4 Conclusions - POLYTECH - ETH Zürich

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1.00.8Eθ/ E l(-)0.60.4G lt0.20.00 15 30 45 60 75 90θ (°)FIGURE 5 Normalized off-axis Young’s modulus, E θ /E l , calculated with E l = 130 GPa (that of atypical foil described in Chapter II), E t = 2 GPa, v lt = 0.4 and values of the shear modulus, G lt , of,resp. , 0.1, 1, and 10 GPa.To reduce the anisotropic properties of the foils, it is common practice to stackdifferently oriented foils, and bind them together to form a laminate. The stiffness ofsuch multi-foil laminates is described by classical lamination theory. Assuming thatthe in-plane strains in all foils are equal and that all foils have the same thickness, theelastic behavior of the laminate follows from the average value of the stiffness tensor,taking into account for each foil the mismatch between the loading and longitudinaldirection. Analogous to the case of a single foil, the Young’s modulus of the laminateas a function of loading angle then follows from the average compliance tensor, whichis the inverse of the average stiffness tensor, albeit not resulting in a simple relation asEquation 1. In general, not surprisingly, the anisotropy of the laminate is reduced withincreasing number of differently oriented foils and may even vanish. This is depictedin Figure 6, which shows the angular dependence of the Young’s modulus of a singlefoil, a [0/ 90], [0/ 60/ 120] and [0/ 45/ 90/ 135] laminate. In this figure, it can beobserved that the in-plane Young’s modulus for the latter two laminates is independentof the loading direction, and such laminates are, therefore, referred to as “quasiisotropic”.The general lay-up that leads to quasi-isotropic laminates is⎡ 180 180 ⎤⎢0/ / /( m − 1)⎣ mm ⎥⎦, where m is the number of different orientations in thelaminate, with m ≥ 3. For all these laminates the in-plane stiffness constants can be-20-
expressed as: 61 21 1 El( El + Et − 2 νltEt)G = Glt+2 8 E −νEl lt t(5)ν =1 1 El( El + Et + 6 νltEt)− Glt+22 8 El −νltEt1 1 E (3E + 3E + 2 ν E )Glt+2 8l l t lt t2El −νltEt(6)E = 2(1 + ν ) G(7)For most oriented polymer foils it holds that E l à E t , G lt . Under these conditions, theabove in-plane elastic constants approach asymptotically the following limitingvalues: 61 El1 ElE ≈ , ν ≈ , G ≈ (8)3 3 8AB1.00.8CDE θ / E l (-)0.60.4AC, D0.2B0.00 15 30 45 60 75 90θ (°)FIGURE 6 Various ply geometries of uniaxially oriented layers and their normalized off-axisYoung’s modulus, E θ /E l , calculated with E l = 130 GPa, E t = 2 GPa, G lt = 800 MPa and v lt = 0.4 (seetext): A Single, unidirectional layer [θ = 0], B Cross-ply [0/ 90], C [0/ 60/ 120], and D [0/ 45/ 90/ 135]laminate.-21-
Page 3: Diss. ETH No. 17603Ultra-high-perfo
Page 7: «I do not propose to say much abou
Page 10 and 11: Ultra-high-performance unidirection
Page 12 and 13: Hauptketten wirken bei den Aramidfa
Page 14 and 15: Planare HochleistungsfolienWie bere
Page 16 and 17: Feuilles de polymères hautes-perfo
Page 19 and 20: 1 BackgroundThe use of polymers in
Page 21 and 22: A third process for the production
Page 23 and 24: 2 From Fiber to Fabric and Film and
Page 25 and 26: iaxially oriented polymer films. Su
Page 27: (often assumed to be equal to that
Page 31 and 32: The properties of such laminated st
Page 33 and 34: 5 References and Notes1. Carothers,
Page 35: 68. The Composite Materials Handboo
Page 39 and 40: 1 IntroductionIt has long been reco
Page 41 and 42: - unlike the present work - focused
Page 43 and 44: allowed to evaporate under air flow
Page 45 and 46: Dynamical mechanical thermal analys
Page 47 and 48: solid-state compressed films of vir
Page 49 and 50: Following pseudo-affine orientation
Page 51 and 52: shown E-λ plots for foils with dif
Page 53 and 54: 55A B C5444333σ D (MPa)2σ D(MPa)2
Page 55 and 56: esulting thermograms are presented
Page 57 and 58: A100 μmλ = 510 2030 40 5070 90 10
Page 59 and 60: A B CD E1 cmFσ (MPa)45403530252015
Page 61 and 62: polymer foils is determined princip
Page 63 and 64: AdhesionIn order to promote adhesio
Page 65 and 66: FIGURE 14 Scanning electron microgr
Page 67 and 68: foil is shown in Figure 15B, and fo
Page 69 and 70: Small deviations from quasi-isotrop
Page 71: 56. Smith, P. ; Lemstra, P. J. J. M
Page 75 and 76: 1 IntroductionIn this chapter, effo
Page 77 and 78: TABLE 1 Young’s modulus, E, and t
Page 79 and 80:
s12A-A0.50.1B-B17BAABs2BA13A-A0.1B-
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ABextruder20 mmFIGURE 4 A. Schemati
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and planar foils were tested in ten
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s11 3 10 33 120s2504540353013 1729
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f1-s11 2 4 913f2-s2A6560555045401 3
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4.4 Air-gap ExtrusionIn view of the
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A100B1001010W ratio / T ratio (-)10
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ABCDFIGURE 11 A. Photographs of as-
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A70B1.2601.0500.8E (GPa)40302010σ
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Finally, the mechanical characteris
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6 References and Notes1. Kwolek, S.
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1 IntroductionIt was already discus
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2 ExperimentalMaterials. The polyme
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3 Results and Discussion3.1 Foil Ex
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3.2 Heat TreatmentAs already demons
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Expectedly, the Young’s modulus o
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the experimentally observed angular
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5 References1. Aoki, H. ; Onogi, Y.
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1 IntroductionCellulose is the main
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2 ExperimentalMaterials. The nutrie
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A0.5 mmBCFIGURE 1 Bacterial cellulo
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Finally, the test-angle dependence
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5 References1. Meyer, K. H. ; Lotma
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1 ConclusionsThe results presented
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10,0001,000σ (MPa/(g/cm 3 ))100101
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1.4 Final ConclusionIn the literatu
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precursor fibers, which, however, a
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3 References1. Gordon, J. E. Proc.
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Group for great unforgettable teamw
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4 Conclusions - POLYTECH - ETH Zürich

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