A theoretical model was established to predict the fatigue behavior of composite materials, with emphasis placed on predictions of the degradation of residual strength and residual stiffness during fatigue cycling. The model parameters were evaluated from three test series including static strength fatigue life and residual strength tests. The tests were applied to two graphite/epoxy laminates. Load sequence effects were emphasized for both laminates and the predicted results agreed quite well with subsequent verification tests. Dynamic as well as static stiffness reduction data were collected by use of a PDP11-03 computer, which performed quite satisfactorily and permitted the recording of a substantial amount of dynamic stiffness reduction data

Jones, D. L.

Yang, J. N.

English

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SEVUENCG EFFECTS UN THE DEGRADATION AND
FAILURE OF COMPOSITE MATERIALS Final
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DETERMINATION OF LOAD SEQUENCE
EFFECTS ON THE DEGRADATION AND
FAILURE OF COMPOSITE MATERIALS
Final Technical Report
NASA Langley Research Center
Grant NSG 1604
Principal Investigators
Jann N. Yang
Douglas L. Jones
School of Engineering and Applied Science
The George Washington University
Washington, D.C. 20052
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ABSTRACT
This report summarizes the research that was performed
under NASA Grant NSG1604, Determination of Load Sequence
Effects on the Degradation and Failure of Composite Materials.
This grant was initiated in March, 1979, and was extended
until its expiration date of August 31, 1980. The Technical
Officer of this grant was Dr. T. Kevin O'Brien of the NASA
Langley Research Center, Hampton, Virginia 23665.
All of the work that was included in the proposal for
this grant has been completed. A theoretical model was
established to predict the fatigue behavior of composite
materials, with emphasis placed on predictions of the
degradation of residual strength and residual stiffness during
fatigue cycling. The model parameters were evaluated from
three test series including static strength fatigue life and
residual strength tests. The tests were applied to two
graphite/epoxy laminates, [±35] 2s
 and [0,90,±45] s . Load
sequence effects were emphasized for both laminates and the
predicted results agreed quite well with subsequent verifi-
cation tests.
Because of the mutual interests of the principal investi-
gators and the technical officer of this grant, the tests on
the [0,90,+45]s laminates were delayed so that dynamic as well
as static stiffness reduction data could be collected. These
data were collected by use of a PDP11-03 computer, which
performed quite satisfactorily and permitted the recording
of a substantial amount of dynamic stiffness reduction data.
1INTRODUCTION
Under the sponsorship of this grant, a theoretical,model
developed under a previous grant, NSG141S, Statistical
Characterization of the Fatigue Behavior of Composite Lamina,
was extended to include load sequence effects on the predic-
tions of fatigue life, residual strength and residual stiff-
ness of composite laminates. The model was applied to two
graphite/epoxy laminates, [±351 2 , and [0,90,±45] 5 . For each
laminate the parameters in the model were evaluated from a
series of static tensile tests (15-25 tests), fatigue life
tests (20-25 tests) and residual strength tests (10-15 tests).
Then several verification test series were performed in which
the tests were performed under two levels of cyclic loading.
A total of approximately 3 00 tests were performed on these
two composite laminates. The agreement between predictions
made from the model and actual test results was good in all
verification test series.
The results of this work have been well received as
indicated by the conference presentations and publications
produced under this grant. The results of this work have
been presented at two conferences; the ASTM Symposium on
Fatigue of Fibrous Composite Materials held in San Francisco
(May 22-23, 1979), and the Third International Conference on
Composite Materials held in Paris (August 26-29, 1980). The
2paper presented at the ASTM conference has been published in
ASTM STP723, Fatigue of Fibrous Composite Materials, and the
paper presented at the Third International Conference on
Composite Materials was included in the conference proceedings.
In addition to these conference presentations, a paper
incorporating some of the analytical work developed under this
grant has been published in the Journal of Composite Materials,
Vol. 14, 1980, pp. 168-176. Abstracts of these three papers
are included with this report. Two additional papers discussing
the application of the theoretical model to both laminates
have been prepared for publication. In addition, a paper
discussing the technique employed for measuring the dynamic
stiffness and presenting some of the dynamic stiffness re-
duction data is being prepared for publication. Since all
of these papers have or are expected to be available in the
open literature only a brief summary of the results will be
included in this report.
3PROGRESS
The research sponsored by this grant encompassed an
extension of the existing theoretical model as well as the
F
	
