Short Fiber-reinforced Plastics Research Articles

Predicting the fiber orientation of injection molded components and the geometry influence with neural networks

The injection molding simulation of short fiber reinforced plastics (SFRP) is time consuming. However, until now it is necessary for predicting the local fiber orientation, to optimize the molding process and to predict the mechanical behavior of the material. This research presents the capabilities of artificial neural networks (NN) in predicting fiber orientation tensor (FOT) during injection molding processes, with a focus on enhancing computational efficiency compared to traditional simulation methods. Three NN architectures are compared based on simulated injection molded plates, with the goal of predicting the effect of the plate geometry on the local fiber orientation. Results indicate that NN outperform the baseline assumption of aligned fibers and demonstrate significant potential for accurate FOT prediction. The computational efficiency of NN, especially during the prediction phase, showcases a reduction in processing time by a factor of 104 compared to traditional simulation methods. This research lays a foundation for further exploration into the feasibility of NN in partly replacing time-consuming simulations for practical applications in injection molding processes.

Pseudograin decomposition of short fiber-reinforced plastics for two-step homogenization using machine learning approach

Decomposing the representative volume element (RVE) of short fiber-reinforced plastics (SFRPs) into several pseudograins (PGs) is essential for understanding its effective mechanical behavior. However, conventional PG decomposition methodologies are limited by their high computational costs due to iteration-based algorithms. To address this, we propose a machine learning-assisted PG decomposition procedure that utilizes a series–parallel artificial neural network (ANN) system to facilitate the time-consuming decomposition process. To validate the effectiveness of our proposal, we implemented a two-step homogenization framework of SFRP that consists of the series–parallel ANN system, Mori-Tanaka model, and Voigt model into ABAQUS user material subroutine (UMAT). The elastic modulus values predicted by the UMAT are found to be in good agreement with both DIGIMAT-MF and experimental values, while also maintaining low computational time.

Progressive pseudograin damage accumulation model for short fiber-reinforced plastics and its application to fatigue life prediction

A progressive pseudograin damage accumulation (PPDA) model is proposed to predict the fatigue life of short fiber-reinforced plastics (SFRPs), combining viscoelastic-viscoplastic (VEVP) two-step homogenization theory with Chaboche fatigue damage model. Each representative volume element (RVE) of SFRPs is decomposed into pseudograins using a two-step homogenization framework. Then, the fatigue life of each pseudograin is predicted using a master S-N curve, which is prepared based on the “normalized fatigue factor” taking into account both the stress ratio and multiaxial stress state. Thereafter, the overall failure of RVE is predicted by a PPDA model, in which each pseudograin fails progressively considering the stress concentration of the living pseudograins, resulting in non-linear fatigue damage evolution. Finally, the PPDA model is successfully implemented into ABAQUS user material subroutine (UMAT), predicting the fatigue lifetime in good agreement with experimental data.

Investigation of strain rate dependent microscopic failure mechanisms in short fiber reinforced plastics using finite element simulations

For predicting the strain rate dependent failure of short fiber reinforced plastics (SFRP) a two-phase simulation model is developed using the finite element method and comparing the results to microscopic specimen tests for uniaxial tension under quasi-static (0.007/s) and dynamic loads (250/s). Experimentally the failure behavior of SFRP is observed to be strain rate dependent. The global strain at failure and the absorbed energy increase with strain rate. Moreover, locally an influence of the strain rate on the amount of material involved in the deformation can be observed. The suggested model can represent these effects accurately. Also, the present micro-mechanical effects and their influence on the strain distribution are investigated by unit cell simulations. Thereby the material model of the fibers, the matrix, and the boundary layer are varied respectively. These reveal the important role of strain rate dependent decohesion leading to a correct representation of the plastically deformed volume. Consequently, the distortion energy density is evaluated and is found to be constant at failure for all strain rates.

