Tension-tension fatigue performances of a pultruded carbon fiber reinforced epoxy plate at elevated temperatures

Composite Structures 215 (2019) 421–431

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Tension-tension fatigue performances of a pultruded carbon fiber reinforced epoxy plate at elevated temperatures ⁎

T

⁎

Pangang Wua, Longjun Xua, , Jianlin Luob,c, , Xueyi Zhangd, Wenfeng Biana a

Department of Civil Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China School of Civil Engineering, Collaborative Innovation Center of Engineering Construction and Safety in Shandong Blue Economic Zone, Qingdao University of Technology, Qingdao 266033, China c Center for Infrastructure Engineering, School of Computing, Engineering and Mathematics, Western Sydney University, Sydney, NSW 2751, Australia d College of Aerospace & Civil Engineering, Harbin Engineering University, Harbin 150001, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Pultruded CFRP plate Tension fatigue performance Elevated temperature Failure mechanism Microstructure

Fatigue performance of pultruded CFRP plate at elevated temperature is essential for the design process and applications in structure rehabilitation and reinforcement. Here, tension-tension fatigue performances of pultruded CFRP plate at room temperature (RT), 50 °C and 83 °C (Tg minus 30 °C) were investigated along with static tension properties. The static tensile strength at different temperature (fut), fatigue life, prediction formula, temperature curves, stiffness curves and fatigue failure mechanisms were comprehensively studied in tandem with microstructure. Results reveal, temperature increase and fatigue load lead to resin thermo-elasto-plastic softening and premature failure; the resultant fatigue life is significantly reduced when temperature is close to 83 °C; the fatigue life at RT, 50 °C and 83 °C exceeds 2 × 106 cycles with 95% reliability under stress level of 49.95%fut, 49.03%fut, and 43.24%fut, respectively.

1. Introduction Carbon fiber reinforced polymer (CFRP) composites possess many desirable characteristics such as high strength with light-weight, superior resistance to fatigue and corrosion, and have been widely applied in structure rehabilitation and strengthening [1–4]. In recent years, unidirectional pultruded CFRP plates with excellent quality, stable properties, and long-term storage advantages, can be successfully manufactured by large-scale industrial pultrusion process, and have been gotten more and more attentions in strengthening existed concrete or steel beams [5]. The variation of temperature is unavoidable in outdoor environment, and pultruded CFRP plate is often exposed to high temperature and fatigue load during retrofitting and strengthening of civil structures. In summer, the temperature of 50 °C is often met for outdoor structural surface temperature, e.g., roof surface of a building may exceed 50 °C in southern China. In addition, the temperature of glass

transition temperature (Tg) minus 30 °C is mainly considered the upper limit temperature of FRPs in civil engineering applications [6], and the CFRP plate also likely serves at high temperatures, which is generally less than Tg minus 30 °C in outdoor environment, so the fatigue performances of a pultruded CFRP plate at such range high temperatures should be fully understood for safe designs and applications [7,8]. Most of researchers mainly focused on the static performances under high temperature of FRP composites. Ferrier et al. [9] reported the static ultimate strength of FRP-strengthened concrete elements decreased with the temperature increasing. Feng et al. [10] presented the results of bending tests on FRP specimens at temperatures from 25 °C to 120 °C, the mechanical properties such as strength and stiffness decreased with temperature increasing. Russo et al. [11] studied residual strength of pultruded FRP specimen after 50, 100 and 200 thermal cycles of loading and unloading from 25 °C to 50 °C, rather than the fatigue life at high temperature. The dynamic fracture behavior of CFRP plate is different from that

Abbreviations: FRP, fiber reinforced polymer; CFRP, carbon fiber reinforced polymer; BFRP, basalt fiber reinforced polymer; Tg, glass transition temperature; fut, ultimate tensile strength at each temperature; SEM, scanning electron microscopy; DMA, dynamic mechanical analysis; R, the minimum stress to maximum stress ratio; S, stress level; N, fatigue life; RT, room temperature; σmax, maximum stress; σult, ultimate tensile strength in the tensile test; A, B, constant parameter; rmax, fatigue stress; Ps(N), probability of the survival after N cycles; Ni, cycle number under the i-th stress level; N¯i , scale parameters of the Weibull distribution; α fi , shape parameters of the Weibull distribution; k ,Y0 , slope and intercept of the fitted line; Yσ , stress value; T, temperature ⁎ Corresponding authors at: No. 2, West Wenhua Road, High-tech District, Weihai, Shandong 264209, China (L. Xu). No. 11, Fushun Road, Shibei District, Qingdao, Shandong 266033, China (J. Luo). E-mail addresses: [email protected] (L. Xu), [email protected] (J. Luo). https://doi.org/10.1016/j.compstruct.2019.02.062 Received 28 December 2018; Received in revised form 31 January 2019; Accepted 15 February 2019 Available online 16 February 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

