246:
Realistically the highest fiber volume ratio is around 70% due to manufacturing parameters and is usually in the range of 50% to 65%. Adding too little fiber reinforcement in the composite will actually deteriorate the properties of the material. Too much fiber volume may also decrease the strength of the composite due to the lack of space for the matrix to fully surround and bond with the fibers. Therefore, there is an optimal space between fibers that will fully exploit the uniform load transfer between fibers. Given the fiber volume fraction, the theoretical elastic properties of a composite can be determined. The
41:
the orientation of the fibers and the architecture of the fibers. The geometric analysis of the composite can be seen in the cross-section of the composite. Voids are often formed in a composite structure throughout the manufacturing process and must be calculated into the total fiber volume fraction of the composite. The fraction of fiber reinforcement is very important in determining the overall mechanical properties of a composite. A higher fiber volume fraction typically results in better mechanical properties of the composite.
1236:
Another method requires accurate measurement of the density of the sample and comparing it to the theoretical density in the equation described in the previous section. The density is determined by weighing the sample in air and then in a liquid of known density. Application of
Archimedesā principle
778:
or void fraction is a measure of the void (i.e., "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0 and 100%. There are many ways to determine if a composite part contains voids, such as industrial CT scanning
40:
material. When manufacturing polymer composites, fibers are impregnated with resin. The amount of resin to fiber ratio is calculated by the geometric organization of the fibers, which affects the amount of resin that can enter the composite. The impregnation around the fibers is highly dependent on
1232:
There are many methods of evaluating the void content of materials (including composites). The first is to exam a polished section, identifying the voids in the section, either manually or using computer-aid analysis and determining the area fraction which corresponds to the volume fraction of the
759:
However, these are ideal situations only used for theoretical analysis. In practical cases there can be variation in fiber diameter and irregular packing. In practice, it's hard to achieve a volume fraction greater than 0.7 and this must be regarded as the realistic limit for commercial materials.
227:
Optical microscopy-based techniques involve potting sectioned samples of the laminate, polished using standard metallographic techniques, and obtaining digital cross-sectional photomicrographs using an optical microscope and magnifications between 100 and 2500. Digital images may be recorded at a
245:
The amount of fiber in a fiber reinforced composite directly corresponds with the mechanical properties of the composite. Theoretically the maximum fiber ratio of round fibers that can be achieved in a composite is 90.8% if the fibers are in a unidirectional hexagonal close packed configuration.
236:
This method involves heating up the composite to a temperature at which resin will melt and fibers remain stable, burning off resin and weighing fibers, the volume fraction can be calculated from the initial weight of composite and fiber's weight. This method is typically used with glass fibers.
218:
This procedure involves the digestion of the polymer matrix using an acid which does not attack the fibers. Following digestion, the remaining fibers are washed, dried, and weighed. Knowing the initial weight of the composite specimen as well as the densities of the fiber and resin, the volume
44:
Calculating the volume of fiber ratio in a composite is relatively simple. The volume fiber fraction can be calculated using a combination of weights, densities, elastic moduli, stresses in respective directions, Poisson's ratios, and volumes of the matrix (resin system), fibers, and voids.
228:
number of locations along the length and through-the-thickness of the laminate. Computer programs aid in the analysis of fiber ratio in the photomicrograph of the polished composite specimen. This method is preferred as a non-destructive approach to determining fiber volume fraction.
767:(usually carbon) fibers are considered to have the highest volume fraction among common fiber architectures. Filament winding is also usually associated with high fiber volume fractions ā with careful control of fiber tension and resin content, values of around 70% are possible.
450:
Fibers are commonly arranged in a square or hexagonal lattice as well as in a layer-wise fiber array. Assuming that each fiber has a circular cross-sectional with the same diameter, the fiber volume fraction of these two kinds of packing are respectively:
538:
617:
1339:
1118:
870:
1503:
The liquid used in this method should have a high density and chemical stability and low vapour pressure and surface tension. The most popular liquid currently in use is perfluoro- 1 - methyl decalin.
