Introduction to composites - fibers

1. Figures taken from: P.K. Mallick. Fiber-Reinforced Composites, Materials, manufacturing, and design. 3rd Ed., CRC Press. 2008 Introduction to composites - fibers CME/MSE 404G. Polymeric Materials Fall 2012 fibers

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9. Properties of commercial fibersaverage values from manufacturers fibers

10. Fibers: 2012references; new research on fibers for composites fibers

11. In-class exercise fibers

12. Each team is to find composites applications for their fibers assignments fibers

13. Team responses fibers

14. Fiber bundles Typical fibers have very small diameters, so that fiber bundles are used for ease of handling. Untwisted = strand, end (glass & Kevlar fibers); =tow (carbon fibers) Twisted = yarn fibers

15. Single fiber test • ASTM D3379 - ASTM D3379-75(1989)e1 Standard Test Method for Tensile Strength and Young's Modulus for High-Modulus Single-Filament Materials (Withdrawn 1998) • A single filament is mounted along the centerline of a slotted tab using adhesive at each end • The tab ends are gripped in the tensile machine and the midsection is cut • Constant loading rate until failure fibers

16. Single fiber mounting for tensile test fibers

17. Tensile property determinations • Definitions • Fu – force at failure • Af = average filament cross-sectional area (planimeter measurement via photos of filament ends • Lf = gage length • C = true compliance (via loading rate) Tensile strength Tensile modulus fibers

18. Typical tensile strengths of fibers Typical fibers have high strength, high orientation Stress-strain curves are nearly linear up to failure Most fail brittlely Most fibers are prone to damage with handling and with contact to other surfaces fibers

19. Model for fiber tensile strengths fibers

20. Model application fibers

21. Typical applications: Weibull distribution • Time to failure: failure rate is proportional to time raised to the nth power, k=n+1 • Cases • 0 < k < 1: failure rate decreases with time. Example = infant mortality or early failure of electrical circuits • k = 1: failure rate is constant over time. Example = random external events • k > 1: failure rate increases with time. Example = aging process fibers

22. Weibull: probability density In-class question: Interpret each curve with respect to a time-to-failure data set. Hint: the integral of each curve = 1. fibers

23. Weibull: cumulative distribution In-class question: Interpret each curve with respect to a time-to-failure data set. Hint: the upper limit of each curve = 1. fibers

24. Failure rates fibers

25. Quantile plots fibers

26. Figure 2.4 fibers

27. Example data: failure strength at a given fiber length fibers

28. Weibull distribution fibers

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30. Quantile plots fibers

31. Problem 2.5. Mallick • MSE 599 P2_5.xlsx fibers

32. Analysis of flaws in high-strength carbon fibres from mesophase pitch Janice Breedon Jones, John Barr, Robert Smith, J. Materials Sci., 14, (1980), 2455-2465 fibers

33. Data taken at two guage lengths, 20 mm and 3.2 mm fibers

34. Effect of gauge length on strengthwhy should there be an effect? fibers

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39. Single mode of failure should show similar Weibull plot slopes Similar slope suggests the same failure modes for each gauge length fibers

40. Extrapolate to 0.3 mm lengthexpected load transfer length for multifilament fibres of this diameter (3.8 Gpa) If the failure mechanisms are similar, we can extrapolate the tensile strength to shorter gauge lengths, estimating the tensile strength for lengths that are difficult to measure experimentally. fibers

41. Flaw strength distributions and statistical parameters for ceramic fibers: the normal distribution M. R’Mili, N. Godin, J. Lamon, Phys. Rev. E, 85, 051106 (2012) Large sets of ceramic fibre failure strengths from tows of 500 – 1000 filaments Flaws generated by ultrasonic Flaw strengths are distributed normally fibers

42. SiC-based Nicalon filaments fibers

43. Quasi-linear regressionfailure of fiber tows For probabilities less than 4%, there is an under-estimate of the number of first failures. This is likely due to the detection of low energy events near the filtering threshold. This is probably not a bimodal distribution of flaws. fibers

44. Comparison of model and fiber failure data Very good indeed. fibers

45. General effect of aspect ratio on tensile strength fibers

46. Dry glass bundle. 3000 filaments Single filament shows a linear stress-strain curve. Bundle shows a nonlinear stress-strain curve prior to maximum stress, and progressive failure after maximum stress. Both effects are due to statistical distribution of the filament strengths. Some fail as the load increase. After the maximum stress, highly loaded fibers continue to fail, but not all at once fibers

47. Fiber production Glass fibers fibers

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49. Types of glass fiberstensile strength = 3.45 GPa; surface flaws reduce this to 1.72 GPa • Continuous strand roving [strand = parallel filaments, n > 204] • Woven roving [roving = group of untwisted strans/ends wound on a cylindrical forming package] • Chopped strands – continuous strands cut to specific lengths; 3.2 – 12.7 for injection molding • Chopped strand mats - 50.8 mm for chopped strand mats • Woven roving mat • Milled glass fibers, 0.79 to 3.2 mm; plastic fillers fibers

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