04_fraksi volume & laminate
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Fibre Volume Fraction and Laminate Thickness
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How much fibre?
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How much reinforcement?Weight fraction Used in manufacture. May refer to fibre or resin - 'GRP' manufacturers will specify a glass content of (e.g.) 25 wt%; a prepreg supplier might give a resin content of 34 wt%.
Volume fraction Used in design to calculate composite properties. Almost always refers to fibre content.
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Weight fraction volume fraction conversionFor the special case of a two-component composite (eg fibre and matrix):
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Chart1
000
0.02464065710.03389830510.0417391304
0.05063291140.06896551720.0842105263
0.07809110630.10526315790.1274336283
0.10714285710.14285714290.1714285714
0.13793103450.18181818180.2162162162
0.17061611370.22222222220.2618181818
0.20537897310.26415094340.3082568807
0.24242424240.30769230770.3555555556
0.28198433420.35294117650.4037383178
0.32432432430.40.4528301887
0.36974789920.44897959180.5028571429
0.41860465120.50.5538461538
0.47129909370.55319148940.6058252427
0.52830188680.60869565220.6588235294
0.59016393440.66666666670.7128712871
0.65753424660.72727272730.768
0.73118279570.79069767440.8242424242
0.81203007520.85714285710.8816326531
0.90118577080.92682926830.9402061856
111
glass
HS carbon
aramid
fibre weight fraction
fibre volume fraction
Volume fraction - weight fraction conversion(epoxy resin matrix)
Sheet1
orientation0.5VfWfE (ud)E (biaxial)E (CSM)densitycostrel. thicknessUDbiaxialCSMUDbiaxialCSM
fibre density25000.0000010.00000208333.0000673.0000323.000023251200.00133.00000416674000.00000000170.00000000170.0000000017111
matrix density12000.050.09881422926.354.64.162512653.19762845850.0080.00000000310.00000000230.00000000211.80682605461.30889713641.1844130916
Ef700.10.18796992489.76.25.32513303.37593984960.0040.00000000410.00000000260.00000000232.37482169161.51794497571.3037226728
Em30.150.268817204313.057.86.487513953.53763440860.00266666670.00000000480.00000000290.00000000242.76886693171.65497425531.3764970251
fibre cost50.20.342465753416.49.47.6514603.68493150680.0020.00000000530.0000000030.00000000253.03528500531.73975682411.4158700556
matrix cost30.250.409836065619.75118.812515253.81967213110.00160.00000000560.00000000310.00000000253.20753766361.78649751541.4312322975
0.30.471698113223.112.69.97515903.94339622640.00133333330.00000000570.00000000310.00000000253.31005189481.80550391551.4293614353
0.350.528700906326.4514.211.137516554.05740181270.00114285710.00000000580.00000000310.00000000253.3608248351.80432020521.415188373
0.40.581395348829.815.812.317204.16279069770.0010.00000000590.00000000310.00000000243.37322351451.78850850071.3923239696
0.450.630252100833.1517.413.462517854.26050420170.00088888890.00000000580.00000000310.00000000243.35724524311.76219453221.3634260393
0.50.675675675736.51914.62518504.35135135140.00080.00000000580.0000000030.00000000233.32041123741.72845341171.3304581513
0.550.718015665839.8520.615.787519154.43603133160.00072727270.00000000570.00000000290.00000000223.26840741091.68958539931.2948741404
0.60.757575757643.222.216.9519804.51515151520.00066666670.00000000560.00000000290.00000000223.20554864481.64731504961.2577509698
0.650.794621026946.5523.818.112520454.58924205380.00061538460.00000000540.00000000280.00000000213.13511837921.6029363681.2198852792
0.70.829383886349.925.419.27521104.65876777250.00057142860.00000000530.00000000270.00000000213.05961918511.55741951821.1818641248
0.750.862068965553.252720.437521754.7241379310.00053333330.00000000520.00000000260.0000000022.98095914541.51148987641.1441172017
Sheet2
wfglassHS carbonaramid
0000
0.050.02464065710.03389830510.0417391304
0.10.05063291140.06896551720.0842105263
0.150.07809110630.10526315790.1274336283
0.20.10714285710.14285714290.1714285714
0.250.13793103450.18181818180.2162162162
0.30.17061611370.22222222220.2618181818
0.350.20537897310.26415094340.3082568807
0.40.24242424240.30769230770.3555555556
0.450.28198433420.35294117650.4037383178
0.50.32432432430.40.4528301887
0.550.36974789920.44897959180.5028571429
0.60.41860465120.50.5538461538
0.650.47129909370.55319148940.6058252427
0.70.52830188680.60869565220.6588235294
0.750.59016393440.66666666670.7128712871
0.80.65753424660.72727272730.768
0.850.73118279570.79069767440.8242424242
0.90.81203007520.85714285710.8816326531
0.950.90118577080.92682926830.9402061856
1111
Sheet2
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
glass
HS carbon
aramid
fibre weight fraction
fibre volume fraction
Volume fraction - weight fraction conversion
Sheet3
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Maximum fibre volume fractionA composite cannot contain 100% fibre. Maximum volume fraction could be achieved only if unidirectional fibres are hexagonally close packed - ie all fibres are touching.
