-,
.
.
D. V .
ROSATO
NONWOVEN FIBERS IN REINFORCED PLASTICS cceptance and use of nonwoven fabrics as reinforcement of structural plastics is steadily rising. Only with nonwoven fiber sheet structures can the full potential of fiber strength be realized. Great advances have been made in developing . - new fibers and resins, in new chemical finishes given to the fiber, in methods of bonding the fiber to the resin, and in mechanical processing methods. Nonwoven fabrics are inherently better able to take advantage of these developments
A
“ i
thin
XPP ~ nqh.-Pt< - w..-n.v___ ..- .-.
Strength of commercial reinforced plastics is far below any theoretical strength. Ordinary glass fibers are three times stronger and stiffer for their weight than steel. Nonwoven elass fiber laminates usuallv have strengths about 50% below that of woven fabric lay-ups. But in special constructions, properly treated fibers have produced laminates as strong as the woven product, better in some cases. Reinforced plastics are usually applied as laminates of several layers. Many variables are important in determining the performance of the finished product. Some of the important ones are: Y
ORIENTATION OF PLIES OF THE LAMINATE TYPEOF RESIN FIBER-RESIN RATIO
TYPE OR TYPES OF FIBERS ORIENTATION OF
FIBERS
WHAT ARE NONWOVEN FABRICS?
.
NONWOVEN FABRICS are fibrous sheets made without spinning, weaving, or knitting. They include felts, bonded fabrics, and papers. The interlocking of fibers is achieved by a combination of mechanical work, chemical action, moisture, and heat-by either textile or papermaking processes. T h e y may consist of one or more classes of fibers.
WOVEN FABRICS are woven or knitted from yarns which are spun from fibers. C O R D A G E includes all types of threads, twine, and rope produced by twisting fibers together. PAPERS are produced by a wet process. T h e line of demarcation between specialty papers and nonwoven fabrics is not clear. T h e term nonwoven fabrics includes nonwoven fibrous sheets made by both textile and-paper processes (72).
FIBER-RESIN BONDING SURFACE FINISH OF FIBERS
METHOD OF
MANUFACTURE OF THE FIBER MAT
FIBERSIZE INITIAL SEPARATION
OF FIBERS
With such a number of variables, the man trying to write specifications may feel that he has walked into a maze. But they also provide flexibility in developing special properties or combinations of properties in a specific product. Some of the many fibers available are listed in the table (page 33). Manufacturing methods play so large a part in determining mechanical properties that modified processing techniques or new types of .. equipment are often required to handle new fibers. This leads to high costs for initial development. In the case of the newer fibers, the knowledge required to realiie their full potential is not yet developed. They are, however, available for experimental or small scale applications. What properties will eventually be developed for fibers formed from quartz, ceramics, beryllium glass, leached glass, graphite, regenerated asbestos, or zirconium silicate? The new technology of growing ultra-strong single crystal whiskers has given us an entirely different type of fiber. Some of these fibers can be used only in nonwoven structures. Many of them are best used in this way. The term “nonwoven fibers” includes nonwoven fibrous sheets made by both textile and paper processes (72). Nonwovens have entered many fields of application in addition to their use as reinforcement (5) and an extensive technology of manufacture has been developed ( 4 , 6 ) . Now, the demands of the space program for better performance of plastic materials (7) has led to the development of new fibers and special methods of production.
