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vinylester composite
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Composites Science and Technology 58 (1998) 1361±1369 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0266-3538/98 $Ðsee front matter
COMPRESSION CREEP OF A PULTRUDED E-GLASS/ VINYLESTER COMPOSITE David W. Scott & Abdul-Hamid Zureick* School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA (Received 19 June 1997; accepted 9 January 1998)
2 PREVIOUS WORK
Abstract This paper presents the results of an experimental investigation pertaining to the long-term behavior of pultruded ®ber-reinforced polymeric materials subjected to longitudinal compressive loading. Material coupons cut from a pultruded vinylester/E-glass I-shape section were subjected to axial compressive loads at various stress levels for time durations up to 10 000 h. The strain measurements over time were recorded and compared to a practical power law formulation, with good agreement. A predictor design equation for the time-dependent longitudinal modulus was developed on the basis of the experimental results. # 1998 Elsevier Science Ltd. All rights reserved
A large volume of work currently exists on the timedependent behavior of composite materials. The vast majority of these investigations have concerned the viscoelastic behavior of laminated composites used extensively in the aerospace industry. Many of these studies form the foundation upon which the present work related to civil engineering construction is based. A review of the pertinent technical literature associated with the experimental characterization of the time-dependent behavior of FRP composites from a variety of material systems and manufacturing processes has recently been completed.1 In what follows we summarize the results from those few investigations which focused on the creep behavior of FRP composite materials used speci®cally in civil engineering applications, as they are directly related to the present work. One of ®rst published investigations on the subject at hand was conducted by Holmes and Rahman2 who tested three glass-reinforced box sections. Each section was loaded to one-third of its estimated short-term ultimate bending strength at a span length of 6 m for approximately 20 months under normal laboratory conditions. Tensile, compressive and shear creep strains taken from the experiments were compared with three viscoelastic models formulated using the ®rst 2000 hours of experimental data. The experimental tensile and shear strains showed relative consistency with the predicted values, while the compression strains did not compare well with any of the models. After 15 000 h of testing, the midspan de¯ection had become approximately twice its elastic value. Mosallam and Bank3,4 investigated the viscoelastic behavior of a portal frame assembly constructed from three pultruded FRP wide ¯ange sections. The wide ¯ange sections were connected using pultruded FRP angles. All of the sections used in the construction of the portal frame were composed of glass continuous strand mat and roving with a vinylester resin. The frame was loaded to approximately one-fourth of the estimated frame failure load under normal laboratory conditions. Results from this work showed that after 10 000 h of
Keywords: B. creep, composites, compression, E-glass, vinylester 1 INTRODUCTION Recent years have found increasing acceptance of ®berreinforced polymeric (FRP) composites manufactured by the pultrusion process as an alternative to traditional materials both in new civil-engineering construction and in the rehabilitation of infrastructure. However, a fundamental lack of understanding of the behavior of these advanced materials in many dierent types of service has limited their application. The viscoelastic nature of FRP composites makes it imperative that the time-dependent behavior of these materials be accounted for in the analysis and design of any structural system. This paper presents the results of an experimental investigation into the creep behavior of pultruded FRP composite materials in compression. The experiments were performed at three dierent stress levels for time durations up to 10 000 h. The experimental data is correlated with a practical creep model that can be used for design purposes. *To whom correspondence should be addressed. 1361
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D. W. Scott, A.-H. Zureick
loading, the girder mid-span de¯ection had increased by approximately 22%, with the majority of the increase occurring in the ®rst 2000 h. The power-law model utilized in the study predicted a decrease of 35% in the viscoelastic section ¯exural modulus over a 10 yr period; the viscoelastic section shear modulus was predicted to decrease by about 46% over the same period. Daniali5 reported on the short- and long-term behavior of two types of pultruded glass/vinylester and glass/ polyester T-shaped beams. One type of beam contained a cavity in the web; the other was formed with a solid web. The beams were tested in a two-span setup at room temperature and at 54 C for stress levels ranging from 50% to 85% of the estimated short-term strength for time durations up to 10 000 h. For the members loaded to 50% of ultimate, the polyester cavity-web beams experienced an increase of approximately 20% in the de¯ection of the system after 10 000 h at room temperature; the vinylester cavity-web beams increased about 15%. The tests at ambient conditions for load levels greater than 50% of ultimate were stopped after 500 h. At the elevated temperatures, the beams with a polyester binder suered drastic reductions in strength, as well as shorter creep life and larger creep de¯ections, when compared with the specimens utilizing a vinylester binder. Mottram6 constructed two panel assemblies from pultruded glass/polyester I-sections sandwiched between pultruded FRP plates. The assemblies were ®rst tested under short-term ¯exural loads, where comparisons revealed a 7% reduction in the stiness of the assembly from the stiness of the original elements; this was attributed to the ¯exibility of the adhesive bonding. The beams were then loaded for 24 h at room temperature. Predictive power law models for the viscoelastic tensile and shear moduli were developed using the data collected from the experiment. These time-dependent moduli were used with Timoshenko beam theory to predict the de¯ection in the panel assemblies for time durations of one week, one year and ten years. The predicted values re¯ected increases of 25%, 60%, and 100%, respectively, over the specimens' initial de¯ection. The author found that creep parameters obtained from testing coupon samples taken from the beams compared very well with the creep parameters taken directly from the assembly. Recently, McClure and Mohammadi7 investigated the compression creep behavior of pultruded FRP angle sections. A total of 11 single angle members with crosssection dimensions 50.8 mm50.8 mm6.4 mm and length 152.4 mm were tested. Additionally, 20 material coupons with dimensions 12.7 mm6.5 mm31.75 mm were cut from the legs of angles of the same cross-section. Both the angles and the coupons were subjected to constant compressive loads for a time duration of 2500 h in normal laboratory conditions. Each angle section was loaded to approximately 45% of its estimated short-term local buckling load. During the ®rst
2500 h the strain in the angle sections increased by an average of 16% over the short-term values, with nearly half of that increase occurring in the ®rst 24 h. The coupon specimens were loaded to 45% of their short term ultimate load; the average stress in the coupons was approximately 3.3 times higher than that in the angles. The coupon strains increased by an average of 13% after 2500 h. A power law model was used to predict creep strains for both the angles and the coupons over the test duration. The authors found little dierence between the experimental and the predicted results for both the angle and coupon experiments; this was to be expected, since the parameters used in the development of the power law model were determined using data from the entire test duration. In summary, there was only a limited amount of experimental work performed to date on the timedependent behavior of FRP composites for civil engineering applications. The viscoelastic eects of dierent stress levels on these materials have not been adequately investigated. In addition, ways to quantify the eects of constant long-term loads for use in reliable design criteria are not widely known and supported. The work described in this paper was performed to ®ll a portion of that need. 3 PRESENT INVESTIGATION 3.1 Specimen details The rectangular prismatic coupon specimens used in this work were cut from each structural plate element in a 102 mm102 mm6.4 mm pultruded FRP wide ¯ange section as shown in Fig. 1. The composite material consisted of a vinylester matrix (Derakane 411TM) reinforced with unidirectional E-glass roving and continuous ®lament mat. Four layers of the E-glass mat were placed alternately with three layers of E-glass rov-
Fig. 1. Coupon locations and nominal dimensions.