Numerical simulation for the tensile failure of randomly oriented short fiber reinforced plastics based on a viscoelastic entropy damage criterion

In this study, we conduct a numerical simulation of the tensile failure of randomly oriented short fiber reinforced plastics (SFRP) by integrating an entropy damage criterion. The Mori-Tanaka theory is used as the model for the composite. The constitutive equation of the resin is defined by a conventional viscoelastic model with a power law considering entropy damage. The dissipated energy is calculated using this constitutive equation and the stress-strain history. Dividing the dissipated energy by the absolute temperature yields an entropy value, which is related to material damage that results in a decrease in the elastic moduli. This deteriorating behavior of the resin is integrated into the Mori-Tanaka theory. The tensile failure simulation is implemented at nine angles ranging from 5° to 85° in 10° increments to determine the relationship between the tensile strengths and off-axis angles. These results are introduced into the layer wise method (LWM) and superimposed to obtain the tensile strength of randomly arranged short fiber reinforced plastics. The calculations are performed by varying the strain rate. The numerical results are in good agreement with the experimental results. Thus, the originality of this study is the introduction of a viscoelastic entropy damage criterion into a conventional micromechanical model.

Fiber contribution on elastic properties of cellulose composites: A multiscale numerical study

AbstractMultiscale finite element analysis based on the asymptotic homogenization theory was carried out for short fiber reinforced plastics (FRP), and the effects of fiber morphologies on mechanical properties were systematically organized. Cellulose microfibers were used as the reinforcing fibers and polypropylene was used as the matrix. In order to quantify the enhancement effect of intrinsic fibers on the mechanical properties, a new indicator based on strain energy, contribution proportion of fiber (CPf) was proposed. In this paper, as the first demonstration of introducing the CPf, unidirectionally oriented short FRP was focused and elastic properties were analyzed for fundamental fiber morphologies. In terms of the fluctuation rate based on the elastic modulus of the matrix, when the volume content of fiber is 3.0 vol%, the elastic modulus of composites varied by 106%, 105%, 97.6%, and 35.1%, respectively, depending on the fiber orientation, fiber aspect ratio, fiber/matrix interface and fiber‐to‐fiber distance. Based on the CPf, fiber morphologies could be divided into two. The first factors are fiber orientation angle and fiber content, which determine the rate of change in mechanical properties with respect to the CPf. The second factors are fiber aspect ratio, fiber/matrix interface, and fiber‐to‐fiber distance, which affect the mechanical properties according to the rate of change determined by the first factors. The complicated influence of the fiber morphologies on the mechanical properties could be unified by introducing the CPf. These computations show that CPf is effective for systematic analysis and design of fiber morphologies.

短繊維強化樹脂の材料試験及び材料同定と材料データベースへの登録

The use of short fiber reinforced plastic (SFRP), which can be injection molded, is expanding. However, it is difficult to obtain the material parameters which is necessary for structural analysis at the design stage. In this paper, we present a case study of a fracture law considering stress triaxiality, which has been the focus of attention in recent years. The parameters of the accumulated plastic strain fracture law, a fracture law considering stress triaxiality, are identified based on the results of conventional fracture laws.

Fatigue Damage Evaluation of Short Carbon Fiber Reinforced Plastics Based on Thermoelastic Temperature Change and Second Harmonic Components of Thermal Signal.

Short fiber reinforced plastics (SFRPs) have excellent moldability and productivity compared to continuous fiber composites. In this study, thermoelastic stress analysis (TSA) was applied to detect delamination defects in short carbon fiber reinforced plastics (SCFRPs). The thermoelastic temperature change ΔTE, phase of thermal signal θE, and second harmonic temperature component ΔTD were measured. In the fatigue test of SCFRP, it was confirmed that changes in ΔTE, θE, and ΔTD appeared in the damaged regions. A staircase-like stress level test for a SCFRP specimen was conducted to investigate the generation mechanism of the ΔTD. The distortion of the temperature change appeared at the maximum tension stress of the sinusoidal load—and when the stress level decreased, the temperature change returned to the original sinusoidal waveform. ΔTD changed according to the change in the maximum stress during the staircase-like stress level test, and a large value of ΔTD was observed in the final ruptured region. A distortion of the temperature change and ΔTD was considered to be caused by the change in stress sharing condition between the fiber and resin due to delamination damage. Therefore, ΔTD can be applied to the detection of delamination defects and the evaluation of damage propagation.