337:
100:
1237:
leads to the following expression for the measured density of the sample in terms of measured weight, where subscripts āaā and āLā refer to water and liquid, respectively:
754:
715:
219:
fraction of both the fiber and matrix in the original laminate may be determined. This method is generally used for composites composed of carbon fiber reinforcement.
1439:
1404:
1221:
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1150:
1023:
994:
965:
936:
902:
439:
410:
369:
202:
173:
132:
672:
1364:
642:
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In the production process, using different fiber architecture methods can obtain different volume fractions. 2D aligned unidirectional fabrics with
461:
1571:
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1242:
1034:
788:
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Theoretical determination of the optimal fiber volume fraction and fiber-matrix property compatibility of short fiber composites.
783:. If the volume fraction of the fibers and matrix is known, the volume voids can also be found using the following equation:
256:
1687:
1682:
250:
of a composite in the fiber direction of a unidirectional composite can be calculated using the following equation:
50:
1527:
37:
1667:
1544:
Stochastic analysis of fibre volume fraction and permeability in fibre bundles with random filament arrangement
1563:
1546:, Composites Part A: Applied Science and Manufacturing, Volume 49, June 2013, Pages 109-118, ISSN 1359-835X.
678:
The maximum fiber volume fraction will occur when the fibers are touching, i.e. r=R. For a hexagonal array
720:
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1625:
TE565 Class
Lecture. NCSU College of Textiles, Raleigh. 14 Sept. 2014. Lecture.
780:
533:{\displaystyle {V_{f}}=({\frac {\pi }{2{\sqrt {3}}}}){({\frac {r}{R}})^{2}}}
1607:
Characterization of Fiber Volume
Fraction Gradients in Composite Laminates
775:
764:
1652:
Science and
Engineering of Short Fibre Reinforced Polymer Composites
376:
372:
139:
135:
612:{\displaystyle {V_{f}}=({\frac {\pi }{4}}){({\frac {r}{R}})^{2}}}
1334:{\displaystyle p={\frac {(W_{apL}-W_{Lpa})}{(W_{a}-W_{L})}}\!}
36:, is the percentage of fiber volume in the entire volume of a
1113:{\displaystyle V_{v}={\frac {({p_{ct}}-{p_{cm}})}{p_{ct}}}\!}
1029:
Another equation used to calculate void volume fraction is:
865:{\displaystyle V_{v}=1-V_{f}-V_{m}={\frac {v_{v}}{v_{c}}}\!}
1605:
Michael T. Cann, Daniel O. Adams and
Claudio L. Schneider,
1189:
is the theoretical density of the composite without voids
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332:{\displaystyle E=(1-{V_{f}}){E_{m}}+{V_{f}}{E_{f}}}
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1366:is the measured density of the composite sample
1609:, Journal of Composite Materials, 2008 42: 447
674:is the center to center spacing of the fibers.
95:{\displaystyle V_{f}={\frac {v_{f}}{v_{c}}}\!}
1650:Fu, Shao-Tun, Bernd Lauke, and Yiu-Wing Mai.
1623:Fiber Finishing, Properties and Architecture.
16:Mathematical element in composite engineering
8:
1560:Engineering Mechanics of Composite Materials
209:Methods to Determine Fiber Volume Fractions
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1591:Principles of composite material mechanics
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1524:An Introduction to Composite Materials
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1593:(2nd ed.). Boca Raton, FL: CRC Press.
7:
1542:A. Endruweit, F. Gommer, A.C. Long.
1441:is the weight of composite in liquid
441:is the elastic modulus of the fibers
412:is the elastic modulus of the matrix
241:Importance of Fiber Volume Fraction
223:Optical microscopy-based techniques
1558:Isaac M Daniel, Ori Ishai. (2006).
1406:is the weight of composite in air
14:
1668:Volume-Weight Fraction Calculator
1641:Polymer Composites, 14(2), 85-93.