Compression creep of a pultruded E-glass/vinylester composite ing to provide the reinforcement pattern. Small pieces cut from various locations on sections having the same ®ber architecture were examined using the modi®ed ignition loss method.8 Results indicated that the glass ®ber volume fraction, Vf, was approximately 0.3, with the ®ller content about 5% by volume. The gage length of each of the coupons was determined so as to prevent a stability failure of the coupon under axial compression. The coupons were cut only in the longitudinal direction, as the cross-section dimensions of the wide ¯ange section precluded taking specimens in the transverse direction. 3.2 Short-term material properties To determine the average initial longitudinal elastic modulus, EL0, and ultimate compression stress, FLc, for the material, short-term tests were conducted on ®ve coupons cut from the same wide ¯ange section that the creep coupons were taken from. The short-term experiments were conducted in a servo-hydraulic testing machine using hydraulic grips to transfer the load to the specimens. The specimens were tested in accordance with ASTM D34109 with one important exception; the width of the coupons was 38 mm as opposed to the maximum 25 mm width given in the standard. This was done based on the tension coupon results of a study of this particular type of material conducted by Wang and Zureick.10 A typical stress±strain diagram for the coupons under short-term loading is given in Fig. 2. A single uniaxial extensometer was used to measure the longitudinal strain in the coupon. This choice was made based on a series of coupon tests performed with backto-back strain gages. The results of these tests showed that coupon bending during the experiments was well within the tolerance set forth by ASTM for the desired strain range. As a result, the use of strains from only one side of the coupon in determining the longitudinal modulus was justi®ed. In order to avoid damage to the
Fig. 2. Typical coupon stress±strain curve for short-term loads.
1363
extensometer the instrument was removed at a stress level of about one-half of the expected ultimate strength. The results of the short-term tests are given in Table 1. 3.3 Long-term experimental set-up Figure 3 shows a schematic illustration of the deadweight lever-arm creep ®xture developed to apply compression loads to the coupons. The ®xture was constructed from structural steel with pillow block roller bearings functioning as the fulcrum. The lever-arm was designed to magnify the load applied to the specimens by a factor of 10. The ®xture is capable of loading three coupons simultaneously at a desired constant load. A set of cages was constructed for each ®xture, which transferred the tensile load applied by the lever arm to each FRP coupon as compression; a typical compression cage is shown in Fig. 4. Three stress levels of 65 MPa, 129 MPa, and 194 MPa were investigated in the present work; these values represent 20%, 40%, and 60%, respectively, of the average ultimate compressive stress from the short-term coupon tests. Stress levels of 20% and 40% of ultimate are well within the linear±elastic range found from the short-term tests. This will be important in later work where determining the model parameters for various stress levels will be desirable. A stress level of 60% of ultimate is very near the level where coupons made from this material have begun to exhibit non-linear behavior. For each stress level a set of three coupons was tested; each set is designated by its matrix material (vinylester), Table 1. Results from short-term compression tests Coupon location Flange 1 Flange 2 Flange 3 Flange 4 Web Average C.O.V (%)
FLc (MPa)
EL0 (GPa)
356 348 304 291 318 323 7.7
21.3 22.9 24.2 21.4 22.7 22.5 4.8
Fig. 3. Schematic diagram of lever arm ®xture used in creep experiments.
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D. W. Scott, A.-H. Zureick
Fig. 4. Compression cage used in creep experiments.
reinforcement material (E-glass), load level and coupon number. For example, the three coupons subjected to a stress level of approximately 20% of ultimate are designated as specimens VG20-1, VG20-2, and VG20-3. The ends of each coupon were milled so as to provide a ¯at surface for the application of the axial compressive load by the cage grips. The coupons were aligned in each ®xture mechanically using plastic shim material to provide a secure seat in the grips. Concrete pads weighing an average of 27 kg each were hung from the ®xture lever-arm to obtain the required stress level. The experiments were conducted under normal laboratory conditions. Figures 5 and 6 show one of the creep ®xtures after the application of load. A series of trial coupons were tested in the compression cages with back-to-back gages to determine the amount of bending induced by the ®xture. The dierence in back-to-back strain readings was minimal (within 2%); therefore, a single three-hundred ®fty (350) ohm uniaxial strain gage was axed to each of the three specimens in each creep ®xture. This minimized the number of channels needed to electronically monitor the strains in the coupons. The strain readings were recorded at the following time intervals: 1. Period 1: Once each 6 min (0.1 h) for the ®rst hour; 2. Period 2: Once each hour for the next 24 h following period 1; 3. Period 3: Once each day for the next 30 days following period 2; 4. Period 4: Once each week for the next month (four weeks) following period 3; 5. Period 5: Once each two weeks thereafter. The specimen strain readings for each of the three stress levels are shown in Figs 7±9. The experiment involving coupons subjected to stress levels of 40% of ultimate have been underway for approximately 10 000 h. The experiments at the other two stress levels have been underway for approximately 5 000 h. Table 2 gives the percent increase over the initial (elastic) strains for several time durations.
Fig. 5. Lever arm creep ®xtures used in the investigations (side view).
3.4 Evaluation of viscoelastic model To bring the results of this investigation to a level suitable for design, the well known power law developed by Findley11 was adopted to model the time-dependent behavior. This formulation was con®rmed as an adequate modeling approach for the 26 yr creep of an unreinforced thermoplastic material.12 As noted earlier, the ®ber volume fraction Vf for this material is approximately 0.3. Therefore, it was assumed that the creep behavior would be more matrix driven, and the Findley model would provide a good approximation. The simplest form of the power law may be written as t 0 mtn
1
where E(t) = total time-dependent creep strain; E0= stress-dependent and temperature-dependent initial elastic strain; m = stress-dependent and temperaturedependent coecient; n = stress-independent material constant; t = time after loading. The evaluation of the empirical constants needed to formulate the power law model may be found from the experimental creep data by ®rst rearranging eqn (1) and taking the log of both sides:
Compression creep of a pultruded E-glass/vinylester composite
1365
Fig. 8. Specimen creep strains for coupons loaded up to 40% of ultimate stress.