Structural Optimization of Locally Continuous Fiber-Reinforcements for Short Fiber-Reinforced Plastics

The integration of continuous fiber-reinforced structures into short or long fiber-reinforced plastics allows a significant increase in stiffness and strength. In order to make the best possible use of the high stiffness and strength of continuous fiber-reinforcements, they must be placed in the direction of load in the most stressed areas. A frequently used tool for identifying the most heavily loaded areas is topology optimization. Commercial topology optimization programs usually do not take into account the material properties associated with continuous fiber-reinforced hybrid structures. The anisotropy of the reinforcing material and the stiffness of the base material surrounding the reinforcement are not considered during topology optimization, but only in subsequent steps. Therefore in this publication, existing optimization methods for hybrid and anisotropic materials are combined to a new approach, which takes into account both the anisotropy of the continuous fiber-reinforcement and the stiffness of the base material. The results of the example calculations not only show an increased stiffness at the same material input but also a simplification of the resulting reinforcement structures, which allows more economical manufacturing.

3D microstructural characterization and mechanical properties determination of short basalt fiber-reinforced polyamide 6,6 composites

This study aimed to quantify the 3D microstructure of short basalt fiber (BF)-reinforced polyamide 6,6 (PA6,6) composites, in an attempt to more accurately predict their mechanical properties. Thermoplastics are often reinforced with short fibers to improve their strength. BF is a natural fibrous material and a potential option for thermoplastic reinforcement. However, injection-molded composite materials, including thermoplastics, have microstructural properties that evolve during the molding process. Thus, a method for quantifying the microstructure of short fiber-reinforced plastic (SFRP) composites is of particular interest with regard to predicting and optimizing the performance thereof. In this study, nondestructive analysis of the internal microstructure of injection-molded, SBF/PA6,6 composites was conducted using micro-computed tomography (μ-CT) imaging. All of the composite components, including the SBFs, PA6,6, and voids, were reconstructed into 3D digital images and subsequently defined as basic structural models. To investigate the effects of fiber length and orientation on the mechanical properties of the composites, longitudinally and transversely fiber-oriented SBF/PA6,6 composite specimens were carefully compared. μ-CT-assisted analytical measurements were then conducted using the reconstruction models and simulation tools to determine the fiber length, orientation distribution, and anisotropic mechanical properties. The resulting microstructure-based predictions yielded valuable information clarifying the relationship between the 3D microstructure and mechanical properties of injection-molded SBF/PA6,6 composites. The results showed a 20% increase in the tensile strength of specimens having SBFs oriented in the longitudinal versus transverse direction. Thus, the anisotropic nature of the composites, attributable to the internally dispersed fibers, has an effect on the composite's mechanical properties. This article provides an important overview of predictive technologies based on the internal microstructure of SFRPs, and insight into the means to further advance this technology.

Analysis and Evaluation of Fiber Orientation Reconstruction Methods

The calculation of the fiber orientation of short fiber-reinforced plastics with the Fokker–Planck equation requires a considerable numerical effort, which is practically not feasible for injection molding simulations. Therefore, only the fiber orientation tensors are determined, i.e., by the Folgar–Tucker equation, which requires much less computational effort. However, spatial fiber orientation must be reconstructed from the fiber orientation tensors in advance for structural simulations. In this contribution, two reconstruction methods were investigated and evaluated using generated test scenarios and experimentally measured fiber orientation. The reconstruction methods include spherical harmonics up to the 8th order and the method of maximum entropy, with which a Bingham distribution is reconstructed. It is shown that the quality of the reconstruction depends massively on the original fiber orientation to be reconstructed. If the original distribution can be regarded as a Bingham distribution in good approximation, the method of maximum entropy is superior to spherical harmonics. If there is no Bingham distribution, spherical harmonics is more suitable due to its greater flexibility, but only if sufficiently high orders of the fiber orientation tensor can be determined exactly.