446:Common Fiber Packing Arrangements
717:= 0.907, and for square packing
32:. Fiber volume ratio, or fiber
1324:
1298:
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1025:is the volume of the composite
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204:is the volume of the composite
1:
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1528:Cambridge University Press
967:is the matrix volume ratio
38:fiber-reinforced composite
938:is the fiber volume ratio
749:{\displaystyle V_{f,max}}
710:{\displaystyle V_{f,max}}
1654:. Woodhead Limited, 2009
1152:is the void volume ratio
904:is the void volume ratio
232:Resin Burning-off Method
1564:Oxford University Press
1499:is the weight of liquid
1434:{\displaystyle W_{Lpa}}
1399:{\displaystyle W_{apL}}
175:is the volume of fibers
1493:
1464:
1435:
1400:
1360:
1335:
1228:Measuring Void Content
1217:
1216:{\displaystyle p_{cm}}
1183:
1182:{\displaystyle p_{ct}}
1146:
1114:
1019:
996:is the volume of voids
990:
961:
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644:is the radius of fiber
638:
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1492:{\displaystyle W_{L}}
1465:
1463:{\displaystyle W_{a}}
1436:
1401:
1361:
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1218:
1184:
1147:
1145:{\displaystyle V_{v}}
1115:
1020:
1018:{\displaystyle v_{c}}
991:
989:{\displaystyle v_{v}}
962:
960:{\displaystyle V_{m}}
933:
931:{\displaystyle V_{f}}
899:
897:{\displaystyle V_{v}}
867:
751:
712:
669:
639:
614:
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436:
434:{\displaystyle E_{f}}
407:
405:{\displaystyle E_{m}}
366:
364:{\displaystyle V_{f}}
334:
199:
197:{\displaystyle v_{c}}
170:
168:{\displaystyle v_{f}}
129:
127:{\displaystyle V_{f}}
97:
28:element in composite
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771:Void Volume Fraction
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1688:Physical quantities
1683:Composite materials
1589:Gibson, R. (2007).
1522:Derek Hull. (1981).
1621:Bradford, Philip.
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667:{\displaystyle 2R}
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22:Fiber volume ratio
1572:978-0-19-532244-6
1359:{\displaystyle p}
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26:mathematical
21:
20:
18:
1233:composite.
30:engineering
1677:Categories
1562:. 2nd ed.
1507:References
781:ultrasound
455:Hexagonal
1312:−
1275:−
1073:−
822:−
809:−
756:= 0.785.
574:π
486:π
273:−
776:Porosity
765:pre-preg
1343:Where:
1122:where:
874:where:
621:where:
375:volume
371:is the
341:Where:
138:volume
134:is the
104:where:
1570:
543:Square
648:and
377:ratio
373:fiber
140:ratio
136:fiber
1568:ISBN
1370:and
1156:and
908:and
382:and
145:and
779:or
1679::
1630:^
1614:^
1598:^
1578:^
1566:.
1551:^
1535:^
1526:.
1515:^
1530:.
1485:L
1481:W
1456:a
1452:W
1427:a
1424:p
1421:L
1417:W
1392:L
1389:p
1386:a
1382:W
1354:p
1325:)
1320:L
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1307:a
1303:W
1299:(
1294:)
1289:a
1286:p
1283:L
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1270:L
1267:p
1264:a
1260:W
1256:(
1250:=
1247:p
1209:m
1206:c
1202:p
1175:t
1172:c
1168:p
1138:v
1134:V
1103:t
1100:c
1096:p
1091:)
1085:m
1082:c
1078:p
1067:t
1064:c
1060:p
1055:(
1049:=
1044:v
1040:V
1011:c
1007:v
982:v
978:v
953:m
949:V
924:f
920:V
890:v
886:V
855:c
851:v
845:v
841:v
835:=
830:m
826:V
817:f
813:V
806:1
803:=
798:v
794:V
742:x
739:a
736:m
733:,
730:f
726:V
703:x
700:a
697:m
694:,
691:f
687:V
662:R
659:2
632:r
604:2
600:)
594:R
591:r
586:(
582:)
577:4
569:(
566:=
560:f
556:V
525:2
521:)
515:R
512:r
507:(
503:)
495:3
490:2
481:(
478:=
472:f
468:V
427:f
423:E
398:m
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357:f
353:V
324:f
320:E
312:f
308:V
303:+
297:m
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288:)
282:f
278:V
270:1
267:(
264:=
261:E
190:c
186:v
161:f
157:v
120:f
116:V
85:c
81:v
75:f
71:v
65:=
60:f
56:V
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