Plotting eqn (2) on logarithmic scales yields a straight line; the intercept at t=1 h represents the value of m while the slope of the line yields n.
The strain data for each coupon from the ®rst 1000 h of the experiment are plotted logarithmically in Figs 10± 12. The resulting values for Eo, m and n from eqn (2) are given in Table 3. The Findley model given by eqn (2) is plotted alongside the experimentally determined creep data in Figs 7±9. The power law formulation proved quite adequate for modeling the creep behavior of the pultruded material. The power law parameters found in the present work may be compared with those found by Mosallam and Bank,3,4 Mottram,6 and McClure and Mohammadi7 on similar material systems. The stress-dependent parameter m varied for each study while the stress-independent material constant n found in the present work was
Fig. 7. Specimen creep strains for coupons loaded up to 20% of ultimate stress.
Fig. 9. Specimen creep strains for coupons loaded up to 60% of ultimate stress.
Fig. 6. Lever arm creep ®xtures used in the investigation (front view).
log t ÿ 0 log m nlog t
2
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D. W. Scott, A.-H. Zureick Table 2. Percent increase in specimen longitudinal strains c
f=0.40 FLc specimen
f=0.20 FL specimen VG20-1
VG20-2
VG20-3
VG40-1
VG40-2
VG40-3
VG60-1
VG60-2
VG60-3
%
%
%
%
%
%
%
%
%
2.3 3.8 5.8 9.0 10.5 13.8 Ð
1.8 3.1 5.5 8.0 9.4 13.4 Ð
1.5 2.6 4.4 6.8 7.9 11.1 Ð
1.8 3.7 5.7 8.2 9.5 13.4 15.6
1.3 2.4 3.4 4.9 6.0 8.9 10.2
1.5 3.2 4.6 6.4 7.8 11.4 13.4
1.9 3.2 5.6 7.8 9.4 13.2 Ð
1.6 2.5 4.5 6.5 7.7 11.1 Ð
1.7 3.2 5.1 7.4 8.8 12.3 Ð
tÿ0 0
Time (h) 1 10 100 500 1000 5000 10 000
tÿ0 0
tÿ0 0
tÿ0 0
Table 3. Creep parameters taken from eqn (2) Stress level f=0.2FL
c
f=0.4FLc f=0.6FLc
f=0.60 FLc specimen
Specimen number VG20-1 VG20-2 VG20-3 VG40-1 VG40-2 VG40-3 VG60-1 VG60-2 VG60-3
0 () m () 2522 2411 2467 4982 5012 5003 7713 7611 7812
56 43 37 101 70 85 148 116 143
n 0.220 0.242 0.243 0.228 0.207 0.222 0.231 0.232 0.226
approximately the same as that determined by Mottram. The coupon tests performed by McClure and Mohammadi also yielded similar results for n as found here. However, the creep experiments performed on full angle sections by McClure and Mohammadi yielded a lower value for n than the coupon tests; no explanation was given by the authors. Since the present work deals with experiments on coupons, it seems reasonable to compare the experimental results to the coupon test results of the authors. The value for n found by Mosallam and Bank diered from those in the other investigations by approximately 40%. It should be noted that
Fig. 10. Evaluation of constants m and n for f=0.2 FLc.
tÿ0 0
tÿ0 0
tÿ0 0
tÿ0 0
tÿ0 0
the studies performed by Mottram, and Mosallam and Bank primarily involved ¯exural tests, while the present work as well as that by McClure and Mohammadi focused on compression experiments. Table 4 gives the average values for n from each of the dierent investigations. 3.5 Prediction of time-dependent modulus The constants Eo and m in eqn (1) may be expressed as hyperbolic functions of stress as shown: " # 3 f f 1 f ::: 3 00 0 00 sinh fe fe 3! fe " # f f 1 f 3 0 ::: m m m sinh fm fm 3! fm 0
Substituting these expressions into eqn (1) yields f f 0 0 n m t sinh t 0 sinh fe fm
4
5
Fig. 11. Evaluation of constants m and n for f=0.40 FLc.
Compression creep of a pultruded E-glass/vinylester composite
1367
Fig. 12. Evaluation of constants m and n for f=0.60 FLc. Table 4. Average values for creep parameter n from dierent investigations Investigator Bank and Mosallam Mottram McClure and Mohammadi present work
n 0.33 0.22 0.25 0.23
where f is the applied stress. The parameters 0 0, m0 , fe and fm are material constants determined empirically from creep experiments at multiple stress levels. If the cubic and higher terms are neglected in the Taylor series expansions given in eqn (3) and (4), then eqn (5) may be approximated as f 0 0 n f mt 6 t 0 fe fm It must be noted that at higher stress levels the creep parameters in Findley's power law may not be approximated as linear functions of stress; that is, it may not be acceptable to neglect the cubic and higher terms in the Taylor series expansions given in eqn (3) and (4). Thus, the simpli®ed expression given in eqn (6) may no longer be valid. In order to check the validity of the simpli®cations shown in eqn (6) for the stress levels in this investigation, it was necessary to obtain values for the material constants 00 , m0 , fe and fm. These constants were determined from plots of eqn (3) and (4), as shown in Fig. 13. The values for fe and fm were selected to linearize the curves; the values of 00 and m0 were then determined from the slopes of the straight lines. Using the values of fe and fm found from the curves in Fig. 13, the ratios ffe and ffm may be determined for each of the stress levels used in the experiments. The maximum values for these ratios occur for the coupons tested at f 0:60 FL c ; for this stress level, the values of the ratios
Fig. 13. Evaluation of creep parameters 0 and fe. f fe
and ffm are 0.562 and 0.803, respectively. These experimental results can be used to predict the long term strain from both the exact expression for the Findley power law given in eqn (5) and the simpli®ed expression given by eqn (6). The dierence between the exact expression and the simpli®ed equation, using the experimental data found in this investigation, is at most 4% at t=75 yr. Up to 15% variation can be viewed as acceptable in civil engineering applications owing to the fact that the loads are non-deterministic. Equation (6) may be rewritten in the form 1 tn 7 t f E 0L Et where E 0L fe0 f0 is an initial longitudinal elastic 0 modulus and represents the time-dependent component. Table 5 gives the values for E 0L and Et for each coupon. Equation (7) may be rearranged to provide an expression for the viscoelastic modulus as follows: EL t
E 0L Et E 0L Et E 0L tn 1 E 0L tn Et
8
Equation (8) may be used to predict the reduction in longitudinal stiness for an FRP material provided the constants from Findley's equation are determined. The worst-case result from the coupon experiments in this investigation predicts a reduction in the longitudinal stiness of approximately 28% over a 75-year service life. One fact must be noted when using the Findley model with the simpli®cations shown in eqn (6); the predicted reduction in longitudinal stiness over time is not dependent on the stress level.
