Fiber Orientation State Research Articles

Fiber Orientation in 3-D Injection Molded Features

Abstract We present a finite element method for predicting the fiber orientation patterns in 3-D injection molded features, and compare the predictions to experiments. The predictions solve the full balance equations of mass, momentum, and energy for a generalized Newtonian fluid. A second-order tensor is used to describe and calculate the local fiber orientation state. A standard Hele-Shaw molding filling simulation is used to provide inlet boundary conditions for the detailed inite element models, which are limited to the local geometry of each feature. The experiments use automated image analysis of polished cross-sections to determine fiber orientation as a function of position. Predictions compare well with experiments on a transverse rib, where the detailed calculation can be 2-D. Results of a 3-D calculation for a flow-direction rib also show generally good agreement with experiments. Some errors in this latter calculation are caused by not simulating the initial filling of the rib, due to computational limits.

Characterization of short glass fiber filled polystyrene by fiber orientation and mechanical properties

AbstractA quasi‐steady state, non‐isothermal, compressible, inelastic, and creeping flow of polymer melt into a thin cavity is analyzed to predict fiber orientation states. Modified Cross model and Tait's state equation are adopted to consider shear‐thinning behavior and compressibility of the polymer melt. Second order tensors are introduced to describe 3‐dimensional fiber orientation. Flow‐induced fiber orientation can be predicted by solving the equations of change for the orientation tensor with a suitable closure approximation. The orthotropic closure is applied except for the case of low interaction coefficient. Fiber orientation develops mainly due to shear flow in the skin layer and due to stretching effect in the core layer. It turns out that the compressibility, which induces additional velocity gradients during packing, reduces development of the fiber orientation. Results are dependent upon the magnitude of the interaction coefficient. The larger the interaction coefficient, the smaller the orientation development and the effect of compressibility. To predict orientation dependent mechanical properties, the orientation averaging for an arbitrary orientation is carried out from the properties of a transversely isotropic unit cell. The compressibility reduces the axial modulus and increases the transverse modulus. Opposite trends are observed for thermal expansion coefficients. It is also observed that the consideration of compressibility reduces the overall anisotropy of the molded product. Effects of compressibility on mechanical properties of the parts are reduced as the interaction coefficient becomes larger.

A model to predict the strength of short fiber composites

AbstractThe material properties of short fiber composites, such as modulus, strength and thermal expansion, are greatly dependent on the fiber orientation state in the composite. Although the orientation pattern is often quite complex, models that allow its prediction have been successfully applied in combination with micromechanical models to calculate moduli and thermal properties. This paper describes the derivation of a model to predict the strength of short fiber composites with arbitrary fiber orientation and fiber length distribution based on classical (micro‐) mechanical theories. The predictions are in good agreement with data measured on short fiber composites with different fiber contents.

Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics

In this paper we present a detailed thermoviscoelastic formulation for the simulation of thermally and pressure induced residual stresses in injection moulded short-fibre-reinforced thermoplastics. The computed residual stresses enable us to predict shrinkage and warpage in the finished products. We also apply an anisotropic version of a rotary diffusion equation to calculate the flow-induced fibre orientation distribution. The predicted fibre orientation state, together with micromechanical theories, allows the incorporation of anisotropy in material properties into the thermoviscoelastic model. Finally we report three numerical examples to indicate the success of the present model.

Fibre orientation in short-fibre-reinforced thermoplastics II. Quantitative measurements by image analysis

To determine the fibre orientation state in short-fibre-reinforced thermoplastics, polished cross-sections are examined. If a circular cross-section is assumed for the fibres, they are pictured as ellipses on the intercepting plane. The picture evaluation is done by image analysis which uses an analysis program specially developed for this problem. User-defined parameters allow an adjustment of the evaluation algorithm, so that fully automated picture processing is possible. To describe the fibre-orientation state orientation tensors are used. Under some assumptions about the fibre orientation state, which are well met in regular plastic components, all tensor components can be obtained from one inclined polished cross section. Measurements on experimental components are made by using the described analysis procedure and confirm the validity of the assumptions.

Fibre orientation in short-fibre-reinforced thermoplastics I. Contrast enhancement for image analysis

Fibre orientation has been investigated in different thermoplastic polymers reinforced by short glass fibres. The aim is to quantify the fibre orientation state from polished cross-sections, whereby a computer-aided image analysis is used to measure the contour of the fibres. To garantee sufficient contrast for different matrix materials in reflected light microscopy a special specimen preparation treatment is given. With this technique results can be achieved with a quality which is comparable with that from scanning electron microscopy.