FIBERS AND THEIR PROPERTIES The most recent methods of testing fibers (2, 3) involve the use of commercially available electronic tensile testers (Instron testers). This type of equipment is highly sensitive and can make individual fiber stressstrain values readily available. Longitudinal and transverse strain can be determined and properties such as Poisson’s ratio calculated for extremely fine fibers. In comparing individual fiber data results can be misleading; test methods can differ slightly, so that the results are not related. Conditions such as gage lengths, rates of loading, and methods of measuring diameters in VOL 5 4
NO. 8
AUGUST 1 9 6 2
31
W
(INCHES)-'
X
I/DIAMETER,
Figure 7 . Average strength of pure iron and pure copper whiskers as a fui.ction of diameter
LT v) I-
W
different sets of data can be correlated. Strength and Toughness. Unfortunatcll-, wlien a material has high strength, it also has high modulus, with poor flexibility and toughness ( I I). (Toughness is calculated from the area under the stress-strain curve.) G l a s fibers such as Type E follow this pattern. Although they have the highest specific strenqth (strength per unit weight) of the fibers listed in Table I, they also have the poorest toughness. Nylon and silk have opposite properties-high toughness but low specific strength. T o improve the toughness and flexibility of a fiber, the most common procedure is to reduce the diameter. Probably the most outstanding example of this phenomenon involves the use of metal whiskers. As shown in Figure 1, strength of metallic whiskers varies inversely with fiber diameter. High-Temperature Operation. A major disadvantage of glassy fibers is their relatively low strength at high temperatures, because of a low temperature softening point. However, new glassy fibers are being developed with exceptionally high strengths at elevated temperatures (Figure 2). Softening point does not tell the entire story regarding high temperature operation. ,4major reason for using the glassy fibers rather than metals is their complete oxidation resistance, even at high temperatures. Whiskers of Metals and Ceramics. Whiskers are single crystal filaments possessing greater strength than the ordinary fiber-actually approaching the maximum theoretical strength of the material. Strength is inversely related to whisker diameter (Figure 1). The high strength is principally due to the absence of dislocations or imperfect shear planes. Fiber surface defects are practically nonexistent. Metal whiskers are usually of high purity and free of work hardness. Whiskers are grown by condensation from supcrsaturated vapor, by growth from chemical solution, or by electrodeposition. Whiskers and other. super-fine
0
\9c
\
\
/
\q.$3 \ \ \
\
\ \
\
9 O0 I300 TEMPERATURE,
Fzpure 2.
2,000
OF,
T e n d e strengths offibers at elevatpd temperatures
180"
FLgu7-e 3. Properties o j a nonzoaen glass Jber-epox) 32
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
r a i n laminate
Table 1.
Fiber Syn thetic-Inorganic Conventional glass (Type E) Beryllium glass Quartz (fused silica) Carbon Aluminum silicate Graphite
Rock Wool Natural-Inorganic Asbestos Metals and Refractories Steel Aluminum Tungsten Tantalum Molybdenum Magnesium Synthetic-Organic Fluorocarbon Polyester Acrylic Polyamide Cellulose acetate Regenerated cellulose (rayon) Natural Organic Cotton Sisal Wool a
Filament.
Staple.
Softens.
Sp. Gr. 2.6 2.6 2.2 1.8 2.7 3.9 1.6 2.2 2.8
Properties of Fibers
Diameter,
Length, In.
P.
...a,b ...a.b a,b
...a , b
up.;,
10
x
Modulus of Elasticity 70". P.S.I. 70-8,P.S.I. Tensile Strength
x
Heat Resistance, O
F.
2.8
12-20 10-25 1-4 2-1 5
GOOc 1500d 1500d 35OOc 6200" 3300d
...
67641
0.6-4
2800d
2-6
5-1 5
400
10.5
5-1 5 8-1 0 1-100 2-20
280 100-350 20 100-600 2-20
up to 4
2-30
up to 4
1-22
2.5
up to 3
0.02
100-200
20-25
2770d
7.8 2.8 19.3 16.6 10.2 1.8
. . .a $
1-25 4-20 20 5 5-20 6-1 5
200-400 60-90 200 70-90
20-30 10 58 28 42
2920e 1212. 61506 53906 47000 12006
20 10-25 10-25 10-40 11-44 10-40
47 100 50 70-120 25 30-105
17 19 28
50-110 120 29
...
a$
up to 1 up to 0 . 5 up to 0 . 5
. . .a , b
2.2 1.4 1.2 1.1 1.3 1.5
. . . aa,$b
1.6 1.3 1.3
up to 2 up to 24 up to 15
Decomposes.
