Intralaminar fatigue crack growth properties of conventional and interlayer toughened CFRP laminate under mode I loading

Composites: Part A 68 (2015) 202–211

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Intralaminar fatigue crack growth properties of conventional and interlayer toughened CFRP laminate under mode I loading N. Sato a,b,⇑, M. Hojo b, M. Nishikawa b a b

Toray Industries Inc. 1515, Tsutsui, Masaki-cho, Iyogun, Ehime, Japan Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto, Japan

a r t i c l e

i n f o

Article history: Received 29 March 2014 Received in revised form 2 September 2014 Accepted 9 September 2014 Available online 17 October 2014 Keywords: B. Fracture toughness B. Fatigue B. Delamination A. Prepreg

a b s t r a c t Intralaminar and interlaminar fatigue crack growth behaviours under mode I loading were investigated with conventional and interlayer toughened unidirectional CFRP laminates. For intralaminar crack growth tests, initial defects were introduced using ‘‘intralaminar film insertion method’’, in which a release film is inserted inside a single lamina prepreg. A fatigue test under a constant maximum energy release rate, Gmax, was carried out using DCB specimens. It was found that the intralaminar fatigue crack growth property of the interlayer toughened CFRP laminates was the same as that of the conventional CFRP laminates. For the interlayer toughened CFRP laminates, the Gmax with a given crack growth rate, da/dN, was much lower for intralaminar crack growth than for interlaminar crack growth. The da/dNGmax curve at zero crack extension, Da = 0, which was estimated by extrapolating the da/dN-Da relationship, was not affected by bridging fibres, and most conservative for the interlayer toughened CFRP laminates. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Various kinds of fracture modes have been discussed, e.g. (a) interlaminar delamination [1,2], (b) intralaminar delamination (parallel to lamination plane), (c) longitudinal intralaminar matrix crack [3–5], (d) translaminar crack progression (fibre breaking) [6,7] and (e) transverse intralaminar matrix crack [8] for fracture toughnesses of carbon fibre reinforced plastic (CFRP) laminates as shown in Fig. 1. CFRP laminates have widely used as a lightweight structural material for aircraft. However the low fracture toughness of CFRP laminates where the crack path is parallel to the fibre direction is often regarded as a limiting factor in the structural design of CFRP components [9]. The most often discussed fracture mode is interlaminar delamination, which is induced by interlaminar normal and shear stresses at the interface of adjacent layers in CFRP laminate [1,2]. The crack growth behaviour for longitudinal intralaminar matrix crack is also a popular and active topic amongst many researchers [3–5]. On the other hand, intralaminar delamination is rarely discussed because insertion of initial defect is quite difficult for the fracture toughness test. The thickness of a single CFRP lamina (intralayer fibre-rich region) is normally not uniform and the boundary of one ply is often wavy. Thus it is very ⇑ Corresponding author at: Toray Industries Inc. 1515, Tsutsui, Masaki-cho, Iyogun, Ehime, Japan. E-mail address: [email protected] (N. Sato). http://dx.doi.org/10.1016/j.compositesa.2014.09.031 1359-835X/Ó 2014 Elsevier Ltd. All rights reserved.

challenging to introduce an initial defect for intralaminar delamination fracture toughness test only within the intralayer region of the CFRP laminate. A few research groups conducted a fracture toughness tests by introducing an initial defect parallel to the lamination plane by machining [10–12]. The main purpose of their researches was to develop an interlaminar delamination fracture toughness test method without the use of an initial film insertion; however the possibility of application of this method to intralaminar delamination fracture toughness study was not discussed. Moreover, crack growths in the intralaminar region were observed and evaluated in some interlaminar delamination fracture toughness tests of multidirectional CFRP laminates as reviewed in Ref. [13]. However the crack growth direction was not corresponded with the fibre orientation direction and the detection of crack front position inside the CFRP laminate is quite difficult due to the edge effect. Therefore, the crack growth behaviour of intralaminar delamination could not be evaluated directly by using their approaches. Here the crack growth behaviour of intralaminar delamination is most likely different from those of interlaminar delamination and longitudinal intralaminar matrix crack. Firstly, the local fibre volume fraction of the interlaminar resin rich region is typically lower than that of intralaminar fibre-rich region [14]. Thus the fracture surface of interlaminar delamination is relatively flat with larger fibre spacings in the thickness direction at the resin rich interlayer region and less broken fibres compared with

