Uncertainty quantification of fiber orientation distribution measurements for long-fiber-reinforced thermoplastic composites

Abstract

We present a detailed methodology for experimental measurement of fiber orientation distribution in injection-molded discontinuous fiber composites using the method of ellipses on two-dimensional cross sections. Best practices to avoid biases occurring during surface preparation and optical imaging of carbon-fiber-reinforced thermoplastics are discussed. A marker-based watershed transform routine for efficient image segmentation and the separation of touching fiber ellipses is developed. The sensitivity of the averaged orientation tensor to the image sample size is studied for the case of long-fiber thermoplastics. A Mori–Tanaka implementation of the Eshelby model is then employed to quantify the sensitivity of elastic stiffness predictions to biases in the fiber orientation distribution measurements.

Keywords

Long-fiber thermoplastics injection molding fiber orientation distribution measurement uncertainty quantification elastic properties

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References

Henning

Ernst

Brüssel

. LFTs for automotive applications. Reinf Plast 2005; 49: 24–33.

Markarian

. Long fibre reinforced thermoplastics continue growth in automotive. Plast Addit Compound 2007; 9: 20–24.

Denault

Vu-Khanh

Foster

. Tensile properties of injection molded long fiber thermoplastic composites. Polym Compos 1989; 10: 313–321.

Hassan

Yahya

Yahaya

et al.

Tensile, impact and fiber length properties of injection-molded short and long glass fiber-reinforced polyamide 6, 6 composites. J Reinf Plast Compos 2004; 23: 969–986.

Karger-Kocsis

Friedrich

. Fracture behavior of injection-molded short and long glass fiber – polyamide 6.6 composites. Compos Sci Technol 1988; 32: 293–325.

Thomason

. The influence of fibre length, diameter and concentration on the impact performance of long glass-fibre reinforced polyamide 6, 6. Compos Part A Appl Sci Manuf 2009; 40: 114–124.

S-Y

Lauke

. Effects of fiber length and fiber orientation distributions on the tensile strength of short-fiber-reinforced polymers. Compos Sci Technol 1996; 56: 1179–1190.

VerWeyst

Tucker

CL III

Foss

et al.

Fiber orientation in 3-D injection molded features: prediction and experiment. Int Polym Process 1999; 14: 409–420.

Bailey

Rzepka

. Fibre orientation mechanisms for injection molding of long fibre composites. Int Polym Process 1991; 6: 35–41.

10.

Toll

Andersson

. Microstructure of long-and short-fiber reinforced injection molded polyamide. Polym Compos 1993; 14: 116–125.

11.

Lafranche

Krawczak

Ciolczyk

et al.

Injection moulding of long glass fiber reinforced polyamide 66: processing conditions/microstructure/flexural properties relationship. Adv Polym Technol 2005; 24: 114–131.

12.

Hine

Davidson

Duckett

et al.

Hydrostatically extruded glass-fiber-reinforced polyoxymethylene. I: the development of fiber and matrix orientation. Polym Compos 1996; 17: 720–729.

13.

Phelps

Tucker

. An anisotropic rotary diffusion model for fiber orientation in short-and long-fiber thermoplastics. J Non-Newton Fluid Mech 2009; 156: 165–176.

14.

Ortman

Baird

Wapperom

et al.

Prediction of fiber orientation in the injection molding of long fiber suspensions. Polym Compos 2012; 33: 1360–1367.

15.

Foss

Tseng

Snawerdt

et al.

Prediction of fiber orientation distribution in injection molded parts using Moldex3D simulation. Polym Compos 2014; 35: 671–680.

16.

Wang J, Nguyen BN, Mathur R, etal.. Fiber orientation in injection molded long carbon fiber thermoplastic composites. In: Proceedings of the Annual Technical Conference of SPE (SPE-ANTEC), The Society of Plastic Engineers, Paper # 2139172, Orlando, 23–25 March 2015.

17.

Nguyen BN, Fifield LS, Kijewski SA, et al. Predictive engineering tools for injection-molded long-carbon-fiber thermoplastic composites-FY 2015 first quarterly report. Richland, WA: Pacific Northwest National Laboratory (PNNL), 2015.

18.

Kawamura

Ikeda

Morita

et al.

Unambiguous determination of 3D fiber orientation distribution in thermoplastic composites using SAM image of elliptical mark and interference fringe. J Compos Mater 2005; 39: 287–299.

19.

Bright

Crowson

Folkes

. A study of the effect of injection speed on fibre orientation in simple mouldings of short glass fibre-filled polypropylene. J Mater Sci 1978; 13: 2497–2506.

20.

Darlington

Smith

. Some features of the injection molding of short fiber reinforced thermoplastics in center sprue-gated cavities. Polym Compos 1987; 8: 16–21.

21.

Shen

Nutt

Hull

. Direct observation and measurement of fiber architecture in short fiber-polymer composite foam through micro-CT imaging. Compos Sci Technol 2004; 64: 2113–2120.

22.

Bernasconi

Cosmi

Hine

. Analysis of fibre orientation distribution in short fibre reinforced polymers: a comparison between optical and tomographic methods. Compos Sci Technol 2012; 72: 2002–2008.

23.

Thi

TBN

Morioka

Yokoyama

et al.

Measurement of fiber orientation distribution in injection-molded short-glass-fiber composites using X-ray computed tomography. J Mater Process Technol 2015; 219: 1–9.

24.

