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Composim Scrmr~ and Techno/op 53 (IYYS) 133% 143 0 199.5 Elsevier Science Limited

0266-3538(95)00012-7

Printed in Northern Ireland. All rights reserved 0266-3S38/YS/$(~.SO

DETERMINATION OF 3D FIBER ORIENTATION DISTRIBUTION IN THERMOPLASTIC INJECTION MOLDING

J. J. McGrath & J. M. Wille

Mechanical Engineering Department, Composites Structures and Materials Center. Michigan State University, East Lansing, Michigan 48824, USA

(Received 2 May 1994; revised version received 26 August 1994; accepted 15 December 1994)

Abstract 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 perfor- mance characteristics of the method are described. The method is non-destructive, operator-independent, eco- nomical and rapid. Scanning to depths of about 1.3mm without cutting is possible at 10 pm spatial resolution at processing rates of <lOmin mm-“. Straightforward modifications should allow processing rates >I mm” min -‘. 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 X2 mm X 0.15 mm. The orientation dis- tribution function is quantified as well as the orientation tensor components. Convenient graphical visualiz- ations of the 30 orientation distribution function and tensor representations are provided.

Keywords: fiber orientation, optical section, automa- tion, injection molding, thermoplastic, composite

1 INTRODUCTION

1.1 Optical sectioning of transparent composites An optical sectioning method for quantifying the orientation state of short fibers in injection molded parts has been developed. The approach makes use of automated sectioning and image analysis of opaque tracer fibers (0.1-0.3 wt%) embedded in transparent composites consisting of a thermoplastic matrix and glass fibers (up to 30 wt%). Transparency of the thermoplastic/glass composite is realized by matching the index of refraction of the thermoplastic matrix and the glass fibers.

Figure 1 illustrates the degree of transparency

133

attained with index of refraction matching as well as the appearance of samples which include opaque tracer fibers. The top photograph is an injection molded specimen 6 mm thick made with polymethyl- methacrylate (PMMA) and 30 wt% BK-10 glass fibers. The middle photograph illustrates the situation when the indices of refraction do not match well and optical sectioning is virtually impossible in a 6 mm thick sample made of PMMA with E-glass. The bottom photograph shows a ‘transparent’ injection molded part (PMMA with 30 wt% BK-10 glass fibers) which includes opaque carbon tracer fibers (0.1 wt%) added for imaging. Orientation of the fibers is evident. Optical sectioning of such specimens can be performed to depths of approximately 1.3 mm.

It is recognized that many matrix/fiber systems are not transparent and that the fiber orientation distributions (FODs) in an arbitrary matrix/fiber system will be the result of the complexities associated with non-linear rheology in a non-isothermal system. Although the specific FOD results obtained here are not expected to apply in general, it has been possible to extend the present method to other matrix/fiber systems by matching the indices of refraction of matrix and fiber. These systems include polycarbonate, SAN and polypropropylene (see Table 1). Since the properties of these materials differ significantly, it should be possible to use this range of properties to understand more about the complexities mentioned above. In addition, future research using the present approach may prove useful in relation to understand- ing the FODs in non-transparent materials when transparent systems with similar properties are used as models.

A schematic representation of the optical sectioning method for quantifying the orientation state of short fibers in injection molded parts is illustrated in Fig. 2. Sequential scanning along the optical axis with a light microscope creates a series of 2D images which can be reconstructed into 3D images from which fiber orientations can be determined.

134 .I. J. McGrath. J. M. Wille

* t

Fig. la. Top: PMMA with 30wt% BK-10 fibers (transpar- ent). Bottom: PMMA with 30 wt% E-glass fibers (opaque).

Fig. 2. Optical sectioning method.

direction corresponds to the flow direction during injection molding, the y (or 2) direction is orthogonal to the flow direction and the z (or 3) direction corresponds to the direction of the optical axis used for sectioning. An orientation tensor can be defined in terms of the dyadic product of the components pl, p2 and p3 of the orientation vector, p, weighted by the orientation distribution function, $(p). The orienta- tion averaged tensor (( ) notat& signifies an orientation average) is defined as

r2n I-” Fig. lb. Injection molded PMMA with 30 wt% BK-10 glass

fibers and 0.1 wt% carbon fibers. (a,) = J J P;P#(P) dP (1)

0 0

1.2 Representation of FODs A number of methods of representing the fiber orientation state have been described in the literature.14 The orientation tensor representation introduced by Advani and Tucker4 has been widely accepted and has been adapted here. It has the advantages of being a compact description of the orientation distribution that is independent of reference system, requiring no a priori assumptions about the shape of the distribution function.

