Properties of hemp fibre polymer composites -An optimisation of ...

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Appendix B: Modelling of porosity content The porosity content in the composites was determined by assuming that a composite on a macroscopic scale can be divided into fibres, matrix and porosity. The volume fraction of porosity Vp can then be calculated as V = 1 −V −V p m f where the subscripts p, m and f denotes porosity, matrix and fibres, respectively. Equations for calculation of volume fractions of porosity, matrix and fibres based on experimentally obtained composite data are outlined in Paper IV. The porosity content in the composites was modelled versus the fibre weight fraction based on techniques developed by Madsen and Lilholt (2003, 2005), in which it is assumed that the volume fraction of porosity is linear dependent on both volume fraction of fibres Vf and of matrix Vm using the porosity constants αf and αm. Wf ρm V f = W f ρm ( 1+ α f ) + ( 1− Wf ) ρ f ( 1+ αm ) ( 1− W f ) ρ f ( 1− Wf ) ρ f Vm = V f = W f ρm W f ρm ( 1+ α f ) + ( 1− W f ) ρ f ( 1+ αm ) V = α V + α V p f f m m This expression for the volumetric distribution between fibres, matrix and porosity is valid when the fibre content is below the maximum attainable volume fraction Vf,max found by Madsen and Lilholt (2002). Vf,max increases versus the compaction pressure applied when the liquid matrix and fibres are compacted before curing. If the weight fraction of fibres corresponds to a higher Vf than Vf,max, matrix will be partly replaced with air in the composite so the porosity content will increase while the fibre content remains constant at Vf,max. The porosity constants αf and αm can be determined by linear regression of Vp versus Vf as shown in Figure 35 using the following formulas. V p c V p = α V f ( 1+ α ) = ( α − α ) m f + α V m f m = α V c α f − αm αm Vp = V f + 1+ αm 1+ αm Expression for the regression line: = a ⋅V + b Vp f m f V f f + α + α m m ( 1− V −V ) f 74 Risø-PhD-11 p
The porosity constants can now be determined based on the regression line as follows: Determination of αm : αm b = 1+ αm c b αm = 1− b ⇔ b( 1+ αm) = αm ⇔αm( 1− b) = b Determination of α f : α f −αm a = ⇔ a( 1+ α m) = α f −αm 1+ α ⇔ α f = a( 1+ αm) + αm c m α f c ⎛1−b b ⎞ b = a ⎜ + ⎟+ ⎝1−b 1−b⎠ 1−b α f a+ b = 1− b Risø-PhD-11 75
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Risø-PhD-11(EN) Properties of hemp
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Contents Preface 6 1 Resumé 7 2 Li
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PhD thesis: Properties of hemp fibr
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1 Resumé Karakterisering af hampef
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2.4 Oral presentations Anders Thyge
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4 Introduction Hemp (Cannabis sativ
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4.2 The outline of the thesis The f
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The only fertilizer used was 360/48
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Temperature [ o C] 35 30 25 20 15 1
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A B Figure 7. A: Model of transvers
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Figure 8. Lignin (a), pectin (b) an
Page 23 and 24: Figure 11. Microfibril angles (MFA)
Page 25 and 26: Teleman, 1997). The crystal structu
Page 27 and 28: to the computing effort and the sub
Page 29 and 30: Figure 15. The structure of hemicel
Page 31 and 32: fibre mats, which are made by air-d
Page 33 and 34: Figure 18. From fibre filament to a
Page 35 and 36: A B C D Figure 20. Chemical structu
Page 37 and 38: water vapour and air are removed fr
Page 39 and 40: 7 Defibration methods Defibration m
Page 41 and 42: Table 5. Fibre yield and cellulose
Page 43 and 44: a b c Composition [% w/w] 100 Compo
Page 45 and 46: 8 Fibre strength in hemp The streng
Page 47 and 48: 8.2 Effect of pre-treatment of hemp
Page 49 and 50: E-modulus [GPa] 90 80 70 60 50 40 3
Page 51 and 52: Second mode: Failure is controlled
Page 53 and 54: structure, which made much higher f
Page 55 and 56: Table 7. Porosity factors determine
Page 57 and 58: Thereby, the effective fibre streng
Page 59 and 60: a b Composite tensile strength σcu
Page 61 and 62: Table 9. Mechanical properties in a
Page 63 and 64: a σ c/ρ c [10 3 m 2 /s 2 ] b Ec/
Page 65 and 66: Fibre strength σ f [MPa] Fibre sti
Page 67 and 68: 11 References Andersen TL, Lilholt
Page 69 and 70: Kaar WE, Cool LG, Merriman MM, Brin
Page 71 and 72: Stowell EZ, Liu TS, 1961. On the Me
Page 73: Appendix A: Comprehensive composite
Page 77 and 78: Appendix D: Density and mechanical
Page 79 and 80: Paper I Changes in chemical composi
Page 81 and 82: Risø-PhD-11 81
Page 89 and 90: Paper II Hemp fiber microstructure
Page 91 and 92: ABSTRACT Characterization of hemp f
Page 93 and 94: METHODS AND TECHNIQUES Treatment of
Page 95 and 96: 2000) and their orientation gave th
Page 97 and 98: By TEM microscopy, the single fiber
Page 99 and 100: Table 1. Chemical composition of th
Page 101 and 102: Table 2. Tensile strength (σ) and
Page 103 and 104: Morvan, C., Jauneau, A., Flaman, A.
Page 119 and 120: Paper IV Comparison of composites m
Page 121 and 122: ABSTRACT Aligned epoxy-matrix compo
Page 123 and 124: the calculation of volume fractions
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solution (pH 4) for 4 h at 85°C. L
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E ⎛ dσ c ⎞ = ⎜ ⎟ ⎝ dε
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Table 2. Chemical composition, stru
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transverse section of the small hem
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Long fibres that pass through the e
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Figure 6. Effect of composite fabri
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DISCUSSION The defibration of hemp
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This investigation showed that the
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Bos, H.L., Molenveld, K., Teunissen
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Thygesen, A., 2006. Properties of h
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Risø-PhD-11 145
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Risø’s research is aimed at solv
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