Tension–tension axial fatigue of E-glass fiber-reinforced polymeric composites: tensile fatigue modulus

Construction and Building Materials, Vol. 12, No. 1, pp. 51]58, 1998 Q 1998 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0950]0618r98 $19.00 q 0.00

PII:S0950–0618(97)00059-7

Tension–tension axial fatigue of E-glass fiber-reinforced polymeric composites: tensile fatigue modulus C. E. DemersU

Civil Engineering Building a72, Room 206B, University of Arizona, Tucson, AZ 85721, USA Received 5 December 1996; revised 19 August 1997; accepted 6 September 1997 Interest in utilizing fiber-reinforced polymeric (FRP) composites in civil engineering applications is increasing. Such applications include bridge structures which undergo cyclic loading. For FRP composite structures subject to cyclic loading, fatigue is an important limit state. Strength and modulus degradation need to be considered as either may be the failure criterion. This study focuses on fatigue modulus degradation from tension]tension axial fatigue tests, constant amplitude loading, with frequency of fatigue load 5 Hz or less for E-glass (and glass) FRP composites without environmental concerns. The evaluation of fatigue modulus data is augmented by laboratory testing of an E-glass/ vinylester unidirectional composite in tension]tension axial fatigue (constant amplitude loading) with frequency of fatigue load at 5 Hz or less. For glass FRP composites exhibiting a primary and secondary tensile modulus, failure is defined as a 3, 5, or 8% decay of normalized tensile fatigue modulus based on whether cyclic maximum and minimum stress is above or below the static knee point stress. For composites exhibiting only a primary tensile modulus, a conservative 3% decrease in tensile fatigue modulus is recommended to define failure until further testing refines all values. Q 1998 Elsevier Science Ltd. All rights reserved. Keywords: FRP composites; E-glass; composites

Introduction

studies needed for the characterization under variable amplitude loading. Utilizing a frequency of fatigue load 5 Hz or less is consistent with civil engineering bridge applications and also limits the evaluation of data whose strength and stiffness are negatively affected by internal heat generation which is caused by high frequency of fatigue load. This evaluation of fatigue modulus data is augmented by laboratory testing of an E-glassrvinylester unidirectional composite in tension] tension axial fatigue of constant amplitude loading with frequency of fatigue load 5 Hz or less. The fatigue modulus degradation is a criterion for failure and also provides an indirect assessment of damage growth in the composite material. E-glass FRP composite fatigue strength degradation as a criterion for failure is evaluated in a previous publication1.

Fiber-reinforced polymeric ŽFRP. composites have traditionally been utilized in aerospace, marine and mechanical applications. As such, extensive analytical and experimental investigations have been conducted. Recently, FRP composites are utilized in civil engineering applications. This requires an understanding of the material behavior under various loading and environmental conditions that are unique to civil engineering structures. For FRP composite structures subject to cyclic loadings, fatigue is an important limit state. Both strength and modulus degradation under fatigue loading need to be considered. This study focuses on fatigue modulus degradation from tension]tension axial fatigue tests of constant amplitude loading with frequency of fatigue load 5 Hz or less for E-glass Žand glass. FRP composites without environmental concerns. Material characterization under constant amplitude loading provides a basic understanding with future U

Tensile modulus, static and fatigue The tensile modulus, E, is the slope of a best fit line to the monotonic ultimate strength curve. However, some

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51

52

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers

Figure 1 Tensile fatigue modulus vs. fatigue life for regions 1]3

FRP composite ultimate strength curves are best fit by two moduli, a primary tensile modulus, EI , and a secondary tensile modulus, EII . Echtermeyer et al.2 observed such a response and defined the intercept of the moduli as the knee point stress, s knee , and knee point strain, e knee . The static secant modulus, Ess , is defined as the slope from ultimate stress, sult , and ultimate strain, e ult , back to zero. Under fatigue loading, the cyclic maximum stress, smax , may be a value above or below the static knee point stress, s knee . The tensile fatigue modulus, Ef , is measured during the unloading portion of a tensile fatigue cycle Žor the tensile part of the fatigue cycle.. It is the slope of the line between cyclic maximum stress and strain and cyclic minimum stress and strain. Under progressive cyclic loading, the tensile fatigue modulus decays from its initial value, Efl , which is measured during the unloading portion of the first fatigue cycle. The normalized fatigue modulus is defined as the ratio between tensile fatigue modulus at any given fatigue life and initial tensile fatigue modulus, EfrEfl . The decay is graphically represented as tensile fatigue modulus vs. fatigue life or log of fatigue life, or as normalized fatigue modulus vs. log of fatigue life. Plots of Ef vs. N may show three regions of modulus degradation as shown in Figure 1. The first region describes an initial decay Žusually for 200]1000 cycles fatigue life., the second region describes a gradual decay which defines the greater part of the fatigue life, and the third region describes a rapid decay over which little increase in fatigue life is achieved. The third region may or may not be present depending on cyclic stress magnitude. The transition from second to third region defines the critical fatigue modulus, Efc .