The orientation of a single fiber is defined in Fig. 3 in terms of the orientation vector, p. The x (or 1)

The orientation distribution function here is defined experimentally in terms of the fiber length in a particular direction normalized with respect to the total fiber length within a defined region of the sample at a location of interest:

(2)

For an ensemble of fibers the orientation averaged tensor can be determined by calculating the P;pj product in a particular direction, multiplying by the

z .(3)

Table 1. Injection molding processing envelope

Melt lemperature

Mold temperature

Volumetric injection rate (max.)

Strain rate (maximum at wall)

Injection/hold pressure

Fiber length

Fiber content

Mold and gate geometry

Materials (injection molded parts have been

made and imaged with these materials)

2OT 5 7‘ 5 3ow.z

20°C 5 7‘ 5 120°C

25cmTs ’ -0 s ’ to 1500s~’

2200 bar (32 OCU psi)

IOO~m t”3mm

0 wt% to 30 wt%

‘arbitrary’

PMMA; polycarbonate

SAN; polypropylene

Fig. 3. Fiber orientation angles.

30 fiber orientation dktribution in thermoplastic injection molding 135

fiber length in that direction and dividing by the total fiber length in the sampled region:

(aji> = F & PiPj

m m

2 EXPERIMENTAL METHODS

2.1 Injection molding system The laboratory injection molding system developed for manufacturing transparent composites of interest is shown in Fig. 4 and described in more detail elsewhere.5-9 The apparatus consists of a modular injection mold, tabletop injection molding unit, and data acquisition equipment. The injection molding system was designed as an economical device capable of producing a range of manufacturing process conditions of commercial interest in order to study the relationship between manufacturing conditions and fiber orientation distributions. The manufacturing process envelope attainable with this device is defined in Table 1.

The mold, shown in Fig. 5 has a sandwich construction allowing a variety of mold and gate geometries to be studied rapidly and inexpensively.

2.2 The imaging system The imaging system was designed to maximize resolution and penetration depth, while minimizing operator intervention. The details of this system are also discussed elsewhere.5-9 A schematic of the imaging apparatus is shown in Fig. 6. The motion controller and frame grabber were used to allow the positioning of the specimen and image acquisition to

Hvdraulic Speed _Regulation

C$iinder

Position Transducer A

Piston

Barrel

ion I I

Fig. A Injection molding system.

be controlled by computer without operator intervention.

2.3 Image analysis

2.3.1 Image processing The image analysis system of Fig. 6 has been applied for automated image analysis of transparent compos- ite specimens as described above. As a specific illustration, top and side views of a specimen are shown schematically in Fig. 7a along with a typical optical scan pattern. An obstacle was introduced in this specimen for the purpose of studying knit lines. A top view photograph of the area around the scan region is shown in Fig. 7b.

An important feature of the software created by Wille6 is its comprehensive and user-friendly nature. An example of one of the graphical user interfaces (GUIs) that characterize data collection and image analysis is shown in Fig. 8. The scan pattern described above is easily programmed, resulting in a highly automated and virtually user-independent mode of operation. The primary source of variation that can be introduced by the operator is in setting the microscope light intensity and the video camera controls. The degree of person-to-person variability is small when tests are performed carefully. The degree of reproducibility is quantified later in this paper.

Control of the x-y traversing as well as depth along the optical axis frame grabs is accomplished by servo/stepper motors. The optics used here produce 2D image areas of 1.077 mm X O-797 mm as shown in Fig. 7a. The resolution of the frame grabber (320 x 400) determines the x and y resolutions for this configuration (3.37 pm X 1.99 pm). The working depth of field along the optical (z) axis was found to be approximately 15 pm with the optics used. Thus the voxel (volume element) size used here is -3 pm x 2 pm X 15 pm. Note the relatively poor z-axis resolution. While the unit area scanned (1.077 mm x 0.797 mm) is fixed for the optical system used, the depth of each scanned domain is variable and easily defined in the software (see Fig. 8). For example, in Fig. 7a, 50 optical slices each 14.9 pm thick were imaged to study fiber orientations in a layer 0.745 mm thick located at the bottom surface of the specimen.