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under static tensile testing, and under-researched on account of the difficulties associated with experimentation [12–15]. A few papers have studied fatigue performance of FRP composites at RT rather than high temperature. Zhao et al. [16] studied the fatigue behaviors of basalt fiber reinforced polymer (BFRP) composites at RT, measured the fatigue life under different stress level. Colombo et al. [17] recorded thermography for fatigue test of BFRP at RT under different fatigue stress levels. The relationship between the fatigue life and high temperature is a crucially important design factor when CFRP plate is used to reinforce structure [18]. However, most of the researchers on the fatigue behavior of FRPs at high temperature focused on the fatigue performance at the temperature over 100 °C. For instance, Montesano et al. [19] compared the difference of fatigue performance of triaxially braided polymer matrix composite at RT and 225 °C. The materials for these studies are mainly used in the field of aerospace, which are not very suitable for civil engineering applications due to the cost of production and service temperature range. Nonetheless, few studies have been carried out to date on the fatigue life of CFRP plate, especially at elevated temperature [20,21]. Several papers investigated the evaluation models used in the fatigue characterization of the FRP composites [19,22–25]. The fatigue performance of CFRP was reported to be dependent on the interfacial adhesion between the fiber and resin matrix [26]. Proper adhesion is essential to optimize the transferring of the loads from the resin matrix to the fibers [27–31]. In the present study, the testing elevated temperatures were selected as room temperature (RT), 50 °C, and (Tg − 30 °C). The quasi-static tensile, tensile-tensile fatigue performances of unidirectional pultruded CFRP plates in three above temperatures were tested, and microstructures of CFRP plates were further characterized by scanning electron microscopy (SEM). The study aims to understand the effects of the high temperatures on the fatigue performances of the unidirectional pultruded CFRP plates. This is necessary for the safe and economic application of such plates in rehabilitation of civil structures, which may encounter elevated temperature conditions.

Flexural Modulus/MPa

60000

Tg=113Ԩ

50000 40000 30000 20000 10000 0

0

40

80

120 160 Temperature/Ԩ

200

240

Fig. 1. Flexural storage modulus of the CFRP plate in bending mode tested by DMA (Heating rate is 5 °C/min with the frequency of 1 Hz).

113 °C, determined by the inflection point of the storage modulus which are generated by a dynamic mechanical analyzer (DMA, Q800 type, TA Instruments Inc., U.S.A.). So (Tg − 30 °C) is 83 °C. The pultruded CFRP plates for the tensile test were cut into 250 mm × 25 mm × 1.46 mm according to ASTM D3039 [33]. The ends of the CFRP specimens were double glued with aluminum tabs, and the three-dimensional size and appearance of CFRP specimens were shown in Fig. 2. A universal tensile machine (DHY-10080 mode, Shanghai Hengyi Company, China) was applied for the tensile test under constant displacement speed of 2 mm/min [33]. Test temperatures were set as RT, 50 °C, and 83 °C, respectively. For the elevated temperature testing, the specimen was wrapped in a heating tape (220 V/100 W, Runjiang, Jiangsu, China) and insulated cotton, and the heating rate is 5 °C/min. The temperatures of the plate surfaces were measured and controlled by a relay controller with an accuracy of 1 °C. When the temperature reaches the specified temperature (50 °C and 83 °C), it needs to be kept for 15 min before the fatigue loads applying, and then, the elevated ambient temperature of specimen almost remains constant during fatigue testing.

2. Experimental procedure 2.1. Materials The unidirectional pultruded CFRP plates with the thickness and width of 1.46 mm × 25 mm were produced by a pultrusion process at the Laboratory for FRP Composites and Structures, Harbin Institute of Technology (Harbin, China). The applied pultrusion machine (mode NLL-5TL) was manufactured by Nanjing Loyalty Composite Equipment Manufacture Company (Nanjing, China), the detailed pultrusion parameters can be found in Ref. [32]. PAN-based carbon fibers (800 tex type, Sinopec Shanghai branch corporation, China) with the diameter of 7 µm were used for fiber reinforcement with about 65% volume content, and its mechanical parameters are shown in Table 1. The epoxy resin was a commercial epoxy with a brand name of Fenghuang, obtained from Xing-chen Chemicals Co. Ltd. (Wuxi, China). The curing agent was methyl tetrahydrophthalic anhydride (MeTHPA), obtained from Qingyang Chemistry Co. Ltd. (Jiaxing, China).

