04_Fraksi Volume & Laminate

Fibre Volume Fraction and Laminate Thickness

How much fibre?

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.

Weight fraction volume fraction conversionFor the special case of a two-component composite (eg fibre and matrix):

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


Volume fraction - weight fraction conversion

Sheet3

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.

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

Maximum fibre volume fractionIn a unidirectional fibre composite, the fibre area fraction is the same as the fibre volume fraction, so:

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%.

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

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.

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.

Laminate thicknessfibrematrixhigh matrix contentlow fibre content= thick laminatelow matrix contenthigh fibre content= thin laminateTwo laminates, both containing 5 plies of reinforcement:

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:

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


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


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


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


ply thickness (mm)

Ply thickness vs fibre volume fraction (HS carbon)

Sheet1


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




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


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?

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!

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


kg/m3

Sheet1

fibre volume fractiondensity

01200

12500

Sheet1

density


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


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


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


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


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




Sheet1


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




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



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



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


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


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


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


GPa

Rule of mixtures elastic modulusHS carbon / epoxy resin

Sheet2

Sheet3

***

04_Fraksi Volume & Laminate

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