	
performance of approximately 300 tests to establish the model
parameters and verify the accuracy of the theoretical pre-
dictions. The developments in each of these areas will be
described briefly in this report.
Development of the Theoretical Model
In the previous grant, NSG1415, a three-parameter fatigue
and residual strength degradation model
Rc (n l ) - Rc (n0 ) - a cKSb (n l
-no)	 (1)
was developed for unnotched composite laminates under cyclic
loading. In Eq. (1), R(nl ) and R(n 0 ) are the residual
strengths at n 1 and n0 cycles respectively, 9 is the scale
parameter of the ultimate strength, and b, c, K are three
parameters to be determined from the test data. The stress
range S is defined as
S = 
amax - amin	 (1-R) Qmax	 (^)
where Qmax and amin represent the maximum and minimum cyclic
stress and R is the stress ratio.
4For ni - n and no - 0 , Eq. (1) reduces to
Rc (n) - Rc (0) - ScKSbn	 (3)
where the ultimate strength R(0) is a statistical variable
assumed to follow a two-parameter Weibull distrubution
a
FR(0) (x) - P[R(0) < x) - 1 - exp [-(x/s) J	 (4)
This model was used to calculate the statistical dis-
tributions of the fatigue life and the residual strength
after a specified number of cycles. It was noted that it
is only necessary to evaluate a, 0, b, c and K from a
limited number of static strength, fatigue life and residual
strength tests. Then the model can be used to predict the
distributions of fatigue life and residual strength under one
or more levels of cyclic loading.
As part of this grant effort a more general degradation
model
Rv(n) - Rv (0) - f [S I R(0) ]nY	(5)
was developed in which Y and v were additional parameters
and
f[S,R(0)] s 1 Ry (0) - a
hY [Rc (0) - ac]Y
5For a given stress ratio, N can can be expressed in terms of
the classical S-N curve as
KSb N . 1
	
(7)
This model was also used to derive expressions For the
fatigue life and residual strength distributions under con-
stant and variable amplitude fatigue loadings. The two
additional parameters v and y can be evaluated along with
a, 0, b, c, K from the same static, fatigue life and residual
strength tests.
The revised model possesses the ability to predict the
effects of load sequence through (i) the difference in
residual strength when fatigue failure occurs (boundary
effect) and (ii) the material memory effect with respect to
previously experienced loads. It permits the isolation of
the memory effect from the boundary effect, with the memory
effect represented by the value of y (y - 1 reprents no
memory effect). The results of this analysis was applied to
both laminates in this test program, with the emphasis placed
or. load sequence effects due to two levels of fatigue loading.
6Experimental Test Program
A test program using coupon specimens of 5208/T300
graphite/epoxy laminates was conducted for the purpose of
generating statistically significant test data and verifying
the validity of the theoretical model. An independent test
program was performed on each of two graphite/epoxy laminates,
[t35] 2s and [0,90,t45] s , totalling nearly 300 specimens
(approximately 150 specimens in each test series).
The testing procedures and approximate numbers of
specimens used for each set of tests; i.e., static strength,
fatigue life, residual strength tests, etc., were essentially
the same for both laminates. The parameters in the theoretical
model were first established by performing 45-65 tests, in-
cluding 15-25 static tensile tests, 20-25 fatigue life tests
and 10-15 residual strength tests. For the fatigue tests, the
test frequency was 10 Hz and the stress ratio was 0.1. Then
additional tests were performed to verify the predicted
fatigue life and residual strength distributions resulting
primarily from dual level fatigue loadings. The dual level
fatigue loadings incorporated one change of load after a
specified number of cycles, i.e., a hig'-low or a low-high
loading program. Three verification test series were per-
formed on each laminate.
An additional aspect of the fatigue behavior considered
L_
7under this grant was the stiffness degradation due to fatigue
F
	