...
. . .a$
. . . aa ,, bb ... ...a J
e
Melts.
f
Sublimes.
fibers are described in Developments in Fiber Technology, p. 55 of this issue. Desirable properties of reinforcing fibers are high melting points, high strength, resistance to oxidation, and low weight. Whiskers which show promise in these areas are : Refractory oxides - alumina (melting point 3722" F.) - silica (melting point 2670' F.) Metals - iron (melting point 2920" F.) - copper (melting point 2000" F.) Tensile strength of iron whiskers at room temperature is reported as high as 2 million p.s.i. with whiskers not exceeding 1.5 microns in diameter. Copper whiskers under 1.3 microns in diameter have a strength of 400,000 p.s.i. Silicon whiskers 1 micron in diameter produce strengths of 550,000 p.s.i. Very little progress has been made in developing reinforced laminates with whiskers as fibers, although, theoretically, maximum high-temperature and highstrength reinforced laminates can be produced. Nonwoven reinforcing sheets using these whiskers would definitely set up manufacturing problems, but progress is being made. Fiber Length. T h e conclusion that short staple fibers will not produce maximum physical properties is not correct. Both experiment and theory have concluded that, with proper adhesion between fibers and
...
40
0
Coeff. of Linear Expansion
6 0.4
6 5-7 1-3 1-8
8-1 0 17-20 4.5 6.6 5.4 8-20
525f 480' 450* 480° 5006 400d
... ... ...
2758 2128 212g
Used up to this temperature.
matrix, maximum strength can be achieved by using relatively short staple fibers rather than continuous filament construction. I n the case of glass fiber constructions, high strength properties have been developed with fibers approximately 0.5 inch in length (Figure 3). The commercial glass fiber mat using 0.5-inch fiber lengths will have a strength approximately 50% below maximum properties obtainable in woven fabric lay-ups. However, in special constructions, properly treated fibers form laminates equivalent to high strength woven laminates. In general, a maximum length of approximately 0.5 inch will result in maximum strength properties. Shorter fiber lengths are used to obtain maximum strength for certain fibers such as asbestos and whiskers (Figure 1). The relatively long staple fibers (approximately 0.5 to 1 inch) are required in some materials to ensure that the fibers are straight. Fibers which curl produce low strength composites. Asbestos Fibers. Nonwoven asbestos fibers produce higher strength reinforced plastics than the woven fabric reinforcements. The reasons are directly related to the fineness and wettability of asbestos fiber. The fibrous structure of asbestos is as important to its industrial value as its mineral value. Asbestos can be sub-divided into fibers so fine that only the electron microscope will reveal them. The basic single fiber of chrysotile is a smooth cylinder approximately 0.02 micron in diameter (850,000 to 1.4 million per linear inch). Because of their fineness, these fibers have an extremely VOL. 5 4
NO. 8
AUGUST 1962
33
For maximum laminate strength the fiber must carry its share of the load
large surface area and cannot be proper1)- wet after they are put together in bundles, as in yarns. There is more freedom to develop suitable coatings for the individual nonwoven fibers. The characteristics of asbestos fiber can be compared with new fibers such a s quartz, aluminum silicate, graphite, pyrofiber, steel, and molybdenum. A s shown in Table I, these individual fibers produce high tensile strengths, high elastic moduli, and high heat-resistant characteristics. Suitable bonding or finishing agents must be developed, and clean surfaces produced to promote maximum bond strength for these special fibers in nonwoven fabrics.
MANUFACTURE OF NONWOVEN FIBROUS STRUCTURE The textile and paper industries are based on two of the oldest arts. Manufacture of nonwovens draws on both of these (6, 8, 12). T o produce nonwovens by a papermaking process: a substitute must usually be found for the hydrogen bonding associated with finely divided cellulosic elements. T o use synthetic fibers, which have smooth, nonscaly surfaces, in a textile process one or more of these treatments must be added to the basic wool felting process : - Chemical treating or etching to provide interlocking.