Previous research Dharan 3 observed the decay of normalized fatigue modulus Ž EfrEfl . for R s 0 axial fatigue tests of a unidirectional glassrepoxy composite at frequency 5 Hz and a constant strain rate. The monotonic stress]strain curve was represented a primary tensile modulus. Gradual decay of the normalized fatigue modulus occurred until a normalized critical fatigue modulus, 0.6, was reached. Thus a 40% decrease in normalized fatigue modulus occurred before the normalized critical fatigue modulus was reached. Agarwall et al.4 observed the decay of fatigue modulus for R s 0.05 axial fatigue tests of a 0r90 Eglassrepoxy composite for stress or strain control. A frequency limit of 0.01]2 Hz limits the data available for study. The monotonic stress]strain curve was represented by a primary and secondary modulus. Regardless of stress or strain control and stress or strain range, the fatigue modulus decreased linearly from its initial value to failure. No critical fatigue modulus or rapid degradation thereafter of tensile modulus was evident. Generally, the limited data showed increasing fatigue modulus decay from 3% to 15% for decreasing stress range. Jessen et al.5 observed the decay of normalized fatigue modulus Ž EfrEfl . for R s 0.05 axial fatigue tests of unidirectional E-glassrpolyester for constant load at frequency 5 Hz. The monotonic stress]strain curve was represented a primary tensile modulus. The cyclic maximum stress was 50% ultimate tensile strength to 88% ultimate tensile strength. Regardless of cyclic maximum stress, a consistent normalized critical fatigue modulus Ž Efc rEfl . 0.96 was achieved. Only 4% decrease in normalized fatigue modulus occurred before

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers the normalized critical fatigue modulus was reached. The tests were stopped at 20% decay of normalized fatigue modulus when damage occurred outside the gage area of the specimens. Failure was interpreted as 20% decay of normalized fatigue modulus to effectively define the fatigue life of these specimens. The normalized critical fatigue modulus, Efc rEfl , was reported greater than the normalized static secant modulus, Ess rEI . Echtermeyer et al.2 observed the decay of fatigue modulus for R s y1 axial fatigue tests of glassr neopentyl glycolrisopolyester at frequency 2]5 Hz and constant load rate. The monotonic ultimate strength curve was represented by a primary tensile modulus and a secondary tensile modulus with the moduli intercept defining the static knee point stress and strain. For fatigue loading, the cyclic maximum stress ranged from 25% ultimate tensile strength to 100% ultimate tensile strength. For cyclic maximum stress below the static knee point stress, failure of the specimens was not achieved. For cyclic maximum stress above the static knee point stress, gradual decay of the fatigue modulus occurred until a critical fatigue modulus Ž12.4 GPa or when normalized with respect to Efl ; 0.80]0.94. was reached. As the cyclic maximum stress decreased, the initial fatigue modulus increased. However, regardless of cyclic maximum stress, a consistent critical fatigue modulus was achieved. The critical fatigue modulus was reported 23% lower than the primary tensile modulus. The critical fatigue modulus was approximately equal to the static secant modulus. Echtermeyer et al. also observed the decay of fatigue modulus for R s y1 axial fatigue tests of glass fiber composites with isophthalic polyester, or vinylester, or rubber modified vinylester, or orthophthalic polyester resin. The critical fatigue moduli, respectively, were 13.4 GPa, 12.8 GPa, 12.7 GPa and 13.3 GPa. The critical fatigue modulus was reported 20]25% lower than the primary tensile modulus. The critical fatigue modulus was approximately equal to the static secant modulus. Hahn et al.6 observed the decay of modulus for R s 0.1 axial fatigue tests of w0r" 45r90xs glassrepoxy laminate for load control at frequency 4 Hz. The monotonic tensile stress]strain curve was represented by a primary tensile modulus although a secondary tensile modulus could have been included. To determine decay of modulus, fatigue testing was periodically interrupted, the specimen loaded at the static loading rate to the cyclic maximum stress magnitude, and the fatigue secant modulus Ž Efs . at a given fatigue life measured. This fatigue secant modulus was normalized with respect to the primary tensile modulus. Gradual decay of this normalized fatigue secant modulus occurred until a normalized critical fatigue secant modulus, ; 0.67, was reached. As the cyclic maximum stress decreased, the normalized initial fatigue secant modulus Ž Efs1rEI . increased. However, regardless of cyclic maximum stress, a consistent normalized critical fatigue secant modulus was achieved. The normalized critical fatigue secant modulus was essentially the same as the normal-

