Composite Materials Research Progress

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244 Maria Pia Cavatorta and Davide Salvatore Paolino events [40]. Strictly speaking, the DD is not a damage variable but rather a point by point measurement of the laminate efficiency of energy absorption, whereas the coefficient η proposed by Liu averages the efficiency of energy absorption over a wide range of impact energies (from very low energies to Pn). E a/P n 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 GVP90_12.31 GE90s_8.00 GE90m_8.00 GE45_4.50 GE90s_4.00 GE90m_4.00 CE60_1.75 CE90_1.55 CE60_0.85 CE90_0.75 CE60_0.40 CE90_0.35 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 E i/P n Figure 3. Energy absorption Master Curve. Figure 3 plots the Master Curve proposed in [19]. Data for the three thicker laminates are again superimposed and very close to the bisector, meaning that the absorbed energy is about equal the impact energy (DD almost one). For thin laminates, the difference is more enhanced pointing out a lower efficiency of energy absorption [3]. As said, no indications can be evinced from Figures 2 and 3 in terms of laminate damage tolerance. In this respect, definition of the DuI, which differentiates between the nature of energy absorption mechanisms, appears rather appealing. In its original definition, the DuI is meant to rank different laminates tested under similar impact conditions, on the basis of a more fragile or more ductile behavior under impact loading. It is worthwhile noticing that in the literature the DuI is basically used to rank different laminates at perforation or fracture (Charpy tests), for which determination of Einitiation and Epropagation poses no trouble. The forcedisplacement curves are open curves and Einitiation is calculated without ambiguity as the area bounded by the force-displacement curve up to Fpeak and the horizontal axis, while Epropagation is calculated as the area bounded by the force-displacement curve from Fpeak to a constant level of force and the horizontal axis (Figure 4a). In the attempt of proving the DuI against other damage variables, computation of the DuI was also applied to impact tests with rebound. When the dart rebounds, the force-displacement curves are closed curves and computation of Einitiation and Epropagation becomes troublesome as different areas could be considered. No references of DuI computation in impact tests with rebound were found in the literature. Considering that in impact events with rebound the energy absorbed by the laminate is equal to the area bounded by the force-displacement curve, in computing the DuI
Damage Variables in Impact Testing of <strong>Composite</strong> Laminates 245 it was decided to calculate Einitiation as the area bounded by the force-displacement curve up to Fpeak and Epropagation as the area bounded by the force-displacement curve after Fpeak so that the sum of the two energies is equal to the overall energy absorbed by the laminate (Figure 4b). In this way, only the portion of impact energy in fact dissipated by the laminate was taken into account and differentiated by the nature of energy absorption mechanisms. Force [kN] 12 10 8 6 4 2 0 Initiation Energy F peak 0 5 10 15 20 25 Displacement [mm] Propagation Energy Figure 4a. An example of force-displacement curve with perforation: filled areas correspond to E initiation (Initiation Energy) and Epropagation (Propagation Energy). Force [kN] 30 25 20 15 10 5 0 Initiation Energy 0 2 4 6 8 10 Displacement [mm] F peak Propagation Energy Figure 4b. An example of force-displacement curve with rebound: filled areas correspond to E initiation (Initiation Energy) and Epropagation (Propagation Energy).
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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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In: Composite Materials Research Pr
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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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110 W.H. Zhong, R.G. Maguire, S.S.
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112 Reinforcement: Advanced materia
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130 Yuanxin Zhou, Hassan Mahfuz, Vi
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140 Heat Flow (W/g) Heat Flow (W/g)
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144 Material Yuanxin Zhou, Hassan M
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146 SEM Analysis Yuanxin Zhou, Hass
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150 Governing Equation For the fibe
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152 ⎧ UU = ⎨ ⎩ ⎧ UD = ⎨
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156 Stress (MPa) 120 80 40 0 Yuanxi
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166 Giangiacomo Minak and Andrea Zu
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170 ⎟ ⎞ ⎠ s ⎜ ⎛ ⎝ = a E
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188 A B E (MPa) D 250000 200000 150
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190 D D 1.0 0.9 0.8 0.7 0.6 0.5 0.4
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Page 208 and 209: 194 Giangiacomo Minak and Andrea Zu
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Page 225 and 226: Research Directions in the Fatigue
Page 241 and 242: Bending force [N] Research Directio
Page 253 and 254: Damage Variables in Impact Testing
Page 257: Damage Variables in Impact Testing
Page 263 and 264: F peak [kN] 16 14 12 10 8 6 4 2 0 D
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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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