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
59 5.4 Boundary Conditions There are several basic assumptions that are common to all of the methods, which are given in the previous chapter. In addition, the boundary conditions used in the finite element analyses are as follows: • Along the planes x, y, and z = 0, the model is restricted to move in the x, y, and z directions respectively. • The boundary planes x, y, and z = l 0 are free to move but have to remain planar in a parallel way for preserving the compatibility with adjacent cells. 5.5 Solution The deformation in the unit cell is caused by a temperature increase of ∆T. During the deformation; x, y, and z = l 0 become, x, y, and z = l respectively and the displacement, ∆l, is determined from the analysis. The CTE of the composite for the direction i is then found using α i ∆l 1 = (5.1) l ∆T 0 For an easier solution, edge of the representative unit cell is taken as unity and also the temperature increase is taken as unity. Then CTE of the composite for the required direction becomes the displacement of the unit cell for that direction. The displacement fields for the unit cell having a fiber volume fraction of 48% is given in Figure 5.6 and Figure 5.7.
60 Figure 5.6 The displacement field in the longitudinal direction for the unit cell having a fiber volume fraction of 48%. Figure 5.7 The displacement field in the transverse direction for the unit cell having a fiber volume fraction of 48%.
- 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
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- 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
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- 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 65 and 66: 56 5.2 Mesh Creation 10-node tetrah
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- 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
60<br />
Figure 5.6 The displacement field in <strong>the</strong> l<strong>on</strong>gitudinal directi<strong>on</strong> for <strong>the</strong> unit cell having a <strong>fiber</strong> volume<br />
fracti<strong>on</strong> <strong>of</strong> 48%.<br />
Figure 5.7 The displacement field in <strong>the</strong> transverse directi<strong>on</strong> for <strong>the</strong> unit cell having a <strong>fiber</strong> volume<br />
fracti<strong>on</strong> <strong>of</strong> 48%.
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