53

ized static secant modulus, Ess rEI . Failure was interpreted to occur when the fatigue secant modulus was reduced to within the range of the static secant modulus. Similar results were achieved with the 10-Hz data. The Hahn et al. data, which was evaluated via the fatigue secant modulus, is not directly comparable with tensile fatigue modulus evaluations by other research as presented. Thus, the Hahn et al. data is given as an overview. A summary of the fatigue test parameters relevant for each reference is given in Table 1.

E-glassr r vinylester unidirectional composite Test procedure The material was comprised of vinylester resin with E-glass reinforcement. The reinforcement was unidirectional with five layers of mat reinforcement placed throughout the thickness. The weight% fiber was 38%. The E-glassrvinylester composite was supplied in plate form. Coupons were dry cut with final dimensions obtained using a water lubricated diamond saw. The coupon dimensions were 2.54 cm wide= 1.27 cm thick = 25.4 cm long Ž1 = 0.5= 10 inch. with the clear distance between grips 15.24 cm Ž6 inch.. The coupon shape was bar form. Tabs were not utilized in this study. All tests were performed on a servo-hydraulic MTS machine. The same actuator speed was used for both fatigue ramp-up and static load. A 50-kip capacity load cell was used to monitor the fatigue load and a uniaxial extensometer was used to measure the specimen strain over a 2.54 cm Ž1 inch. gage length. A temperature voltmeter, sensitivity " 0.18C, was used to monitor the specimen surface temperature during testing. A computerized data acquisition system was used to record the loadrstrain data. The constant amplitude fatigue tests were conducted at room temperature in stress control for: normalized maximum stress Ž smaxrsult . 0.8, R ratios 0.05, 0.1, 0.5, 0.9 and test frequencies 1, 3, 5 Hz.; normalized maximum stress Ž smaxrsult . 0.6, R ratios 0.05, 0.1, 0.5, 0.9 and test frequencies 1, 3, 5 Hz; normalized maximum stress Ž smaxrsult . 0.4, R ratios 0.1, 0.5 and test frequencies 1, 5 Hz. A total of 50 fatigue tests were conducted with a maximum of four repeats per normalized maximum stress, R ratio and test frequency combination. For 5 Hz frequency and R values Ž; R s 0.1., specimen surface temperature rise was observed during fatigue testing. However, no distinct trend in the data suggested internal heating had a significant effect on fatigue life1. A summary of the fatigue test parameters relevant for this E-glassr vinylester composite is given in Table 1. Material properties In a monotonic tensile strength test, the material exhibited a bilinear stress]strain behavior with a well defined knee point. The primary tensile modulus was

0r90 Ž15 ply.a

0r" 45r90a

Unidirectional

w4x

w6x

w5x

Unidirectionala

w1x

Vinylester

Neopentyl Glycolrisopolyester

Polyester

Epoxy

Epoxy

Epoxy

Resin

c

b

Continuous fiber reinforcement. Five layers: combination of woven roving and chopped strand mat. Rectangular section with thickness flaring into wedge shape. d Reduced gage. e Constant load rate. f Decay of normalized fatigue modulus.

a

1

w3x

b

Unidirectionala

w3x

a

Type of reinforcement

Reference

Table 1 Tensile fatigue modulus references

Bar

Bar

Rod

d

Dogbone

Dogbone

ASTM D638 Type Ic

Specimen shape

1, 3, 5

2]5

5

4

0.01]2

0.25]6

Frequency ŽHz.

0.1, 0.5, 0.9

y1

0.05

0.1

0.05

0

R

Stress

2

e

Stress

Stress

Stress Strain

Strain

Load control

38 wt.

}

60 vol.

64 wt.