2.3. Fatigue test The tension-tension fatigue tests of unidirectional pultruded CFRP plates were conducted on a servohydraulic dynamic testing machine (Instron 8801 type, Instron Company, U.S.A.) according to ASTM D3479 [34]. The minimum stress to maximum stress ratio (R), and the load frequency was set as 0.1, 16 Hz, respectively. The applied maximum stress level (S) was selected ranging from 65% to 85% of the ultimate tensile strength at each temperature (fut). The test temperatures were also set as RT, 50 °C, and 83 °C. At RT testing, the surface temperature of the specimen was changed with fatigue loading, and recorded as well as ambient temperature. At elevated temperature testing, the surface temperature of the specimen was constant, so it was not necessary to record. The fatigue tests were carried out under the load control [16]. The stiffness of the specimen under each fatigue loading cycle was calculated as the division result of (maximum load – minimum load)/(maximum deformation – minimum deformation). Normalized values of the stiffness under the same S at different temperatures were calculated and compared. For each S, four repeats

2.2. Static tensile test The storage modulus curve of the CFRP plate with the increase of temperature was presented in Fig. 1. The Tg of the CFRP plate was Table 1 Mechanical parameters of carbon fiber. Nominal diameter

Ultimate strength

Elasticity modulus

Breaking elongation

Fiber count

Volume density

7 μm

4900 MPa

250 GPa

1.91%

12 K

1.73 g/cm3

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Table 2 Static tensile properties of the unidirectional pultruded CFRP plate at different temperatures. Temperature (°C)

RT 50 83

Load (kN)

Stiffness (GPa)

Mean

StDev

Mean

StDev

70.810 69.350 68.255

1.466 1.474 2.452

166 169 162

14.416 8.281 9.283

Ultimate strength fut (GPa)

1.94 1.90 1.87

Fig. 2. (a) 3D outlines sizes; (b) appearance of CFRP specimen by pull-extrusion process.

were tested according to the JSCE-E535-1995 standard “test method for tensile fatigue of continuous fiber reinforcing materials” [35]. For the elevated temperature testing, the CFRP plate specimen was wrapped with a heating tape (220 V/100 W, Runjiang, Jiangsu, China) and insulated cotton, and was connected to automatic temperature control equipment (PY-SM5 type, Pinyi Electrical Appliance Co., Ltd., China). The surface temperatures of the plate were measured and controlled by a relay controller with an accuracy of 1 °C. The equipment setup for fatigue tests of CFRP plate at RT and elevated temperatures (50 °C and 83 °C) were shown in Fig. 3 (a), Fig. 3 (b), respectively. When the temperature reaches the specified temperature, it needs to be kept for 15 min before the fatigue loads applying. Then, the temperature of specimen remains constant during testing at elevated temperature. The microscopic fracture interfaces of the CFRP plate after fatigue failure under different S at elevated temperatures were observed by a scanning electronic microscopy (SEM, Quanta 200F type, FEI Company, U.S.A.).

Fig. 4. Load-displacement curves at three kinds of temperatures.

temperatures, and the data are obtained by the sensors on the upper and lower chuck. As shown, there is a sliding phenomenon between tester chuck and specimens at the early stage of loading under different temperature environment, and the displacement includes the end sliding in the loading process, which leads to a large dispersion on the corresponding curve slope. It is worth to pointing out that the fluctuations on static tensile stiffness hardly have impacts on dynamic failure mode during fatigue testing. For a unidirectional CFRP plate, the tensile properties are mainly dominated by the fibers [36]. Thus, the increase of testing temperatures, but still lower than Tg of the CFRP plates, do not significantly affect the tensile properties. As found in Fig. 1, the storage modulus in flexural exhibits a slight decrease in the heating range below 83 °C, which is similar to the change of tensile stiffness.

3. Results and discussions 3.1. Static tensile results Table 2 presents static tensile strengths and stiffness of CFRP plates under RT, 50 °C, and 83 °C. Clearly, with the temperature increases, both the tensile strength and stiffness are slightly reduced, notwithstanding there exist obvious unremarkable fluctuations and deviations on tensile strength, and stiffness along the temperature increasing. These phenomena may attribute to the initial defects remaining in the CFRP plate during pull-extrusion process and unavoidable bondingslips between the end of specimen and tester chuck at high temperature. Fig. 4 shows the load-displacement curves at three kinds of

