Flow-induced anisotropic viscosity in short fiber reinforced polymers

The commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh-Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth-order fiber orientation tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mean field homogenization and experimental investigation of short and long fiber reinforced polymers

The effective elastic material properties of short fiber reinforced polypropylen are determined by means of the self-consistent (SC) method and the interaction direct derivative (IDD) method. In order to account for thermoelastic effective material properties, a Hashin-Shtrikman (HS) based two-step homogenization method with variable reference stiffness is used. The influence of the reference stiffness, dependent on a scalar parameter is investigated. Information on the microstructure are derived by computed tomography scans (µCT) and considered within the homogenization schemes. Thermomechanical properties of a long fiber reinforced polymer (LFRP) and a short fiber reinforced polymer (SFRP) are obtained by means of dynamic mechanical analysis (DMA). Simulation results for SFRP are compared to experimental results. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mean and full field homogenization of artificial long fiber reinforced thermoset polymers

Based on two artificial microstructures representing a long fiber reinforced thermoset material, the effective linear elastic material properties are calculated by both a mean and a full field homogenization method. Concerning the mean field method, the effective elastic material properties are approximated using the homogenization scheme by Mori and Tanaka, formulated explicitly in terms of orientation averages. This allows to use orienation tensors of 2nd and 4th order describing the orientation information on the micro level. The full field method is based on the fast Fourier transformation (FFT), for which the effective material properties are determined by volume averaging. The comparison between both methods show good agreements, the deviations are in the range between 2% and 12%. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A comparison of mean field homogenization schemes for short fiber reinforced thermoplastics

Different mean field homogenization methods are applied to a short glass fiber reinforced polybutylene terephthalate. The different models' predictions for the anisotropic effective elastic properties are assessed and compared to experimental data from tensile tests. Additionally, the estimation of fiber stresses and the influence of the fiber length distribution is studied. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A RVE-based micro mechanical model for short fiber reinforced plastic materials including matrix damage and fiber fracture

The representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Failure of particulate reinforced polymers

In this presentation, a review is given on the main effects of mineral particulate fillers (with an aspect ratio of about unity) on the deformation and fracture of amorphous and semicrystalline thermoplastic and thermosetting polymers. Elastomeric modifiers, polymer blends, and filled elastomers are not considered here. Fillers are generally used to reduce cost as well as the thermal sensitivity of mechanical properties of the matrix material and to improve, if possible, the strength and toughness. The addition of particulate fillers influences all stages of the fabrication and use of the resulting composites. We focus on the effects of a stiff second phase on elastic moduli, matrix structure, and on deformation, creep, and failure mechanisms. As the main mechanisms, particle-matrix debonding, void formation, and matrix microshear yielding are identified. Toughness is less sensitive to the quality of adhesion since particle-matrix debonding and formation of voids can be tolerated. If well controlled, debonding contributes to deformation (formation of voids should be well distributed in space and time). Reference is also made to the surprising and positive effect of CaCO₃ particles on the toughness and impact resistance of HDPE, which increases at small interparticle distances due to interfacial effects on lamellar growth in the ligament area. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 305–316, March–April, 2000.     

Electro- and magnetostatics of reinforced polymers

On the basis of previously proposed models of reinforced media with regular structure, a method is developed for determining the electromagnetic fieldand dielectric and magnetic constants of reinforced polymers treated as ideal dielectrics. The solution obtained describes the static electromagnetic field and is suitable for investigating the propagation in reinforced media of electromagnetic waves whose length exceeds the distance between adjacent fibers. The dependence of the macroscopic constants on the orientation and volume content of the reinforcement is investigated.Institute of Mechanics, AS UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1130–1133, November–December, 1968.     

A new and efficient approach for modeling short fiber reinforced materials within RVEs using an embedded element technique

This paper focuses on the numerical homogenization by using representative volume elements (RVE method). A new approach is presented that is capable of speeding up the modeling process and reducing the computation time of RVEs significantly. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Initial stresses in reinforced and filled polymers

The methods of the statistical theory of elasticity are used to calculate the average stresses in the components of uniaxially reinforced and randomly filled polymers arising in the process of fabricating the material as a result of the different linear expansion coefficients of the components and chemical shrinkage of the resin. Expressions are also obtained for the macroscopic characteristics of the media — moduli of elasticity, linear expansion coefficients, and shrinkage coefficients. The results are compared with experimental data and with the results of computations based on the equations proposed by other authors. The relations obtained for the dependence of the stresses in the components on their properties offer a satisfactory explanation for the experimentally established positive correlation between the shrinkage and the compressive strength of a composite based on furan resin.Gomel' State University. Kirov Urals Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 1, pp. 90–96, January–February, 1973.     