Since the area scanned in the x-y plane is approximately 1 mm2, it is convenient to consider some characteristics of a scanned volume of approximately 1 mm3 produced by a sequence of 70 optical sections. For specimens containing 0.1 wt% carbon fibers each image area (1.077 mm x

O-797 mm x 14.9 pm) contains approximately 30 fibers and >lOO fibers in 1 mm3. At the x-y resolutions of 3 pm x 2 pm a carbon fiber diameter (10pm)

136 J. J. McGrath, J. M. Wille

Fig. 6. The imaging system.

Fig. 5. Mold design.

oriented in the z direction is comprised of several pixels in both lateral directions. At an optical axis (z) resolution of 14.9 pm, each optical section is

Light Source

-4

servo Specimen

Video Camera Servo f7iiilk SC!VO

TOP CLAMPING PIATE

UPPER CAvnY PLATE

MIDDIS CAVITY PLATE

LOWER CAVITY PLATE

SUPPORT PIATE

BolToY CLAMPING PLATE

approximately one fiber diameter thick. It will be shown below that the relatively poor resolution along the optical axis does not introduce significant bias or produce unacceptably inaccurate fiber lengths or orientations.

Both glass and carbon fibers were cut with a custom-made, computer-controlled fiber chopper. Fibers were cut to a relatively mono-disperse distribution with an average length -900 pm. However, following the injection process, fiber lengths were found to be -300 pm in length. Consequently a typical fiber length would be approximately l/3 the length of one side of a cubic 1 mm3 volume element.

Scanning and digitizing an individual image (l-079 mm x O-797 mm x 14.9 pm) can be performed at a rate of approximately 5-10s frame-l (5- 10 min mm-‘) with the equipment defined here. A typical study such as that shown in Fig. 7a consisting of 18 X 12 X 50 images would require some 18 h to process, but the process is highly automated. Significant enhancements in processing times can be

30 fiber orientation distribution in thermoplastic injection molding 137

- L= 82.5 mm-

r I J ,I

_$

H = 3.2 mm

(50 images, 14.9 um spacing)

Fig. 7a. Top and side views of automated imaging pattern.

Eig. 7b. Photograph of fiber orientation around an obstacle in an injection molded part. Close up of part shown in Fig.

7a above.

realized by upgrading the computer, incorporating a frame grabber with a higher data transfer rate, utilizing faster servos and/or stepper motors and optimizing the image processing algorithms. An order of magnitude enhancement is probable.

A typical optically-sectioned image (1.079 mm X

0.797 mm X 14.9 pm) within a localized region of a transparent composite specimen such as that shown in Fig. 7b would appear under the microscope as shown

Fig. 9. Photograph of carbon fibers in injection molded part with 30 wt% BK-10 glass fibers and O-1 wt% carbon fibers.

in the photomicrograph of Fig. 9. A sequence of such images is digitized and a 3D reconstruction of the fibers in a defined volume element can be represented as shown in Fig. 10. Fibers are represented as contiguous voxels, typically several voxels in diameter and many voxels long, as would be expected on the basis of the voxel resolution described earlier.

A detailed description of the image acquisition and processing is beyond the scope of the present treatment. A brief description is included here. Optical sectioning relies on the relatively narrow depth of field of the optical microscope used. Objects which lie within the depth of field of the optics are visible while those outside the depth of field are not. The depth of field of the optics used was calculated to be approximately 5 pm. In actual fact fibers were found to be rather sharply focused in such a narrow band, but parts of fibers were significantly less visible as non-focused objects over a total depth range of some 17 pm. Sequential optical sectioning at 15 pm intervals (fiber diameter - 13 pm) in conjunction with a simple thresholding operation to eliminate out-of-

Fig. 8. Typical graphical user interface (GUI) for software developed.