3.2. Fatigue parameters Fig. 5 presents the temperature curves of the RT test under 65%fut, 75%fu t and 85%fut. The surface temperature of the specimen rapidly rises in the first few thousand cycles and then its varying trend becomes relatively stable comparing with that in ambient temperature. The greater the S is, the more heat produces by interface friction, and the choice of frequency also affects the generation of heat. The frequencies adopted are normally within the range from 0.1 Hz to 25 Hz, and the temperature rise on the specimen surface is normally limited to 10 °C, otherwise, the temperature rise of the specimen should be recorded [34]. This is also one of basic parameters for comparison with other experimental results. The whole process of fatigue test at elevated temperature is controlled by equipment to stabilize the temperature, so the specimen surface temperature at elevated temperature tests is not discussed in this paper. The temperatures (surface temperature minus ambient temperature) generated by the fatigue load are all less than 10 °C during most periods of fatigue loading, which meet the requirements, and illustrate the rationality of our frequency selection. Fig. 5

Fig. 3. Equipments of fatigue test: (a) RT; (b) elevated temperatures. 423

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45

a)

42

Temperature/Ԩ

39

Specimen temperature Ambient temperature

36 33 30 27 24

Fig. 6. Fractural damage appearances of CFRPs under 75%fut stress level: (a) RT; (b) 50 °C; (c) 83 °C; (d) fail in anchorage area.

21 18

0

50000

100000

150000

200000

conditions. Actually, the cooling components of servo-hydraulic dynamic testing machine is continuously generate a lot of heat during the fatigue loading, and room temperature is also affected by changes in outdoor temperature throughout the day. The above factors account for the ambient temperature being a little higher, and varying throughout the testing day. It is noting, increasing air flux during the test can rapidly reduce the above temperature, and elevated temperature tests have good temperature control measures, and as a result of that, the corresponding temperature almost retains to be constant. During the loading process of fatigue test at elevated temperature, only a few tests under higher S show that the surface temperature before failure exceeds the control temperature, and then the specimen is damaged quickly (similar to the third stage of Fig. 5 (c). The macroscopic failure appearance of CFRP specimen varies with the testing temperatures (Fig. 6). As the temperature increases, the fracture mode seems to be less brittle, which attributes to the thermoelasto-plastic melting of the resin matrix [37]. Fig. 6 (d) reveals that the specimen abnormal failure in the anchorage area at hundreds of thousands of cycles. Indeed, the fatigue testing mode is the upper-end fixed and lower-end kept moving under the load control, resulting in a slightly higher temperature at lower-end of the CFRP specimen. At the same time, the local stress concentration caused the end stress to be higher than the design stress, and led to the failure of the specimen at the end. However, it is worth noting that this failure mode cannot meet the requirements of the standard and needs to be retested, so none of the data presented in this paper is the case. The probability of this failure mode can be effectively reduced by reducing the width of the plate and/or increasing the end bonding width. Table 3 shows the N of the CFRP plate under different maximum S, i.e., 65%fut, 75%fut and 85%fut, at RT, 50 °C and 83 °C, respectively. The probability plots of a set of fatigue data using the two-parameter

Fatigue life 45

b)

42

Specimen temperature Ambient temperature

Temperature/Ԩ

39 36 33 30 27 24 21 18

0

50000

100000

150000

200000

Fatigue life

45

c)

42

Temperature/Ԩ

39 Specimen temperature Ambient temperature

36 33 30 27 24 21 18

0

5000

10000 Fatigue life

15000

Table 3 The tension-tension fatigue lives of CFRP plates under different stress levels at RT, 50 °C and 83 °C.

20000

Group No.

Stress levels (S)

Fig. 5. The temperature curves of the specimen and ambient environment during the fatigue test: (a) 65%fut; (b) 75%fu t; (c) 85%fut.

(a) and Fig. 5 (b) do not show the rapid heating curve before failure, because the temperature before failure is not recorded under low S. The N under lower S is long and there is not enough warning before failure, while the N under 85% fut is short and the sound of the specimen changes obviously before failure. At the end of the fatigue testing, the increase of the number of cracks results in the increase of friction heat generation, which is a normal phenomenon that the temperature suddenly increases significantly before failure. Fig. 5 shows that the room temperatures are higher than 23 °C during the fatigue loading, attributing to the limited experimental 424