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Maximum fibre volume fractionThe triangular unit cell has area 3 R2.The unit cell contains an area of fibre (three 60o segments) equal to pR2 / 2
2R3R
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Maximum fibre volume fractionIn a unidirectional fibre composite, the fibre area fraction is the same as the fibre volume fraction, so:
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Maximum fibre volume fractionTheoretically, a unidirectional fibre composite could have Vf 90%. In practice, fibres cannot be perfectly aligned. Maximum volume fraction depends both on the fibre form and method of manufacture - for a unidirectional fibre composite: Vf 60-70%.
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Maximum fibre volume fractionFor other forms of reinforcement, maximum volume fraction also depends on the detailed arrangement of the fibres. The following values are typical:
stitched non-crimp0.6 woven fabric0.4 - 0.55 random (chopped strand mat)0.15 - 0.25
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How much fibre?Commercial reinforcements are characterised by their areal weight (Aw). This is simply the weight (usually given in g) of 1 m2 of the reinforcement. Aw depends on many factors - fibre density, tow or bundle size, weave style, etc.Aw may range from 50 g/m2 or less (for lightweight surfacing tissues), up to more than 2000 g/m2 for some heavyweight non-crimp fabrics.
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Laminate thicknessThe thickness of a composite laminate depends on the amount of reinforcement and the relative amount of resin which has been included. For a given quantity of reinforcement, a laminate with a high fibre volume fraction will be thinner than one with a lower fibre volume fraction, since it will contain less resin.
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Laminate thicknessfibrematrixhigh matrix contentlow fibre content= thick laminatelow matrix contenthigh fibre content= thin laminateTwo laminates, both containing 5 plies of reinforcement:
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Laminate thicknessFibre volume fraction is thus inversely proportional to laminate thickness.
If the fibre content and laminate thickness are defined, we can calculate the fibre volume fraction:If the fibre content and volume fraction are defined, we can calculate the laminate thickness:
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Chart6
0.81.21.82.4
0.53333333330.81.21.6
0.40.60.91.2
0.320.480.720.96
0.26666666670.40.60.8
0.22857142860.34285714290.51428571430.6857142857
0.20.30.450.6
0.17777777780.26666666670.40.5333333333
0.160.240.360.48
0.14545454550.21818181820.32727272730.4363636364
0.13333333330.20.30.4
0.12307692310.18461538460.27692307690.3692307692
0.11428571430.17142857140.25714285710.3428571429
0.10666666670.160.240.32
0.10.150.2250.3
Area weight
200 g/m2
300 g/m2
450 g/m2
600 g/m2
fibre volume fraction
ply thickness (mm)
Ply thickness vs fibre volume fraction (glass)
Sheet1
orientation0.5VfWfUDbiaxialCSMdensitycostrel. thicknessUDbiaxialCSMUDbiaxialquasi-isotropic
fibre density18000.0000010.00000153.0000673.0000323.000023251200.00063.000003555.55555555560.00000000170.00000000170.0000000017111
matrix density12000.050.07317073176.354.64.162512303.14634146340.01111111110.00000000340.00000000250.00000000221.9654944721.42383937821.28842363
Ef700.10.14285714299.76.25.32512603.28571428570.00555555560.00000000480.00000000310.00000000272.79301671421.78524800561.5333021543
Em30.150.209302325613.057.86.487512903.41860465120.00370370370.00000000610.00000000360.0000000033.50150552942.0928782961.7407163521