Bay

Tucker

. Stereological measurement and error estimates for three-dimensional fiber orientation. Polym Eng Sci 1992; 32: 240–253.

25.

Eberhardt

Clarke

. Fibre-orientation measurements in short-glass-fibre composites. Part I: automated, high-angular-resolution measurement by confocal microscopy. Compos Sci Technol 2001; 61: 1389–1400.

26.

Eberhardt

Clarke

Vincent

et al.

Fibre-orientation measurements in short-glass-fibre composites – II: a quantitative error estimate of the 2D image analysis technique. Compos Sci Technol 2001; 61: 1961–1974.

27.

Vélez-García

Wapperom

Baird

et al.

Unambiguous orientation in short fiber composites over small sampling area in a center-gated disk. Compos Part A Appl Sci Manuf 2012; 43: 104–113.

28.

Blanc

Germain

Baylou

et al.

Fiber orientation measurements in composite materials. Compos Part A Appl Sci Manuf 2006; 37: 197–206.

29.

Averous

Quantin

Lafon

et al.

Determination of 3D fiber orientations in reinforced thermoplastics, using scanning electron microscopy. Acta Stereol 1995; 14: 69–74.

30.

Lee

Chung

et al.

Measurement and numerical simulation of three-dimensional fiber orientation states in injection‐molded short-fiber-reinforced plastics. J Appl Polym Sci 2003; 88: 500–509.

31.

Advani

Tucker

III CL

. The use of tensors to describe and predict fiber orientation in short fiber composites. J Rheol 1987; 31: 751–784.

32.

Bay

Tucker

CL III

. Stereological measurement and error estimates for three-dimensional fiber orientation. Polym Eng Sci 1992; 32: 240–253.

33.

Hayes

Gammon

. Optical microscopy of fiber-reinforced composites, Materials Park, OH, USA: ASM international, 2010.

34.

Reinhard

Heidrich

Debevec

et al.

High Dynamic Range Imaging: acquisition, display, and image-based lighting, Burlington, MA, USA: Morgan Kaufmann, 2010.

35.

Zalevsky

. Extended depth of focus imaging: a review. J Photon Energy 2010; 1: 018001–018001.

36.

Soille

. Morphological Image Analysis: principles and applications, Secaucus, NJ, USA: Springer Science & Business Media, 2013.

37.

Mori Y, Takahashi H and Oka R. Image-to-word transformation based on dividing and vector quantizing images with words. In: First international workshop on multimedia intelligent storage and retrieval management, (MISRM), Orlando, Florida, 30 October 1999, pp.1–9.

38.

Maree R, Geurts P, Piater J, et al. Random subwindows for robust image classification. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005 CVPR 2005, San Diego, CA, USA, 20–25 June 2005, pp.34–40. Piscataway, NJ, USA: IEEE.

39.

Wang

Wiederhold

. SIMPLIcity: semantics-sensitive integrated matching for picture libraries. IEEE Trans Pattern Anal Mach Intell 2001; 23: 947–963.

40.

Mezaris V, Kompatsiaris I and Strintzis MG. An ontology approach to object-based image retrieval. In: 2003 International Conference on Image Processing, 2003 ICIP 2003 proceedings, Barcelona, Spain, 14–17 September 2003, pp.II-511–514, vol. 513. Piscataway, NJ, USA: IEEE.

41.

Chan

Vese

. Active contours without edges. IEEE Trans Image Process 2001; 10: 266–277.

42.

Tremeau

Borel

. A region growing and merging algorithm to color segmentation. Pattern Recognit 1997; 30: 1191–1203.

43.

Carson C, Belongie S, Greenspan H, et al. Blobworld: image segmentation using expectation-maximization and its application to image querying. In: IEEE Trans Pattern Anal Mach Intell 2002; 24: 1026–1038.

44.

Shi

Malik

. Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 2000; 22: 888–905.

45.

Clarke A and Eberhardt C. Microscopy Techniques for Materials, Boca Raton, Fl, USA: Science Woodhead Publishing, CRC Press, 2002.

46.

Otsu

. A threshold selection method from gray-level histograms. Automatica 1975; 11: 23–27.

47.

Roerdink

Meijster

. The watershed transform: definitions, algorithms and parallelization strategies. Fund Informat 2000; 41: 187–228.

48.

Beucher

Meyer

. The morphological approach to segmentation: the watershed transformation. Opt Eng 1992; 34: 433–433.

49.

Meyer

Beucher

. Morphological segmentation. J Vis Commun Image Represent 1990; 1: 21–46.

50.

Fitzgibbon

Pilu

Fisher

. Direct least square fitting of ellipses. IEEE Trans Pattern Anal Mach Intell 1999; 21: 476–480.

51.

Zhang

. Parameter estimation techniques: a tutorial with application to conic fitting. Image Vis Comput 1997; 15: 59–76.

52.

Jain AK. Fundamentals of digital image processing, Upper Saddle River, NJ, USA: Prentice-Hall, Inc, 1989.

53.

Nguyen

Bapanapalli

Holbery

et al.

Fiber length and orientation in long-fiber injection-molded thermoplastics – part I: modeling of microstructure and elastic properties. J Compos Mater 2008; 42: 1003–1029.

54.

Tucker

CL III

Liang

. Stiffness predictions for unidirectional short-fiber composites: review and evaluation. Compos Sci Technol 1999; 59: 655–671.

55.

Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, 1957, pp.376–396. London, UK: The Royal Society.

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