70.4 wt.

48 vol.

Fiber Ž%.

f

Specimen separation

Specimen separation

20%

}

}

Unknowne

Failure mode

1]5

}

4

}

}

}

Tests per sample

1.67

1.62

1.9

}

2.1

}

Failure strain

54

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers

55

Table 2 E-glassrvinylester composite material properties

sknee ŽMPa.

eknee Ž me .

sult ŽMPa.

sult CV Ž%.

eult Ž me .

EI ŽGPa.

EI CV Ž%.

EII ŽGPa.

EII CV Ž%.

Ess ŽGPa.

92.15

5065.03

238.65

5.12

16724.77

17.94

0.96

12.95

2.62

14.27

calculated from the stress]strain data between 1000 me and 3000 me Žor the closest available data point. as recommended by ASTM D3039 7. The secondary tensile modulus was calculated from the stress]strain data between 8000 me and 13 000 me Žor the closest available data point.. Table 2 summarizes the test results including the number of specimens tested Ž n., average knee point strain Ž s knee ., average knee point strain Ž e knee ., average primary tensile modulus Ž EI ., average secondary tensile modulus Ž EII . and coefficients of variation ŽCV.. Tensile fatigue modulus As previously defined, the tensile fatigue modulus is measured during the unloading portion of a tensile fatigue cycle. The initial fatigue modulus value changes approximately 15.4]21.2 GPa regardless of cyclic maximum stress. This is attributed to the inherent fiberrresin variability typical within composites. A typical plot of tensile fatigue modulus, Ef , vs. fatigue life, N, is shown in Figure 1 which demonstrates the three regions of modulus degradation. The E-glassrvinylester composite data shows fatigue modulus degradation containing regions 1]2]3; regions 1]2; or regions 2]3. Fatigue modulus degradation region 3 is less pronounced or non-existent as cyclic maximum stress and minimum stress increase. Therefore the data are grouped according to maximum stress and minimum stress above or below the static knee point stress and are labeled as categories I]V. Category I: Category II:

smax ) s knee smin ) s knee smax ) s knee smin ; s knee

Ž1. Ž2.

Category III:

smax ) s knee smin - s knee

Ž3.

Category IV:

smax ; s knee smin - s knee

Ž4.

Category V:

smax - s knee smin - s knee

Ž5.

Within each category, the data is arranged by normalized maximum stress and R ratio. For category I with normalized maximum stress either 0.6 or 0.8 Žand some category II as shown in Figure 2 ., specimen failure occurs before fatigue modulus degradation region 3 is achieved. One category I specimen for which the fatigue test is terminated at 1.35 million cycles Žrun-out. does not exhibit tensile fatigue modulus degradation.

Another category I specimen exhibits a 3% increase in tensile fatigue modulus at failure Žan example of ‘strain hardening’.. For category II or category III with normalized maximum stress 0.8, some specimens begin to show fatigue modulus degradation region 3 before failure occurs as shown in Figure 2. For category IV or category III with normalized maximum stress 0.6, most specimens show advanced fatigue modulus degradation region 3 before failure occurs as shown in Figure 2. Overall, either the tensile fatigue modulus at failure or the critical fatigue modulus approximately ranges from 14.0 GPa to 19 GPa. Generally, for duplicate tests with identical normalized maximum stress and R ratio parameters, the tensile fatigue modulus at failure or the critical fatigue modulus increases with increasing fatigue life. The lower values of the tensile fatigue modulus at failure or the critical fatigue modulus approach the static secant modulus, 14.3 GPa. Test frequency 1, 3, or 5 Hz do not appear to affect fatigue modulus degradation. The percent decay of normalized fatigue modulus Ž EfrEfl . to either specimen failure or to normalized critical fatigue modulus Ž Efc rEfl . is presented in Table 3. The test data do show, regardless of fatigue life: a 3% decrease in normalized fatigue modulus for categories I and II; a 6% decrease in normalized fatigue modulus for category III; an 8% decrease in normalized fatigue modulus for category IV. The test data do not extend into category V which represents long fatigue life studies.

