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
53 used to make the measurement and there is no methodology available to generalize the measurement for use in complex geometries. 4.2.5 Displaying Results After the analyst has defined geometry, element, and node discretization, boundary conditions, loads, and material constitutive relationships, the finite-element code can assemble the equilibrium equations governing the structure. These equations can vary from hundreds to thousands for typical problems. The finiteelement code solves this system of equations. As a result of this solution, a massive amount of information is computed displacements of all nodes and stresses, strains, temperatures, heat fluxes etc. in all elements. Fortunately, this information can be displayed with advanced graphics techniques as constant-stress contours or with a color-coded representation of the particular stress range of interest. These results can then be assessed in terms of engineering performance requirements. In order to judge whether failure will occur, material data defining failure limits in terms of stress or strain are generally required.
CHAPTER FIVE MICROMECHANICAL ANALYSIS BY ANSYS 5.1 Model Development In the present work, the effective coefficient of thermal expansion (CTE) of different kinds of fiber reinforced composites is studied by micromechanical modeling using finite element method. To determine the both longitudinal and transverse CTEs of composites, three dimensional steady state analyses were undertaken. Representative unit cell models for different fiber volume fractions and different kind of materials were produced using finite element program ANSYS. The representative unit cell used for the current analysis is a cylinder which is embedded in a cube with unit dimension. Fibers are assumed to have a square packing arrangement. The radius of the cylinder is determined with respect to fiber volume fraction of the composite. Figure 5.1 shows the unit cell considered in the micromechanical analysis. Using the advantage of symmetry, only an octant of the unit cell, indicated in Figure 5.2, is modeled to describe the behavior of the unit cell and of an entire continuum of unit cells for the finite element analysis. To compare the results of finite element solutions for different types of composites with the results of the analytical methods and to determine the expansion behavior of different material systems with respect to fiber content, models having fiber volume fractions from 10% to 80% with increments of 10% have been composed. Furthermore, comparison between finite element solutions and experimental results have been made upon the models having 40%, 47%, 48%, 54%, 57%, 63%, 65%, and 68% fiber volume fractions. 54
- Page 11 and 12: 2 coefficients of thermal expansion
- Page 13 and 14: 4 coefficients coincide to give res
- 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
- Page 61: 52 displacements and/or rotations a
- Page 65 and 66: 56 5.2 Mesh Creation 10-node tetrah
- Page 67 and 68: 58 carbon fibers were assumed to ha
- 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
53<br />
used to make <strong>the</strong> measurement and <strong>the</strong>re is no methodology available to generalize<br />
<strong>the</strong> measurement for use in complex geometries.<br />
4.2.5 Displaying Results<br />
After <strong>the</strong> analyst has defined geometry, element, and node discretizati<strong>on</strong>,<br />
boundary c<strong>on</strong>diti<strong>on</strong>s, loads, and material c<strong>on</strong>stitutive relati<strong>on</strong>ships, <strong>the</strong> finite-element<br />
code can assemble <strong>the</strong> equilibrium equati<strong>on</strong>s governing <strong>the</strong> structure. These<br />
equati<strong>on</strong>s can vary from hundreds to thousands for typical problems. The finiteelement<br />
code solves this system <strong>of</strong> equati<strong>on</strong>s. As a result <strong>of</strong> this soluti<strong>on</strong>, a massive<br />
amount <strong>of</strong> informati<strong>on</strong> is computed displacements <strong>of</strong> all nodes and stresses, strains,<br />
temperatures, heat fluxes etc. in all elements. Fortunately, this informati<strong>on</strong> can be<br />
displayed with advanced graphics techniques as c<strong>on</strong>stant-stress c<strong>on</strong>tours or with a<br />
color-coded representati<strong>on</strong> <strong>of</strong> <strong>the</strong> particular stress range <strong>of</strong> interest. These results can<br />
<strong>the</strong>n be assessed in terms <strong>of</strong> engineering performance requirements. In order to judge<br />
whe<strong>the</strong>r failure will occur, material data defining failure limits in terms <strong>of</strong> stress or<br />
strain are generally required.
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