Failure life (N) RT

50 °C

83 °C

847,409 742,421 806,684 230,061

253,979 360,578 647,698 478,331

1,016,668 174,157 139,512 256,552

CP1

65% 65% 65% 65%

fut fut fut fut

CP2

75% 75% 75% 75%

fut fut fut fut

173,327 64,617 59,639 3407

56,454 7702 102,790 116,305

346,185 9552 168,966 11,912

CP3

85% 85% 85% 85%

fut fut fut fut

2783 19,996 26,252 19,983

19,088 8815 19,941 7066

37,628 610 8815 31,571

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higher the temperature is, and the worse the fatigue performance of CFRP will be [4]. High temperature renders the mechanical properties of the resin to deteriorate, more or less, can drop the N of pultruded CFRP plate. In addition, when the testing temperature is closed to Tg − 30 °C, the decrease of the N is much more remarkable, and the discreteness of N becomes larger than those at RT and 50 °C. Therefore, when FRP is applied to design, it should not be designed according to static performance but according to the most adverse performance degradation. According to ASTM E739-91, the S-N curves of the CFRP plate can be considered in linear when the fatigue data are plotted in appropriate coordinates. Linear or linearized S-N relationships are considered as Eq. (1) [1],

rmax =

σmax = Alg(N ) + B σult

(1)

where, σmax refers to the maximum stress under the fatigue test, σult refers to the maximum stress for the tensile test, and N is the corresponding number of fatigue cycles to failure; while A and B are the constant parameters. According to Eq. (1), the similar equation for three temperatures is accordingly obtained,

RT:rmax = −0.1629 lg (Nf ) + 1.4839

(2)

50 °C: rmax = −0.1647 lg (Nf ) + 1.4746

(3)

83 °C: rmax = −0.2004lg(Nf ) + 1.5956

(4)

The S-N curves of the CFRP plates at three temperatures are shown in Fig. 8. As found, the S-N curves of CFRP plate at three temperatures well follow Eq. (1). Fig. 8 reveals that the fatigue data exhibits high deviations under each S. It is noting, there are no lateral fibers in the pultruded CFRP plate to bear the transverse load compared with those with other production processes, so the possibility of spitting is increased in the longitudinal direction if there exists a large stress difference along the transverse direction of the unidirectional plate [37], and the residual stress in the plate after splitting increases abruptly with induced damage. In order to compare the fatigue properties of FRP in different production processes, Fig. 9 compares the fatigue performance at RT from different literatures. The statistical distribution of N is similar to Ref. [39] that each S has three or four repeated according to the JSCE-E5351995 standard. For the fitting method, the more points repeated are, the greater the deviation of N is, therefore, the dispersion of fatigue data is relatively large (Table 3). As the same N, the limit stress of pultruded

Fig. 7. Weibull probability plots of fatigue data: (a) RT; (b) 50 °C; (c) 83 °C.

Weibull distribution are presented in Fig. 7. It shows that the fatigue data can good fit Weibull distribution [38]. It is obvious that, despite there only exist very small gaps between the static tensile strength or stiffness modulus at different temperatures (Table 2), the N of the CFRP plates is sensitive to the testing temperatures, especially when the temperature is approaching 83 °C in the fatigue test. On the whole, the

Fig. 8. S-N curves of the pultruded CFRP plate tested at three kinds of temperatures. 425

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Fig. 9. S-N curves comparison of CFRPs with different production processes at RT.

Fig. 10. S-N fitting curves under Whitney’s method with 95% reliability at three kinds of temperatures.

unidirectional CFRP plate is lower compared with those in Ref. [19] and Ref. [39]. In one hand, transverse stress between the fibers in the pultruded plate can only be transferred by the resin, which renders the plate apt to split, and the N accordingly reduced. On the other hand, the actual stress (more than 1.2 GPa) of the pultruded plate in the fatigue test is very high compared to Ref. [4] (less than 300 MPa), and excellent unidirectional tensile properties even cause abnormal failure in the anchorage area of the CFRP specimen at about hundreds of thousands of cycles (Fig. 6 d). In addition, the bearing capacities of CFRP produced by hand lay-up method in Ref. [39] haven’t covered the positive effects of resin, which makes the corresponding test results be higher than the unidirectional pultruded CFRP specimen. As known, Whitney’s method [1] is also widely used, which is developed on two assumptions: the S-N relationship is represented by a classic power law, such as Eq. (1), and the probability of the survival after N cycles is given by a two-parameter Weibull distribution,

Ps (Ni ) = exp [( -Ni/ N¯i )]α fi , i = 1, 2, 3, 4

at 83 °C is the top one at three temperatures when specimen is subjected to high S. Similar phenomena can also be found in Ref. [19]. This phenomenon maybe due to the toughness of resin increases at high temperature and the specimen is more adaptable to large strain under high S. Limit value of allowable S of pultruded CFRP plate should be greater owing to abnormal failure in anchorage area of the specimen under 75%fut (Fig. 6 d), and providing better fatigue performance for the pultruded plate. In order to further predict the S-N curve formula of unmeasured temperature from RT to 83 °C, the following assumptions are given, (1) From RT to 50 °C: It is assumed that the S-N curves of interpolation temperature can be evenly divided into spatial domains according to interpolation position because the S-N curves at RT and 50 °C are very close and almost parallel. The slope is approximately the average of the two lines, and the intercept is determined by the temperature difference by the linear difference method. (2) From 50 °C to 83 °C: Because the S-N curves at 50 °C and 83 °C are obviously not parallel, the intersection point can be predicted and calculated. It is assumed that the S-N curve in this temperature range rotates equally but proportionally around the intersection point, which is effective and cost saving on test expenses.