Discussion Under cyclic loading, the tensile fatigue modulus degrades to a value either in region 2 or in region 3. Region 3 represents rapid degradation of tensile fatigue modulus with minimal increase in fatigue life. Therefore the intersection between region 2 and region 3, the critical fatigue modulus, is a conservative maximum value of tensile fatigue modulus. For very high values of cyclic normalized maximum or minimum stress, the specimen fails before the tensile fatigue modulus decays to the critical fatigue modulus. Therefore, specimen failure is defined as a percent decrease in tensile fatigue modulus which is limited to the critical fatigue modulus. The percent decay of normalized fatigue modulus Ž EfrEfl . to specimen failure or to normalized critical fatigue modulus Ž Efc rEfl . is shown in Table 3 for composites exhibiting both primary and secondary tensile moduli. The Echtermeyer 2 and Agarwall et al.4 data support the more conservative results of the E-

w4x

w2x

w1x

Reference

0.80 0.60

sma xrsult

0.9 0.9

R ratio

Category I sma x ) s knee smin ) s knee

3% 3%

EfrE fl

0.80

smaxrsult

0.5

R ratio

Category II smax ) s knee smin ; s knee

3%

EfrEfl

0.73 0.79 0.84 0.91

1.00 0.62

0.80 0.60

smaxrsult

0.05 0.05 0.05 0.05

y1 y1

0.1, 0.05 0.5, 0.1, 0.05

R ratio

Category III smax ) s knee smin - s knee

8% 15% 5% 3%

6% 10%

6% 5%

EfrEfl

0.44

0.40

smaxrsult

Table 3 Percent reduction of normalized fatigue modulus Ž EfrEfl . to specimen failure or to normalized critical fatigue modulus Ž Efc rEfl .

y1

0.1, 0.5

R ratio

Category IV smax ; s knee smin - s knee

20%

8%

EfrEfl

0.25

smaxrsult

y1

R ratio

Category V smax - s knee smin - s knee

18%

EfrEfl

56

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers

57

Figure 2 Normalized fatigue modulus vs. log of fatigue life for categories I]IV

glassrvinylester data. For categories I and II, a 3% decrease in normalized fatigue modulus is achieved before either the normalized critical fatigue modulus is reached or failure of the specimen occurs. For category III, a 5% decrease in normalized fatigue modulus is achieved before either the normalized critical fatigue modulus is reached or failure of the specimen occurs. For category IV, an 8% decrease in normalized fatigue modulus is achieved before either the normalized critical fatigue modulus is reached or failure of the specimen occurs. For category V, approximately 20% decrease in normalized fatigue modulus is achieved before either the normalized critical fatigue modulus is reached or failure of the specimen occurs. Category V represents long-life fatigue studies. Table 4 shows the normalized fatigue modulus degradation to failure or to normalized critical fatigue modulus and also the normalized critical fatigue modulus vs. the normalized static secant modulus. The normalized fatigue modulus 0.6 from the Dharan 3 data is significantly lower than the values 0.80]0.94 from the Echtermeyer et al.2 , 0.96 from the Jessen et al.5, 0.85]0.97 from the Agarwall et al.4 , or 0.70]0.97 from the E-glassrvinylester composite data. It is uncertain, due to the limited data, as to why the Dharan data is so much lower. A similar range of fatigue modulus degradation is achieved by Agarwall et al.4 , Jessen et al.5, Echtermeyer et al.2 , and E-glassrvinylester composite data. The Echtermeyer et al.2 data and the Eglassrvinylester composite data show 20]21% decay of Žnormalized. tensile fatigue modulus is approximately equal to the Žnormalized. static secant modulus. Otherwise, the Žnormalized. critical fatigue modulus is greater

Table 4 Normalized fatigue modulus and normalized critical fatigue modulus vs. the normalized static, secant modulus Efc

Reference

Failure or Efc rEfl

EfcrEfl vs. EssrEI

w3x

0.60

w4x

0.85]0.97

w5x

0.96 Consistent

Efc rEfl ) EssrEI

w2x

12.4 GPa Consistent

0.80a ]0.94

Efc rEfl ; EssrEIa Efc rEfl ) EssrEI

Demers

14]19 GPa

0.79a ]0.97 Variesb

Efc rEfl ; EssrEI Efc rEfl ) EssrEI

a For this value of Efc rEfl Žcolumn 3., then EfcrEfl ; EssrEI Žcolumn 4.. b Varies according to cyclic maximum stress and cyclic minimum stress magnitude.

than the Žnormalized. static secant modulus, also for the Jessen et al.5 data. This limited data suggests that defining specimen failure as decay of the Žnormalized. tensile fatigue modulus to within the range of the Žnormalized. static secant modulus is not conservative. Failure may occur well before the Žnormalized. tensile fatigue modulus decays to within the range of the Žnormalized. static secant modulus.