Finishing with an adhesive binder to adhere fiber to fiber. - Mechanically interlocking or stitching Jibers across the sheet. - Blending dzferent fibers, including scalelike fibers or longu fibers which are used as carriers. -
At the present time, only one major difference exists between nonwoven textiles and papers-the method of fiber deposition. The textile process uses mechanical devices or air, while the paper process uses water as the method of controlling and depositing textile fibers. The major difference between a wet-formed nonwoven (paper product) and air- or machine-formed nonwoven (textile product) is the relationship of fiber length to fiber straightness. The air processes of fiber deposition usually produce curled fiber structures. The wet processes tend to keep fibers straight.
Composition of Type E Conventional G l a s s Fibers
Comjonent
wt.% 54.0
14.5 22.5
8.5 0.5 34
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Wet Process. Two standard types of wet process paper machines used in manufacturing useful nonwoven sheets are the Fourdrinier and cylinder machines. Modifications have been made in these machines so that a satisfactory resin or matrix situation can be accomplished. The general paper product is highly dense, so that saturation with laminating resins is difficult. Saturability can be improved by reducing paper thickness, including resins in the pulp mix, using foaming or dispensing agents in the pulp (so that when paper is dried the fibers are partially separated), air-blowing paper during drying, or increasing hole diameters or porosity in wire screen or felt carriers. Dry Process. The manufacture of dry process nonlvoven sheets can be divided into two steps:
-formation of the web -application of bonding agent Web, mat, and felt are terms for the nonwoven sheet. The web may be formed by mechanical carding of fibers, an air-laying process, or an air-flotation system. The techniques provide latitude in orientation of fibers. Fibers can be deposited so that they are roughly parallel and in the machine direction. Other patterns include orthotropic and isotropic layups. The particular equipment and method of operation is influenced by such fiber characteristics as strength, stiffness, length, diameter, flexibility, surface condition, abrasion resistance, softness, ease of fiberizing, tenacity, and resilience. A major limiting factor in the use of one t) pe of heat resistant-high strength synthetic monofilament fiber is its inability to rub fiber to fiber without destruction. However, these fibers can be surface treated or blended with other fibers to permit processing in mechanical equipment. The air flotation process lays down fibers on a large conveyor belt. The deposited fiber is sprayed with resin binder to develop a strong web or sheet. This process is typical of the methods used to produce the large quantities of nonwoven glass fiber mats for the reinforced plastics industry. The air-laying process is a relatively new procedure, and is more versatile than the air-flotation process. Fiber Orientation and degree of compactness can be very closely controlled. This process uses air pressure or vacuum with varying speed conveyor belts. The fibers are distributed into a web by aerodynamic controls. Bonding. In some cases, nonwoven reinforcing sheets can be treated with the laminating resin or matrix during the manufacturing process. No separate operation of applying a bonding agent to the fiber web is required. The resin can be applied by saturation or spray techniques immediately after the web is made. The completely resin-treated web is called a prepreg. For use in reinforced laminates, unimpregnated fibrous structures must have sufficient strength for further processing with laminating resin or matrix. This strength can be achieved by mechanical interlocking of fibers during manufacture, use of thermoplastic fibers, and 'or application of q-nthetic resins, either wet or
dry (74). Numerous bonding resins are available to :
MECHANICAL PROPERTIES
- provide fiber adhesion during resin impregnation
The behavior of a part under the influence of external forces which tend to stretch, compress, or twist, depends on three major factors: shape of the part, dimensions of the part, and nature of its material. The nature of a material with respect to its behavior under the influence of external forces is described by strength, stiffness, elasticity, resilience, and toughness. Complete knowledge of the behavior of a substance with respect to these five primary qualities involves a knowledge of its behavior under three forces : tensile, compressive, and shearing. The influence of time, temperature, and moisture of the above mentioned properties is also important. Investigations have been conducted to develop the basic theory and to relate properties of textile fiber to the tensile properties of nonwoven fabrics (without matrix or laminating resin). I n developing these relationships, the individual characteristics