Composite Materials Research Progress

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224 W. Van Paepegem, I. De Baere, E. Lamkanfi et al. The following equation was derived, with μij the coefficient of friction between parts i and j (i,j=A,B,C): F cosα −μBCsin α (1 −μACμBC)cos α −( μBC −μAC )sinα P= + RA 2 sinα + μ cosα sinα + μ cosα BC BC For both grips displayed in Figure 16, the angle α is set equal to 10 degrees. In [45] it was shown that the grips in Figure 17 can be replaced by their equivalent contact pressure, calculated from Equation (1), because the simulated contact pressure with the finite element model of Figure 17 perfectly corresponds with the analytically calculated contact pressure. Next a detailed finite element model of the end tab region has been developed. Figure 19 shows the model of this setup, both mesh and boundary conditions are illustrated. The specimen is meshed using C3D20R elements using a global element size of 2 mm. Where stress concentrations were expected, the element size was reduced to 0.5 mm. The thickness of the specimen was 2.4 mm, which is also the thickness of the tabs, as has already been mentioned. The material properties for the composite specimen are given in Table 1. For the boundary conditions, the displacement along the 1 and 2 axis was inhibited for planes B1 (on top) and B2 (at the bottom), simulating the ‘rough’ boundary condition from the previous paragraph. Since contraction of the specimen is possible in the 3-direction due to the Poisson effect, the movement along the 3-axis was allowed for both planes. In order to prevent movement of the entire sample along the 3 axis, the central line of plane C (at the back) was fixed. Figure 19. Illustration of the model for the end tab region [45]. Two time steps were modelled. In the first, the contact pressure p, calculated from Equation (1), was imposed. In the second, a tensile stress of 600 MPa was applied on surface A. The exact value of the stress does not matter, since the stress concentration factors are compared. (1)
<strong>Research</strong> Directions in the Fatigue Testing of Polymer <strong>Composite</strong>s 225 In that way, a detailed analysis of the stress concentration factors in the end tab region was studied for several clamping conditions and end tab geometries. Detailed results can be found in [45]. 4.2. Friction in Single-Sided 3-Point Bending Fatigue In uni-axial fatigue tests on fibre-reinforced composites, the stress-strain hysteresis loop can be used as a measure for stiffness degradation and energy dissipation. In case of three-point bending fatigue tests, the hysteresis loop of the bending force versus midspan displacement can yield similar information. In this numerical study, it is shown that the shape of the hysteresis loop can be affected significantly by friction at the supports, especially for large deflections. As such, the area of the closed hysteresis loop is no longer a measure for energy dissipation and damage growth. Figure 20 shows typical hysteresis loops of the bending force versus midspan deflection at several times during fatigue life for the [90°/0°]2s carbon/PPS laminate. The amplitude of the midspan deflection was 14.5 mm and the testing frequency was 2.0 Hz. The hysteresis loops are gone through in clockwise direction (loading – unloading). The problem treated here, is the typical shape of the hysteresis curve. One would expect that the dissipated energy during such a hysteresis cycle is used for initiation and propagation of microscopic fatigue damage, but in the case of this material, ultrasonic C-scans could not detect any significant fatigue damage in the specimens (apart from the last stage in fatigue life). Therefore it was assumed that the effect could be induced by friction at the supports, given the very large midspan displacements for a short span length. Bending force [N] Typical hysteresis curves in bending for [90°/0°] 2s carbon/PPS laminate 700 600 500 400 300 200 100 Cycle 1 Cycle 80 000 Cycle 160 000 Cycle 191 000 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Deflection [mm] Figure 20. Typical hysteresis curves in bending for [90°/0°] 2s carbon/PPS laminate.
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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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Page 188 and 189: 174 Giangiacomo Minak and Andrea Zu
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Page 218 and 219: 204 Conclusion Giangiacomo Minak an
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Page 225 and 226: Research Directions in the Fatigue
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Page 241 and 242: Bending force [N] Research Directio
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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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