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)     

Optimization of the injection molding process for short-fiber-reinforced composites

A fast and effective methodology integrating the finite-element and Taguchi methods is presented to determine the optimal design conditions of the injection molding process for short-fiber-reinforced polycarbonate composites. The finite-element-based flow simulation software, M-flow, was employed to simulate the molding process to obtain the fiber orientation distributions required. The Taguchi optimization technique was used to identify the optimal settings of injection molding parameters to maximize the shear layer thickness. The effects of four main parameters — the filling time, melt temperature, mold temperature, and injection speed — on the fiber orientation or the shear layer thickness were investigated and discussed. It is found that the dominant parameter is the filling time. The best levels of the four parameters to acquire the thickest shear layer are also identified.     

Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials

The kinematics of shearing deformation in fiber reinforced materials can lead to fibers that (a) first shorten, (b) then return to their original length, and (c) then elongate. In a hyperelastic constitutive treatment this can cause the shear stress to be a nonmonotone function of the amount of shear if the fibers are sufficiently more stiff than the matrix. Here, we explore how this effects the emergence and development of kink surfaces in the context of a variety of boundary value problems. Kink surfaces are surfaces across which the deformation gradient is discontinuous. For fiber reinforced materials such surfaces generate an abrupt change in the fiber orientation (a kink). We characterize the appearance of kink surfaces in terms of three general mechanisms: fade-in, pair creation, and boundary emission. Each has a counterpart for kink surface disappearance. These mechanisms are highly sensitive both to changes in the original fiber orientation field, including spatial variation in this field, and to changes in the nature of the applied boundary conditions. A variety of examples are presented.     

Emergence and disappearance of load induced fiber kinking surfaces in transversely isotropic hyperelastic materials

The kinematics of shearing deformation in fiber reinforced materials can lead to fibers that (a) first shorten, (b) then return to their original length, and (c) then elongate. In a hyperelastic constitutive treatment this can cause the shear stress to be a nonmonotone function of the amount of shear if the fibers are sufficiently more stiff than the matrix. Here, we explore how this effects the emergence and development of kink surfaces in the context of a variety of boundary value problems. Kink surfaces are surfaces across which the deformation gradient is discontinuous. For fiber reinforced materials such surfaces generate an abrupt change in the fiber orientation (a kink). We characterize the appearance of kink surfaces in terms of three general mechanisms: fade-in, pair creation, and boundary emission. Each has a counterpart for kink surface disappearance. These mechanisms are highly sensitive both to changes in the original fiber orientation field, including spatial variation in this field, and to changes in the nature of the applied boundary conditions. A variety of examples are presented.     

Determination of the modulus of elasticity of the amorphous regions of chemical fibers

A method of calculating the orientation index and modulus of elasticity of the elements of a two-phase fiber model is presented. The effect of orientational drawing on the variation of these characteristics has been investigated for nylon [capron] fibers.Mekhanika Polimerov, Vol. 3, No. 3, pp. 409–412, 1967     

Statistical theory of defect buildup in composite materials and the scale-factor effect in reliability

A statistical theory of fracture based on the concept of defect buildup is applied to composite materials with a definite fiber orientation. On the premise that the concentration of defects that precede a fracture is sufficiently low, asymptotic distributions of defectiveness are established and asymptotic expressions for the reliability function are derived. It appears feasible to use this theory for predicting the reliability and the scale-factor effect for structures made of oriented composite materials.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 247–255, March–April, 1976.     

Rationalization of the shape of wound membrane shells of revolution composed of high-modulus material

A method of designing composite membrane shells of revolution under axisymmetric loading is described. The properties of the shell material are analyzed. It is shown that for shells of high-modulus material in the presence of tensile membrane stresses the fibers fail in the matrix. A fiber arrangement and shell geometry ensuring isotensoid properties are proposed for this case. A technological and weight analysis is presented.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 5, pp. 822–828, September–October, 1975.     