Effects of Aspect and Area Ratio of Fiber on the Accuracy of Intensity Method in Measurement of Fiber Orientation-Angle Distribution

To investigate accuracy of intensity method for measurement of the fiber orientation distribution, fiber orientation function is calculated by drawing simulation figures for the fiber orientation as varying fiber aspect ratio, fiber area ratio, and fiber orientation state, respectively. The values of fiber orientation function measured by intensity method are compared with the calculated values of fiber orientation function. The results show that measurement accuracy of the fiber orientation angle distribution by intensity method is affected by the fiber aspect ratio when the total length of oriented fiber is same. The average gradient of fiber orientation function is 0.94 for 1000mm of the total fiber length and is 0.93 for 2000 mm when the fiber aspect ratio is over 50. Measurement accuracy by intensity method is about 94% and the reliable data can be obtained by intensity method.

Residual Stresses in Short-Fibre Reinforced Injection-Moulded Thermoplastic Parts

Having the prediction of the warpage and shrinkage behaviour of injection-moulded short-fibre reinforced thermoplastics in mind, a model is developed to calculate the residual stresses. In accordance with the structure and the behaviour of these materials, a layerwise orthotropic, viscoelastic constitutive equation is used. As a cause for the stress development, a process determining the history of cooling under pressure is considered. The volume expansion of the matrix is described using a time-dependent viscoelastic free volume concept. From this, the viscoelastic functions for thermal expansion are derived as well as a time-dependent temperature shift factor. The material law of the composite is developed with the help of micromechanical considerations assuming viscoelastic matrix and elastic fibre behaviour. The residual stresses are calculated for a specially designed testing device which possesses regions of different fibre orientation. Measured fibre orientation tensors are used as simulation input. In the following, the calculated stress profiles were compared with measured values, which were determined using the layer removal technique. The calculated and measured profiles are in good agreement and show a strong influence of the fibre orientation state. The highest occurring stresses are in the same order of magnitude as the long-term strength of these materials.

The Optimized Quasi-Planar Approximation for Predicting Fiber Orientation in Injection-Molded Composites1

Abstract Fiber filled injection-molded plastic parts contain complex fiber orientation patterns. This fiber orientation state affects material properties, including both elastic modulus and strength, and the calculation of shrinkage and warpage. Several models are available for predicting fiber orientation, which are based on the theory of Folgar and Tucker [1]. A particular simplification of these models, here called the quasi-planar (QP) approximation, was introduced by Gupta and Wang [2]. Here we develop a substantially improved version of that model, which we call the optimized quasi-planar (OQP) approximation. The OQP approximation is formed by optimizing the QP approximation against a more general fiber orientation model. Details of the current and improved models are discussed, and the typical behavior of the old and new models is explored. In addition, simulations are performed using C-MOLD, a commercial software package that implements the QP approximation, to determine the final fiber orientation state in an end-gated strip. The resulting fiber orientation data is then used to predict the elastic modulus as a function of position, and both predictions are compared to available experimental data for fiber orientation and elastic modulus. The results show that the OQP approximation improves the fiber orientation prediction and the subsequent elastic modulus prediction compared to the QP model, though the OQP approximation is still less accurate than the full three-dimensional model.

Numerical Solution of Fiber Orientation in a Backward-Facing Step Channel

As a fundamental study on anisotropic channel flow, two-dimensional fiber orientation was investigated in a main flow as well as in a recirculating flow within a salient corner of a backward-facing step channel. For a large number of fibers (N=1800, aspect ratio γa=5 and 10000) having a random initial orientation, the orientation distribution after injection was computed with the Jeffery's equation along streamlines in Newtonian flows. This distribution, which was described by the second-order orientation tensor and the orientation ellipse determined on a statistical basis, was compared with the actual distribution found from experiments.For large γa, both experiments and computations indicated that steady orientation was achieved after several circulation and all fibers aligned almost completely along the streamlines in a recirculating flow. For small γa, the computations predicted that almost complete orientation was achieved at steady state but a preferred orientation angle lay obliquely to the streamlines. When fibers almost completely aligned along the streamlines flowed into an expanding part of a channel, this orientation state remained in a main flow at high Reynolds numbers Re, because of gradual divergence of main flow, but their preferred orientation angle lay obliquely to the streamlines in the central region of the channel. In contrast, for low Re that resulted in the main flow abruptly diverging at the expanding part, the fibers were less oriented and their preferred orientation angle in the central region increased just at downstream side of the expansion entrance. This worse orientation was expected to remain in a wider downstream region for lower Re.All above results provided a clue for rigorous computation of fiber suspension flows, which is carried out by coupling flow field with fiber orientation state, through a complex channel often inducing a recirculating flow.