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intralaminar delamination [15]. It is also mentioned that the resinrich interlayer region is possibly tougher than the matrix-fibre interfaces region where high residual stresses can be accumulated [16]. Secondly the level of fibre misorientation in X–Y plane (parallel to intralaminar delamination) is often higher than that in X–Z plane (parallel to longitudinal intralaminar matrix crack) [17]. The fracture properties for intralaminar delamination are supposedly the same order of magnitude as those for longitudinal intralaminar matrix crack due to the fracture mechanisms which involves fracture primarily in the fibre-rich areas. However, due to the difference in the level of fibre misorientation, the fibre bridging effect for longitudinal intralaminar matrix crack is more significant than that for intralaminar delamination. The fracture toughness of longitudinal intralaminar matrix crack possibly gives non conservative values. In addition, it is important to note that the cracks in the CFRP laminate are often generated and propagated within the fibre-rich ‘‘intralayer region’’ of the prepreg, as shown in Fig. 1b. For example, Lorriot indicated that the crack is possibly initiated from the intralayer region for a CFRP laminate tensile test caused by edge delamination [18]. Liebig also indicated that voids in CFRP laminate are located not only in the resin-rich interlayer region but also in the fibre-rich intralayer region [19]. These voids in intralayer fibre-rich region are introduced by volatile components in the matrix resin or incomplete resin impregnation [20,21]. Since these intralaminar voids emerge as sites for crack initiation, the initiation can possibly be located at both the interlayer and intralayer regions. Hence, the evaluation of accurate intralaminar delamination fracture properties is quite important. Furthermore, understanding the difference between interlaminar and intralaminar delamination crack propagation properties is more important for interlayer toughened CFRP laminates, which has recently been used in primary and secondary structures of aircraft [1,22]. In this materials system, the tough resin layer is localised in the interlayer region of CFRP laminates to improve the interlaminar delamination fracture toughness and CAI (Compression After Impact) strength [1,22,23]. Therefore fracture toughness for intralaminar crack growth must be lower than the interlaminar delamination crack growth. Many researchers have actively discussed interlaminar delamination static crack growth characteristics [24–28] and interlaminar delamination fatigue crack growth characteristics [29–31] of interlayer toughened CFRP laminates under mode I loading. Their results demonstrate the static and

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fatigue crack growth resistances which decrease with increasing crack length when the location of the crack path progresses from the toughened interlayer region to a non-toughened intralaminar fibre-rich region during crack growth [24,25,29]. When the crack path progresses inside the intralaminar fibre-rich region, the intralaminar fracture toughness starts to increase owing to the fibre bridging effect [3]. Since both the detrimental and incremental factors are overlapping, it is impossible to evaluate the minimum intralaminar fracture toughness by using an interlaminar delamination crack growth test for the interlayer toughened laminates. An intralaminar crack growth test is essential to evaluate the minimum fracture properties, in particular at the initial stage of crack growth to minimise the fibre bridging effect. In our previous study, a new initial defect insertion method, the ‘‘intralaminar film insertion method’’, was proposed for evaluating the intralaminar fracture toughness of CFRP laminates [32]. In this method, a release film is inserted inside a single lamina of a prepreg to introduce an initial defect within the intralayer region for the intralaminar crack growth test. By using this method, the intralaminar fracture toughness without fibre bridging effect was evaluated for conventional CFRP laminate and interlayer toughened CFRP laminate from the initial value to the propagation value for the first time. Understanding the intralaminar fatigue crack growth behaviour is also important to assure and enhance the durability of aircraft structures under long-term cyclic loadings. Although limited reports are available on fatigue crack growth behaviour of longitudinal intralaminar matrix crack [33], there are no reports yet on the fatigue properties for intralaminar delamination. In addition, the fatigue crack growth behaviour of CFRP laminates still remains to be elucidated, thus many active discussions have been continuously held [34–36]. Here, one of the common problems in these studies is the increase in crack growth resistance owing to the fibre bridging effect for fatigue crack growth [37]. Since the crack growth behaviour depends on the crack length, it is difficult to obtain a minimum threshold value for fatigue crack growth using conventional load-shedding tests [29,38,39]. This effect is significant particularly under mode I loading [39–41]. For a more conservative approach, the crack propagation rate at zero crack extension (Da = 0) can be evaluated to avoid the fibre bridging effect which has only been discussed by a few research groups [39–43]. Amongst them, the only acknowledged approach to obtain the relationship between crack propagation rate at Da = 0 and the energy release rate is to measure the fatigue crack growth rate using a constant maximum energy release rate tests proposed by Hojo et al. and Tanaka et al. [39,40]. Although this approach has already been applied to studies for carbon fibre (CF)/PEEK and CF/epoxy laminates [39,40], the evaluation of intralaminar fatigue fracture has not been conducted. In the present study, a new fatigue test method was proposed by combining the intralaminar film insertion method and the delamination fatigue crack growth test method under a constant maximum energy release rate to obtain the intralaminar delamination fatigue crack growth properties of CFRP laminates. Using this method, intralaminar delamination fatigue crack growth properties were evaluated for conventional unidirectional CFRP laminates and interlayer toughened unidirectional CFRP laminates for the first time. 2. Materials and methods 2.1. Materials