138 J. J. McGrath, J. M. Wille

Fig. 10. Unthinned (top) and thinned (bottom) digitized 3D fiber images.

plane information proved to be quite satisfactory (see results below). A 3D thinning algorithm was developed for the work described here. The details of this method will be described elsewhere. The primary purpose of the algorithm is to determine the locations of fiber ends and intersections, which are then used for quantifying fiber lengths and orientations. This skeletonizing algorithm reduces structures comprised of a group of voxels down to a chain of single voxels lying along the medial axis of the fiber. The algorithm satisfies the following criteria: (i) it does not disturb the connectivity of the image; (ii) it does not shorten voxel chains; and (iii) it must remove voxels in a uniform manner such that the remaining voxels lie on the medial axis of the fiber. Endpoints are identified in the resultant thinned image as voxels with only one neighbor whereas voxels with more than two neighbors are intersections. No additional correction factors are implemented to account for fiber shortening or lengthening introduced by the algorithm.

The results of such thinning will produce an image such as shown in the bottom of Fig. 10 from an image such as that shown in the top of Fig. 10. Thinned images are stored as l-bit data in a compressed (animation) format requiring about 25 kbyte mmP3 ( = 25 Mbyte cm-‘) of sampled volume.

It is beyond the scope of this paper to describe the extent to which the FOD results are influenced by individual complexities such as lighting variations through the thickness of the part or thresholding operations used to produce optical sections, etc. A global assessment of the adequacy of the present approach is provided by referring to the calibration results presented below.

2.3.2 Fiber orientation and length determination Fiber ends and intersections are identified from thinned images. Ambiguity may arise when fibers apparently overlap. The optical axis resolution may not permit determining whether a small number of long fibers overlap at the intersection or a larger number of shorter fibers come together. In the present treatment the distinction is not critical since the total fiber length in a specified direction in the discretized orientation space will be the same in either case. Therefore the orientation tensor and the 3D histogram will not be influenced by this ambiguity.

Once each fiber is defined as described above, individual voxels in thinned images (Fig. lob) are treated as point masses and the moment of inertia tensor of each fiber is calculated. The direction of each fiber is then defined to be that corresponding to the eigenvector associated with the minimum principal moment of, inertia. Total fiber length in specified directions is then determined from voxel sizes and number of voxels.

2.3.3 The fiber orientation state The fiber orientation distribution (FOD) for a defined volume (such as that shown in Fig. 7a) may be determined by dividing orientation space into discrete solid angle increments and summing the total fiber length in each direction (centered on a solid angle increment). In this manner a 3D histogram represent- ing the FOD may be created. A unit sphere at ‘sea level’ corresponds to no fibers detected in any direction. The magnitudes of peaks above this reference level correspond to the total amount of fiber detected in a particular direction.

Representative FODs visualized as 3D histograms are shown in Fig. 11. The top case illustrates the FOD for two fibers orthogonal to one another. The bottom case illustrates a more complex situation with a larger number of fibers which happen to be more or less aligned in a single direction. The software developed by Wille6 produces such 3D histograms which can be manipulated (rotated/zoomed) on the computer monitor for rapid visualization.

30 fiber orientation distribution in thermoplastic injection molding 139

Fig. 11. Representative fiber orientation distribution (FOD) 3D histograms.

2.3.4 The fiber orientation tensor As discussed earlier, the fiber orientation state is conveniently represented in tensor format. For a defined sample volume (e.g. 1.077 mm x 0.797 mm x O-745 mm in Fig. 7a) an orientation-averaged tensor may be defined by computing the aij components of each fiber.

This orientation tensor may be thought of as an ellipsoid. The orientation and lengths of the principal axes of the ellipsoid may be determined from the eigenvalues and eigenvectors of the orientation tensor for each volume of interest. Such an ellipsoid is shown in Fig. 12. The orientation information relative to the flow direction (x or l), orthogonal direction (y or 2) and optical axis (z or 3) are shown. The rotation angle, 4, is defined as the angular displacement from the flow direction in the x-y plane, the elevation angle, W, is defined as the angular displacement of the major axis from the x-y plane and the rotation angle,

Z

T ; (j’ B --. Y . . --__ 0 ’ --_,

X

Fig. 12. Ellipsoidal representation of orientation tensor.

p, is defined as the angular displacement of the intermediate axis about the major axis. It should be noted that such ellipsoids are convenient functional approximations of the discretized 3D histogram introduced above.