Conclusions The presented data on axial fatigue of glass FRP composites with frequency of fatigue load 5 Hz or less,

Fiber-reinforced polymeric composites: tensile fatigue modulus: C. E. Demers

58

shows that the tensile fatigue modulus decays under axial fatigue loading. Under high cyclic normalized maximum stress, failure may occur before the tensile fatigue modulus decays to the critical fatigue modulus. Therefore failure is defined as a percent decrease in tensile fatigue modulus which is limited by the critical fatigue modulus. The critical fatigue modulus may be equal to or greater than the static secant modulus. Thus defining failure as decay of tensile fatigue modulus to within the range of the static secant modulus is not conservative Žas failure may occur before.. Also, defining failure as a generic percent decay of tensile fatigue modulus, regardless of cyclic maximum or minimum stress magnitude, is not conservative. Therefore for glass FRP composites exhibiting a primary and secondary tensile modulus, failure has been redefined as a percent decay of normalized tensile fatigue modulus based on whether cyclic maximum and minimum stress is above or below the static knee point stress. Recommended values are: Category I:

smax ) s knee smin ) s knee

failure when EfrEfl decays 3%

Ž6.

Category II:

smax ) s knee smin ; s knee

failure when EfrEfl decays 3%

Ž7.

Category III:

smax ) s knee smin - s knee

failure when EfrEfl decays 5%

Ž8.

Category IV:

smax ; s knee smin - s knee

failure when EfrEfl decays 8%

Ž9.

Category V:

smax - s knee smin - s knee

failure when EfrEfl decays 20%

The host institution for this program is the School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia. The excellent laboratory work was conducted by Patrick Bair, graduate student. All the above are gratefully acknowledged for support of this project. Special thanks also to Dennis Senal for his assistance with the graphics.

Notation The following symbols are used in this paper: CV EI EII Ef Efl Efc Efs Efsl Ess EfrEfl Efc rEfl Efs rEI EfslrEI Ess rEI N R sknee eknee sult eult smax smin smaxrsult smin rsult

Coefficient of variation Ž%. Primary tensile modulus Secondary tensile modulus Tensile fatigue modulus Initial tensile fatigue modulus Critical fatigue modulus Fatigue secant modulus Initial fatigue secant modulus Static secant modulus Normalized fatigue modulus Normalized critical fatigue modulus Normalized fatigue secant modulus Normalized initial fatigue secant modulus Normalized static secant modulus Fatigue life smin rsmax Knee point stress Knee point strain Ultimate stress Ultimate strain Cyclic maximum stress Cyclic minimum stress Normalized cyclic maximum stress Normalized cyclic minimum stress

Ž 10 . Category V represents long fatigue life studies. The data is insufficient to project for E-glass FRP composites whether a 20% decrease in normalized tensile fatigue modulus defines failure for category V. For composites exhibiting only a primary tensile modulus, the data base is too small for definitive conclusions. Thus, utilizing a very conservative 3% decrease in tensile fatigue modulus to define failure is recommended. Further testing is needed to refine these values and to observe the decay of fatigue modulus during long life studies Žgreater than one million cycles..

Acknowledgements This research is funded by the National Science Foundation Visiting Professorships for Women Program.

References 1 Demers, C. E., Tension]tension axial fatigue of E-glass fiber-reinforced polymeric composites: fatigue life diagram. Construction and Building Materials, 1997, paper accepted for publication 2 Echtermeyer, A. T., Buene, L., Engh, B. and Sund, O. E., Significance of damage caused by fatigue on mechanical properties of composite laminates. SAMPE, 1993, 38B, 1]10 3 Dharan, C. K. H., Fatigue failure mechanisms in a unidirectionally reinforced composite material, ASTM STP. Fatigue of Composite Materials, 1975, 569, 171]188 4 Agarwall, B. D. and Dally, J. W., Prediction of low-cycle fatigue behaviour of GFRP: an experimental approach. Journal of Materials Science, 1975, 10, 193]199 5 Jessen, S. M. and Plumtree,A., Fatigue damage accumulation in pultruded glassrpolyester rods. Composites, 1989, 20(6), 559]567 6 Hahn, H. T. and Kim, R. Y., Fatigue behavior of composite laminate. Journal of Composite Materials, 1976, 10, 156]180 7 ASTM D3039. Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials