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AD-773 960
TENSILE (COMPRESSIVE) PROPERTIES OF GLASS-EPOXY COMPOSITES AS A FUNCTION OF VOLUME FRACTION
M. J. Michno, Jr. , et al
Monsanto Research Corporation
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Prepared for:
Office of Naval Research Advanced Research Projects Agency
December 1973
DiSTRIBSiED BY:
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J REPORT TITLE
Tensile (Compressive) Properties of Glass-Epoxy Composites as a Function of Volume Fraction
4 DESCRIPTIVE HO J FS (Typv ol rnporl .mil inctustvv liatcs)
*. AU T HORlSI fFiri? name, mid'llv ini'utl, last nitmf)
M. J. Michno, Jr., and F. J. Shea
RLPOR T DATE
December 1973 9tf. CONTRMCT OR GRANT NO
N0001'4-67-C-02l8 h. PROJEC T NO
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^ZL 7b. NO. OF REFS
8a. ORIGINATOR'S REPORT NUMBERIS)
HPC 73-163
9b. OTHER REPOR i NO(S) (Any other numbers that may be assigned thta report)
0 DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited
II SUPPLEMENTARY NOTES 12 SPONSORING MILI TARY ACTIVITY
Office of Naval Research Washington, D. C.
I i AHSTKAC T
The mechanical performance of unidirectionally reinforced glass epoxy composites was studied as volume fraction filler was varied over the range 30-70 percent. Experimentally determined quantitites included: longitudinal and transverse tensile strength, ultimate strain, modulus; and Polsson's ratio; and longitudinal and tr^.isverse compressive strength. Data analysis Indicated that all properties varied linearly with volume fraction. Longitudinal properties and Polsson's ratio were interpreted in terms of the rule of mixtures.
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S^t urity dttft^Iliratior
Mechan ics Volume fraction Reinforcsd Plastics Tensile Strength Compressive Strength Moduli U;timate Stra ins Poisson's Ratio
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HPC 73-163 ITEM A002
TENSILE (COMPRESSIVE) PROPERTIES OF GLASS-EPOXY COMPOSITES
AS A FUNCTION OF VOLUME FRACTION
by
«
M. J. Michno, Jr. and F. J, Shea
December 1973
D D C ^n?\
Ffn U 1ST4
E Monsanto/Washington University Association
High Performance Composites Program Sponsored by ONR and ARPA
Contract No. N000U-67-C-0218, ARPA Order 876
Approved for Public Release: Distribution Unlimited.
The views and conclusions contained In this document are those of the authors and should not be Interpreted as necessarily representing the official policies either expressed or Implied, of the Advanced Research Projects
Agency or the U. S. Government.
ii M-
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FOREWORD
The research reported herein was conducted by the staff of
Monsanto/Washington University Association under the sponsorship of
the Advanced Research Projects Agency, Department of Defense, through
a contract with the Office of Naval Research, NOOOIi»-67-C-02l8 (formerly
NOOOU-Se-C-OO^K ARPA Order No. 876, ONR contract authority NR-SSö-MV
^-13-66, entitled "Development of High Performance Composites."
The prime contractor Is Monsanto Research Corporation. The
Program Manager Is Dr. Rolf Buchdahl (Phone 311»-694-l»721).
The contract Is funded for $7,000,000 and expires 30 June, 197'*.
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TENSILE (COMPRESSIVE) PROPERTIES OF GLASS-EPOXY COMPOSITES
AS A FUNCTION OF VOLUME FRACTION
INTRODUCTION
Filament winding is a ccnmonly employed viable technique for
producing glass-reinforced plastic comr^ents. Processing variables
which affect the mechanical performance of these components include
widing tension, mandrel temperature, and winding speed [1]. Winding
tension directly controls the volume fraction filler (v^). Herein we
consider the effect of variable vf on the strength of glass-epoxy
composites.