Efficient Multiscale Methods for Viscoelasticity and Fatigue of Short Fiber-Reinforced Polymers

To predict the nonlinear mechanical behavior of components made of short fiber-reinforced plastics (SFRP) under long term and cyclic loading, coupled process and component simulations are required. The injection molding process leads to locally varying fiber orientations within the component. This varying microstructure [1] significantly influences the viscoelastic and fatigue behavior. The interaction between the microstructure [2] and the nonlinear macroscopic properties is resolved by a coupled fast Fourier transformation and finite element two-scale method (FFT-FEM), where the fiber orientation tensor is obtained by analyzing μCT images or by the corresponding process simulation. The aim of this work is to reduce the numerical costs of such a multiscale method. In a first step, the highly efficient micro-scale solver FeelMath [3,4] using an FFT-based preconditioner is presented. Afterwards, a numerical scheme based on a precomputed database trained with FeelMath simulations on the microscale and a model order reduction algorithm, is discussed. The combination of these ideas reduces the numerical effort, such that the method is applicable for industrial problems. Comparative studies of the fully coupled and reduced model document the high accuracy of this approach. The overall performance of this methodology is demonstrated by three-dimensional, industrial applications.

Macro-mechanical modeling and experimental validation of anisotropic, pressure- and temperature-dependent behavior of short fiber composites

In this article, firstly a comprehensive experimental characterization of short fiber reinforced plastic (SFRP) composites sheets is presented. The micro-computed tomography (μCT) is utilized at first to analyze the degree of anisotropy of the SFRP sheets. Then, destructive tests are applied to investigate the mechanical behavior of the sheets at different loading states. The experimental results are presented and discussed thoroughly. Secondly, based on the findings from the experiments conducted, the numerical modeling of the SFRP sheets is discussed. Therein, a user-defined macro-mechanical constitutive model is suggested to represent the sophisticated constitutive behavior of SFRP composites. A brief description of the model and the parameter identification is provided. The performance of the model is assessed and verified via the FE simulation of the destructive characterization tests. Furthermore, the model is employed in the simulation of biaxial stretching experiments of SFRP sheets. The experimental–numerical correlation results demonstrate the validity, accuracy, and applicability of the employed modeling procedure.

First-order perturbation-based stochastic homogenization method applied to microscopic damage prediction for composite materials

In this paper, a first-order perturbation-based stochastic homogenization method was developed to predict the probabilities of not only macroscopic properties but also microscopic strain damage in multiphase composite materials, considering many random physical parameters. From the stochastic solution of microscopic strains, damage propagation was analyzed to predict where progressive damage would occur in the microstructures of composites subject to a given macroscopic strain. As an example, a short fiber-reinforced plastic, consisting of short fibers, matrix, and interphase, was used to show the influence of random physical parameters for each constituent material on the variability of the homogenized properties and microscopic strain. In another example, a coated particle-embedded composite material was stochastically analyzed to consider even slight influences of uncertainty in the mechanical properties of the coating material and show damage propagation in this coating layer. Characteristic displacements representing material heterogeneity were thoroughly investigated and extensively used with the aim of reducing the computational cost of finding them in a nonlinear analysis of the microscopic damage propagation.

Topology Optimization for Injection Molding of Short Fiber‐Reinforced Plastics

AbstractWe investigate an approximate approach for compliance‐based topology optimization of short fiber‐reinforced plastic (SFRP) parts. The approximation consists in the replacement of the costly filling and fiber orientation simulation by the solution of an eikonal equation, which determines the principal fiber orientation. The optimization problem is then solved using the classical SIMP method in combination with a transversely isotropic material law and a projected gradient method. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimal Experimental Design to Identify the Average Stress‐Strain Response in Short Fiber‐Reinforced Plastics

AbstractWe show how to use optimal experimental design methods for the parameter identification of short fiber reinforced plastic (SFRP) materials. The experimental data is given by computer simulations of representative volume elements (RVE) of the SFRP material. The experiments are designed such that a minimal number of RVE simulations is required and that the model response attains a minimal variance for a class of strains and fiber orientations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Residual Stress Evaluation of Short-Fiber Reinforced Plastics by X-Ray Diffraction