of fiber, bonding, geometry, and manufacturing process are evaluated. It is assumed that the Hookean theory of material holds. To develop nonwoven fabric theories, a small element of the product, a unit cell, is defined. Size of the unit cell is chosen so that it contains only continuous strands of fibers. All fiber ends are outside of the unit cell dimensions. The bond between fibers is sufficient to allow the strain in any fiber to be approximately equal to the strain induced by parallel displacement of the boundaries of the unit cell. The fibers do not buckle under load. Stress-strain curves of the unit cells and of the individual fibers can be developed. I n an ideal nonwoven structure the components of fiber, bond, and geometry would be fully utilized-that is, failure is in the fiber and not in the bond. In such an analysis, woven structures are theoretically not as efficient in utilizing these components. Mechanical Behavior of Laminat e 6. Stress-bearing materials are called isotropic when the engineering properties are the same in all directions. Materials which do not have this characteristic are anisotropic. One particular type of anisotropy, orthotropy, occurs when an essentially two-dimensional material possesses two definite axes of symmetry at: right angles to each other. Paper, wood, and woven fabric laminates are orthotropic. -4naly tical theories have been developed for wood, plywood, and woven fabric-reinforced plastics to predict the behavior of orthotropic materials when the principal stresses are not along the axes of symmetry. These theories can be applied to the engineering properties of nonwoven fabrics. The analysis takes into account the effect of free fiber lengths between bonded areas, characteristic fiber flexibility, and binder content of nonwovens. I n developing this analysis, certain simplifying assumptions have to be made. However, some degree of confidence can be placed in the resulting theory. I n the stress analysis of metals, the differential element is chosen to be infinitely small, and is assumed to be
-permit resin to saturate sheet -permit chemical interaction between fiber and resin - have no detrimental efects after laminate is manufactured.
a‘
Many of the nonwoven fibers now in preliminary development stages must be bonded to form a strong web. These bonded sheets also make available to industry a product which can be resin-treated into diversified prepregs using different prepreg processes and resins. Finishes. I n the past decade, extensive work has been conducted to develop new chemical finishes designed to have one part of the chemical (polymer) adhere to the fiber and another part adhere to the resin. These chemical finishes applied to fibers can also reduce or eliminate resin crazing or strains adjacent to the fiber. Recent advances in developing chemical finishes are noted in Developments in Fiber Technology, page 55. Reinforced plastic laminates can reach maximum strength at room and elevated temperatures only when the base of fiber and resin can handle its share of the load and is resistant to heat degradation. Improvement in these areas continues. One of the major advances in reaching the objective has been through fiber finishes. I t is possible to combine finishes and binders for webs using only one operation or polymer (73). Most of the work to date concerns finishes for glass fibers. These include : vinyltrichlorosilane, styrene, ethylene oxide, epichlorhydrin, phenylsilane, and vinyldimethylethoxysilane. Different finishes are used to obtain maximum strength with different resins. Special finishes can be applied to nonwoven fibers more readily than to woven fabrics. Glass fibers or yarns generally require a special slippery coating (such as starch) to permit weaving. After weaving, this coating is removed by heat treating or chemical cleaning and then the finish is applied. Most of the synthetic inorganic fibers require this treatment also. With nonwovens, the finishes can be applied either prior to or after forming webs without any other special treatment. Degree of Fiber to Resin Adhesion. The problem of evaluating the characteristics of the fiber-to-fiber bond will continue to plague the industry. Various chemical and mechanical measuring techniques have been developed but no satisfactory general procedure has been found. Special test procedures do exist for specific fiber and resin products. The most obvious and conventional procedure for determining satisfactory bond is to determine the final physical properties of cured composites. Presumably bonding is best when the highest specific fiber properties are obtained, based on using maximum fiber density. Obviously then, highest strength will be obtained when using the smallest diameter fibers so that the final structure will be composed almost entirely of load-bearing fibers (Figure 4). As the smaller diameter, high strength fibers are used, the matrix will become principally a chemical coupling agent.