Fig. 1. Schematic drawings of delamination in cross-section of non-toughened CFRP laminate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Conventional unidirectional CFRP laminates and interlayer toughened unidirectional CFRP laminates were prepared. The former are also referred to as ‘‘non-toughened CFRP’’, and the latter

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as ‘‘toughened CFRP’’ in this paper. Details of the specimen fabrication are also described in a separate paper [32]. 2.1.1. Non-toughened CFRP PAN-based intermediate modulus, high tensile strength CF (T800S, Toray Industries Inc.) was used as the reinforcing fibre. The components of the matrix resin used in the study were similar to those in the study of Kishi et al. [44]. Di-glycidyl ether of Bisphenol A epoxy (jER828, EEW 189 g/mol), 4,40 -diamino diphenyl sulfone (4,40 -DDS, Seikacure-S, Wakayama Seika Kogyo Co., Ltd.) and polyethersulfone (PES5003P, Sumitomo Chem. Corp.) were mixed with a ratio of 100:33:15 by weight. Prepregs were fabricated using the drum winding method, each of which had a nominal cured ply thickness of 0.2 mm. These prepregs were stacked unidirectionally, and the CFRP laminates were cured in an autoclave at 180 °C for 2 h. The nominal fibre volume fraction of the CFRP laminates was 60%. 2.1.2. Interlayer toughened CFRP For interlayer toughening, PA12 particles (Diamid, Daicel-Evonik Ltd.) with an average diameter of 20 lm were used. The particles were placed on the surface of the prepreg described in the previous section. The content of the particles was 5 wt% in the prepreg. Using this prepreg, the interlayer toughened CFRP laminates were cured in an autoclave. Note that curing this prepreg simply at 180 °C may melt PA12 particles and thereby eliminate them in the interlayer region, because their melting point is about 176 °C [45]. Thus, the laminates were precured at 150 °C for 1 h and postcured at 180 °C for 2 h. The nominal fibre volume fraction of the toughened CFRP laminates was 53%. The volume fraction of the intralaminar fibre-rich region for the toughened CFRP laminate was 60%. This value was calculated from the areal weight and density of carbon fibre, and thickness of the intralayer fibre-rich region.

2.1.3. Specimens and initial defects Four kinds of CFRP laminates were prepared as shown in Fig. 2. The present study focuses only on the ‘‘interlaminar delamination’’ and ‘‘intralaminar delamination’’ displayed in Fig. 1. These two types of delamination are referred as ‘‘interlaminar’’ and ‘‘intralaminar’’ hereafter in this paper. The stacking sequence for the interlaminar crack growth test was [020], and a PTFE film (thickness 12 lm) was inserted at the central ply interface (between the 10th and 11th plies) during the lay-up process, then cured to produce the ‘‘CFRP (interlaminar)’’ laminates. The stacking sequence for intralaminar crack growth test was [019], and a PTFE film was inserted inside of the central ply (10th ply) during the layup process, and then cured to produce the ‘‘CFRP (intralaminar)’’ laminate. Details of the method of inserting the PTFE film into the 10th ply are described in the next section. In all cases, a precrack was not introduced. 2.1.4. Intralaminar film insertion method In the intralaminar film insertion method proposed in our previous study [32], a release film is directly inserted within the fibrerich region of one prepreg ply to induce crack initiation for the crack growth test. A specific procedure of the intralaminar film insertion method is summarised as follows. Fig. 3 shows a schematic drawing of the prepreg cross section for each step in the intralaminar film insertion method. In the first step, CF tows were aligned in one-direction as a sheet, and this CF sheet was then placed between resin films (Fig. 3a). In the second step shown in Fig. 3b, resin temperature was kept at 40 °C, which was lower than that of the conventional process in this study, to keep the high viscosity of the resin during the prepreg fabrication. Here, the resin was impregnated only in the surface regions of the fibre sheet. The temperature of the prepreg sheet was reduced to room temperature. This semi-impregnated prepreg was opened in the out

Fig. 2. Schematic drawings of initial defect region for non-toughened and toughened CFRPs.