Projections of these ellipsoidal representations of local FODs as ellipses onto the x-y, X-Z and y-z planes are useful for rapid visualization of local and global fiber orientation states. Figure 13 shows the projection of measured FOD ellipsoids onto the x-y plane for the sample with an obstacle introduced earlier (Fig. 7b). Flow was from left to right. The long, thin ellipses (lines) near the top and bottom indicate significant fiber alignment near the mold walls as expected. Similarly, the thin ellipses (lines) between the obstacle and the walls as well as downstream of the obstacle indicate significant alignment in the flow direction. The latter effect is taken to be associated with the presence of the expected knit line. The more circular ellipses upstream of the obstacle correspond to a more random fiber alignment and give the appearance of a flow ‘stagnation’ effect. All of these findings are quantified in the tensor representation of course but this form of visualization has proven to be a powerful tool to rapidly comprehend and record FOD results.

3 RESULTS

3.1 Calibration of FOD determinations The accuracy and reproducibility of the FOD determinations obtained from the optical sectioning method described here have been evaluated. Since the details are presented elsewhere&’ only a summary is given here for the sake of completeness. A sequence of calibration tests was performed which included evaluating the software using well-defined pseudo- data followed by increasingly more complex optical situations.

For a pseudo-data set comprised of fibers with known properties (fiber lengths and orientations) the software developed here calculated the average measured fiber length as 586 pm (a 2.3% error) with a standard deviation of 52 ,um. The calculated orienta- tion tensor for a uniform fiber distribution was very close to the ideal result (i.e. a diagonal tensor with a,, = a22 = aj3 = O-3333) indicating a very accurate determination of the angular orientation (certainly within the error expected due to angular discretiza- tion). Taken together these results were acceptable confirmations that the software successfully processed images with known properties (fiber lengths and orientations).

The next level of complexity involved real samples with single fibers in known orientations. In these instances the software must cope with non-idealities introduced by the optical system. The results indicate

140 J. J. McGrath, J. M. Wille

Fig. 13. Typical projection of the tensor ellipsoid onto the x-y plane.

that the orientation is correctly determined to within 2” accuracy and the length to within 3% accuracy.

Because the resolution along the optical axis (z) is poor relative to that laterally (x-y plane), the accuracy of the experimentally determined tilt angles (out of the x-y plane in the z direction) is important to examine critically. Single carbon fibers embedded in epoxy and suspended in air were rotated incrementally in the x-z and y-z planes. The results for the X-Z and y-z tests were comparable to those in the x-y plane. Specifically the error in orientation was limited to less than 3”, the errors were random and were within the limits expected from the degree of solid angle discretization and the experimental uncertainty. Fiber lengths were much longer than the fields of view so no fiber lengths were determined by the software for these tests. These results suggest that the image analysis developed is capable of producing acceptably accurate results in relatively simple samples.

The question then arises as to whether accurate FODs can be derived from the complex images inherent to samples with opaque tracer fibers and high glass fiber densities as described here. In the absence of an ideal calibration standard in which fiber lengths and orientations are well-defined, the software performance was evaluated by testing for self- consistency of fiber orientations and lengths in a single specimen scanned from four orthogonal directions. The details of this test are also described in detail elsewhere.“’

A small volume calibration specimen (1 mm X 1 mm X 10 mm; PMMA with 30 wt% BK-10 fibers and O-1 wt% carbon fibers) was cut from an injection molded specimen. This specimen was then scanned

from four orthogonal directions (*y and +z). Orientation tensors and 3D histograms were deter- mined for all four directions. One direction was taken to be the standard and results from the other three directions (tensors and histograms) were transformed mathematically back to the reference direction so that the results for all four scan directions could be compared directly with one another. Representative comparisons of the 3D histograms are shown in Fig. 14. Ideally the 3D histograms and all components of the orientation tensors ((aij)) would match exactly, regardless of which direction the specimen was scanned. While neither histogram nor tensors match exactly, the agreement is considered acceptable.