Generalized warpage parameter

AbstractA warpage index (Δψm) was introduced for studying warpage characteristics of a plastic part injection molded from PA66 compounded with 30 wt% glass fiber. Δψm is defined as Δψm = (Δψm)max – (Δψm)min, where ψm = ψ(θ)max, where ψ(θ) = (ε(θ) – α(θ)ΔT)/| α(θ)ΔT|, where ε is the total strain, α is the linear thermal expansion coefficient, ΔT is temperature difference, and θ is the angle along which ε and α are calculated. Finite element analysis was used for calculating flow field in injection, fiber orientation, material anisotropy and warpage. ψm is calculated in each finite element, and Δψm is calculated in a whole finite element model. Δψm is a measure of the ratio of actual shrinkage to the amount of shrinkage that would occur if an element freely shrank. The characteristics of Δψm were studied. It has been found that warpage is null if Δψm = 0, but that null warpage generally does not indicate Δψm = 0. It is shown that Δψm quantitatively represents the warped and unwarped state. Δψm distinguishes the null warpage state with possible buckling from the null warpage state without possible buckling. It has been shown that material anisotropy is possibly described with Δψm, and that the cause of warpage is self‐restrictive deformation in an injection molded part. It has been deduced that it is generally not possible to eliminate warpage only by controlling material properties. Δψm is obtainable for a plastic part with complex geometry and complex fiber orientation state, and for arbitrary materials. Applications of Δψm are left for future study.

Prediction of fiber orientation in the thickness plane during flow molding of short fiber composites

AbstractFiber orientations caused by the flow in the thickness plane during injection molding of short fiber reinforced polymer composites has been simulated. The Lagrangian scheme was employed for the finite element analysis. Flow fields were solved by using a penalty method with Uzawa's scheme and orientation fields were also solved by using the second order orientation tensor. A generalized Newtonian fluid whose rheological behavior is independent of fiber orientation was assumed. Automatic mesh generation using an elliptic grid generator was developed for quadrilateral elements. Mold filling and orientation analyses were performed for a cavity of rectangular cross section. To determine the orientation state in other cross‐sectional geometries, numerical analyses were also performed for two different typical cross sections. As the result, orientation of short fibers in the flow field was analyzed qualitatively and quantitatively. According to the state of short fiber orientation in the thickness plane, the orientation field can be classified into three regions in the flow direction and three layers in the thickness direction. Orientation of short fibers was mainly influenced by elongational and shear flows. It was observed that critical values are present for upper limits of orientation. Effects of initial orientation at the inlet on the orientation field were examined.

Void Ratio and Warpage of an Injection Molded Plate

Warpage of a plate with holes (voids) were investigated with warpage index (φm) and with finite element analysis. φm is proportional to the difference of total strain and thermal strain. φm indicates the degree of restriction in thermal shrinkage in an injection molded part. In thermal stress analysis, φm is calculated with respect to thermal load which is proportional to the product of linear thermal expansion coefficient and temperature difference. A plate with holes is a representation of an internal structure of a plate made with a processing method in which voids are intentionally generated inside the plate. Gas-injection molding or foam-injection molding are two examples of this processing method. Thermal stress analysis and buckling analysis were conducted for plates with voids, which were injection molded with PA66 compounded with 30 weight% glass flber. Correlations among volumetric void fraction, buckling mode, buckling temperature and φm were studied. For obtaining anisotropic material properties, flow field in injection molding was calculated, the interaction between the flow field and glass fiber was simulated, and fiber orientation states were calculated. Clear correlation between void fraction and warpage was found.

Determination of 3D fiber orientation distribution in thermoplastic injection molding

An automated optical section method for quantifying the orientation state of short fibers in injection molded parts is presented. The method is based on imaging tracer fibers in index of refraction-matched transparent composites. The experimental methods and performance characteristics of the method are described. The method is non-destructive, operator-independent, economical and rapid. Scanning to depths of about 1.3 mm without cutting is possible at 10 μm spatial resolution at processing rates of < 10 min mm −3. Straightforward modifications should allow processing rates >1 mm 3 min −1. Calibration tests suggest that fiber orientation is quantified to within the accuracy expected based on the degree of solid angle discretization chosen for analysis (5 ° here). Reproducible fiber orientation distributions are realized for sample domain sizes of about 2 mm × 2 mm × 0.15 mm. The orientation distribution function is quantified as well as the orientation tensor components. Convenient graphical visualizations of the 3D orientation distribution function and tensor representations are provided.

Image Simulation and Evaluation of Fiber Orientation Distribution

Abstract A new method is presented for analyzing fiber orientation distribution in fiber reinforced composites. A fiber orientation state in fiber reinforced composites is first obtained from soft X-ray image by making contract micro-radiograph (CMR). The distribution of the fiber orientation is measured by a fiber orientation index G(θ) as proposed in this paper. Furthermore, a computer simulation for the fiber orientation distribution is carried out in order to evaluate the fiber orientation index G(θ). It has been found that the value of the fiber orientation G(θ) decreases with an increase in the scatter of the fiber orientation distribution. Not only the direction but also the degree of the fiber orientation can be shown from the curve of the fiber orientation index G(θ). The result shows that this method is easy and useful to evaluate the fiber orientation distribution in fiber reinforced composites.