Investigation of the modulus of elasticity of carbon fibers

A simplified analysis of the dependence of the elastic properties and electrical conductivity of a carbon fiber on its orientation index is presented. The experimentally confirmed inverse correlation between the electrical resistivity and the speed of sound makes it possible to calculate the modulus of elasticity of carbon fibers from data on the bulk resistivity.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 5, pp. 846–850, September–October, 1971.     

Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow

The modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are firstly derived. A new successive iteration method is developed to calculate the mean orientation distribution of fiber, and the mean and fluctuation-correlated quantities of suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The obtained results show that the flow rate of the fiber suspension is large under the same pressure drop in comparison with the rate of Newtonian fluid in the absence of fiber suspension. Fibers play a significant role in the drag reduction. The amount of drag reduction augments with increasing of the fiber mass concentration. The relative turbulent intensity and the Reynolds stress in the fiber suspension are smaller than those in the Newtonian flow, which illustrates that the fibers have an effect on suppressing the turbulence. The amount of suppression is also directly proportional to the fiber mass concentration.     

Homogenization of Elastic Properties of Short Fiber Reinforced Composites Based on Discrete Microstructure Data

Since the microstructure of short fiber reinforced composites is inhomogeneous, the application of micromechanical models is useful, that take into account their characteristics like the fiber orientation and the aspect ratio of fibers. Two different methods are considered in this work: A two-step approach is utilized to get approximately the upper and lower bounds of the elastic properties. Furthermore, an approximation for the elastic properties is calculated by the self-consistence method. Both methods use discretely microstructural information including the length, the diameter and the orientation of each single fiber. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relation between molecular orientation characteristics determined from birefringence and acoustic data and the effect of orientation on the strength of polycaprolactam fibers

The mean molecular orientation calculated from birefringence and acoustic data has been investigated in relation to the degree of stretching for polycaprolactam fiber. A correlation has been found between the characteristics calculated by these two independent methods. It is shown that the molecular orientation factor calculated from the speed of sound does not depend on crystallinity if the measurements are made below the glass transition temperature. It is confirmed that the strength of the fiber depends importantly on the degree of orientation of the molecular segments in the amorphous zones.Mekhanika Polimerov, Vol. 3, No. 1, pp. 3–7, 1967     

A Coupled Model for the Left Ventricle Including Regional Differences in Structure

Modeling cardiac function is an important task to increase the understanding of the physiological response of the heart and to determine how complex structural heart components influence the biomechanical behavior of the heart. In this communication a coupled model of orthotropic ventricular myocardium is presented using fiber and sheet orientations that is matching regionally measured experimental data. This approach generates a more realistic and homogenized stress distribution when compared to a model with a generic fiber and sheet orientation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational modeling of shape memory fibers in conforming and non-conforming compound structures

In this work a material model for shape memory alloy (SMA) fibers is presented. A constitutive model is provided which aims for computational use. The presented model incorporates all relevant material nonlinear phenomena. It takes pseudoplasticity into account as well as pseudoelasticity and further the shape memory effect (SME). The constrained SME (CSME) and the two-way SME are covered by the presented material model. The constitutive model is implemented in a one-dimensional truss formulation and in a 3D-rebar element. Both formulations are used to model fiber composite structures. Those are described by the use of a non-conforming and a conforming mesh on the mesoscale. The numerical examples show the capability of the formulation. Different meshing strategies for the fiber–matrix compound are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

张量封闭模型与三维取向分布对纤维悬浮槽流稳定性的影响

应用3种不同的纤维方向张量封闭模型,数值模拟了纤维悬浮槽流的流动稳定性问题,从而研究封闭模型和纤维的三维取向分布对稳定性分析的影响．结果发现,采用3种不同封闭模型所得到的流动稳定特性与纤维参数之间的关系是相同的,但采用三维混合封闭模型时,由于纤维的取向与流向的偏差程度较大,所以纤维对流动的不稳定性具有最强的抑制作用．而采用二维混合封闭模型时,由于纤维在平面取向条件下,其轴线整体上趋于呈流向排列,使得对流体的作用削弱,导致纤维对流动不稳定性抑制的作用最弱．     

Nonlinear finite element analysis of functionally graded plates integrated with patches of piezoelectric fiber reinforced composite

In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates.     

Evolution of the Fiber Density in Biological Tissues

An important challenge in the field of biomechanics is to understand and to model the properties of fibrous tissues. We consider a matrix-fiber composite for which the matrix microstructure and its mechanical properties are taken to be constant. The initial fiber distribution is assumed to be unstructured and the mechanical properties of the fibers evolve during deformation. Further we assume that the fiber creation rate is constant while the fiber degeneration is stretch-dependent. In particular, this study investigates the change of the fiber orientation density when a sudden simple shear is applied to the material. The fiber orientation density depends on the current deformation, the history of the deformation, and the deformation state of the fibers at the time of their creation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element buckling and postbuckling solutions for multilayered composite panels

A study is made of the buckling and postbuckling responses of flat, unstiffened composite panels subjected to various combinations of mechanical and thermal loads. The analysis is based on a first-order shear deformation von Karman-type plate theory. A mixed formulation is used with the fundamental unknowns consisting of the strain components, stress resultants and the generalized displacements of the plate. The stability boundary, postbuckling response and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented for both solid panels and panels with central circular cutouts. The results show the effects of the variations in the fiber orientation angles, aspect ratio of the panel, and the hole diameter (for panels with cutouts) on the stability boundary, postbuckling response and sensitivity coefficients.     

Computation of the Coupled Dynamics of Fibers in a Spray

The PUR-fiber-spray molding technology is a manufacturing process which produces polyurethane-based (PUR) composites by spraying the matrix together with reinforcing fibers in a tool form or on a substrate. Thereby chopped fibers are laterally (sidewise) injected in the polyurethane-air spray cone for wetting before the entire composite is spread on the substrate, where it starts curing. To investigate and compute the fiber orientation and density distribution in the final composites manufactured by this process, a new approach simplifying the multiply coupled interaction of the three phases is presented in this paper. Hereby it is presumed that the final position and orientation of a fiber on a substrate results from its dynamics and coupled interactions with air, PUR-droplets and other fibers within the spray cone. Thus, a model of the process is built, that computes the transient behavior of the air-liquid droplets mixture by the CFD code ANSYS Fluent and its influence on the dynamics of the fibers by an extra code called FIDYST. For this multiphase problem two approaches are presented for the droplet-fiber coupling using a concept called “homogenization” of the liquid phase (droplets in the continuous phase). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of load transfer in thermo–elastic membranes

The flexural stiffness can be negligible in the analysis of extremely thin walled shell structures. Modeling these structures as membranes simplifies the theoretical formulation and reduces the computational effort. However, in case of compressive in–plane loads, the prediction of the load transition behavior by means of the membrane theory may be incorrect, if the wrinkling phenomenon is not taken into account. Therefore wrinkling algorithms were established in the past. Thermal strains influence the occurrence of wrinkling and the state of membrane forces. In order to analyze thermo-mechanical effects in conjunction with membrane wrinkling, the Roddeman wrinkling theory was modified. For small strains the incorporation of thermal effects into the wrinkling algorithm is straight forward. A method for large strains was developed and elaborated for thermoelastic rubber–like materials. The wrinkling algorithm is easy to implement into existing FE-programs. Results of numerical analysis are presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of Mechanical Properties in Tissues Undergoing Deformation-Related Fiber Remodeling Processes

We consider a biological fibrous soft tissue in which fibers are distributed in all directions. The mechanical properties of the fibers evolve due to a continuous remodeling process. The model to describe these fiber properties is based on the strain energy density of the protofibers and a survival kernel which describes the deformation-related property changes. In particular, this study investigates the development of the fiber orientation density for different choices of the fiber creation rate and fiber dissolution rate models. It has been shown that the fiber orientation density depends on both the history of the deformation and the deformation state of the fibers at the time of their creation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)