TENSILE STRESS-RUPTURE AND CREEP
CHARACTERISTICS OF TWO
GLASS-FABRIC-BASE
PLASTIC LAMINATES
No. 1863
June 1937
INFORMAT!fl9 RFV1EWED'
AND REAFFiRMED
1965
This Report is One of a Series
Issued in Cooperation with the
ANC-17 PANEL ON PLASTICS FOR AIRCRAFT
of the Departments of the
AIR FORCE, NAVY, AND COMMERCE
1P1111111119[.:.,.
1
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FOREST PRODUCTS LABORATORY
MAD/SON 5. WISCONSIN UNITED STATES DEPARTMENT OF AGRICULTURE
FOREST SERVICE
I n Cooperaboo with the University of Wisconsin
TENSILE STRESS-RUPTURE AND CREEP CHARACTERISTICS
1
OF TWO GLASS-FABRIC-BASE PLASTIC LAMINATES —
By
KENNETH H. BOLLER, Engineer
2
Forest Products Laboratory, —
Forest Service
U. S. Department of Agriculture
Summary
Stress-rupture and strain-time relationships were obtained from tests up
to 1,000 hours on two glass-fabric-base plastic laminates normally used
in aircraft design. One was made with a typical polyester resin and 181
Volan A glass fabric, the other with a typical epoxy resin and 181 Volan A
glass fabric. Data were obtained to show the effect of tensile loading at
0° to the warp direction under atmospheric conditions of 73° F. and 50
percent relative humidity and at 45° to the warp under the same atmospheric conditions and at 73° F. in water. The data show that the stressrupture curve may be approximated by straight lines on semilogarithm
coordinates, ° r = cro - M log t, and that the strain-time relationship may
be shown as a function of the applied stress and time. The strain, e t , at
any time, t, may be expressed as E t =
sinh cr/ cre + t o m' sinh o-/ crm.
The constants were evaluated and are presented.
e'
The data show that the stress-rupture characteristics of the material
tested for this report at 0° to the warp are similar to that reported in
Forest Products Laboratory Report 2039. The data here reported, however, show the lower stresses at which the material fails when loaded at
45° to the warp and it shows that the creep strains at 45° loading are up
to 6 times greater than creep strains at 0° to loading.
1
— This progress report is one of a series (ANC-17, Item 56-1) prepared
and distributed by the U. S. Forest Products Laboratory under U. S.
Navy, Bureau of Aero autics No. NAer 01768 and U. S. Air Force
Contract No. DO 33(616)56-9. Results here reported are preliminary
and may be revised as additional data become available.
2
—Maintained at Madison, Wis. , in cooperation with the University of
Wisconsin.
Rept. No. 1863
-1-
Introduction
The stress-rupture and strain-time behavior of plastics is important in
the design of machine parts and structural members. It is known that
plastics, as well as metals and wood, may fail under long-continued
stresses that are less than their ultimate short-time strength. It is also
known that the deformations caused by long-term loads may become excessive and render materials unsuitable for service.
Much research is being done on the creep characteristics of various
structural materials at both room and elevated temperatures to obtain
design criteria and empirical formulas that represent the data. However, to develop design criteria especially suitable for use in aircraft
and missile design, it was essential to obtain the stress-rupture and
strain-time relationships of glass-fabric-base plastics in more than one
direction. Relationships that result from a tensile stress in the plane of
the laminations at 0° and 45° to the warp direction were desired. At 0°
to the warp, data were desired for normally dry conditions, 73° F. and
50 percent relative humidity. At 45° to warp, the data were desired for
the same dry condition and at 73° F. in water. Since aircraft applications were the primary consideration, the loads were to be applied for
periods up to 1,000 hours.
Even though the primary objective of this investigation was to obtain
stress-rupture data at 45° to the warp for comparison with those at 0°
to the warp, a secondary objective was to obtain some comparative creep
data. Tensile strains were measured, and a mathematical evaluation of
these data is presented.
This work was conducted at the Forest Products Laboratory from January
1956 to May 1957 at the request of and in cooperation with the ANC-17
Panel on Plastics for Aircraft.
Laminates Tested
Two types of glass-fabric-base plastic laminates were evaluated. One
was made with a typical polyester resin, Paraplex P-43, the other with
a typical epoxy resin, Epon 828 CL. Both were fabricated with 181 Volan
A fabric laid up with adjacent plies parallel. One panel 1/8 inch thick by
36 inches square was made of each type of laminate.