Part Buckling in Injection Molding (I)

Warpage of two injection molded parts with similar geometry was investigated to clarify the key parameters for determining the qualitative warpage mode in injection molding. The geometry of one part (Case 1) included small ribs in addition to the geometry of the other part (Case 2). The basic geomerty of Case 1 and Case 2 were plate with three rectangular ribs, and were identical to each other. PET compounded with 30 weight % short glass fiber was used in the study. It was experimentally found that the warpage mode of Case 1 did not qualitatively coincide with that of Case 2. From thermal stress analysis and buckling analysis, it was shown that the difference of the fiber orientation states between Case 1 and Case 2 was not adequate for generating a qualitative difference in warpage mode between the two parts. The numerical analysis indicated that the Case 2 warpage was caused by the anisotropic material properties which were induced from the fiber orientation state. On the other hand, the buckling analysis indicated that the measured Case 1 warpage required an external force applied to the part during the injection molding. The possiblity was shown that external force influences to the warpage modes of injection molded parts. The detail investigations on the existence of the external force and on how the external force affects to the part warpage are left for the future study.

Effect of fiber orientation on the fracture toughness of brittle matrix composites

The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. The orientation distribution of the fibers is likely to be biased, and not in an ideal random or aligned state. A micromechanical model is formulated for the post-cracking behavior using the force-displacement relation for an arbitrary fiber bridging a crack, the fiber orientation density function, and the fiber location density function. This model is then used to determine an effective traction law for the bridging fibers, as well as the steady state bridging toughness increment. In most cases, the results may be placed in the form of a product of the aligned fiber results times a modifying integrated orientation factor. The friction shear st ress on fiber pull-out is allowed to vary during pull-out, modeling the effects of matrix breakdown, fiber surface smoothing or wear debris accumulation. Results are presented for a variety of representative planar and three-dimensional fiber orientation states.

The toughness of brittle matrix composites reinforced with discontinuous fibers

The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. Using a fundamental crack opening-restraining traction law for the resistance to crack propagation provided by an arbitrarily oriented fiber which bridges a crack, together with the fiber orientation and location density functions, a micromechanical model is developed. This model determines the effective crack opening-traction law of the bridging fibers. The steady-state toughness increment is obtained by integrating the contributions of the individual fiber pull out energies. This model includes the observed effect that fibers at large angles to the crack face normal may break rather than pull out. The shear stress at the fiber-matrix interface is allowed to vary during pull out, simulating fiber or matrix damage. Results are presented for a variety of representative fiber orientation states and interfacial shear cases.

Fiber–fiber interactions in homogeneous flows of nondilute suspensions

A theoretical model for calculating the average interfiber spacing in nondilute short fiber suspensions is presented. The approach adopts the Doi–Edwards theory to model spacing between rigid rod‐like polymer molecules to determine the interfiber spacing. Modifications have been introduced to the Doi–Edwards theory in order to obtain accurate estimates of interfiber spacing at all orientation states and for fibers of finite diameter. A parametric study has been conducted to explore the influence of the relevant dimensionless parameters: the fiber volume fraction, the fiber aspect ratio, and the probability distribution function of the fiber orientation state on the average spacing between the fibers. An approach has been suggested to use this spacing to characterize fiber–fiber interactions in flowing suspensions. Numerical predictions of flow‐induced fiber orientation based on this approach are presented.

Fiber orientation in Fiber Suspension Flow through a Parallel Plate Channel and an Abrupt Contraction Channel

The orientation of fibers has been investigated experimentally in fiber suspension flows of both Newtonian and viscoelastic fluids through a parallel plate channel and a planar channel with an abrupt contraction, and the development of the fiber orientation has been examined while the fibers flow along the channel. The effects of shear thinning and elasticity on the fiber orientation have been discussed.The fibers lie tangent to the streamlines with an increase in viscoelasticity in the flow through a parallel plate channel and a channel with an abrupt contraction. This phenomenon is essentially equivalent to the phenomenon that a slender body, namely a straight circular cylinder with a large length to diameter ratio, rotates towards a vertical orientation when falling through a quiescent polymer solution. High fiber alignment to the streamlines, thus, is attributed to the shear thinning and elsticity of the suspending fluids; however, elastic effect is most dominant.The state of fiber orientation is strongly influenced by the drastic change of the velocity field due to viscoelasticity and flow rate: the fibers align in a manner of wine-glass shape as the contraction is approached and then the distribution of fibers abruptly expands in the immediate downstream region of the contraction in a highly elastic fluid flow.