(5)

where, Ni is the cycle number under the i-th stress level; N¯i and αfi are the scale and shape parameters of the Weibull distribution under the ith S; Ps (Ni ) is the probability of survival after Ni cycles; during the actual calculation, N¯i is substituted by N¯oi , the characteristic number of the cycles for each S obtained by a normalized method [40]. Through the curve fitting of log (Yσ ) versus log (N¯oi ) according to the S-N curve shown in Eq. (6), k and Y0 are the slope and intercept of the fitted line, respectively. With the determined k, Y0 and αf , the S-N curve at any specified level of reliability can be calculated by,

Yσ = Y0 { −ln[PS (N )]}1/ αf kN−1/ k

According to the above two assumptions, S-N curve for increasing the temperature term (T) (RT ≤ T ≤ 83 °C) can be given,

rmax = −0.1638lg(Nf ) + 1.4746 + 0.00042 × (T − 28), RT < T < 50 °C (7)

(6)

Table 4 shows the formula parameters and fitting results by Whitney’s method at 95% of reliability, which have enough reliabilities. Whitney’s method can reduce the dispersion of data through several iterations and is recognized as an efficient method. As prediction of formulas shown in Table 4, when the N reaches 2 million cycles, the limit values of allowable S are 49.95%fut, 49.03%fut and 43.24%fut at RT, 50 °C and 83 °C, respectively (Fig. 10). It’s noting, Fig. 10 presents a new phenomenon that the S-N fitting curve based on Whitney’s method

rmax = −[0.1647 + 0.00108 × (T − 50)]lg(Nf ) + 1.29127 + 0.00367T , 50 ° C⩽ T ⩽ 83 °C

(8)

The S-N curves at 40 °C and 66 °C are calculated using the above method, and the corresponding results are shown in Fig. 11. The S-N curves at 40 °C and 66 °C have the proper and linear distributions, which proves that the method has good applicability and can roughly predict the S-N curve at any temperature.

Table 4 Formula parameters and fitting results by Whitney’s method. Temperature

αf

1/k

Y0

Fitting formula

RT

1.4753

0.1233

1.7212

Yσ = 1.7212 × {−ln[PS (N )]}0.0836 × N−0.1233

50 °C

1.4808

0.1194

1.6797

Yσ = 1.6797 × {−ln[PS (N )]}0.0806 × N−0.1194

83 °C

0.9659

0.1675

2.6463

Yσ = 2.6463 × {−ln[PS (N )]}0.1734 × N−0.1675

426

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Fig. 11. The prediction formulas based on S-N curves at different temperatures.

The same assumptions can also be applied to Whitney’s method, and prediction formulas are obtained,

(T − 28) 22 × {0.0106 + 0.00039lg{−ln[PS (N )]}}, RT < T < 50 °C,

lg(Yσ ) = −0.1213lg(N ) +

(9)

lg(Yσ ) = −[0.1194 + 0.00146(T − 50)] × lg(N ) + 0.01032T + 0.8058 + (0.00282T − 0.06018) × lg{−ln[PS (N )]}, 50 ° C⩽ T ⩽ 83 °C, (10) WhenPS (N ) is set to 0.95, the prediction formulas are as follow:

(T − 28) × 0.0101 22 + 0.16243 , RT < T < 50 °C ,

lg(Yσ ) = −0.1213lg(N ) +

(11)

lg(Yσ ) = −[0.1194 + 0.00146(T − 50)]lg(N ) + 0.00749T + 0.88343, 50 ° C⩽ T ⩽ 83 °C ,

(12)

The prediction curves at 40 °C and 66 °C based on Whitney’s method are calculated with 95% reliability, and the results are shown in Fig. 12. The S-N curves at 40 °C and 66 °C also have the proper and linear distributions. The above predicted results shown in Fig. 11 and Fig. 12 can proved that the method has good applicability and the corresponding prediction formulas can effectively predict the fatigue performance of the CFRP plate at any temperature in that range. Fig. 13 presents the