A useful measure of the level of FOD self- consistency, irrespective of scan direction is realized by another representation of the results. Comparison of the ellipsoid orientation angles defined in Fig. 12 for the ellipsoids derived from the four scan directions suggest that orientation is being determined accurately to within -4” and that total fiber lengths are being determined accurately to within l-2%. These results for complex images are comparable to those obtained for simpler images and are expected based on the degree of solid angle discretization applied (tessella- tion order of 3 = regular icosahedron with faces subdivided three times). Apparently no significant bias or error is introduced when scanning complex images containing 0.1 wt% carbon fibers, even when z-direction resolution is -15 pm.

the

3.2 Comparison of optical sectioning and surface ellipse methods Another means of assessing the performance of the optical sectioning method described here is to

30 fiber orientation distribution in thermoplastic injection molding 141

I-- t

(a) Scanned from -.z (b) Scanned from -y

24 i-7

(c) Scanned from +z (d) Scanned from +y

Fig. 14. Comparison of orientation distribution functions for four orthogonal scans.

compare the results obtained from this method with results obtained from a traditional technique such as the surface ellipse technique.

The detailed results of such a comparison are given elsewhere.“’ The important conclusion from that work is that a very good correlation of the results obtained by the two different methods was obtained when representative tensor components were deter- mined at the same locations in a single specimen and compared. This is taken as another affirmation of the validity of the optical sectioning method.

3.3 Reproducibility The reproducibility of the present approach has been examined from several viewpoints. Important sources of variability may be introduced by (i) small numbers of tracer fibers; (ii) operator-to-operator variability; and (iii) non-reproducible injection molding process- ing conditions.

Because the number of opaque tracer fibers is relatively small (-100) in the characteristic volume considered here (1 mm”) there is the possibility of significant variability of FOD determinations for a given sample examined with multiple scans at a single location by a single person. It has been found that scanning a single cell (-1.077 mm X O-797 mm X

0.700 mm) can lead to unacceptable variability in tensor component determinations when multiple

determinations of the tensor components for a specified sample area are measured. This is not the case when the scanning area is larger (-3 mm X

3 mm X O-15 mm). In such cases the standard devia- tion of the mean is typically a few percent of the mean value of the respective tensor components. This is expected theoretically on the basis of increased numbers of fibers in the sampled volume.

Another useful measure of reproducibility is related to the variability that is associated with having different investigators sample a single specimen at a specified location. Figure 15 reveals the typical degree of reproducibility found for two persons operating the system (scan volumes were 1.077 mm X 0.797 mm X

1.0 - al 1 -Operator 1

0.6 - al 1 - Operator 2

?I 0.6 P g 0.4 m

- a33 Operator 1

o.oL-=e=-J - a33- Operator 2

-1 0 1 z/b

Fig. 15. Person-to-person reproducibility of tensor com- ponents. Same location, single sample.

142 J. J. McGrath. J. M. Wille

0.15 mm in each case). The error bars represent ing shear thinning phenomena which may be occurring standard errors. during injection.

To conduct meaningful studies related to the influence of manufacturing conditions on FODs, the variation of FODs produced by a specified set of manufacturing conditions from specimen to specimen should be significantly less than the variation of FODs produced by changes in the manufacturing conditions. The variation of FODs detected in four samples produced by fixed manufacturing conditions is illustrated in Fig. 16. The scan volumes were three x-wise scans of l-077 mm X 0,797 mm X 0.15 mm in each case. The error bars represent standard errors. An interesting aspect of this figure is the asymmetry of

4 SUMMARY AND CONCLUSIONS

the fiber thickness displaced mold.

Taken

orientation distribution through the part which is associated with the gate being from the vertical axis of symmetry in the

as a whole these reproducibility results

A new method of quantifying the fiber orientation distributions within short fiber reinforced composites has been developed. The technique makes use of a transparent model composite system comprised of opaque tracer fibers and glass fibers with index of refraction that matches that of the thermoplastic matrix. A sparse population of opaque carbon tracer fibers are imaged and assumed to be representative of the glass fiber orientation state. The advantages and the capabilities of the method have been outlined in some detail. One limitation of the approach is the need to work with fiber/matrix combinations with matching indices of refraction. However a number of such combinations have been identified and prelimi- nary research has been initiated with them. Another limitation is that high tracer fiber densities are desirable for statistical sampling purposes but this results in decreased penetration depth for optical sectioning. Nevertheless, even with a relatively limited set of such model composites, it appears that a number of interesting issues may be addressed with this approach for a range of properties and manufacturing conditions. The use of other model transparent composites systems as well as non- dimensional representation may offer the possibility to extend the results of this method with such model systems to completely opaque composites.

