Composite Materials Research Progress

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152 ⎧ UU = ⎨ ⎩ ⎧ UD = ⎨ ⎩ C1 C 2 C3 ⎧ = ⎨ ⎩ ⎧ = ⎨ ⎩ * τ / + 1, k i i j 0 * τ −1/ , k i i j 1 2 1 0 0. 75 ⎧0 ⎪ = ⎨1 ⎪ ⎩2 Yuanxin Zhou, Hassan Mahfuz, Vijaya Rangari et al. element (i,j)~(i,j+1) unbroken element (i,j)~(i,j+1) broken interface (i,j)~(i+1,j) unbroken interface (i,j)~(i+1,j) broken interface (i-1,j)~(i,j) unbroken interface (i-1,j)~(i,j) broken element broken no element broken element broken no element broken both side matrix broken single side matrix brokes no matrix broken C 4 C 5 1 i ≠ 1 = ⎨⎧ ⎩0 i = 1 1 i ≠ n = ⎨⎧ ⎩0 i = n Using the successive over-relaxation, we have [ ] [ ] ( )[ ] 1 k q k q k q− U = U + 1− λ U i, j λ (15) i, j where, λ is the relaxation factor, which controls the convergence speed of solution, and q is the times of iteration. k k i, j U i, j is the right side of Equation (14). After U i, j is obtained, the stress of the segment of fiber and matrix can be calculated from following expression:
An Experimental and Analytical Study of Unidirectional Carbon Fiber… 153 For fiber element: For matrix element U i+ 1, j −U i, j σ i, j = E f (16a) X U i+ 1, j −U i, j σ i, j = Em (16b) X The strain and stress of composites were calculated from average stress of all elements. c n m n m 1 ⎡ ⎤ = × ( ) ( ) ⎢∑∑σ 2i+ 1, j 1− V f + ∑∑σ 2i, jV f 2N + 1 M ⎥ ⎣ i−0 1 1 1 ⎦ σ (17) Strength of Fiber Element and the Failure Criterion VKΔt ε c = (18) L Strength assignment to the fiber elements In simulating, the strength of the fiber elements should be predetermined. According to the Weibull statistical constitutive model the strength of the fiber follow Equation (4). If we assume L in Equation (4) equal to mesh length Δx, here σΔx can be obtained from the scale parameter σ0 at experimental length Lo. n×m random array ηi,j, equally distributed in the range of (0,1), are produced by the computer, and we let η i, j β ⎡ Δx ⎛ S ⎤ i, j ⎞ = P ( Δx, S ) = ⎢− ⎜ ⎟ i, j exp ⎥ (19) ⎢ L0 ⎣ ⎝ σ 0 ⎠ ⎥ ⎦ From the Equation (19), we can get the strength of fiber element The failure criterion The failure criterion of fiber is i, j ≥ S i, j 1 i, j ⎡ L0 = − ln j σ ⎤ β ( ηi, ) 0 S ⎢ ⎥ (20) ⎣ Δx ⎦ σ fiber element broken (21a)
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COMPOSITE MATERIALS RESEARCH PROGRE
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Copyright © 2008 by Nova Science P
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vi Contents Chapter 9 Recent Advanc
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viii Lucas P. Durand scale transiti
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x Lucas P. Durand machine. In paral
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In: Composite Materials Research Pr
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Multi-scale Analysis of Fiber-Reinf
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T300 fibers (Soden et al., 1998; Ag
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1 I L = L : r v Multi-scale Analysi
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I E ⎡0 ⎢ ⎢0 ⎢ ⎢ ⎢ ⎢0
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Applied macroscopic load Correspond
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Optimization of Laminated Composite
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⎧σ x ⎫ ⎡ mE ⎪ ⎪ ⎢ x
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and γ 2 γ 0 Optimization of Lamin
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4 x 10 5 4 3 2 1 Compliance (Nmm) 0
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3.5 3 2.5 2 1.5 1 Optimization of L
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Page 115 and 116: Optimization of Laminated Composite
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Page 124 and 125: 110 W.H. Zhong, R.G. Maguire, S.S.
Page 126 and 127: 112 Reinforcement: Advanced materia
Page 144 and 145: 130 Yuanxin Zhou, Hassan Mahfuz, Vi
Page 154 and 155: 140 Heat Flow (W/g) Heat Flow (W/g)
Page 158 and 159: 144 Material Yuanxin Zhou, Hassan M
Page 160 and 161: 146 SEM Analysis Yuanxin Zhou, Hass
Page 164 and 165: 150 Governing Equation For the fibe
Page 170 and 171: 156 Stress (MPa) 120 80 40 0 Yuanxi
Page 180 and 181: 166 Giangiacomo Minak and Andrea Zu
Page 184 and 185: 170 ⎟ ⎞ ⎠ s ⎜ ⎛ ⎝ = a E
Page 202 and 203: 188 A B E (MPa) D 250000 200000 150
Page 204 and 205: 190 D D 1.0 0.9 0.8 0.7 0.6 0.5 0.4
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202 Giangiacomo Minak and Andrea Zu
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204 Conclusion Giangiacomo Minak an
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206 Giangiacomo Minak and Andrea Zu
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Research Directions in the Fatigue
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Bending force [N] Research Directio
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Damage Variables in Impact Testing
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F peak [kN] 16 14 12 10 8 6 4 2 0 D
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Eletromechanical Field Concentratio
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MV/m. Eletromechanical Field Concen
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276 S.C. Tjong developed in the pas
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278 S.C. Tjong ultrasonic waves gen
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280 S.C. Tjong applications. Goujon
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282 S.C. Tjong nanoparticles were p
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284 S.C. Tjong where DL is lattice
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286 S.C. Tjong stress is temperatur
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288 S.C. Tjong threshold stress res
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290 S.C. Tjong NC Al, and the NC Al
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292 S.C. Tjong (a) (b) Figure 19. T
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294 S.C. Tjong Apart from forming u
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296 S.C. Tjong [29] Saravanan, M.;
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298 braids, 115 broadband, 211 bubb
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300 endothermic, 139 endurance, 32
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302 isostatic pressing, 279, 288 It
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304 piezoelectricity, 261 pitch, 12
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306 67, 69, 70, 71, 72, 73, 84, 94,
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Composite Materials Research Progress

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