1368
D. W. Scott, A.-H. Zureick Table 5. Creep parameter n, elastic modulus EL0 and time-dependent component Et from eqn (10)
Stress level
Specimen ]number
f=0.20FLc
VG20-1 VG20-2 VG20-3 VG40-1 VG40-2 VG40-3 VG60-1 VG60-2 VG60-3 Average C.O.V. (%)
f=0.40FLc f=0.60FLc
n
EL0 (GPa)
Et (GPa)
Et/EL0
0.220 0.242 0.243 0.228 0.207 0.222 0.231 0.232 0.226 0.228 4. 6
24.2 22.7 22.9 22.9 22.7 24.2 21.3 22.1 22.1 22.8 3.9
1165 1514 1747 1280 1847 1521 1312 1676 1356 1491 14.6
48.1 66.7 76.3 55.9 81.4 62.9 61.6 75.8 61.4 65.6 15.3
The Findley power law model is only valid if the material undergoes the ®rst stage of creep deformation, often referred to as primary creep. This type of behavior is characterized by a decrease in the rate of creep over time. At lower stress levels (relative to ultimate), most FRP materials used in civil engineering applications undergo such behavior. At higher stress levels, a material may experience an increase in the rate of creep with time up to the point of failure. This type of behavior is referred to as tertiary creep. In this investigation, we found that the Findley power law was adequate to model the behavior of the material loaded to 60% of its ultimate strength for a time duration of approximately 5000 h; however, the behavior of the material could change in the future if it begins to undergo tertiary creep. At the present time, we recommend that the sustained stress level not exceed 33% to ensure that the Findley model provides a valid description of the material behavior. 3.6 Proposed design equation for time-dependent modulus EL(t) Based on the results of the present work, it is possible to formulate a design equation for estimating the longterm longitudinal elastic modulus EL(t) for FRP composites manufactured by the pultrusion process with glass reinforcement primarily in the longitudinal direction and a resin matrix similar in composition to that of Derakane 411TM. From a civil engineering design standpoint, it is more practical to specify the time t in years instead of hours. In doing so, we obtain EL t
E 0L
1
E 0L Et
8760tn
EL t
E 0L 1 8760t
0:25
E 0L 1 8760t
0:25
t0:25
E 0L t E 0L 0:25 1 10 t 10
where t is a time-dependent reduction factor given by t
1 1
10 0:25 t
11
The true numerical value for (8760)0.25 is 9.6744. However, to simplify the expression given in eqn (10), we decided to use the conservative approximation (8760)0.25&10. This makes the proposed equation more practical to the designer. The parameter EE0t can be L found using Findley's model from creep strain data of only 1000 h in duration. The creep strains may be used with eqn (2) to determine the constants m and n. Assuming the applied stress remains constant, the timedependent component Et mf can then be determined. If the elastic modulus EL0 is known, then may calculated and used in eqn (11).
9
The value of the material coecient n found in this work and in other research studies was fairly consistent for this class of materials. Thus, a convenient value of n=0.25 is selected for use in the design equation. If we further introduce the parameter EE0t , then eqn (9) L may expressed in the following form:
Fig. 14. Normalized viscoelastic modulus versus time.
Compression creep of a pultruded E-glass/vinylester composite
1369
ACKNOWLEDGEMENTS This work is supported by the Federal Highway Administration under Contract No. DTFH61-93-C0012. E. Munley serves as Program Director. REFERENCES
Fig. 15. Average normalized viscoelastic modulus versus time.
The predicted normalized time-dependent moduli EEL t 0 L as a function of time are presented graphically in Fig. 14 using the experimental results from the coupon tests. These curves show the variation in results within each stress level. The time-dependent reduction factor t given by eqn (11) is also plotted in Fig. 14 to compare with values predicted using the coupon test results. A value of =45 was chosen as a lower-bound value of the ratio EE0t found from the experiments in the present L work. The value for t diers from those predicted using the experimental data by a range of 15% to 27% at t=75 yr. A plot of EEL t versus time using average 0 L values for n and from the coupon tests is shown in Fig. 15; the error bars at each data point represent two using standard deviations. The predicted results for EEL t 0 L average values from the coupon experiments dier from eqn (11), which uses n=0.25 and =45, by approximately 20% at t=75 yr. This shows the degree of conservatism in choosing a lower bound value for and using the convenient value n=0.25.
1. Scott, D., Lai, J. and Zureick, A., Creep behavior of ®ber-reinforced polymeric composites: a review of the technical literature. J. Reinf. Plastics and Composites, 1995, 14, 588±617. 2. Holmes, M. and Rahman, T. A., Creep behavior of glass reinforced plastic box beams. Composites, 1980, 4, 797±802. 3. Mosallam, A.S. and Bank, L.C., Creep and recovery of a pultruded FRP frame. In: Advanced Composite Materials in Civil Engineering Structures, ASCE, ed. S. Iyer and R. Sen, 1991, pp. 24±35. 4. Bank, L. C. and Mosallam, A. S., Creep and failure of a full size ®ber reinforced plastic pultruded frame. Compos. Eng., 1992, 2(3), 213±227. 5. Daniali, S., Short-term and long-term behavior of two types of reinforced plastic beams. In 46th Annual Conference, Composites Institute, February 1991, pp. 13A-1 through 5. 6. Mottram, J. T., Short and long-term structural properties of pultruded beam assemblies fabricated using adhesive bonding. Compos. Struct., March 1993, 387±395. 7. McClure, G. and Mohammadi, Y., Compression creep of pultruded E-glass-reinforced-plastic angles. J. Mater. in Civil Eng., 1995, 7(4), 269±276. 8. Ye, B. S., Svenson, A. L. and Bank, L. C., Mass and volume fraction properties of pultruded glass ®bre-reinforced composites. Composites, 1995, 26, 725±731. 9. ASTM D3410M-95, Standard test method for compressive properties of polymer matrix composite materials with unsupported gage section by shear loading. American Society for Testing and Materials, West Conshohocken, PA. 10. Wang, Y. and Zureick, A. H., Characterization of the longitudinal tensile behavior of pultruded I-shape structural members using coupon specimens. Compos. Struct., 1994, 29, 463±472. 11. Findley, W.N., Creep characteristics of plastics. In 1944 Symposium on Plastics, 1944 ASTM. 12. Findley, W. N., 26-year creep and recovery of poly(vinyl chloride) and polyethylene. Polym. Eng Sci., 1987, 27(8), 582±585.