	
cycling. Measurements of the static stiffness degradation
were made for the [13S] 2s laminates but a rather limited
V amount of data was taken due to the necessity of frequently
interrupting the fatigue cycling. In addition, removal and
replacement of the extensometer caused problems in obtaining
reliable and accurate results.
Two improvements in the testing procedure were subse-
quently instituted and it was concluded by the technical
officer and the principal investigators that the tests on the
[0,90,t45] s
 should be delayed until these improved techniques
could be used. Both improvements contributed significantly
to the collection of a greater amount of more accurate stress-
strain data. One improvement was the use of a Dual Sensor
Strain Transducer (DSST) for measuring the strains in the
[0,90,±45] s
 specimens. This unit was designed to be retained
on composite materials during cyclic loading and led to con-
sieirable improvement in the repeatability of the stress-
strain data. The second improvement was the purchase and
utilization of a PDP11-03 computer for recording the dynamic
stress-strain response of these laminates. The computer was
programmed to record previously specified stress-strain
cycles from which the dynamic stiffness values were calculated.
The acquisition and use of this computer resulted in a con-
siderable increase in the data that could be recorded during
these fatigue tests. The static and dynamic stiffness data
are also being prepared for publtcation at the present time,
so they will not be included in this report.
9CONCLUSIONS
A theoretical fatigue model previously developed by the
principal investigators has be<sn generalized and used to
predict the effect of load sequence on the fatigue life and
residual strength degradation of two graphite/epoxy laminates.
Previous models have incorporated contributions due to the
differences in residual strength at failure (boundary effect),
while this research program incorporated the effects of pre-
viously applied load3 at different load levels (meroory effect)
into the model.
The model was applied to two graphite/epoxy laminates
[±35) 2s and [0,90±45] s to predict load sequence effects on
the distributions of fatigue life and residual strength for
high-low and low-high fatigue cycling. The model parameters
were first evaluated for each laminate by a series of static
strength, fatigue life and residual strength tests (40-65
tests). Comparisons were then made between the predicted and
actual distributions and the agreement was found to be good
for all verification tests. The results of these tests have
been prepared for publication.
In addition, static and dynamic stiffness reduction
data were generated recorded and reduced with the use of a
PDP11-03 computer. The stiffness reduction data is also
being evaluated and prepared for-publication.
A B S T R A C T
LOAD SEQUENCE EFFECTS ON THE FATIGUE
OF UNNOTCHED COMPOSITE MATERIALS 
J. N. Yang and D. L. Jones
School of Engineering and Applied Science
The George Washington. University
Washington, D.C. 20052
ABSTRACT
A comprehensive version of a fatigue and residual
strength degradation moc?el previously developed by the
authors is proposed. This theoretical model is capable of
predicting the statistical distributions of the fatigue life
and the residual strength as well as the effect of load
sequence, after variable amplitude or spectrum loadings, on
these distributions. The model has been verified by the
use of existing test data on glass epoxy laminates. It is
shown that the correlation 'between the model and the test
results is good.
1Presented at the ASTN1 Symposium on Fatigue of Fibrous
Composite Materials and published in ASTM STP 723,
1\merican Society for Testing and Materials.
STATISTICAL FATIGUE OF UNNOTCHED COMPOSITE LAMINATES 
J. N. Yang and D. L. Jones
School of Engineering and Applied Science
The George Washington University
Washington, D.C. 20052
ABSTRACT
The complex structure of composite materials has led to
the development of a number of statistical models of damage
accumulation processes under fatigue loadings. This paper
presents a phenomenological approach to fatigue damage accumula-
tion, which incorporates as special cases various statistical
models developed previously by the authors and other researchers.
The relative merits of each model in predicting the fatigue
behavior under various loading programs are discussed in this
paper.
On the basis of extensive experimental data, it has been
assumed for all of these models that the residual strength is a
monotonically decreasing function of the number of cycles of
applied loading. All of the model parameters can be evaluated
from two sets of test results: (i) a series of ultimate strength
1 Proceedings of the Third International Conference on Composite
Daterials, August, 1950, Paris.
tests, and (ii) a series of fatigue tests, including some fatigue
life and some residual strength tests. Once the model parameters
have been evaluated, the model can predict the statistical dis-
tributions of the fatigue life and the residual strength under
constant or variable amplitude cyclic loads. A considerable
amount of test data generated by the authors and other re-
searchers has been examined to determine the accuracy of this
model. Tests have been performed on several different graphite/
epoxy composite laminates, including [0/90/45/-45] s , [t45]2s,
[±3'1]2s, and [90/45/-45/0] s . The model parameters were
evaluated for all of these materials and comparisons were then
made between the predicted and actual material response under
various types of proof and fatigue loadings. In general, the
predicted response has agreed closely with the actual response
and several typical examples are presented in this paper.
PROOF TEST AND FATIGUE OF UNNOTCHED
COMPOSITE LAMINATES 
J. N. Yang
School of Engineering and Applied Science
The George Washington University
Washingtoa, D. C. 20052
and
C. T. Sun
School of Aeronautical and Astronomical Engineering
Purdue University
Lafayette, Indiana 47907
ABSTRACT
A comprehensive fatigue and residual strength degradation
model has been used to predict the effect of proof. loads (or
high load) on the statistical fatigue behavior of c) polite
laminates. The validity of the theoretical model .±s confirmed
by the experimental tests results. The correlation between
the test results and the theoretical distributions of the
fatigue life and the residual strength for composite specimens
with or without the effect of proof loads is shown to be very
good.
l Reprinted from Journal of Composite Materials, Vol. 14(April,
1950), pp. 108-170.


Determination of load sequence effects on the degradation and failure of composite materials

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