Fig. 13. Normalized stiffness degradation curves of the pultruded CFRP plates: (a) 65%fut; (b) 75%fu t; (c) 85%fut.

normalized stiffness degradation versus the normalized failure cycles at three temperature cases. Fig. 14 shows the difference of stiffness degradation curves at RT of the pultruded CFRP plate and the traditional laminated plate. The stiffness of our pultruded CFRP does not decrease significantly but increases slightly at the beginning of fatigue loading,

Fig. 12. The prediction formulas based on Whitney’s method with 95% reliability at different temperatures. 427

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from the surface deterioration [42]. Under 65%fut, micro-cracks transverse to the fiber direction are formed in the resin matrix region, while no fiber debonding can be found at RT (Fig. 15 a). At the increased temperatures (i.e., 50 °C and 83 °C), no such micro-cracks are found in the resin matrix region, and also no fiber debonding is occurred (Fig. 15 b and c). Based on the above observation, a good bonding between the fiber and the resin matrix exists for the present CFRP plate under lower S is achieved. With higher fiber volume content, FRP composites have better mechanical properties [43]. Fig. 15 shows that resin matrix has obvious brittleness at RT, while obvious thermo-elasto-plastic melting phenomenon appears under higher temperature and S. Increased temperatures can soften the resins matrix, resulting in decreased elastic mechanical properties, even at the test temperatures below Tg − 30 °C. In such situation, the resins become plastic deformable and the ability to transfer shear stress to the fiber reinforcement is reduced [44]. Figs. 15–17 show that the failure interface has significant thermoelasto-plastic melting phenomenon in the resin matrix at the 83 °C, and this phenomenon also occurs at fracture surfaces at 50 °C under 85%fut stress level, which indicate both fatigue load and external temperature influence thermo-elasto-plastic melting phenomenon in the resin matrix. This phenomenon can correspond to the third stage of stiffness degradation curves and the rising temperature curve. At the end of N, the cracks increase sharply in the specimen, resulting in reduced stiffness and more friction heat generation, which leads to extremely high temperature and thermo-elasto-plastic melting phenomenon in the failure interface. In high temperature tests, specimens were wrapped by thermal insulation cotton, and the heat cannot be dissipated in time, so the melting phenomenon is more obvious. It can reasonably explain the stiffness has an oblique descent after the inflection point in the stiffness degradation curves (Fig. 15 b and c) and the temperature of the specimen increases suddenly in the temperature curve (Fig. 5 c). In the case of constant frequency, the higher the S of fatigue test is, the more heat can be produced by friction. The coupling of different friction heating and external temperature leads to different interface appearance and different N. This can mutual verify the results of different N under different S (Table 3 and Fig. 8). Moreover, macroscopic failure appearance also ascertains that there lays melting phenomenon at high temperature for the resin matrix on the outer surface of the fiber (Fig. 6 c). At a given atmospheric temperature, the higher the fatigue load is, the more obvious the deformation will be. Fatigue load leads to the premature break of the weak interface between epoxy matrix and stretched fibers, and thus the resultant N is reduced. On the one hand, because the elastic modulus of fibers and resins are obviously different, cracks are more likely to occur under higher S, and friction at the crack produces more heat (compare Fig. 16a with Fig. 16 c). Therefore, the higher the fatigue load is, the shorter the N is. On the other hand, the resin matrix presents brittleness at RT, whereas it is thermo-elastoplastic softening at higher temperature. This is due to the big gap of elastic modulus between the fiber and resin, and brittleness of resin at RT (Fig. 17), which is not suitable for large strain. So the resin matrix has positive advantage to large deformation at high temperatures. On the whole, at lower S, the leading factor in the decline of N is that the resin property decreases under high temperature, whereas the leading factor in the decline of N is that the resin cannot adapt to large deformation at higher S. The above consequences can also be proved that fitting curves at 83 °C is the top one (Fig. 10 and Fig. 12) when the specimen is simultaneously subjected to high S.