Composites Science and Technology 58 (1998) 1361±1369 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0266-3538/98 $Ðsee front matter
COMPRESSION CREEP OF A PULTRUDED E-GLASS/ VINYLESTER COMPOSITE David W. Scott & Abdul-Hamid Zureick* School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA (Received 19 June 1997; accepted 9 January 1998)
2 PREVIOUS WORK
Abstract This paper presents the results of an experimental investigation pertaining to the long-term behavior of pultruded ®ber-reinforced polymeric materials subjected to longitudinal compressive loading. Material coupons cut from a pultruded vinylester/E-glass I-shape section were subjected to axial compressive loads at various stress levels for time durations up to 10 000 h. The strain measurements over time were recorded and compared to a practical power law formulation, with good agreement. A predictor design equation for the time-dependent longitudinal modulus was developed on the basis of the experimental results. # 1998 Elsevier Science Ltd. All rights reserved
A large volume of work currently exists on the timedependent behavior of composite materials. The vast majority of these investigations have concerned the viscoelastic behavior of laminated composites used extensively in the aerospace industry. Many of these studies form the foundation upon which the present work related to civil engineering construction is based. A review of the pertinent technical literature associated with the experimental characterization of the time-dependent behavior of FRP composites from a variety of material systems and manufacturing processes has recently been completed.1 In what follows we summarize the results from those few investigations which focused on the creep behavior of FRP composite materials used speci®cally in civil engineering applications, as they are directly related to the present work. One of ®rst published investigations on the subject at hand was conducted by Holmes and Rahman2 who tested three glass-reinforced box sections. Each section was loaded to one-third of its estimated short-term ultimate bending strength at a span length of 6 m for approximately 20 months under normal laboratory conditions. Tensile, compressive and shear creep strains taken from the experiments were compared with three viscoelastic models formulated using the ®rst 2000 hours of experimental data. The experimental tensile and shear strains showed relative consistency with the predicted values, while the compression strains did not compare well with any of the models. After 15 000 h of testing, the midspan de¯ection had become approximately twice its elastic value. Mosallam and Bank3,4 investigated the viscoelastic behavior of a portal frame assembly constructed from three pultruded FRP wide ¯ange sections. The wide ¯ange sections were connected using pultruded FRP angles. All of the sections used in the construction of the portal frame were composed of glass continuous strand mat and roving with a vinylester resin. The frame was loaded to approximately one-fourth of the estimated frame failure load under normal laboratory conditions. Results from this work showed that after 10 000 h of
Keywords: B. creep, composites, compression, E-glass, vinylester 1 INTRODUCTION Recent years have found increasing acceptance of ®berreinforced polymeric (FRP) composites manufactured by the pultrusion process as an alternative to traditional materials both in new civil-engineering construction and in the rehabilitation of infrastructure. However, a fundamental lack of understanding of the behavior of these advanced materials in many dierent types of service has limited their application. The viscoelastic nature of FRP composites makes it imperative that the time-dependent behavior of these materials be accounted for in the analysis and design of any structural system. This paper presents the results of an experimental investigation into the creep behavior of pultruded FRP composite materials in compression. The experiments were performed at three dierent stress levels for time durations up to 10 000 h. The experimental data is correlated with a practical creep model that can be used for design purposes. *To whom correspondence should be addressed. 1361
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D. W. Scott, A.-H. Zureick
loading, the girder mid-span de¯ection had increased by approximately 22%, with the majority of the increase occurring in the ®rst 2000 h. The power-law model utilized in the study predicted a decrease of 35% in the viscoelastic section ¯exural modulus over a 10 yr period; the viscoelastic section shear modulus was predicted to decrease by about 46% over the same period. Daniali5 reported on the short- and long-term behavior of two types of pultruded glass/vinylester and glass/ polyester T-shaped beams. One type of beam contained a cavity in the web; the other was formed with a solid web. The beams were tested in a two-span setup at room temperature and at 54 C for stress levels ranging from 50% to 85% of the estimated short-term strength for time durations up to 10 000 h. For the members loaded to 50% of ultimate, the polyester cavity-web beams experienced an increase of approximately 20% in the de¯ection of the system after 10 000 h at room temperature; the vinylester cavity-web beams increased about 15%. The tests at ambient conditions for load levels greater than 50% of ultimate were stopped after 500 h. At the elevated temperatures, the beams with a polyester binder suered drastic reductions in strength, as well as shorter creep life and larger creep de¯ections, when compared with the specimens utilizing a vinylester binder. Mottram6 constructed two panel assemblies from pultruded glass/polyester I-sections sandwiched between pultruded FRP plates. The assemblies were ®rst tested under short-term ¯exural loads, where comparisons revealed a 7% reduction in the stiness of the assembly from the stiness of the original elements; this was attributed to the ¯exibility of the adhesive bonding. The beams were then loaded for 24 h at room temperature. Predictive power law models for the viscoelastic tensile and shear moduli were developed using the data collected from the experiment. These time-dependent moduli were used with Timoshenko beam theory to predict the de¯ection in the panel assemblies for time durations of one week, one year and ten years. The predicted values re¯ected increases of 25%, 60%, and 100%, respectively, over the specimens' initial de¯ection. The author found that creep parameters obtained from testing coupon samples taken from the beams compared very well with the creep parameters taken directly from the assembly. Recently, McClure and Mohammadi7 investigated the compression creep behavior of pultruded FRP angle sections. A total of 11 single angle members with crosssection dimensions 50.8 mm50.8 mm6.4 mm and length 152.4 mm were tested. Additionally, 20 material coupons with dimensions 12.7 mm6.5 mm31.75 mm were cut from the legs of angles of the same cross-section. Both the angles and the coupons were subjected to constant compressive loads for a time duration of 2500 h in normal laboratory conditions. Each angle section was loaded to approximately 45% of its estimated short-term local buckling load. During the ®rst
2500 h the strain in the angle sections increased by an average of 16% over the short-term values, with nearly half of that increase occurring in the ®rst 24 h. The coupon specimens were loaded to 45% of their short term ultimate load; the average stress in the coupons was approximately 3.3 times higher than that in the angles. The coupon strains increased by an average of 13% after 2500 h. A power law model was used to predict creep strains for both the angles and the coupons over the test duration. The authors found little dierence between the experimental and the predicted results for both the angle and coupon experiments; this was to be expected, since the parameters used in the development of the power law model were determined using data from the entire test duration. In summary, there was only a limited amount of experimental work performed to date on the timedependent behavior of FRP composites for civil engineering applications. The viscoelastic eects of dierent stress levels on these materials have not been adequately investigated. In addition, ways to quantify the eects of constant long-term loads for use in reliable design criteria are not widely known and supported. The work described in this paper was performed to ®ll a portion of that need. 3 PRESENT INVESTIGATION 3.1 Specimen details The rectangular prismatic coupon specimens used in this work were cut from each structural plate element in a 102 mm102 mm6.4 mm pultruded FRP wide ¯ange section as shown in Fig. 1. The composite material consisted of a vinylester matrix (Derakane 411TM) reinforced with unidirectional E-glass roving and continuous ®lament mat. Four layers of the E-glass mat were placed alternately with three layers of E-glass rov-
Fig. 1. Coupon locations and nominal dimensions.