D. V Rosato holds the posztzon o f Corporate Marketing Manager, Northeastern Territory, for Telecomputing Corporation, Newton, Mass.
AUTHOR:
VOL. 5 4
NO. 8
AUGUST 1 9 6 2
35
.
uniform and homogeneous. This is donc although minute voids or cracks are known to be present. A similar approach can be used in nonwoven analogies. The theory of fiber reinforced laminated structures has been a satisfactory approach to many industry problems. Development of data and know-how in the glass fabric-reinforced plastic industry is considered a major accomplishment. Most of the work has specifically concerned woven reinforcements, although some information is available for products using nonwoven glass, cotton, asbestos, and rayon fibers. The laminated theory approach applies to both woven and nonwoven reinforcements. It is possible to make a laminate that is isotropic in the plane of the laminate from orthotropic laminations. This is done by varying the orientation of each ply. The elasticity and strength of the isotropic material can be predicted from a know-ledge of the properties of parallel laminates made of the same material. Laminate strength is related to fiber strength. A statistical approach permits systematic mathematical and practical evaluation in applying certain fibers in efficient and useful nonwoven structures. Laminate Properties as Related to Nonwoven Fiber Orientation. The subject of fiber orientation in reinforced plastics has been of interest to mathematicians and engineers. It will continue to stimulate interest since various unknown factors remain. These can be related to chemical factors (coupling agents), mechanical factors (Hooke's law), orientation (manufacturing process), and structural, heat-resistance, or electrical characteristics. Certain assumptions can be made, however, which permit developing a theoretical and practical approach to improve reinforced composite constructions. Fiber orientation, bond, and amount of fiber are keys to developing maximum efficiency (Figures 4 and 5 ) . In a nonivoven laminate construction, assume that the fibers are infinitely thin and rigidly joined where they cross each other. -4 square unit cell composed of these fibers (assumed uniformly distributed) is subject to stresses u1 and u z parallel to its sides, which cause strains € 1 and € 2 , respectively. Consider a fiber crossing the unit cell so as to make the angle 0 with the u1 direc-
Table II.
Properties of Reinforced Laminates Tensile E x 70-0 Strength, P.S.I. P. r.
s.
Matrzx Typical organic resin Alumina Ethyl silicate
0 . 3 to 0 . 5 0 . 1 to 0 . 3 0.1
4000-10,000 1000-3000 500-2000
tion. Its unstrained length within the cell is sec 0. When the cell is strained by amounts e1 and €2, the strain in the fiber will be (€1 cos20 € 2 sin%) (7, 9 ) . If the effective fiber modulus is E, then the load carried by the fiber will be E j (el cos2t9 e2 sin20). The number of fibers at angle 0 crossing the base line of the cell i b proportional to cos 0. If the fibers are distributed as a function J ( O ) , then the number of fibers crossing the base line at angle 0 will be cos0 f ( 0 ) . The total load in all these fibers (at angle 0) is:
+
+
Ef(E1cos2B
.