A general tensor polynomial strength criterion proposed by Tsal
and Wu [2] appears to have wide applicability and for specially
orthotropic material under plane biaxial stresses (In the absence of
shear stress) assumes the form:
F.a, + F.o. + F-.a. + I n 2^2 in r22CF2 + 2F12al02 " , (0
o. ■ longitudinal stress
o« ■ transverse stress
F., F - 2nd rank strength tensors (contracted notation)
F.., F.-, F.. - '♦th rank strength tensors
The normal stress Interaction tensor F.2 can be determined only from
tests under combined states of stress. However, the non-Interacting
components of the strength tensors can be experimentally de^rmined from
simple states of stress:
Fi -x J_ X' F2 " Y ' Y'
11 1
XX' 22 I
YY'
(2)
(3)
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'
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u
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'Hü. I ili.H'iptB—M—i
where X, X', Y, Y' are uniaxial tensile and compressive strengths along
longitudinal and transverse directions respectively. D-termination of
X, X', Y, Y' as a function of v^. would allow calculation of F,, F„, F,.. f 12 11'
and F2 as a function of vf. If additional determinations of ^«(v,)
were made the applicability of Eq. (1) for a range of vf could be
ascertained. Other commonly employed failure criteria such as maximum
strain require knowledge of the ultimate strains at failure and the
elastic constants. Hence, in addition to strength data we seek to
determine as a function of vf longitudinal and transverse moduli
(E.., E ); longitudinal and transverse ultimate strains (e,." .
e2 ); and Poisson's ratio v.«.
MATERIALS AND SPECIMENS
Compos'tes were prepared using ehe same materials and filament
winding techniques as reported in detail elsewhere [3]. The matrix
resin was Epon 828 plus Shell Curing Agent Z(20 phr*). The filler was
PPG 1062-T6** E glass roving. Unidirectional composites were prepared
by filament winding on a rectangular mandrel with four 6 In. x 8 in.
faces. After winding the mandrel was placed in a vacuum chamber for
45 min. to remove any entrapped air from the samples. The mandrel was
then remounted on the filament winder and the final volume fraction was
established by clamping steel plates to the mandrel faces, the final
thickness of the sample being cortrolled by contact with preselected
shims. Winding stresses in the glass were then relieved by cutting the
glass tape across two corners of the mandrel. The composites were then
B-staged while rotating on the mandrel under heat lamps. Final curing
was at 100oC for 30 mln. followed by 2 hours at 150oC.
* Parts per hundred resin
** Manufactured by PPG Industries, Inc.
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TENSILE SPECIMENS
Straight sided specimens 1/2 in. wide and 6 In. long were cut
from the plates at 0° and 90° to the fiber direction. These were
tabbed with glass fabric reinfo.ced laminates to establish a gage
length of 3 in.
Several hoop wound tubular samples at selected volume fractions
were also tested In tension.
COMPRESSION SPECIMENS
Compression samples were prepared by adhesive bonding unidirectional
composite sheets to either side of a 1/2 in. thick a'uminum honeycojib.
The resultant sandwich plate was then cut Into strips 1 in. wide by
1 1/2 in. long with the fiber direction either parallel or perpendicular
to the length. The honeycomb of the rectangular sandwiches was then
machined away (slotted) at the mldsection. The slotting produced an
unsupported mid-length of approximately 0.3 In. Care was taken to
eliminate adhesive from the composite faces along this unsupported
length. As In the case of tensile samples, several hoop wound tubular
samples at selected volume fractions were tested to determine transverse
compress Ive strength.
EXPERIMENTAL DETAILS
The tensile specimens were tested In an Instron tester at a
cross-head speed of 0.2 in/min. An extensometer was used to continuously
record strains to complement the continuous load record. All tests were
conducted at room temperature (750F). Composite stress and modulus
were calculated based upon the original cross sectional area and the
recorded loads.
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Compressive samples were also tested in an Instron tester at a
crosshead rate of 0.2 in/min. Details of the testing followed those
recommended in [k] and included the use of a lightly clamped lateral
guide (outside the unsupported length). This method of testing resulted
In the desired compressive failure mode within the unsupported length
of the specimen and avoided end brooming or crushing and premature
buckling failure. The ultimate load at failure was reduced to the
ultimate stresses at failure based on the original cross sectional area
of each face plate and the assumption that each face plate carried one
half of the total load.
All tests on tubular samples were conducted on an MTS closed-loop
servo control system. The tubes were Instrumented with strain gages to
determine ultimate strains and Polsson's ratio.
TEST RESULTS AND DISCUSSION
Stress-strain curves for both 0° and 90° composites were essentially
linear to failure. The resulting graphs are shown in [3] and are not
duplicated here.
