A numerical study on the thermal expansion coefficients of fiber
A numerical study on the thermal expansion coefficients of fiber A numerical study on the thermal expansion coefficients of fiber
57 Figure 5.4 A representative meshed unit cell having a fiber volume fraction equal to 68%. Mesh refinement is performed until the changes in the results are sufficiently small. A representative meshed unit cell having 12678 elements and 19046 nodes is shown in Figure 5.4, and the mesh on the fiber matrix interface is shown in Figure 5.5. Figure 5.5 The finite element mesh on the fiber matrix interface for fiber volume fraction of 68%. 5.3 Material Properties The constituent property data used in the analyses are given in Tables 5.1, 5.2, and 5.3. The data in Table 5.1 is taken from the investigation of Sideridis (1994). The unidirectional glass fiber composites used in his investigation consisted of an epoxy matrix (permaglass XE5/1, Permali Ltd, UK) reinforced with long E-glass fibers having a diameter of 0.012 mm. The properties of transversely isotropic carbon fibers and other isotropic matrix materials are taken from the
58 carbon fibers were assumed to have same properties. All of the epoxies were assumed to have same properties except CE339, which has a larger CTE. This larger value of CTE is due to the rubber particles in this rubber toughened epoxy. Table 5.1 Material properties, at room temperature, used for the composite consisting of isotropic glass fibers and isotropic epoxy matrix (Sideridis, 1994). Material E (GPa) G (GPa) ν α (10 -6 /ºC) Epoxy 3.5 3.89 0.35 52.5 Glass fiber 72 40 0.2 5 Table 5.2 Matrix properties at room temperature (Bowles, & Tompkins, 1989). Matris E (GPa) G (GPa) ν α (10 -6 /ºC) 934 epoxy 4.35 1.59 0.37 43.92 5208 epoxy 4.35 1.59 0.37 43.92 930 epoxy 4.35 1.59 0.37 43.92 CE339 epoxy 4.35 1.59 0.37 63.36 PMR15 polymide 3.45 1.31 0.35 36 2024 Aluminum 73.11 27.58 0.33 23.22 Borosilicate glass 62.76 26.20 0.20 3.24 Table 5.3 Carbon fiber properties at room temperature (Bowles, & Tompkins, 1989). Fiber E 1 (GPa) E 2 (GPa) G 1 (GPa) G 2 (GPa) ν 1 ν 2 α 1 (10 -6 /ºC) α 2 (10 -6 /ºC) T300 233.13 23.11 8.97 8.28 0.2 0.4 − 0.54 10.08 C6000 233.13 23.11 8.97 8.28 0.2 0.4 − 0.54 10.08 HMS 379.35 6.21 7.59 2.21 0.2 0.4 − 0.99 6.84 P75 550.40 9.52 6.9 3.38 0.2 0.4 − 1.35 6.84 P100 796.63 7.24 6.9 2.62 0.2 0.4 − 1.40 6.84
- Page 15 and 16: 6 concentration from pure metal to
- Page 17 and 18: 8 high strength-to-weight and stiff
- Page 19 and 20: 10 polymers. Thermosetting polymers
- Page 21 and 22: 12 Metals are strong and tough. The
- Page 23 and 24: 14 Table 2.1 Properties of reinforc
- Page 25 and 26: 16 2.2.2.2 Carbon Fibers Carbon is
- Page 27 and 28: 18 use is in aircraft industry foll
- Page 29 and 30: 20 strength and a reasonable Young
- Page 31 and 32: 22 1. Processing the conventional f
- Page 33 and 34: 24 (orthorhombic) of polyethylene h
- Page 35 and 36: 26 Whiskers are monocrystalline sho
- Page 37 and 38: 28 3.2 Factors Affecting the Coeffi
- Page 39 and 40: 30 3.2.4 Thermal Cycling The primar
- Page 41 and 42: 32 3.3.1 Mechanical Dilatometry Thi
- Page 43 and 44: 34 absolute accuracy of about ± 0.
- Page 45 and 46: 36 3.3.3 Strain Gauges This relativ
- Page 47 and 48: 38 • The composite is macroscopic
- Page 49 and 50: 40 3.4.1.3 Equation of Van Fo Fy In
- Page 51 and 52: 42 and the thermal expansion coeffi
- Page 53 and 54: 44 P P 11 33 2 A 22 − A = Det A A
- Page 55 and 56: 46 • A perfect bonding exists at
- Page 57 and 58: CHAPTER FOUR FINITE ELEMENT METHOD
- Page 59 and 60: 50 No matter how the geometry is cr
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- Page 63 and 64: CHAPTER FIVE MICROMECHANICAL ANALYS
- Page 65: 56 5.2 Mesh Creation 10-node tetrah
- Page 69 and 70: 60 Figure 5.6 The displacement fiel
- Page 71 and 72: 62 small differences between these
- Page 73 and 74: 64 Table 6.1 Comparison of the expe
- Page 75 and 76: 66 Longitudinal CTE (1/°C) 2.25E-0
- Page 77 and 78: 68 Longitudinal CTE (1/°C) 2.00E-0
- Page 79 and 80: 70 Longitudinal CTE (1/°C) 4.00E-0
- Page 81 and 82: 72 Longitudinal CTE (1/°C) 1.00E-0
- Page 83 and 84: 74 Ishikava, T., Koyama, K., & Koba
57<br />
Figure 5.4 A representative meshed unit cell having a <strong>fiber</strong> volume fracti<strong>on</strong> equal to 68%.<br />
Mesh refinement is performed until <strong>the</strong> changes in <strong>the</strong> results are sufficiently<br />
small. A representative meshed unit cell having 12678 elements and 19046 nodes is<br />
shown in Figure 5.4, and <strong>the</strong> mesh <strong>on</strong> <strong>the</strong> <strong>fiber</strong> matrix interface is shown in Figure<br />
5.5.<br />
Figure 5.5 The finite element mesh <strong>on</strong> <strong>the</strong> <strong>fiber</strong> matrix interface for <strong>fiber</strong> volume fracti<strong>on</strong> <strong>of</strong> 68%.<br />
5.3 Material Properties<br />
The c<strong>on</strong>stituent property data used in <strong>the</strong> analyses are given in Tables 5.1, 5.2,<br />
and 5.3. The data in Table 5.1 is taken from <strong>the</strong> investigati<strong>on</strong> <strong>of</strong> Sideridis (1994). The<br />
unidirecti<strong>on</strong>al glass <strong>fiber</strong> composites used in his investigati<strong>on</strong> c<strong>on</strong>sisted <strong>of</strong> an epoxy<br />
matrix (permaglass XE5/1, Permali Ltd, UK) reinforced with l<strong>on</strong>g E-glass <strong>fiber</strong>s<br />
having a diameter <strong>of</strong> 0.012 mm. The properties <strong>of</strong> transversely isotropic carb<strong>on</strong><br />
<strong>fiber</strong>s and o<strong>the</strong>r isotropic matrix materials are taken from <strong>the</strong> <str<strong>on</strong>g>study</str<strong>on</strong>g> <strong>of</strong> Bowles and<br />
Tompkins (1989). The c<strong>on</strong>stituent properties used in <strong>the</strong>ir analyses are given in Table<br />
5.2 and 5.3. Some <strong>of</strong> <strong>the</strong>se data was experimentally measured values and were taken<br />
from various literature sources which include both research papers and<br />
manufacturers’ product data sheets. However, many <strong>of</strong> <strong>the</strong> transverse <strong>fiber</strong> properties<br />
represent values that were calculated from composite properties. T300 and C6000
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