The X-ray diffraction method is used to evaluate the residual stress in injection-molded plates of short-fiber reinforced plastics (SFRP) made of crystalline thermoplastics, polyphenylene sulphide (PPS), reinforced by carbon fibers with 30 mass%. The stress in the matrix in the skin layer was determined using Cr-Kα radiation with the sin2 ψ method. The X-ray evaluation of stress in carbon fibers was not possible because of high texture. A new method was proposed to evaluate the macrostress in SFRP from the measurement of the matrix stress. According to micromechanics analysis of SFRP, the matrix stresses in the fiber direction and perpendicular to the fiber direction, and shear stress can be expressed as linear functions of the applied (macro-) stresses in the fiber direction and perpendicular to the fiber direction, and shear stress. The proportional constants are named stress-partitioning coefficients. Using skin-layer strips cut parallel, perpendicular and 45° to the molding direction, the stress in the matrix was evaluated under the uniaxial applied stress and the stress-partitioning coefficients of the above equations were determined. Once the relations between the macrostress and matrix stress are established, the macrostress in SFRP can be evaluated from the measurements of the matrix stresses using X-rays.

Effect of fiber orientation on fatigue crack propagation in short-fiber reinforced plastics

The influence of the fiber orientation on the crack propagation behavior was studied with single edge-notched specimens which were cut from an injection-molded plate of short-fiber reinforced plastics (SFRPs), at five fiber angles relative to the loading axis, i.e. θ=0° (MD), 22.5°, 45°, 67.5°, 90° (TD). Macroscopic crack propagation path was nearly perpendicular to the loading axis for the cases of MD and TD. For the other fiber angles, the crack path was inclined because the crack tended to propagate along inclined fibers. In the relation between the crack propagation rate and the stress intensity factor range, ΔK, the propagation rate of fatigue cracks was slowest for MD, and increased with increasing fiber angle. When the crack propagation rate was correlated to ΔK/E (E=Young’s modulus), the relations for different orientations merged into a single relation. Based on the results of stress-ratio effect, it was concluded that the crack propagation rate was mainly controlled by ΔK at low rates and by the maximum stress intensity factor Kmax at high rates. For injection molded plates, the existence of the core layer accelerated crack propagation in MD direction, and decelerated in TD direction. Mechanisms of crack propagation were discussed based on microscopic observation of the near crack-tip region and fracture surfaces.

短繊維強化樹脂複合材料の残留応力の新X線測定法

The X-ray diffraction method is used to measure the residual stress in injection-molded plates of short-fiber reinforced plastics (SFRP) made of crystalline thermoplastics, polyphenylene sulphide (PPS), reinforced by carbon fibers with 30 mass%. Based on the orientation of carbon fibers, injection molded plates can be modeled as three-layered lamella where the core layer is sandwiched by two skin layers. The stress in the matrix in the skin layer was measured by Cr-Kα radiation by the sin2ψ method. Since the X-ray penetration depth is shallow, the state of stresses measured by X-rays in FRP can be assumed to be plane stress. The X-ray measurement of stress in carbon fibers was not possible because of high texture. A new method was proposed to evaluate the macrostress in SFRP from the measurement of the matrix stress. According to micromechanics analysis of SFRP, the matrix stresses in the fiber direction, σ1m and perpendicular to the fiber direction, σ2m, and shear stress τ12m can be expressed as the functions of the applied (macro) stresses, σ1A, σ2A, τ12A as follows: σ1m = α11σ1A + α12σ2A, σ2m = α21σ1A + α22σ2A, τ12m = α66τ12A, where α11, α12, α21, α22, α66 are stress-partitioning coefficients. Using skin-layer strips cut parallel, perpendicular and 45° to the molding direction, the stress in the matrix was measured under the uniaxial applied stress and the stress-partitioning coefficients of the above equations were determined. Once these relations are established, the macrostress in SFRP can be determined from the measurements of the matrix stresses by X-rays. Microscopic phase stresses due to the mismatch of the thermal expansion coefficient between matrix and fiber was negligible in X-ray stress measurement of the skin layer.

OS2118 射出成形した短繊維FRP平板における疲労き裂進展に及ぼす板厚の影響

OS2118 射出成形した短繊維FRP平板における疲労き裂進展に及ぼす板厚の影響