Rept. No. 1863
-2-
The polyester panel, 12 plies thick, had ari average total thickness of 0.131
inch, a specific gravity of 1.79, a resin content of 39.16 percent, and a
Barcol hardness of 65.5. This panel was cured at a pressure of 10 pounds
per square inch at 220° F. for 20 minutes, then at 250° F. for 70 minutes.
Quality control specimens were cut from this panel and tested according to
Federal Specification L-P-406b. Results showed that the strength parallel
to warp was greater than that required by Specification MIL-P-8013B. The
average properties were as follows: (1) at 73° F. and 50 percent relative
humidity, the average maximum stress was 49,980 pounds per square inch
as compared with the specified 40,000 pounds per square inch, the stress at
the secondary proportional limit was 29,550 pounds per square inch, and the
secondary modulus of elasticity was 2,465,000 pounds per square inch; (2)
after a 2-hour boil the maximum stress was 47,640 pounds per square inch
as compared with the specified 38,000 pounds per square inch, the secondary proportional limit was 26,080 pounds per square inch, and the secondary modulus of elasticity was 2,432,000 pounds per square inch.
The epoxy panel, 13 plies thick, had an average total thickness of 0.122 inch,
a specific gravity of 1.86, a resin content of 33.57 percent, and a Barcol
hardness of 70.4. This panel was cured in a hot press at 215° to 220' F. ,
at contact pressure for 12 minutes then at a pressure of 25 pounds per square
inch for 48 minutes. Quality control specimens, cut from this panel and
tested according to Federal Specification L-P-406b, showed greater strength
than called for in Specification MIL-R-9300A and MIL-P-25421. The average properties are as follows: (1) at 73' F. and 50 percent relative humidity,
the initial proportional limit was 15,690 pounds per square inch, the secondary proportional limit was 44,020 pounds per square inch, and the maximum
stress was 60,240 pounds per square inch. For maximum stress, the specification value is 47,000 pounds per square inch. The initial and secondary
moduli of elasticity were 3,560,000 and 2,592,000 pounds per square inch
respectively; (2) after a 2-hour boil, the initial proportional limit was 15,260
pounds per square inch, the secondary proportional limit was 47,070 pounds
per square inch, and maximum stress was 59,450 pounds per square inch.
For maximum stress, the specification value is 45,000 pounds per square
inch. The initial and secondary moduli of elasticity were 3,457,000 pounds
per square inch and 2,594,000 pounds per square inch respectively.
Additional control specimens were tested to evaluate the short-time tensile
strength of the material at 0' to the warp direction and under the same conditions at which the long-time specimens would be tested. The short-time
specimens were closely matched with the long-time specimens and tested
according to Method 1011 of Federal Specification L-P-406b.
Rept. No. 1863
-3-
These test results are as follows: (1) The dry maximum stress of the polyester laminate at 0° to the warp was 50,560 pounds per square inch, and that
of the epoxy laminate was 58,320 pounds per square inch. These values agree
with the quality control sampling. (2) The dry maximum stress of the polyester laminate at 45° to the warp was 21,650 pounds per square inch, and that
of the epoxy laminate was 22,800 pounds per square inch. (3) The wet maximum stress of the polyester laminate at 45° to the warp was 14,690 pounds
per square inch, and that of the epoxy laminate was 21,810 pounds per square
inch. The wet specimens -in these tests were conditioned in water at 73° F.
for 60 days before they were tested. Strain data were also observed on these
creep-control specimens. The envelopes of tensile stress-strain data for
these six conditions are shown in figures 1 to 6.
Method of Test
Data for the stress-rupture and strain-time relationships were obtained in
tension by using the type 2 specimen described in Method 1101 of Federal
Specification L-P-406b. The specimen was held by 1/4-inch steel plates
that were clamped together by four bolts. The load was applied to the specimen through these plates with universal joints, a knife-edged lever system,
and weights in creep machines like the one shown in figures 7 and 8.
These tensile-creep machines were in a room conditioned at 73 • F. and 50
percent relative humidity. Dry tests were made at this condition. Wet tests
were made in these machines with the specimens under water at 73° F. The
water in the tank of the creep machine was maintained at a constant level.
The lever-arm system was calibrated to determine the ratio of the load suspended from the arm to the load on a load cell in the machine. The load cell
was a steel tensile specimen 1/8 inch thick that had been previously calibrated
for its load-strain characteristics. The lever-arm ratio for each machine
was determined and creep tests were made on plastic specimens with the
lever arm level.