Tabulated test results appear In the Appendix. Data gathered
includes: longitudinal propcties X, e^ , E^ (Table Al) and,
X' (Table A2); transverse properties Y, e " , E«. (Table A3) and Y',
-e«.ult (Table AM; Polsson's ratio v. (Table A5). C )mpresslve modul I 22 2]
and ultimate strains were not determined for longitudinal samples.
Compressive moduli for transverse samples were approximately equal to
the transverse tensile moduli.
H
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-
:
Data include the observed values of the various quantities and
when appropriate the average values of several observations at a given vf.
Clearly scatter exists and a statistical treatment of the experimental
data Is In order.
In all cases a simple linear relationship was sought and data
were fit to the best straight line employing the least square technique.
The resulting relations
X ■ 225.^
ult 11
11
X'
0.97v
S.O'JV
Y = 5-6^
.u,t - - 1.12v L
E22 - 6.09v
v - is.yAv
ips and associated standard deviations (SD) are:
CO
(5)
(6)
(7)
(8)
(9)
(10)
(ID
+ 6.86; SD = 10.59 (Ksi)
+ 1.62; SD = .Zk {%)
+ 1.70; SD - .50 (Msi)
+68.8C.; SD «= 7.28 (Ksi)
+ 4.13; SD - 0.95 (Ksi)
+ 1.09; SD •= .08 it)
- I.M; SD - 0.26 (Msi)
+13.71; SD ■ 1.6A (Ksi)
These relationships are depicted graphically in Figure 1-8. The solid
lines and shaded region represent the appropriate linear dependency
upon volume fraction plus and minus one standard deviation. The open
circles Indicate a single experimental observation and an open circle
with a scatter band represents the actual experimental scatter about
the average valje. In the case of ultimate longitudinal strain e,,
(Fig. 2) an attempt was made to fit the best horizontal line i.e.
e ult - const, however such a fit resulted in a standard deviatior. which
exceeded the standard derivation of a linear relationship.
if one considers the longitudinal data (Figs. 1-3) the product of the
ultimate strain and modulus for a given vf accurately predict the ultimate
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tensile strength at that v. I.e.
vf " " vf (12)
This result is to be expected in view of the fact that behavior was
nearly linear to failure.
Examination of the transverse tensile data (Figs. 5-7) discloses
the transverse modulus E . (Fig. 7) increases with v, at a greater rate
than does the transverse tensile strength Y (Fig. 5). Hence, the
transverse ultimate strain e (Fig. 6) must decrease with Increasing v.
If for any given v, strength and strain are to be nearly linearly
related, I.e.
■ (e"1' E„) vf v, 22 22 f (13)
A simple computation based on Eq. (8)-(10) verifies that Eq. 13 Is
essentially correct.
A point worth noting is that the transverse strength data Y (Fig. 5)
and Y' (Fig. 8) Include several test results from tubular samples (see
Appendix 1). Thene results agree favorably with the results of tests
on tensile strip or sandwich strip samples Indicating that free edge
and/or size effects were accounted for within observed scatter.
RULE OF HIXTURCS
Longitudinal Properties
The linear form for longitudinal strength and moduli as a function
of v. Indicates that Interpretation in terms of the rule of mixture
Is possible. Consider longitudinal tensile strength X (Eq. b). We wish
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-; <mmm
to express this equation in the form:
X - X-v, + X (1 - vj f f m f
where,
X = composite strength
X, ■ strength of the fiber
X ■ strength of the matrix at composite ultimate strain
v, ■ volume fraction filler.
(IM
Us ing Eq. (5) and say v, ■ 0.50 we determine e ult 11 2.11%. We know [3]
that the modulus of the matrix is E « O.hk Msi hence it follows the m
Xm ■ 3.21* Ksi. Composite strength at v » .50 is determined from Eq. {k)
to be X ■ 119.60 Ksi. We can then incorporate Eq. (U) and back
calculate Xf. The result is Xf - 230 Ksi and the r.jle of mixtures Eq. (14)
can be written:
X - 230vf + 9-24(1 - vf) Ksi (15)
X, based upon the above calculation is a little lower than the value one
would anticipate for virgin E-glass fibers; however, it may be representative
of the strength of a typical fiber after filament winding.
A similar calculation for longitudinal compresslve strength results in
*■
X' - 170.3vf + 9-24 (1 - vf) Ksi (16)
Of course, this computation assumes the tensile and compresslve moduli and
ultimate strains ar« equal, a fact not verified.