Fig. 3. Schematic drawing of the prepreg cross section for each step in the intralaminar film insertion method.

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of plane direction, and a PTFE release film (thickness 12 lm) was inserted in the intralayer region, as shown in Fig. 3c. Finally, the semi-impregnated prepreg was kept at 70 °C for 10 min, and the resin was completely impregnated in the sheet (Fig. 3d). This special prepreg ply was located at the centre of the laminate and enclosed within 18 other normal plies of the prepreg during the lay-up process, and the unidirectional laminates were cured in an autoclave. In this way, CFRP (intralaminar) laminates, in which a release film was inserted in the intralayer region, were fabricated. 2.2. Test methods 2.2.1. Static DCB test The specimen used was 12.7 mm wide and 4 mm thick. Two 10 mm  10 mm aluminium blocks with / = 4 mm hole were attached at the loading points. Note that the distance from a loading point to the end of the initial defect was 25 mm. Epoxy adhesive (TE2220, Toray Fine Chemical Co. Ltd., cured at room temperature for 24 h) was used to bond the aluminium block to the CFRP laminate. In order to determine crack length during the DCB test more easily, one side of the specimen was painted with a white marker. An optical microscope (Magnification: 25, resolution: 10 lm) mounted on a stage that could be moved along the length of the specimen was used to measure the crack length. A computer-controlled 5 kN servo hydraulic testing machine (Servopulser EHF-FM005K1, Shimadzu Corp.) was used for the test. Loading rates of 0.5 mm/min and 1.0 mm/min were used for Da = 0–20 mm and Da = 20–50 mm, respectively. During the DCB test, the specimen was loaded until the crack extended to about 50 mm, and then the specimen was unloaded. The testing environment was 65% RH at 23 °C. The specimens prior to the static test were kept in the same room, in which the servo hydraulic testing test machine was installed for mainly less than three months. The water absorption of the specimens is expected to be small [46]. Three tests were carried out for each laminate. 2.2.2. Fatigue DCB test under constant maximum energy release rate Gmax As briefly explained in the introduction, constant Gmax tests is necessary when the fatigue crack growth resistance increases with the crack extension. Several test methods had been proposed for fatigue crack growth tests under a constant Gmax, for instance, (a) the use of springs at loading points [41], (b) the use of tapered adherents [49], and (c) changing the load level during the fatigue test using computer control [40,50,51]. However, in methods (a) and (b), test fixtures should be designed in accordance with the stiffness of each laminate. In the present study, four kinds of laminates of different stiffnesses were evaluated, thus methods (a) and (b) were not useful from the view point of time or cost consumption. In addition, these test methods were reported in only a few papers and thus are not well-established. Thus, method (c), which was proposed by Hojo et al. and Tanaka et al. [39,40], is the only suitable way to carry out the fatigue crack growth tests. A fatigue DCB test was carried out using the same apparatus and the same environment as those for the static DCB test, and with a computer-controlled fatigue test system established in previous studies [50,51]. With this system, specimen compliance was computed from the complete load–displacement profile data obtained during the fatigue test, and the applied peak load was adjusted to keep the Gmax constant. The specific calculation method for the peak load for the fatigue test under a constant Gmax was described in Section 2.2.4. In this study, the Gmax for the fatigue tests was selected to be within 90–140 J/m2 for non-toughened CFRP (intralaminar), non-toughened CFRP (interlaminar) and toughened CFRP (intralaminar), within 200–300 J/m2 for

