Composite Materials Research Progress

More documents

Recommendations

Info

154 Yuanxin Zhou, Hassan Mahfuz, Vijaya Rangari et al. σ fiber element unbroken (21b) i, j ≤ S i, j The failure criterion of interface is τ ≥ τ i, j m interface broken (22a) τ ≤ τ i, j m interface unbroken (22b) where, τm is the ultimate shear stress of matrix. The failure criterion of matrix is ε ≥ ε i, j m matrix element broken (23a) ε ≤ ε i, j m matrix element unbroken (23b) where, εm is the failure strain of the matrix Simulation Procedure Based on the above numerical constitutive model, a computational program is compiled to simulate the microscopic dynamic failure process of unidirectional composites. The simulation procedure is illustrated as following: (A) Randomly assign a statistical strength Si,j (i=2,4,...2n, J=1,2,…m) to the fiber element, definitely assign the tensile strength to the matrix and the shear strength to the interface. (B) Solve Equation (14) by iteration formula (15) using Ui,j k−1 , Ui,j k−2 and the boundary conditon at time t=kΔt, obtain the displacement field Ui,j k (i=1,2,...2n+1,j=1,2,...m). (C) Determine whether the element or the interface breakage (or the matrix element unloading) has happened, if new breakage occurs, take the breakage into account and repeat steps (B) and (C) until no new breakage occurs, else calculate the apparent stress σc and strain εc using Equation (17) and (18). (D) Increase a time step and repeat step (B) and (C) till the composites failure happens. Here the "composites failure" is defined as the state when the stress σc drops from σmax to about 50% of σmax. Experimental Results of Fiber, Matrix and <strong>Composite</strong> The statistical parameters of fiber were obtained from tension tests of T700 fiber bundles. The tensile stress-strain curve of fiber bundle in Figure 22 shows considerable amount of nonlinearity. The specimen failed gradually after reaching the maximum stress due to the tensile strength distribution of fibers. Three parameters were determined from each stress-strain
An Experimental and Analytical Study of Unidirectional Carbon Fiber… 155 curve: elastic modulus (E), tensile strength ( σ b ), and failure strain ( ε b ). Elastic modulus or Young's modulus is the initial slope of the stress-strain curve. Tensile strength is the maximum stress at the peak load and the strain corresponding to the tensile strength is the failure strain. The average values of these three properties are: E = 210GPa σ = 1. 93GPa ε = 1. 07% b Based on fiber bundles model and statistical theory of fiber strength [34], the Weibull parameters for tensile strength of carbon fibers also can be obatined: Stress (GPa) 2.00 1.60 1.20 0.80 0.40 0.00 σ 2. 70GPa β = 9. 03 L 100mm 0 = T700 Carbon Fiber Experimental Results Simulated Results 0.000 0.005 0.010 0.015 0.020 Strain Figure 22. Stress strain curve of carbon fiber. b 0 =
Page 3:
COMPOSITE MATERIALS RESEARCH PROGRE
Page 6 and 7:
Copyright © 2008 by Nova Science P
Page 8 and 9:
vi Contents Chapter 9 Recent Advanc
Page 10 and 11:
viii Lucas P. Durand scale transiti
Page 12 and 13:
x Lucas P. Durand machine. In paral
Page 15 and 16:
In: Composite Materials Research Pr
Page 17 and 18:
Multi-scale Analysis of Fiber-Reinf
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
T300 fibers (Soden et al., 1998; Ag
Page 27 and 28:
Page 29 and 30:
1 I L = L : r v Multi-scale Analysi
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
I E ⎡0 ⎢ ⎢0 ⎢ ⎢ ⎢ ⎢0
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Applied macroscopic load Correspond
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Optimization of Laminated Composite
Page 69 and 70:
Page 71 and 72:
⎧σ x ⎫ ⎡ mE ⎪ ⎪ ⎢ x
Page 73 and 74:
and γ 2 γ 0 Optimization of Lamin
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
4 x 10 5 4 3 2 1 Compliance (Nmm) 0
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
3.5 3 2.5 2 1.5 1 Optimization of L
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118: Optimization of Laminated Composite
Page 119 and 120: Optimization of Laminated Composite
Page 121: Optimization of Laminated Composite
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 166 and 167: 152 ⎧ UU = ⎨ ⎩ ⎧ UD = ⎨
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
Page 218 and 219:
204 Conclusion Giangiacomo Minak an
Page 220 and 221:
206 Giangiacomo Minak and Andrea Zu
Page 223 and 224:
Page 225 and 226:
Research Directions in the Fatigue
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Bending force [N] Research Directio
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Damage Variables in Impact Testing
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
F peak [kN] 16 14 12 10 8 6 4 2 0 D
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Eletromechanical Field Concentratio
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
MV/m. Eletromechanical Field Concen
Page 285 and 286:
Page 287:
Page 290 and 291:
276 S.C. Tjong developed in the pas
Page 292 and 293:
278 S.C. Tjong ultrasonic waves gen
Page 294 and 295:
280 S.C. Tjong applications. Goujon
Page 296 and 297:
282 S.C. Tjong nanoparticles were p
Page 298 and 299:
284 S.C. Tjong where DL is lattice
Page 300 and 301:
286 S.C. Tjong stress is temperatur
Page 302 and 303:
288 S.C. Tjong threshold stress res
Page 304 and 305:
290 S.C. Tjong NC Al, and the NC Al
Page 306 and 307:
292 S.C. Tjong (a) (b) Figure 19. T
Page 308 and 309:
294 S.C. Tjong Apart from forming u
Page 310 and 311:
296 S.C. Tjong [29] Saravanan, M.;
Page 312 and 313:
298 braids, 115 broadband, 211 bubb
Page 314 and 315:
300 endothermic, 139 endurance, 32
Page 316 and 317:
302 isostatic pressing, 279, 288 It
Page 318 and 319:
304 piezoelectricity, 261 pitch, 12
Page 320 and 321:
306 67, 69, 70, 71, 72, 73, 84, 94,
show all

Composite Materials Research Progress

Create successful ePaper yourself

Delete template?

Save as template?