suggest that for the model composite system used here: (i) a moderate degree of spatial averaging (-2 mm X 2 mm) is required to increase the number of fibers sampled; (ii) results are independent of the system operator and; (iii) for defined manufacturing conditions, the injection molding system produces multiple samples that yield highly reproducible FODs.

3.4 Comparison of optical sectioning FODs with FODs reported in the literature Fiber orientation distributions determined using this optical sectioning method have been compared with fiber orientation distributions published in the literature.” This is somewhat difficult since such published quantitative data are sparse and not all of the processing parameters were matched exactly. It has been suggested that quantitative estimates of the degree of similarity can be made using non- dimensional representation.657 A comparison yields semiquantitative to quantitative similarity of FODs with all general trends being similar. There are indications that the observed quantitative differences are a result of differences in the rheology of the thermoplastic/glass fiber matrices related to interest-

- all-averaged from Measurenients on three Soecimen produckd under the same Conditions

a33-averaged from Measurements on three Specimen produced under the same Conditions

Fig. 16. Sample-to-sample reproducibility of tensor com- ponents. Same location in four samples.

ACKNOWLEDGEMENTS

The majority of this work is based on the PhD dissertation of J. M. Wille. Much of the funding was provided by the Michigan Research Excellence Fund. Contributions to this work were made by the following students: T. Weber, S. Reimann, M. Westerbecke, N. Schbche, J. Ladewig and B. Lian. The Graduate Center for Material Research at the University of Missouri-Rolla supplied the BK-10 glass fibers.

REFERENCES

McGee, S. H. & McCullough, R. L., Characterization of fiber orientation in short-fiber composites. J. Appt. Phys., 55 (1984) 1394-403. Hermans, J. J., The elastic properties of fibre reinforced materials when the fibers are not aligned. Proc. Konigl. Nederl (Akad. van Weteschappen Amsterdam, Series B), 70 (1967) l-9. Wetherhold, R. C. & Scott, P. D., Prediction of thermoelastic properties in short-fiber composites using image analysis techniques. Comp. Sci. Technol., 37 (1990) 393-410.

30 fiber orientation distribution in thermoplastic injection molding 143

4. Advani, S. G. & Tucker III, C. L., The use of tensors to describe and predict fiber orientation in short fiber composites. J. Rheol., 31(1987) 751-84.

5. Wille, J. M. & McGrath, J. J., Automated light microscopic measurement of 3-D fiber orientation in injection molding. Proceedings of the American Society for Composites, Sixth Technical Conference. Technomic Publishing, Lancaster, PA, USA, 1991, pp. 183-8.

6. Wille, J. M., Automated measurement of 3-D fiber orientation distribution in injection-molded composites. PhD thesis, Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA, 1993.

7. Schbche, N., Fiber orientation in transparent short fiber-reinforced thermoplastics. RWTH diploma thesis. Department of Mechanical Engineering Michigan State University, East Lansing, MI, USA, 1993.

8. Wille, J. M., Lian, B. & McGrath, J. J., Three- dimensional fiber orientation distributions in injection- molded, short fiber-reinforced thermoplastics. In Proceedings of the 1993 Advanced Composites Con- ference. ESD Publishing, Ann Arbor, USA, 1993, pp. 349-58.

9. Lian, B., Ladewig, J., Wille, J. M. & McGrath, J. J., Three-dimensional orientation distributions in injection- molded, short fiber-reinforced thermoplastics. Pro- ceedings of the 1994 ANTEC Conference, Society of Plastics Engineers, Brookfield, CT, USA, 1994, pp. 2316-20.

10. Bay, R. S. & Tucker III, C. L., Fiber orientation in simple injection moldings. In MD-29, Plastics and Plastic Composites: Material Properties, Part Perfor- mance, and Process Simulation. ASME, Philadelphia, PA, USA, 1991, pp. 445-92.