e 2 sin2@cosOJ(0)
Therefore, the total stress is :
S_,i2 ,/2
u1 =
cos20
+ c 2 sin20)cosOf(0) d0
Investigators have determined that this expression is dependent on the total number of fibers in the unit cell. To determine the number of fibers, consider u1 as a specific stress by dividing by the number of fibers:
+ 2 sin20)cos20J(0) d0
E, (61cos28 g1
= fi2
S-& 7r 12
-,I2
f(0)de
A similar expression can be written for U Z . If fibers are uniformly distributed, the rewlt is: =
3/ 8
c ~ 2=
8
UI
u1
+ Er'aj + '13 Ef'Ci
'/ 3 E L ) €1)
Then if E1 and E2 are Young's moduli in the directions and u2, and u1 = 0 and uz = 0, the result is:
E1 = E2
u1
= - = '/3
E,
€1
F o r E of f i b e r
Actwl
Theoretical---w
b L
F or E o f resin
Resin Content, % by wt,
o j matrix content on strength and elastic moduli o j reinforced laminates
Figure 4. Effect
36
INDUSTRIAL AND ENGINEERING CHEMISTRY
E m 'Et
Figure 5. Elastic moduli ratio as. stress ratio for oarious$ber to total volume ratios
Similarly, the strength is 1/3 of the fiber strength. Also Poisson’s ratio is and shear modulusor modulus of rigidity G = E J / 8 . These results agree with some of the actual values obtained with nonwoven laminates. Graphs can be plotted to relate the properties of laminates with known properties of fibers (Table I), matrixes (Table 11), and the volume ratio of fiber and matrix. T o obtain the theoretical maximum strength, it is assumed that the fibers are straight, base properties of fiber do not appreciably change during fabrication, satisfactory bond exists between fiber and matrix, and Hooke’s law holds. Correlations between the theoretical and actual values will result in fixed constants to take care of discrepancies (10). Since reinforced laminates follow Hooke’s law, stress is proportional to strain, and the calculated value of modulus of elasticity becomes a known and reliable value. In developing equations to produce Figures 5 and 6, consider a laminate or composite made up of fibers and matrix subjected to an external load P. Figure 7 shows equations for the relationship of stress (u), modulus of elasticity ( E ) ,strain (e), volume of matrix (V,), volume of Vf). fiber ( V f ) ,and volume of laminate ( V , = V, The resultant equations are:
I‘
Ict m 4
F-tf-+I
Figure 7. Basisf o r developing graphs
h and w are constant
v, =
+ tfh,, + VfAf
t,hw
Pl = U L A ~=
+
For a given strain there is almost no movement between matrix and fiber: €1
and when f i m
(3)
= Em = €3
+ V , = 1:
NOMENCLATURE
A = area subject to P E = modulus of elasticity h = height
P
=
load
t = thickness
(4) urn
+
UI
Substituting Equations 1 and 2 in E, = ___
Q
€1
the result is:
El
=
Vf (E, - E,)
.-
+ Em
V
(5)
=
volume
w = width E = strain =
stress
Subscripts f = fiber 1 = laminate m = matrix (resin)
Vl
Figure 6 expresses Equation (5) graphically. LITERATURE CITED
._
50
0 Lo
in
0
-E x
W
I
-
d
W
‘0
5
I
5
50
10 ( Et-
E,,,
)
100
x IO6 FIEI.
Figure 6. Elastic moduli of laminated components us. elastic moduli the composite f o r various fiber to total volume ratios
of
(1) Aeronautical Standards Group, Department of Defense, “Plastics for Flight Vehicles,” Military Handbook, MILHDBK-17, NOV.5, 1959. (2) Bacon, R., Bowman, J. C., Bull. Am. Phys. Sac. 2, 131 (1956). (3) Brenner, S. S., Acta Met. 4, 62 (1956). (4) Carroll-Porczynski, C. Z . , “Inorganic Fibers,’’ Academic Press, New York, 1958. (5) Chem. Eng. 66, 118 (Aug. IO, 1959). ( 6 ) Fiicrst, P. E., Modern Plastics 35, 115 (October 1958). (7) Heller, .I. T., Norris, C. B., ASTIA 202503, October 1958. (8) Nicely, D. C., IND.ENG.C H E W 51, 910-11 (August 1959). (9) Olson, 0. H., Islinger, J. S., WADC TR 59-500,Pt. I, March 1960. (IO) Otto, W., J . Am. Chem. SOC.38, No. 3, 122 (1955). (11) Petterson, D. R., IND.ENG.CHEM.51, 902-3 (August 1959). (12) Rosato, D. V., “Asbestos,” Reinhold, New York, 1959. (13) Rosato. D. V., Brit. Plastics 33, 348-51 (August 1960). (14) Sherwood, N. H., IND.ENG.CHEM.51, 907-9 (August 1959). VOL. 5 4
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AUGUST 1962
37