Compression creep of a pultruded E-glass/vinylester composite ing to provide the reinforcement pattern. Small pieces cut from various locations on sections having the same ®ber architecture were examined using the modi®ed ignition loss method.8 Results indicated that the glass ®ber volume fraction, Vf, was approximately 0.3, with the ®ller content about 5% by volume. The gage length of each of the coupons was determined so as to prevent a stability failure of the coupon under axial compression. The coupons were cut only in the longitudinal direction, as the cross-section dimensions of the wide ¯ange section precluded taking specimens in the transverse direction. 3.2 Short-term material properties To determine the average initial longitudinal elastic modulus, EL0, and ultimate compression stress, FLc, for the material, short-term tests were conducted on ®ve coupons cut from the same wide ¯ange section that the creep coupons were taken from. The short-term experiments were conducted in a servo-hydraulic testing machine using hydraulic grips to transfer the load to the specimens. The specimens were tested in accordance with ASTM D34109 with one important exception; the width of the coupons was 38 mm as opposed to the maximum 25 mm width given in the standard. This was done based on the tension coupon results of a study of this particular type of material conducted by Wang and Zureick.10 A typical stress±strain diagram for the coupons under short-term loading is given in Fig. 2. A single uniaxial extensometer was used to measure the longitudinal strain in the coupon. This choice was made based on a series of coupon tests performed with backto-back strain gages. The results of these tests showed that coupon bending during the experiments was well within the tolerance set forth by ASTM for the desired strain range. As a result, the use of strains from only one side of the coupon in determining the longitudinal modulus was justi®ed. In order to avoid damage to the
Fig. 2. Typical coupon stress±strain curve for short-term loads.
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extensometer the instrument was removed at a stress level of about one-half of the expected ultimate strength. The results of the short-term tests are given in Table 1. 3.3 Long-term experimental set-up Figure 3 shows a schematic illustration of the deadweight lever-arm creep ®xture developed to apply compression loads to the coupons. The ®xture was constructed from structural steel with pillow block roller bearings functioning as the fulcrum. The lever-arm was designed to magnify the load applied to the specimens by a factor of 10. The ®xture is capable of loading three coupons simultaneously at a desired constant load. A set of cages was constructed for each ®xture, which transferred the tensile load applied by the lever arm to each FRP coupon as compression; a typical compression cage is shown in Fig. 4. Three stress levels of 65 MPa, 129 MPa, and 194 MPa were investigated in the present work; these values represent 20%, 40%, and 60%, respectively, of the average ultimate compressive stress from the short-term coupon tests. Stress levels of 20% and 40% of ultimate are well within the linear±elastic range found from the short-term tests. This will be important in later work where determining the model parameters for various stress levels will be desirable. A stress level of 60% of ultimate is very near the level where coupons made from this material have begun to exhibit non-linear behavior. For each stress level a set of three coupons was tested; each set is designated by its matrix material (vinylester), Table 1. Results from short-term compression tests Coupon location Flange 1 Flange 2 Flange 3 Flange 4 Web Average C.O.V (%)
FLc (MPa)
EL0 (GPa)
356 348 304 291 318 323 7.7
21.3 22.9 24.2 21.4 22.7 22.5 4.8
Fig. 3. Schematic diagram of lever arm ®xture used in creep experiments.
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D. W. Scott, A.-H. Zureick
Fig. 4. Compression cage used in creep experiments.
reinforcement material (E-glass), load level and coupon number. For example, the three coupons subjected to a stress level of approximately 20% of ultimate are designated as specimens VG20-1, VG20-2, and VG20-3. The ends of each coupon were milled so as to provide a ¯at surface for the application of the axial compressive load by the cage grips. The coupons were aligned in each ®xture mechanically using plastic shim material to provide a secure seat in the grips. Concrete pads weighing an average of 27 kg each were hung from the ®xture lever-arm to obtain the required stress level. The experiments were conducted under normal laboratory conditions. Figures 5 and 6 show one of the creep ®xtures after the application of load. A series of trial coupons were tested in the compression cages with back-to-back gages to determine the amount of bending induced by the ®xture. The dierence in back-to-back strain readings was minimal (within 2%); therefore, a single three-hundred ®fty (350) ohm uniaxial strain gage was axed to each of the three specimens in each creep ®xture. This minimized the number of channels needed to electronically monitor the strains in the coupons. The strain readings were recorded at the following time intervals: 1. Period 1: Once each 6 min (0.1 h) for the ®rst hour; 2. Period 2: Once each hour for the next 24 h following period 1; 3. Period 3: Once each day for the next 30 days following period 2; 4. Period 4: Once each week for the next month (four weeks) following period 3; 5. Period 5: Once each two weeks thereafter. The specimen strain readings for each of the three stress levels are shown in Figs 7±9. The experiment involving coupons subjected to stress levels of 40% of ultimate have been underway for approximately 10 000 h. The experiments at the other two stress levels have been underway for approximately 5 000 h. Table 2 gives the percent increase over the initial (elastic) strains for several time durations.
Fig. 5. Lever arm creep ®xtures used in the investigations (side view).
3.4 Evaluation of viscoelastic model To bring the results of this investigation to a level suitable for design, the well known power law developed by Findley11 was adopted to model the time-dependent behavior. This formulation was con®rmed as an adequate modeling approach for the 26 yr creep of an unreinforced thermoplastic material.12 As noted earlier, the ®ber volume fraction Vf for this material is approximately 0.3. Therefore, it was assumed that the creep behavior would be more matrix driven, and the Findley model would provide a good approximation. The simplest form of the power law may be written as t 0 mtn
1
where E(t) = total time-dependent creep strain; E0= stress-dependent and temperature-dependent initial elastic strain; m = stress-dependent and temperaturedependent coecient; n = stress-independent material constant; t = time after loading. The evaluation of the empirical constants needed to formulate the power law model may be found from the experimental creep data by ®rst rearranging eqn (1) and taking the log of both sides:
Compression creep of a pultruded E-glass/vinylester composite
1365
Fig. 8. Specimen creep strains for coupons loaded up to 40% of ultimate stress.