Fig. 14. Normalized stiffness degradation curves comparison of pultruded and laminated CFRP under 75%fut.

which indicates that the synergistic mechanical effect between fibers in pultruded CFRP plates are much better when compared with laminated plates. This may be due to the fibers have been stretched simultaneously and prestressed by a pultrusion process, while the steady-decreasing trend on the stiffness of the laminated plate, reflecting steady internal damage, may attribute that the upper and lower ends of the specimen cannot be completely in the same plane. As shown in Fig. 13, stiffness degradation curves of pultruded CFRP plates undoubtedly exist the “sudden death” phenomena, and the stiffness degradations are not obvious before the inflection points. At the same S, there lay little differences in the stiffness degradation curves at three temperatures. The x-coordinate corresponding to the inflection point is close to 1 under 65%fut. However, the x value is about 0.9 when the specimen is under 85%fut or under 75%fut at 83 °C, which indicates there exist a gradual dropping on stiffness. This phenomenon is related to the third stage of the curve in Fig. 5 (c), the sharp increase in the temperature of the specimen is a signal that the crack increases and the crack becomes larger, which means the stiffness goes down. A few tests under 85%fut (at 50 °C and 83 °C) or under 75%fut (at 83 °C) show that the temperature of the specimen is exceed the control temperature few minutes before the specimen was destroyed while the heating device is to stop working. This is because heat from interface friction can be quickly dissipated under lower S; however, friction heat is too much to timely dissipate under higher S, resulting in a rapid rise in pre-failure temperature. The sum from frictional heat (between the fibers in the crack) and environment temperature exceeds a certain value, the properties of resin matrix probably deteriorated, rendering the failure of the specimen. The stiffness value can be used as a parameter to evaluate the fatigue state [41]. The stiffness degradation curves show that most values of stiffness decrease by less than 3% before inflection point. It is not surprised that the fatigue performances of the unidirectional pultruded CFRP plate in tension-tension mode are fiber dominant. Similarly, from the stiffness degradation curves, no great differences can be found at different temperatures before the inflection point. Compared with the traditional laminated plate, the stiffness degradation curve of pultruded CFRP plate is better at predicting residual N, because the horizontal segment of stiffness curves is more stable before the inflection point. 4. Microstructure analysis

5. Conclusions

Figs. 15–17 present SEM photographs of the CFRP specimen fracture surfaces after fatigue failure under different S. The resin matrix of FRP composite has the basic function of joining the fibers, acting as an element of distribution of loads between them and protecting them

This study has experimentally studied the static tension and tensiontension fatigue performances of the unidirectional pultruded CFRP plate at evaluated temperatures. The following conclusions can be drawn. 428

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Fig. 15. SEM images of fractured sections of CFRP plates under 65%fut (red rectangles- resin crack; yellow-green circles- resin melting): (a) RT; (b) 50 °C; (c) 83 °C.

Fig. 16. SEM images of fractured sections of CFRP plates under 75%fut (red rectangles- resin crack; purple rounded rectangles- resin ripples; yellow-green circlesresin melting): (a) RT; (b) 50 °C; (c) 83 °C. 429

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Fig. 17. SEM images of fractured sections of CFRP plates under 85%fut (purple rounded rectangles- resin ripples; yellow-green circles- resin melting): (a) RT; (b) 50 °C; (c) 83 °C.

Xian in the Laboratory for FRP Composites and Structures for kind support which was instrumental in the success of this research. The research was supported by the National Natural Science Foundation of China (No. 51678208, 51878364), Natural Science Foundation of Shandong Province (Project No. ZR2018MEE043 and ZR2017ZC0737), the Project Supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. HIT.NSRIF.201709), and the Co-operative Innovation Center of Engineering Construction and Safety in Shandong Blue Economic Zone.

(1) The static tension performances of the CFRP plate are very slightly affected by elevated temperature with the range less than Tg minus 30 °C. By contrast, their fatigue performances significantly deteriorate as temperature increases near to Tg minus 30 °C. (2) The thermo-elasto-plastic softening of the resin at high temperature is the most fundamental reason for the decrease of fatigue life, and both ambient temperature and friction heat by fatigue loading are sources of high temperature. Notwithstanding, high temperature has somewhat positive impacts as well on the stress transfer and distribution when specimens are subjected to high fatigue load, because of possible thermo-elasto-plastic softening of resin matrix that allows larger deformation. (3) According to the Whitney’s model, the maximum stresses for fatigue life of more than 2 million for the CFRP plate at room temperature, 50 °C and 83 °C are estimated to be 49.95%fut, 49.03%fut and 43.24%fut, respectively, with 95% reliability. (4) The S-N curves for unmeasured temperatures in the range from room temperature to 83 °C are further predicted by means of the Whitney’s method. This feature allows design of composite structures with a specified reliability at any temperature in a specified range. (5) The fatigue lives of the CFPR plate at elevated temperatures in predesigned reliability will be explored and mutual verification with those deduced from the Whitney’s model. The performance degradation of the pultruded CFRP in many other harsh environments also need to be further studied and characterized, which will be conducive to the popularization, application and design safety of this production process.

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Acknowledgements The authors would like to acknowledge the support of Prof. Guijun 430

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