Rule of mixtures Interpretation of the linear longitudinal modulus
vs. v, (Eq. 6) results In
E11 - ll.lvf + .44 (1 - vf) (Msi) (17) ht
A
The back calculated E^ - 11.1 (Ms!) agrees favorably with commonly
accepted valu«s of modulus for E-glass.
Poisson's Ratio
Poisson's ratio v.« can also be closely approximated by a rule of
mixture formulation [5]. The appropriate relationship is:
v 12 vfvf
vfvf + v-. (1 " V,) m (18)
where
v, - Poisson's ratio of the fiber
v - Poisson's ratio of the matrix
v, ■ volume fraction fiber
Using the values of v, - .25 and v ■ .35 reported In [6] the rule
of mixture prediction for v.. was calculated and is presented In Fig. 9.
This figure also depicts the experimentally determined values v9 .
These values of v. were used along with knowledge of E,, to calculate *! "
S.» ■ S2. (compliance coef.). The corresponding value of v.« was then
calculated from knowledge of E.. and the relationship -v.» = S.-E...
Clearly a great deal of scatter exists but the rule of mixtures prediction
appears to apply to the range 58% 1 Vr £ 75*
CONCLUSIONS
Longitudinal and transverse tensile strength, ultimate strain, and
moduli data can be well correlated by linear relationships over a volume
fraction range 30-70 percent. Longitudinal and transverse compresstve
strength data are also linearly related to vf In this range. In particular
'rule of mixtures' models for longitudinal strength, and modulus are
appropriate. Knowledge of X(v,), X^v,), Y(vr). and Y'(vr) allows
strength tensor components F., F.., F., F«, to be determined as a function
8
*)
of v,. Reported values of ultimate strains and Polsson's ratio would
a'low computation of the maximum strain failure criterion predictions
as a function of v.. Data available limit this prediction to
58^ £ vf <^ 75% and to quadrants one and four of either principal strain
or stress space.
^ l
I REFERENCES
1. Oesai, R. R. and Kalnin, I, L., "The Effect of Filament Winding Process Variables on the Performance of Carbon or Fiberglass Reinforced NOL Rings," 24th Annual Technical Conference, Reinforced Plastics/Composites Division, SPI, 1969-
2. Tsai, S. W. and Wu, E. M., "A General Theory os Strength for Anisotropie Materials," J. Composite Materials, Vol. 5, p. 58, 1971.
3. Lavengood, R. E, and Ishai, 0., "The Mechanical Performance of Cross-Plied Composites," Polymer Engineering and Science, Vol. 11, No. 3. p. 226, 1971.
k. Structural Design Guide for Advanced Composite Application, Advanced Composites Division, ARML, Chap. 7, Test Methods, 2nd Edition, January 1971.
5. Ashton, J. E. Halpin, J. C, and Petit, P. H. , Primer on Composite Materials: Analysis, Technomic, I969.
6. Lavengood, R. E. and Ishai, 0., "Deformational Characteristics of Unidirectional Glass Epoxy Corrposites In flexure", Jour, of Matls., JMLSA, Vol. 5, No. 3, p. öM, 1970.
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Fig. 1. Longitudinal Tensile Strength vs vf
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Fig. 2. Ultimate Longitudinal Strain vs vf
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Fig. 3. Longitudinal Modulus vs vf
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Fig. <♦. Longitudinal Compressive Strength vs v^
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Fig. 5. Transverse Tensile Strength vs v-
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Fig. 6. Ultimate Transverse Strain vs v.
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Fig. 8. Transverse Compresslve Strength vs v-
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Fig. 9. Poisson's Ratio vs v.
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I
2
•— r>.r».\Oroj-in\o rAcr\j-r~Jloooor^m cvoon .— \oo — oor^tri»- Jf o^o^o^ooc^\o^a^ .— c^^ooolo^o^oo .— oo CMCM-^^CM.— oo^- *-' — — — — ——— CM— CMCMCMl— — CMCM CMCMCM CMCMCMCMCMCMCMCMCM
\
- -
-p^v
■
vf(*)
ii8
58
59
61
63
75
TABLE A5 - POISSON'S RATIO
^1
.133
.148
.081
.120
.103
.112
.098
.106
.109
.112
.077
.068
• 117
'
ii