Tensile strain was measured with a creep extensometer (fig. 9). It magnifies
the strain in the specimen through a series of mechanical and optical levers
(fig. 10). The magnification ratio of each extensometer was determined by
comparing strain observations on the load cell with scale or dial readings on
the extensometer. A magnification of 1 inch on the dial equaled a strain of
0.004 inch per inch on the specimen. A magnification of 1 inch on the optical
scale equaled a strain of 0.0001 inch per inch on the specimen. A combination of these two ranges was used. For tests of laminates at 0° to the warp,
Rept. No. 1863
-4-
the dial was used to observe the elastic and initial deformation. Then creep
strains were observed on the optical scale. For tests of laminates at 45° to
the warp, the dial was used throughout.
An attempt was made to measure the total strains with SR4 gages attached to
a spring clip instead of with the lever system shown in figure 9. This was
done on specimens tested at 45° to the warp when dry. It was satisfactory
for short periods of time for large strains. It was abandoned, however, because the creep in the spring clip and gage were excessive for small strain
measurements and could not be tolerated.
The load that was applied to the various specimens depended on the quality of
the panel, which had been determined from the short-time tensile strength.
Stress levels were chosen at 5 percent intervals beginning at 80 percent of
the maximum and decreasing until the specimen supported its load for 1,000
hours. This procedure necessitated the choice of additional intermediate
percentages in order to fill out and complete the stress-rupture curve. It
also limited the data for stress-time-strain relationship to the high percentages of stress.
The loading weights, computed from stress chosen, the cross section of the
specimen, and the lever ratio of the creep machine, were supported on a jack
while the specimen was being installed in its creep-machine. The weights
were then lowered slowly, so that the total load was applied to the specimen
in about Z minutes. While the load was being applied, the strains were observed. Sometimes the gears in the extensometer had to be reset because of
limitations in travel. The moment at which, in the opinion of the operator,
the specimen completely supported the weights marked the beginning of time
and of the observed creep strain. The next observation was made 1 minute
later, and succeeding ones at intervals that increased approximately geometrically. Timers that were shut off automatically when failure occurred
were used to measure the interval of time required to cause failure.
Presentation of Data
Tables 1 to 4 present the stress-rupture and the strain-time data for the two
materials. In each table the stress applied is shown in column 1 and is expressed as a percentage of the short-time ultimate tensile strength in column
Z. The time required for each specimen to fail at the constant stress level
is shown in column 3. If a specimen had not failed after 1,000 hours, it was
removed and the actual number of test hours was noted. These data are also
Rept. No. 1863
-5-
shown in figures 11 to 12, where the steady-stress values are plotted as
ordinates on a uniform scale, and the time elapsing until failure occurred
is plotted in hours on a logarithm scale as abscissa.
Strains were computed from either the dial or the optical-scale readings.
The strains noted at the beginning of the test are listed in column 4 of the
tables. These initial strains at zero time scattered more than the envelope
of strains obtained from the short-time tests (figs. 1 to 6). They scattered
on both sides of the average line for the specimens loaded at 45 • , but for
those loaded at 0° they were generally less than the envelope values. The
exact cause of this discrepancy is unknown. Several possible causes are
known, however, such as a small previous strain history or inability to
measure the strain from zero load.
Whatever the cause, it is believed that the creep strains observed after
zero-time were more accurate than those strains observed during loading.
For the analysis of strain due to the constant stress, therefore, the strain
values observed after zero-time were added to a mean strain value obtained
from the envelope of short-time stress-strain curves. This correction, in
reality, shifts the strain-time plot uniformly parallel to the strain axis.
Column 5 presents these mean strain values at the respective stress levels
at what would have been zero time. In columns 6 to 11 a total strain is presented that is equal to the observed creep strains plus the corrected zerohour strain. The observed creep strains at these periods had been picked
from a plot of strain versus time on semilogarithm coordinates. Straintime curves from data of columns 6 to 11 of tables 1 to 4 are presented in
figures 13 to 18 for the two materials tested.
Discussion of Results
Stress - rupture
Figures 11 and 12 show the characteristic reduction of stress with increase
in time as a stress-rupture curve. Data obtained from each test condition
may be represented by a single straight line. A straight line has been drawn
through all the data for each test condition from 1/100 to 1,000 hours to
represent the average trend. Equations for these lines are shown in the
figures. The equations are of the form y = b - m log x or Tr = o-o - M log t,
where o-r is the rupture stress in pounds per square inch at time, t, in hours;
cro is the stress or ordinate intercept at 1 hour; and M is the slope of the
Rept. No. 1863
-6-
curve. This relationship, with the constants shown on the figures, serves
as a guide to maximum stress that can be endured between 1 and 1,000 hours.