Micromechanical modeling of talc particle reinforced thermoplastic polymers

The present work aims at investigating the mechanical behavior of talc particle reinforced thermoplastic polymers. Therefore, micromechanical analyses are performed utilizing detailed finite element models of the explicitely resolved microstructure. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical strength analysis of fiber reinforced plastics

Strength of an unidirectional lamina is computed with a representative volume element. An approximative “voxel” meshing method is used in conjunction with continuum damage mechanics to simulate crack growth in the RVE. Two material models for the nonlinear material behaviour of the epoxy resin are compared. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane stress finite element analysis of filler reinforced polymers

The characteristics of polymers such as force-deformation behaviour, strength, fatigue and wear resistance, can be tailored by embedding it with filler particles. The influence of the fillers on the material behaviour significantly depends on the size and geometric form of the filler aggregates, which vary under mechanical loading. The concept of super element is used to model filler particles. This is now coupled with the polymer matrix to generate a finite element model of filler reinforced polymers. In this work, we investigate the effect of filler geometry and volume fraction of fillers on the overall stiffness of the filler reinforced polymer. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of Gromov hyperbolic short graphs

To decide when a graph is Gromov hyperbolic is,in general,a very hard problem.In this paper,we solve this problem for the set of short graphs(in an informal way,a graph G is r-short if the shortcuts in the cycles of G have length less than r):an r-short graph G is hyperbolic if and only if S9r(G)is finite,where SR(G):=sup{L(C):C is an R-isometric cycle in G}and we say that a cycle C is R-isometric if dC(x,y)≤dG(x,y)+R for every x,y∈C.     

Micro-macro modelling of fiber reinforced composites exhibiting elastoplastic deformation

Fiber reinforced plastics such as carbon fiber-reinforced composites are typically characterized by their high siffness to weight ratio making them particularly attractive in lightweight construction. In addition, the architecture of these materials means that the correct modelling of their orthotropy is very important. In this work, volume averaged stress-strain responses are generated from a micro representative volume element (RVE). A nonlinear macro constitutive material model accounting for anisotropic plasticity is proposed. The model is fitted and compared to the micro stress-strain response. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A constitutive model for continuous fiber reinforced polymer plies

In the present paper a constitutive model is reviewed which can be used to predict the non-linear behavior of continuous fiber reinforced laminates with polymeric matrix materials. The constitutive model considers stiffness degradation and plastic strain accumulation at the length scale of the individual plies (laminae). These effects are modeled via two different phenomenological approaches, however, their interaction is considered when the constitutive equations are solved by an implicit integration scheme. To demonstrate the predictive capabilities of the individual model parts, examples are given where the above mentioned effects are decoupled. This way, their impact on the laminate's response can be studied independently. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale modeling of continuous fiber and fabric reinforced rubber components

Fabric or continuous fiber reinforced rubber components (e.g. tires, air springs, industrial hoses, conveyor belts or membranes) are underlying high deformations in application and show a complex, nonlinear material behavior. A particular challenge depicts the simulation of these composites. In this contribution we show the identification of the stress and strain distributions by using an uncoupled multiscale modeling method, see [1]. Within this method, two representation levels are described: One, the meso level, where all constituents of the composite are shown in a discrete manner by a representative volume element (RVE) and secondly, the macro level, where the structural behavior of the component is defined by a smeared anisotropic hyperelastic constitutive law. Uncoupled means that the RVE does not drive the macroscopic material behavior directly as in a coupled approach, where a RVE boundary value problem has to be solved at every integration point of the macro level. Thus an uncoupled approach leads to a tremendous reduction in numerical effort because the boundary value problem of a RVE just has to be solved at a point of interest, see [1]. However, the uncoupled scale transition has to fulfill the HILL–MANDEL condition of energetic equivalence of both scales. We show the calibration of material parameters for a given constitutive model for fiber reinforced rubber by fitting experimental data on the macro level. Additionally, we demonstrate the determination of effective properties of the yarns. Finally, we compare the energies of both scales in terms of compliance with the HILL–MANDEL condition by using the example of a biaxial loaded sample and discuss the consequences for the mesoscopic level. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)