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

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Abstract

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.

Introduction

Because of the market-imposed pressure to shorten development times, computer-aided simulation analysis has acquired significant importance in recent years. These simulations include the production process as well as the part behaviour in service. For short-fibre-reinforced thermoplastics (SFRT), which are widely used in technical applications, this means the calculation of the fibre orientation (FO) from flow conditions during the injection-moulding process1, 2, 3. The resulting FO state is the basis for calculation models, to determine the anisotropic part characteristics, like stiffness4, 5, thermal expansion[6] and strength[7]. Knowledge of the real FO in the component is of great importance as an interface for the model calculations mentioned. The results of the FO calculations from mould-filling simulations, which are often part of commercial injection-moulding simulation software8, 9 can be verified. On the other hand, micromechanical models — and their assumptions — for predicting the part behaviour can only be checked with correct, measured input parameters.

In addition to the injection-moulding process, knowledge of the FO state is of essential interest for every process, where fibre reinforcement is used. This also includes all manufacturing techniques processing long fibres, like the sheet-moulding compound (SMC) or resin-transfer moulding (RTM) processes. The FO state can be used in defining quality-control criteria as well as the input parameters — through micromechanical models — for finite-element calculations.

As a measuring technique for determining the quantitative FO state, the evaluation of polished cross sections is employed. Therefore a freely programmable image-analysis software (analySIS 2.1, SIS-Soft-Imaging Software Gmbh., D-48153 Münster) is used. The cross sections are either magnified by light microscopy, whereby a special contrasting process is used, and digitised by a video camera or they are directly taken to the image analysis from the scanning electron microscope[10]. Since many images are necessary for the analysis of one cross section, one has to use a controllable specimen-fixing device together — in case of the light microscope — with an automatic focus system. With the help of the algorithm in Section 3a complete automation of the analysis is possible.

Section snippets

Fundamentals

In accordance with the theory of fibre orientation in flow and with the ideas of Ref.[11] all investigations done concerning this work showed a constant fibre concentration in the whole part as well as in the thickness direction. The only exception is the edge zone. This spatially very narrow region is marked by a lower fibre concentration[12].

Image evaluation

For determining the orientation of a fibre in space, which is given by two orientation angles (Fig. 1), a circular cross-section is assumed. The fibres are therefore pictured as ellipses on the cutting plane. The orientation of the major axis is identical to the angle ϕ. The other orientation angle, θ, can easily be calculated from the ratio of the minor axis, b, to the major axis, a, and from the associated angular relation in the following wayθ=arccosba.

Only the sign of the angle stays

Usage of inclined polished samples

From the cutting ellipse the orientation of a fibre is not uniquely determined: two states are possible. Because of this, not all tensor components can be determined from one polished cross section. Which components remain undetermined is discussed for the second-order tensor.

Therefore a cutting ellipse in the 1-2 plane is considered. The realisation point of the fibre on the unit sphere can be above or below the 1-2 plane. Therefore the sign of the third component remains undetermined. From

Measurements

The application of the discussed analysing schema is shown on two examples, where the FO state of a SFRT component is investigated. The component itself and both measurement points are shown in Fig. 10. The component was specially designed for this research project[26].

Conclusions

To describe the orientation distribution in SFRTs orientation tensors are used which represent a compact, general and short formulation. For the measurement of the fibre orientation in SFRT components polished cross sections are evaluated. An image-analysis system is used to measure the ellipses, and a specially developed evaluation algorithm is employed. The major advantages compared to commercial software are improved object detection and a significant reduction in measurement errors through

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