The maximum tensile stress values endured in the short-time control tests,
(as determined from the curves of figures
aafter 1,000 hours, cr l
000'
sl''
follow:
11 and 12), and the percentage' ratios of o1,000/crs1
Tensile stress
Material
o-
sl
1,000 p. s. i.
cr1,000
1,000 p. s.
cr1,000
Percent
Polyester laminate
Tested 0° to warp, Dry
jDry
Tested 45° to warp, Wet
50.56
21.65
14.69
30.60
15.00
9.00
60.60
69.30
61.40
Epoxy laminate
Tested 0° to warp, Dry
Dry
Tested 45° to warp,
Net
58.32
22.80
21.81
34.20
17.90
11.10
58.70
78.60
50.80
The epoxy laminate has the highest stress in each of the three test conditions
from dry strength at 0° to warp to wet strength at 45° to warp. The 1,000hour strength of the polyester laminate, however, is a higher percentage of
its short-time strength for two of these test conditions.
It should be noted that the 45° wet strength of the polyester laminate after
1,000 hours is 61.4 percent of its short-time strength, and the 45° wet strength
of the epoxy laminate after 1,000 hours is 50.8 percent of its short-time
strength. Even though the strength of the epoxy resin laminate at 45° to the
warp is not affected by wet conditions in a short-time test, the slopes of the
stress-rupture curves indicate (figs. 11 and 12) that stress and time might
affect the epoxy laminate more than the polyester laminate. Exacting analysis
of these comparative data is not possible, however, because of the scatter of
test data.
Creep
Many types of engineering and structural materials undergo progressively increasing strains with time while they are at constant stress. The variability
and complexity of this strain-time relationship depend on the material, the
Rept. No. 1863
-7-
stress or stress orientation, temperature, and other factors. Most materials
follow the classic strain-time pattern in three stages after the initial strain
that results from the application of the load. The first is a transition stage
of decreasing strain rate. The second is a stage of minimum strain rate,
and the third is an increasing strain-rate-stage to failure. Numerous attempts have been niade to equate the strain to all of the variables that affect
it, including time.— Of all the formulas that could represent the strain-time
behavior of reinforced plastics at room and elevated temperatures, for short
as well as long periods of time, the best equations for total strain, E t , and
creep rate, V, that might be usable in aircraft applications appeared to be in
the form of y = a + bxn or E t = E 0 + mtn and V = V in sinh o-/cr . These relationships were suggested for plastics and have been used to some extent by
William Findley and his associates. 4' -5The application of these relationships to the data in the investigation required
an evaluation of the constants. At each stress level, the total strain, Et , at
time, t, including the initial strain due to application of the load, would be
represented by the equation E t = E0 + mt n, where E t is total strain in inches
per inch, and t is time in hours. E m, and n are constants for that stress
level.
Since there are three unknown constants, a minimum of three points on the
curve would be required for their solution. If those three points, E 1 ' 2'
and E 3 , at t 1 , t 2 , and t 3 were chosen so that t 2 = (t i t 3 ) /Z-, then
log
-
Z t2
log —
ti
E
2
El
or
E =
E3 (1
E3 -4- f
E2
2
ZE
2
3
—Kempner, Joseph and Hoff, N. J. Bibliography of Creep for Structural
Engineers. WADC TR 56-40, 1956.
4
Findley, W. H. , Adams, C. H. , and Worley, W. J. The Effect of the 2
Laminated Plastics as Interpreted by the Hyperbolic-sine Law and Activation Energy Theory. ASTM Proceedings, 48, p. 1217, 1948.
—'Findley, W. H. and Khosla, Gautam. An Equation for Tensile Creep of 3
Unfilled Thermo Plastics. Soc. of Plastics Eng. Journal, 17(12),
December 1956.
Rept. No. 1863
-8-
Then the third constant would be computed as follows:
tln
Since, however, there were usually more than three points on the strain-time
curve from 0.016 hour to failure for each stress level, the value of c o or n
was approximated by the preceeding equations and then ',.he values of e t - c o
= mtn were plotted on log-log coordinates, the log (E t - c o ) versus log m +
n log t. If the resulting points were a straight line, the first approximation
was correct. If not, another value of c o was used, and the plotting was repeated. The values of c o , m, and n that best agreed with the data are shown
in columns 12, 13, and 14 of tables 1 to 4. Hence, the equation with these
constants represents the test data for each stress level.
In order to make these strain-time constants useful at stress levels other
than those for which they were computed, they must be related to stress.
