achieved through experimental observation, but cannot be generalized; or are inadequately detailed when achieved through existing analytical methods. This makes it possible, therefore, to conduct a quantitative analysis on the distribution of yarn orientation and fiber volume fraction inside a preform. Yet the value of this new model reaches far beyond that of the braiding process. As a general tool, it is advantageous for other textile processes, such as twisting, weaving and knitting and for the investigation of textile preform deformation during the consolidation process. The new numerical approach described here is identified as digital-element simulation rather than as finite-element simulation because of a special yarn discretization process. With the conventional finite-element approach, the element preserves the physical properties of the discretized body. In contrast, with this model the element itself does not preserve physical properties: physical properties are imitated by the element link. The concept is similar to digital discretization. Therefore, the term ‘digital element’ is more appropriate. The size of the element must be very small compared to the size normally employed in finite element analysis.

The effect of fiber volume fraction on filament wound composite pressure vessel strength

This paper is a continuation of previous research reported in Ref. [1] . The previous paper discussed the relationship between fiber volume fraction in filament wound composite vessels and failure pressure. This research included a design of experiment investigation of manufacturing and design variables that affect composite vessel quality and strength. Statistical analysis of the data shows that composite vessel strength was affected by the manufacturing and design variables. In general, it was found that the laminate stacking sequence, winding tension, winding-tension gradient, winding time, and the interaction between winding-tension gradient and winding time significantly affected composite strength. The mechanism responsible for increases in composite strength was related to the strong correlation between fiber volume fraction in the composite and vessel strength. Cylinders with high-fiber volume in the hoop layers tended to deliver high-fiber strength. This paper further examines the relationship between fiber volume fraction and fiber strain to failure. Data from unidirectional strand tests and additional vessel tests are presented. A computer program that is based on the thermokinetics of the resin and processing conditions is used to calculate the fiber volume fraction distribution in the filament wound vessel. The strand's strength-versus-fiber volume data together with the computer program are used to predict composite vessel burst pressure. In general, good agreement with experimental data is observed.