fibre cost50.20.272727272716.49.47.6513203.54545454550.00277777780.00000000710.00000000410.00000000334.10710201382.35409813031.9158407683
matrix cost30.250.333333333319.75118.812513503.66666666670.00222222220.0000000080.00000000450.00000000364.62358908922.57519358662.0630872429
0.30.391304347823.112.69.97513803.78260869570.00185185190.00000000880.00000000480.00000000385.06276951552.76154286212.1862278089
0.350.446808510626.4514.211.137514103.89361702130.00158730160.00000000940.00000000510.0000000045.43477756732.91775961472.28849595
0.40.529.815.812.3144040.00138888890.000000010.00000000530.00000000415.74833703333.04781156792.372670356
0.450.551020408233.1517.413.462514704.10204081630.00123456790.00000001040.00000000550.00000000426.01097558843.15511901822.4411444637
0.50.636.51914.62515004.20.00111111110.00000001080.00000000560.00000000436.22920355853.24263694252.4959844001
0.550.647058823539.8520.615.787515304.29411764710.0010101010.00000001110.00000000580.00000000446.40866350513.31292367392.5389774296
0.60.692307692343.222.216.9515604.38461538460.00092592590.00000001140.00000000580.00000000456.55425580643.36819852862.5716725934
0.650.735849056646.5523.818.112515904.47169811320.00085470090.00000001160.00000000590.00000000456.67024441813.41039031662.5954149064
0.70.777777777849.925.419.27516204.55555555560.00079365080.00000001170.0000000060.00000000456.76034621283.44117829862.611374219
0.750.818181818253.252720.437516504.63636363640.00074074070.00000001190.0000000060.00000000456.82780666483.46202686742.620569647
Sheet1
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
UD
biaxial
CSM
fibre volume fraction
tensile modulus (GPa)
Rule of mixtures tensile modulus (glass fibre/polyester)
Sheet2
fibre volume fraction200 g/m2300 g/m2450 g/m2600 g/m2
0.10.81.21.82.4
0.150.53333333330.81.21.6
0.20.40.60.91.2
0.250.320.480.720.96
0.30.26666666670.40.60.8
0.350.22857142860.34285714290.51428571430.6857142857
0.40.20.30.450.6
0.450.17777777780.26666666670.40.5333333333
0.50.160.240.360.48
0.550.14545454550.21818181820.32727272730.4363636364
0.60.13333333330.20.30.4
0.650.12307692310.18461538460.27692307690.3692307692
0.70.11428571430.17142857140.25714285710.3428571429
0.750.10666666670.160.240.32
0.80.10.150.2250.3
Sheet2
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
200 g/m2
300 g/m2
450 g/m2
600 g/m2
fibre volume fraction
ply thickness (mm)
Ply thickness vs fibre volume fraction (glass)
Sheet3
-
Chart5
0.27777777780.41666666670.55555555560.83333333331.3888888889
0.22222222220.33333333330.44444444440.66666666671.1111111111
0.18518518520.27777777780.37037037040.55555555560.9259259259
0.15873015870.23809523810.31746031750.47619047620.7936507937
0.13888888890.20833333330.27777777780.41666666670.6944444444
0.12345679010.18518518520.24691358020.37037037040.6172839506
0.11111111110.16666666670.22222222220.33333333330.5555555556
0.1010101010.15151515150.2020202020.3030303030.5050505051
0.09259259260.13888888890.18518518520.27777777780.462962963
0.08547008550.12820512820.17094017090.25641025640.4273504274
0.07936507940.1190476190.15873015870.23809523810.3968253968
0.07407407410.11111111110.14814814810.22222222220.3703703704
0.06944444440.10416666670.13888888890.20833333330.3472222222
Area weight
100 g/m2
150 g/m2
200 g/m2
300 g/m2
500 g/m2
fibre volume fraction
ply thickness (mm)
Ply thickness vs fibre volume fraction (HS carbon)
Sheet1
orientation0.5VfWfUDbiaxialCSMdensitycostrel. thicknessUDbiaxialCSMUDbiaxialquasi-isotropic
fibre density18000.0000010.00000153.0000673.0000323.000023251200.00063.000003555.55555555560.00000000170.00000000170.0000000017111
matrix density12000.050.07317073176.354.64.162512303.14634146340.01111111110.00000000340.00000000250.00000000221.9654944721.42383937821.28842363