Figures 19 to 24 show the constants at each stress level versus the stress.
Smooth curves have been drawn through the points to represent average
and m are
values. The equations for these curves through values of shown as y = a sinh bx. The value for n was assumed to be a constant, which
— Using this form for c o and m,
agrees with Findley's investigations. 4
E D
=E' sinh
m = ml
a-
a-
m
where e', m', and e , and o- are constants. These constants were determ
mined by successive approximations until the curves represented the data as
6 It is unfortunate that there are not more tests at the
shown in the figures. —
lower stress levels, so that these relationships could be more accurately defined. The curves, however, define the relationships in the region for which
stress-rupture data are available. With this relationship of the constants to
the stress, the total strain equals
E
t
cr
o= e l Binh — + t nm" Binh
aem
6
—Nadal, A. and Mcyetty, P. G. Hyperbolic Sine Chart for Estimating Working Stresses of Alloys at Elevated Temperatures. ASTM Proceedings,
Vol. 43, p. 735.
Rept. No. 1863 -9-
A summary of the values of the constants that define the relationship of
strain to time, and stress and the stress-rupture curves at room temperature
is given in table 5.
The constants and relationships given in table 5 may be used to compute the
total strains of these two materials at stresses and durations of stress, provided those stresses and periods of duration are kept within the limits of the
stress-rupture curve. Strains have been computed for 1/10, 10, and 1,000
hours of loading. They are shown in figures 19 to 24 in conjunction with the
short-time stress-strain curve.
dE
Creep rates may also be computed. Since the creep rate, V, equals
at
relationship given in table 5 becomes
V= (n m t sinh
the
Cr
n-1
—) t
o-m
This is now a basis for comparing creep rates of the two materials at a selected
time and stress level. For example, at room temperature, the creep rate of
the polyester laminate in tension at 0° to warp at 30,000 pounds per square inch
for 100 hours would be 1.78 x 10 -6 inch per inch per hour, compared to 2.36 x
10 -6 inch per inch per hour for the epoxy laminate under similar conditions.
This shows that there is not too much difference under these conditions between
the strain rates of these two materials.
The creep rate for the 45° loading in the wet test, however, shows a greater
difference. For the polyester laminate, the rate at 8,000 pounds per square
inch at 100 hours is 78 x 10 -6 inch per inch per hour, compared to 27 x 10 -6
inch per inch per hour for epoxy laminate. The creep rate of the polyester
laminate is, therefore, 2.9 times faster than that of the epoxy laminate.
Conclusions
Stress-rupture and creep characteristics were obtained from tensile tests of
typical 181 parallel laminates made of polyester and epoxy resins. Tests
were made at 0° and 45° to the warp direction for periods up to 1,000 hours.
Based on the results of these tests, the following conclusions are given:
(1) Stress-rupture curves were essentially straight lines when plotted on
semilog paper. There was no pronounced endurance limit or leveling off of
the curve for periods up to 1,000 hours. The straight-line relationship denoting the maximum tensile stress, Crr , that the material can endure in time, t,
Rept. No. 1863
-10-
can be expressed by crr = cro - M log t where o- 0 is the stress corresponding
to rupture in 1 hour and M is the slope of the curve, a constant.
(2) Strain-time curves are presented for periods up to 1,000 hours. At 0°
loading, the creep of both polyester and epoxy laminates was very small after
the full test load was applied. At 45° loading, however, the strain at failure
was usually about 2 or 3 times but as much as 6 times greater than the strain
observed immediately after the test load was applied.
(3) The stress-rupture strength of the epoxy laminate up to 1,000 hours under
each test condition was greater than the corresponding strength of the polyester laminate. At any stress level between 1/100 and 1,000 hours, the epoxy
laminate withstood the stress longer than the polyester laminate. For two of
the three test conditions, however, the rate of strength reduction was greater
for the epoxy than for the polyester laminate.
(4) The relationship between strain,
expressed by the equation
E
with time, t, and stress,
t,
Cr,
may be
cr
E t = sinh — + to m' sinh
crecr
and cr were
For the two materials tested, the constants, E t , cre , n,
determined. Thus it is possible to calculate and compare strains at any time
and stress within the limits of the stress-rupture curve.
of the epoxy laminate at 0° to load)
am
ing were about the same as those for the polyester laminate, but at 45° they
were substantially slower for the epoxy than for the polyester laminate.
(5) Creep rates, V = (n m l sixth
Rept. No. 1863
-11-
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M 97 57 8 F
Rept. No. 1863
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