Plotting eqn (2) on logarithmic scales yields a straight line; the intercept at t=1 h represents the value of m while the slope of the line yields n.
The strain data for each coupon from the ®rst 1000 h of the experiment are plotted logarithmically in Figs 10± 12. The resulting values for Eo, m and n from eqn (2) are given in Table 3. The Findley model given by eqn (2) is plotted alongside the experimentally determined creep data in Figs 7±9. The power law formulation proved quite adequate for modeling the creep behavior of the pultruded material. The power law parameters found in the present work may be compared with those found by Mosallam and Bank,3,4 Mottram,6 and McClure and Mohammadi7 on similar material systems. The stress-dependent parameter m varied for each study while the stress-independent material constant n found in the present work was
Fig. 7. Specimen creep strains for coupons loaded up to 20% of ultimate stress.
Fig. 9. Specimen creep strains for coupons loaded up to 60% of ultimate stress.
Fig. 6. Lever arm creep ®xtures used in the investigation (front view).
log t ÿ 0 log m nlog t
2
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D. W. Scott, A.-H. Zureick Table 2. Percent increase in specimen longitudinal strains c
f=0.40 FLc specimen
f=0.20 FL specimen VG20-1
VG20-2
VG20-3
VG40-1
VG40-2
VG40-3
VG60-1
VG60-2
VG60-3
%
%
%
%
%
%
%
%
%
2.3 3.8 5.8 9.0 10.5 13.8 Ð
1.8 3.1 5.5 8.0 9.4 13.4 Ð
1.5 2.6 4.4 6.8 7.9 11.1 Ð
1.8 3.7 5.7 8.2 9.5 13.4 15.6
1.3 2.4 3.4 4.9 6.0 8.9 10.2
1.5 3.2 4.6 6.4 7.8 11.4 13.4
1.9 3.2 5.6 7.8 9.4 13.2 Ð
1.6 2.5 4.5 6.5 7.7 11.1 Ð
1.7 3.2 5.1 7.4 8.8 12.3 Ð
tÿ0 0
Time (h) 1 10 100 500 1000 5000 10 000
tÿ0 0
tÿ0 0
tÿ0 0
Table 3. Creep parameters taken from eqn (2) Stress level f=0.2FL
c
f=0.4FLc f=0.6FLc
f=0.60 FLc specimen
Specimen number VG20-1 VG20-2 VG20-3 VG40-1 VG40-2 VG40-3 VG60-1 VG60-2 VG60-3
0 () m () 2522 2411 2467 4982 5012 5003 7713 7611 7812
56 43 37 101 70 85 148 116 143
n 0.220 0.242 0.243 0.228 0.207 0.222 0.231 0.232 0.226
approximately the same as that determined by Mottram. The coupon tests performed by McClure and Mohammadi also yielded similar results for n as found here. However, the creep experiments performed on full angle sections by McClure and Mohammadi yielded a lower value for n than the coupon tests; no explanation was given by the authors. Since the present work deals with experiments on coupons, it seems reasonable to compare the experimental results to the coupon test results of the authors. The value for n found by Mosallam and Bank diered from those in the other investigations by approximately 40%. It should be noted that
Fig. 10. Evaluation of constants m and n for f=0.2 FLc.
tÿ0 0
tÿ0 0
tÿ0 0
tÿ0 0
tÿ0 0
the studies performed by Mottram, and Mosallam and Bank primarily involved ¯exural tests, while the present work as well as that by McClure and Mohammadi focused on compression experiments. Table 4 gives the average values for n from each of the dierent investigations. 3.5 Prediction of time-dependent modulus The constants Eo and m in eqn (1) may be expressed as hyperbolic functions of stress as shown: " # 3 f f 1 f ::: 3 00 0 00 sinh fe fe 3! fe " # f f 1 f 3 0 ::: m m m sinh fm fm 3! fm 0
Substituting these expressions into eqn (1) yields f f 0 0 n m t sinh t 0 sinh fe fm
4
5
Fig. 11. Evaluation of constants m and n for f=0.40 FLc.
Compression creep of a pultruded E-glass/vinylester composite
1367
Fig. 12. Evaluation of constants m and n for f=0.60 FLc. Table 4. Average values for creep parameter n from dierent investigations Investigator Bank and Mosallam Mottram McClure and Mohammadi present work
n 0.33 0.22 0.25 0.23
where f is the applied stress. The parameters 0 0, m0 , fe and fm are material constants determined empirically from creep experiments at multiple stress levels. If the cubic and higher terms are neglected in the Taylor series expansions given in eqn (3) and (4), then eqn (5) may be approximated as f 0 0 n f mt 6 t 0 fe fm It must be noted that at higher stress levels the creep parameters in Findley's power law may not be approximated as linear functions of stress; that is, it may not be acceptable to neglect the cubic and higher terms in the Taylor series expansions given in eqn (3) and (4). Thus, the simpli®ed expression given in eqn (6) may no longer be valid. In order to check the validity of the simpli®cations shown in eqn (6) for the stress levels in this investigation, it was necessary to obtain values for the material constants 00 , m0 , fe and fm. These constants were determined from plots of eqn (3) and (4), as shown in Fig. 13. The values for fe and fm were selected to linearize the curves; the values of 00 and m0 were then determined from the slopes of the straight lines. Using the values of fe and fm found from the curves in Fig. 13, the ratios ffe and ffm may be determined for each of the stress levels used in the experiments. The maximum values for these ratios occur for the coupons tested at f 0:60 FL c ; for this stress level, the values of the ratios
Fig. 13. Evaluation of creep parameters 0 and fe. f fe
and ffm are 0.562 and 0.803, respectively. These experimental results can be used to predict the long term strain from both the exact expression for the Findley power law given in eqn (5) and the simpli®ed expression given by eqn (6). The dierence between the exact expression and the simpli®ed equation, using the experimental data found in this investigation, is at most 4% at t=75 yr. Up to 15% variation can be viewed as acceptable in civil engineering applications owing to the fact that the loads are non-deterministic. Equation (6) may be rewritten in the form 1 tn 7 t f E 0L Et where E 0L fe0 f0 is an initial longitudinal elastic 0 modulus and represents the time-dependent component. Table 5 gives the values for E 0L and Et for each coupon. Equation (7) may be rearranged to provide an expression for the viscoelastic modulus as follows: EL t
E 0L Et E 0L Et E 0L tn 1 E 0L tn Et
8
Equation (8) may be used to predict the reduction in longitudinal stiness for an FRP material provided the constants from Findley's equation are determined. The worst-case result from the coupon experiments in this investigation predicts a reduction in the longitudinal stiness of approximately 28% over a 75-year service life. One fact must be noted when using the Findley model with the simpli®cations shown in eqn (6); the predicted reduction in longitudinal stiness over time is not dependent on the stress level.