Ef700.10.14285714299.76.25.32512603.28571428570.00555555560.00000000480.00000000310.00000000272.79301671421.78524800561.5333021543
Em30.150.209302325613.057.86.487512903.41860465120.00370370370.00000000610.00000000360.0000000033.50150552942.0928782961.7407163521
fibre cost50.20.272727272716.49.47.6513203.54545454550.00277777780.00000000710.00000000410.00000000334.10710201382.35409813031.9158407683
matrix cost30.250.333333333319.75118.812513503.66666666670.00222222220.0000000080.00000000450.00000000364.62358908922.57519358662.0630872429
0.30.391304347823.112.69.97513803.78260869570.00185185190.00000000880.00000000480.00000000385.06276951552.76154286212.1862278089
0.350.446808510626.4514.211.137514103.89361702130.00158730160.00000000940.00000000510.0000000045.43477756732.91775961472.28849595
0.40.529.815.812.3144040.00138888890.000000010.00000000530.00000000415.74833703333.04781156792.372670356
0.450.551020408233.1517.413.462514704.10204081630.00123456790.00000001040.00000000550.00000000426.01097558843.15511901822.4411444637
0.50.636.51914.62515004.20.00111111110.00000001080.00000000560.00000000436.22920355853.24263694252.4959844001
0.550.647058823539.8520.615.787515304.29411764710.0010101010.00000001110.00000000580.00000000446.40866350513.31292367392.5389774296
0.60.692307692343.222.216.9515604.38461538460.00092592590.00000001140.00000000580.00000000456.55425580643.36819852862.5716725934
0.650.735849056646.5523.818.112515904.47169811320.00085470090.00000001160.00000000590.00000000456.67024441813.41039031662.5954149064
0.70.777777777849.925.419.27516204.55555555560.00079365080.00000001170.0000000060.00000000456.76034621283.44117829862.611374219
0.750.818181818253.252720.437516504.63636363640.00074074070.00000001190.0000000060.00000000456.82780666483.46202686742.620569647
Sheet1
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
UD
biaxial
CSM
fibre volume fraction
tensile modulus (GPa)
Rule of mixtures tensile modulus (glass fibre/polyester)
Sheet2
fibre volume fraction100 g/m2150 g/m2200 g/m2300 g/m2500 g/m2
0.20.27777777780.41666666670.55555555560.83333333331.3888888889
0.250.22222222220.33333333330.44444444440.66666666671.1111111111
0.30.18518518520.27777777780.37037037040.55555555560.9259259259
0.350.15873015870.23809523810.31746031750.47619047620.7936507937
0.40.13888888890.20833333330.27777777780.41666666670.6944444444
0.450.12345679010.18518518520.24691358020.37037037040.6172839506
0.50.11111111110.16666666670.22222222220.33333333330.5555555556
0.550.1010101010.15151515150.2020202020.3030303030.5050505051
0.60.09259259260.13888888890.18518518520.27777777780.462962963
0.650.08547008550.12820512820.17094017090.25641025640.4273504274
0.70.07936507940.1190476190.15873015870.23809523810.3968253968
0.750.07407407410.11111111110.14814814810.22222222220.3703703704
0.80.06944444440.10416666670.13888888890.20833333330.3472222222
Sheet2
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
00000
100 g/m2
150 g/m2
200 g/m2
300 g/m2
500 g/m2
fibre volume fraction
ply thickness (mm)
Ply thickness vs fibre volume fraction (HS carbon)
Sheet3
-
Example calculations
1. What will be the thickness of a laminate consisting of 2 layers of 450 g/m2 chopped strand mat if a resin to glass ratio (by weight) of 2:1 is used?
2. What fibre volume fraction is achieved if 3 layers of 800 g/m2 glass woven roving are compression-moulded to a thickness of 2 mm?
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Rules of Mixturefor Elastic Properties
-
'Rules of Mixtures' are mathematical expressions which give some property of the composite in terms of the properties, quantity and arrangement of its constituents.
They may be based on a number of simplifying assumptions, and their use in design should tempered with extreme caution!
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DensityFor the special case of a fibre-reinforced matrix:
since Vf + Vm = 1
-
Rule of mixtures density for glass/epoxy compositesrfrm
Chart2
1200
2500
density
fibre volume fraction
kg/m3
Sheet1
fibre volume fractiondensity
01200
12500
Sheet1
density
fibre volume fraction
kg/m3
Sheet2
Sheet3
-
Micromechanical models for stiffness
-
Unidirectional plyUnidirectional fibres are the simplest arrangement of fibres to analyse.They provide maximum properties in the fibre direction, but minimum properties in the transverse direction.fibre directiontransverse direction
-
Unidirectional plyWe expect the unidirectional composite to have different tensile moduli in different directions.These properties may be labelled in several different ways:E1, E||E2, E
-
Unidirectional plyBy convention, the principal axes of the ply are labelled 1, 2, 3. This is used to denote the fact that ply may be aligned differently from the cartesian axes x, y, z.132
-
Unidirectional ply - longitudinal tensile modulusWe make the following assumptions in developing a rule of mixtures:Fibres are uniform, parallel and continuous.Perfect bonding between fibre and matrix.Longitudinal load produces equal strain in fibre and matrix.
-
Unidirectional ply - longitudinal tensile modulusE1 = Ef Vf + Em ( 1-Vf )
Note the similarity to the rules of mixture expression for density.
In polymer composites, Ef >> Em, soE1 Ef Vf
-
This rule of mixtures is a good fit to experimental data
(source: Hull, Introduction to Composite Materials, CUP)
-
Unidirectional ply - transverse tensile modulusThe simplified model lumps fibre and matrix together, and assumes that both components experience the same stress:
s2s2or
-
If Ef >> Em, E2 Em / (1-Vf)Note that E2 is not particularly sensitive to Vf.If Ef >> Em, E2 is almost independent of fibre property:
Chart1
33
3.3175355453.3333333333
3.71024734983.75
4.20841683374.2857142857
4.86111111115
5.75342465756
7.04697986587.5
9.090909090910
12.804878048815
E2 - exact
E2 - approx
fibre volume fraction
E2 (GPa)
Rule of mixtures - transverse modulus (glass/epoxy)
Sheet1
Ef70
Em3
VfE2 - exactE2 - approx
033
0.13.3175355453.3333333333
0.23.71024734983.75
0.34.20841683374.2857142857
0.44.86111111115
0.55.75342465756
0.67.04697986587.5
0.79.090909090910
0.812.804878048815
Sheet1
E2 - exact
E2 - approx
fibre volume fraction
E2 (GPa)
Rule of mixtures - transverse modulus (glass/epoxy)
Sheet2
Sheet3
-
carbon/epoxyglass/epoxyThe transverse modulus is dominated by the matrix, and is virtually independent of the reinforcement.
Chart2
33
3.3175355453.328611898
3.71024734983.7380699894
4.20841683374.2623941959
4.86111111114.9578059072
5.75342465755.9243697479
7.04697986587.3590814196
9.09090909099.7107438017
12.804878048814.2712550607
E2 - glass
E2 - carbon
fibre volume fraction
E2 (GPa)
Rule of mixtures - transverse modulus
Sheet1
Ef70235
Em3
VfE2 - glassE2 - carbon
033
0.13.3175355453.328611898
0.23.71024734983.7380699894
0.34.20841683374.2623941959
0.44.86111111114.9578059072
0.55.75342465755.9243697479
0.67.04697986587.3590814196
0.79.09090909099.7107438017
0.812.804878048814.2712550607
Sheet1
E2 - glass
E2 - carbon
fibre volume fraction
E2 (GPa)
Rule of mixtures - transverse modulus
Sheet2
Sheet3
-
The transverse rule of mixtures is not particularly accurate, due to the simplifications made - Poisson effects are not negligible, and the strain distribution is not uniform:
(source: Hull, Introduction to Composite Materials, CUP)
-
Generalised rule of mixtures for tensile modulusE = hL ho Ef Vf + Em (1-Vf )
hL is a length correction factor. Typically, hL 1 for fibres longer than about 10 mm.
ho corrects for non-unidirectional reinforcement:
o
unidirectional
1.0
biaxial
0.5
biaxial at (45o
0.25
random (in-plane)
0.375
random (3D)
0.2
-
Chart4
3.0000673.0000323.00002325
6.354.64.1625
9.76.25.325
13.057.86.4875
16.49.47.65
19.75118.8125
23.112.69.975
26.4514.211.1375
29.815.812.3
33.1517.413.4625
36.51914.625
39.8520.615.7875
43.222.216.95
46.5523.818.1125
49.925.419.275
53.252720.4375
UD
biaxial
CSM
fibre volume fraction
tensile modulus (GPa)
Rule of mixtures tensile modulus (glass fibre/polyester)
Sheet1
orientation0.5VfWfUDbiaxialCSMdensitycostrel. thicknessUDbiaxialCSMUDbiaxialquasi-isotropic
fibre density18000.0000010.00000153.0000673.0000323.000023251200.00063.000003555.55555555560.00000000170.00000000170.0000000017111
matrix density12000.050.07317073176.354.64.162512303.14634146340.01111111110.00000000340.00000000250.00000000221.9654944721.42383937821.28842363
Ef700.10.14285714299.76.25.32512603.28571428570.00555555560.00000000480.00000000310.00000000272.79301671421.78524800561.5333021543
Em30.150.209302325613.057.86.487512903.41860465120.00370370370.00000000610.00000000360.0000000033.50150552942.0928782961.7407163521
fibre cost50.20.272727272716.49.47.6513203.54545454550.00277777780.00000000710.00000000410.00000000334.10710201382.35409813031.9158407683
matrix cost30.250.333333333319.75118.812513503.66666666670.00222222220.0000000080.00000000450.00000000364.62358908922.57519358662.0630872429
0.30.391304347823.112.69.97513803.78260869570.00185185190.00000000880.00000000480.00000000385.06276951552.76154286212.1862278089
0.350.446808510626.4514.211.137514103.89361702130.00158730160.00000000940.00000000510.0000000045.43477756732.91775961472.28849595
0.40.529.815.812.3144040.00138888890.000000010.00000000530.00000000415.74833703333.04781156792.372670356
0.450.551020408233.1517.413.462514704.10204081630.00123456790.00000001040.00000000550.00000000426.01097558843.15511901822.4411444637
0.50.636.51914.62515004.20.00111111110.00000001080.00000000560.00000000436.22920355853.24263694252.4959844001
0.550.647058823539.8520.615.787515304.29411764710.0010101010.00000001110.00000000580.00000000446.40866350513.31292367392.5389774296
0.60.692307692343.222.216.9515604.38461538460.00092592590.00000001140.00000000580.00000000456.55425580643.36819852862.5716725934
0.650.735849056646.5523.818.112515904.47169811320.00085470090.00000001160.00000000590.00000000456.67024441813.41039031662.5954149064
0.70.777777777849.925.419.27516204.55555555560.00079365080.00000001170.0000000060.00000000456.76034621283.44117829862.611374219
0.750.818181818253.252720.437516504.63636363640.00074074070.00000001190.0000000060.00000000456.82780666483.46202686742.620569647
Sheet1
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
UD
biaxial
CSM
fibre volume fraction
tensile modulus (GPa)
Rule of mixtures tensile modulus (glass fibre/polyester)
Sheet2
Sheet3
Chart3
3.0002273.0001123.00008325
14.358.67.1625
25.714.211.325
37.0519.815.4875
48.425.419.65
59.753123.8125
71.136.627.975
82.4542.232.1375
93.847.836.3
105.1553.440.4625
116.55944.625
127.8564.648.7875
139.270.252.95
150.5575.857.1125
161.981.461.275
173.258765.4375
UD
biaxial
quasi-isotropic
fibre volume fraction
tensile modulus (GPa)
Rule of mixtures tensile modulus (T300 carbon fibre)
Sheet1
orientation0.5VfWfUDbiaxialquasi-isotropicdensitycostrel. thicknessUDbiaxialCSMUDbiaxialquasi-isotropic
fibre density18000.0000010.00000153.0002273.0001123.000083251200.00063.000003555.55555555560.00000000170.00000000170.0000000017111