1368
D. W. Scott, A.-H. Zureick Table 5. Creep parameter n, elastic modulus EL0 and time-dependent component Et from eqn (10)
Stress level
Specimen ]number
f=0.20FLc
VG20-1 VG20-2 VG20-3 VG40-1 VG40-2 VG40-3 VG60-1 VG60-2 VG60-3 Average C.O.V. (%)
f=0.40FLc f=0.60FLc
n
EL0 (GPa)
Et (GPa)
Et/EL0
0.220 0.242 0.243 0.228 0.207 0.222 0.231 0.232 0.226 0.228 4. 6
24.2 22.7 22.9 22.9 22.7 24.2 21.3 22.1 22.1 22.8 3.9
1165 1514 1747 1280 1847 1521 1312 1676 1356 1491 14.6
48.1 66.7 76.3 55.9 81.4 62.9 61.6 75.8 61.4 65.6 15.3
The Findley power law model is only valid if the material undergoes the ®rst stage of creep deformation, often referred to as primary creep. This type of behavior is characterized by a decrease in the rate of creep over time. At lower stress levels (relative to ultimate), most FRP materials used in civil engineering applications undergo such behavior. At higher stress levels, a material may experience an increase in the rate of creep with time up to the point of failure. This type of behavior is referred to as tertiary creep. In this investigation, we found that the Findley power law was adequate to model the behavior of the material loaded to 60% of its ultimate strength for a time duration of approximately 5000 h; however, the behavior of the material could change in the future if it begins to undergo tertiary creep. At the present time, we recommend that the sustained stress level not exceed 33% to ensure that the Findley model provides a valid description of the material behavior. 3.6 Proposed design equation for time-dependent modulus EL(t) Based on the results of the present work, it is possible to formulate a design equation for estimating the longterm longitudinal elastic modulus EL(t) for FRP composites manufactured by the pultrusion process with glass reinforcement primarily in the longitudinal direction and a resin matrix similar in composition to that of Derakane 411TM. From a civil engineering design standpoint, it is more practical to specify the time t in years instead of hours. In doing so, we obtain EL t
E 0L
1
E 0L Et
8760tn
EL t
E 0L 1 8760t
0:25
E 0L 1 8760t
0:25
t0:25
E 0L t E 0L 0:25 1 10 t 10
where t is a time-dependent reduction factor given by t
1 1
10 0:25 t
11
The true numerical value for (8760)0.25 is 9.6744. However, to simplify the expression given in eqn (10), we decided to use the conservative approximation (8760)0.25&10. This makes the proposed equation more practical to the designer. The parameter EE0t can be L found using Findley's model from creep strain data of only 1000 h in duration. The creep strains may be used with eqn (2) to determine the constants m and n. Assuming the applied stress remains constant, the timedependent component Et mf can then be determined. If the elastic modulus EL0 is known, then may calculated and used in eqn (11).
9
The value of the material coecient n found in this work and in other research studies was fairly consistent for this class of materials. Thus, a convenient value of n=0.25 is selected for use in the design equation. If we further introduce the parameter EE0t , then eqn (9) L may expressed in the following form:
Fig. 14. Normalized viscoelastic modulus versus time.
Compression creep of a pultruded E-glass/vinylester composite
1369
ACKNOWLEDGEMENTS This work is supported by the Federal Highway Administration under Contract No. DTFH61-93-C0012. E. Munley serves as Program Director. REFERENCES
Fig. 15. Average normalized viscoelastic modulus versus time.
The predicted normalized time-dependent moduli EEL t 0 L as a function of time are presented graphically in Fig. 14 using the experimental results from the coupon tests. These curves show the variation in results within each stress level. The time-dependent reduction factor t given by eqn (11) is also plotted in Fig. 14 to compare with values predicted using the coupon test results. A value of =45 was chosen as a lower-bound value of the ratio EE0t found from the experiments in the present L work. The value for t diers from those predicted using the experimental data by a range of 15% to 27% at t=75 yr. A plot of EEL t versus time using average 0 L values for n and from the coupon tests is shown in Fig. 15; the error bars at each data point represent two using standard deviations. The predicted results for EEL t 0 L average values from the coupon experiments dier from eqn (11), which uses n=0.25 and =45, by approximately 20% at t=75 yr. This shows the degree of conservatism in choosing a lower bound value for and using the convenient value n=0.25.
1. Scott, D., Lai, J. and Zureick, A., Creep behavior of ®ber-reinforced polymeric composites: a review of the technical literature. J. Reinf. Plastics and Composites, 1995, 14, 588±617. 2. Holmes, M. and Rahman, T. A., Creep behavior of glass reinforced plastic box beams. Composites, 1980, 4, 797±802. 3. Mosallam, A.S. and Bank, L.C., Creep and recovery of a pultruded FRP frame. In: Advanced Composite Materials in Civil Engineering Structures, ASCE, ed. S. Iyer and R. Sen, 1991, pp. 24±35. 4. Bank, L. C. and Mosallam, A. S., Creep and failure of a full size ®ber reinforced plastic pultruded frame. Compos. Eng., 1992, 2(3), 213±227. 5. Daniali, S., Short-term and long-term behavior of two types of reinforced plastic beams. In 46th Annual Conference, Composites Institute, February 1991, pp. 13A-1 through 5. 6. Mottram, J. T., Short and long-term structural properties of pultruded beam assemblies fabricated using adhesive bonding. Compos. Struct., March 1993, 387±395. 7. McClure, G. and Mohammadi, Y., Compression creep of pultruded E-glass-reinforced-plastic angles. J. Mater. in Civil Eng., 1995, 7(4), 269±276. 8. Ye, B. S., Svenson, A. L. and Bank, L. C., Mass and volume fraction properties of pultruded glass ®bre-reinforced composites. Composites, 1995, 26, 725±731. 9. ASTM D3410M-95, Standard test method for compressive properties of polymer matrix composite materials with unsupported gage section by shear loading. American Society for Testing and Materials, West Conshohocken, PA. 10. Wang, Y. and Zureick, A. H., Characterization of the longitudinal tensile behavior of pultruded I-shape structural members using coupon specimens. Compos. Struct., 1994, 29, 463±472. 11. Findley, W.N., Creep characteristics of plastics. In 1944 Symposium on Plastics, 1944 ASTM. 12. Findley, W. N., 26-year creep and recovery of poly(vinyl chloride) and polyethylene. Polym. Eng Sci., 1987, 27(8), 582±585.