matrix density12000.050.073170731714.358.67.162512303.14634146340.01111111110.00000000770.00000000460.00000000384.4414711072.66188959372.2169728981
Ef2300.10.142857142925.714.211.32512603.28571428570.00555555560.00000001280.00000000710.00000000577.39965995354.08868478873.2609013359
Em30.150.209302325637.0519.815.487512903.41860465120.00370370370.00000001730.00000000920.00000000729.94052577895.31254939274.1554998584
fibre cost50.20.272727272748.425.419.6513203.54545454550.00277777780.0000000210.0000000110.000000008512.12031319936.36090404894.9209827703
matrix cost30.250.333333333359.753123.812513503.66666666670.00222222220.00000002430.00000001260.000000009713.98707419537.25717022165.5746136117
0.30.391304347871.136.627.97513803.78260869570.00185185190.00000002710.00000001390.000000010615.58197904698.02141060226.1311779243
0.350.446808510682.4542.232.137514103.89361702130.00158730160.00000002940.00000001510.000000011516.94039749368.67085721196.6033730821
0.40.593.847.836.3144040.00138888890.00000003140.0000000160.000000012218.09279392239.2203486177.0021310092
0.450.5510204082105.1553.440.462514704.10204081630.00123456790.00000003310.00000001680.000000012719.06547137619.68269326727.3368863452
0.50.6116.55944.62515004.20.00111111110.00000003450.00000001750.000000013219.881192147110.0689725297.6158000856
0.550.6470588235127.8564.648.787515304.29411764710.0010101010.00000003570.0000000180.000000013620.55969721210.38879429537.8459467306
0.60.6923076923139.270.252.9515604.38461538460.00092592590.00000003670.00000001850.000000013921.118142433810.65050593148.0334714157
0.650.7358490566150.5575.857.112515904.47169811320.00085470090.00000003750.00000001890.000000014221.571466027710.86137364368.1837222532
0.70.7777777778161.981.461.27516204.55555555560.00079365080.00000003810.00000001910.000000014421.932699056811.0277340218.3013621333
0.750.8181818182173.258765.437516504.63636363640.00074074070.00000003860.00000001940.000000014622.213228554411.15512243928.3904634471
Sheet1
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
UD
biaxial
quasi-isotropic
fibre volume fraction
tensile modulus (GPa)
Rule of mixtures tensile modulus (T300 carbon fibre)
Sheet2
Sheet3
-
Chart1
0.150.156.4875
0.20.27.65
0.250.258.8125
0.30.39.975
0.350.3511.1375
0.415.812.3
0.4517.40.45
36.5190.5
39.8520.60.55
43.20.60.6
46.550.650.65
49.90.70.7
UD
biaxial
random
fibre volume fraction
GPa
Rule of mixtures elastic modulusglass fibre / epoxy resin
Sheet1
Ef70
Em3
VfUDbiaxialrandom
0.156.4875
0.27.65
0.258.8125
0.39.975
0.3511.1375
0.415.812.3
0.4517.4
0.536.519
0.5539.8520.6
0.643.2
0.6546.55
0.749.9
Sheet1
UD
biaxial
random
fibre volume fraction
GPa
Rule of mixtures elastic modulusglass fibre / epoxy resin
Sheet2
Sheet3
-
Chart3
0.150.150.150.15
0.20.20.20.2
0.250.250.250.25
0.30.30.30.3
0.350.350.350.35
0.40.40.40.4
0.4553.440.462545.39
116.55944.62550.15
127.8564.648.787554.91
139.270.252.950.6
150.5575.857.11250.65
161.981.461.2750.7
UD
biaxial UD
quasi-isotropic UD
plain woven
fibre volume fraction
GPa
Rule of mixtures elastic modulusHS carbon / epoxy resin
Sheet1
Ef230
Em3
VfUDbiaxial UDquasi-isotropic UDplain woven
0.15
0.2
0.25
0.3
0.35
0.4
0.4553.440.462545.39
0.5116.55944.62550.15
0.55127.8564.648.787554.91
0.6139.270.252.95
0.65150.5575.857.1125
0.7161.981.461.275
Sheet1
UD
biaxial UD
quasi-isotropic UD
plain woven
fibre volume fraction
GPa
Rule of mixtures elastic modulusHS carbon / epoxy resin
Sheet2
Sheet3
***
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