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toughened CFRP (interlaminar). In this study, the numbers of evaluated specimens were six for non-toughened CFRP (intralaminar), five for non-toughened CFRP (intralaminar), four for both nontoughened CFRP (intralaminar) and toughened CFRP (interlaminar). In all the fatigue tests, the stress ratio R of the minimum load to the maximum load was kept constant at 0.5. The frequency of stress cycling was 10 Hz. Note that the temperature of the specimen side surface was measured by an infrared thermometer immediately after the fatigue DCB test and no significant temperature increase was detected. Crack length was computed from specimen compliance during the DCB test using Eq. (2), described in Section 2.2.4. 2.2.3. Crack growth rate at zero crack extension (da/dN at Da = 0) During the fatigue DCB test, a zone of bridged fibres forms, which leads to an increase in fracture toughness. In order to obtain the minimum threshold value of Gmax for fatigue crack growth, the relationship between the crack growth rate, da/dN and Gmax should be obtained at zero crack extension (Da = 0). One method for obtaining the minimum threshold value of Gmax for fatigue crack growth is the delamination growth onset method, which was proposed by Martin and co-workers [42,43], and is also as ASTM 6115 [53]. In this method, fatigue DCB tests were carried out to investigate the relationship between number of cycles for delamination onset and the energy release rate, and a minimum value of Gmax for delamination onset is determined as the threshold from the relationship. However, the scatter of the threshold value is large, and many fatigue tests are required to guarantee the reliability of the threshold value. In addition, test results in the high cycle fatigue range (107–108 cycles) are required to obtain the true minimum threshold value of Gmax [52]. Hojo et al. and Tanaka et al. proposed the method of obtaining da/dN at Da = 0 from the results of a fatigue crack growth test under constant Gmax [39,40]. Both the minimum threshold value for Gmax and da/dN-Gmax relationship can be obtained with a limited number of specimens in this method. Fig. 4 shows the representative da/dN-Da relationship for a CF/PEEK laminate obtained by a fatigue DCB test under a constant Gmax. da/dN increased at the initial stage of crack growth, after that the da/dN decreased with increasing crack extension owing to the fibre bridging effect. At the initial stage of crack growth in a fatigue DCB test, the crack growth is not uniform in the width direction owing to the distribution of the energy release rate [54,55]. When the crack extension is obtained from the compliance change during the fatigue test, da/dN is low at the initial stage [39]. The same tendency was reported for CF/epoxy [33,40]. Thus, da/dN at Da = 0 was estimated

Fig. 4. Representative da/dN-Da curve of a fatigue DCB test under constant Gmax for CF/PEEK laminate [39].

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by extrapolating the relationship between da/dN and Da in the range in which the relationship was linear. Here, the approximate line is expressed as,

da=dN ¼ A 10bDa

ð1Þ

where A is the da/dN at Da = 0 and b is a coefficient, which controls the gradient of da/dN-Da relationship. 2.2.4. Calculation methods for energy release rate G and target peak load PPeak for fatigue DCB test The energy release rate G was calculated using the modified compliance method [56] as discussed in JIS K 7086 and ISO15024 [47,57,48]. The relationship between the specimen compliance C and the crack length a is approximately expressed as

a ¼ a0 þ a1 ðBC Þ1=3 2h

ð2Þ

where 2h is the specimen thickness, and a1 and a0 are fitting coefficients based on the elastic modulus of the laminate. The energy release rate G is expressed as

G¼

 2 3 P ðBC Þ2=3 2ð2hÞ B a1

ð3Þ

where P and B are the applied load and specimen width, respectively. For the fatigue DCB test, the target peak load is changed in order to keep the Gmax constant during the test, while specimen compliance is increasing. Here, the target peak load PPeak is calculated using Gmax by

PPeak ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2a1 ð2hÞB2 Gmax 3ðBC Þ2=3

ð4Þ

Here, data reduction methods for static DCB test and fatigue DCB test are summarised as follows; (Static DCB test) (1) Load–displacement data was collected every 0.5 s during DCB test. In parallel, crack extension were visually measured after every 5 mm of the crack extension using a microscope. (2) After the test, a1 and a0 in Eq. (2) were determined from the load, displacement, and crack extension data by a curve-fitting method. Here, the compliance C was defined as C = u/P. (3) Fracture toughness GIC and GIR was calculated by using the load–displacement data and a1 and Eq. (3).

(5) Crack propagation rate da/dN was calculated from the slope of a–N relationship (between crack length and number of cycle) by least square method. 3. Results and discussion 3.1. Static DCB test Fig. 5 shows the relationship between the fracture toughness, GIR, and the crack extension, Da (R-curve). Each line indicates the average values of fracture toughness of the three specimens. The initial values of fracture toughness were about 150 J/m2 for nontoughened CFRP (interlaminar), non-toughened CFRP (intralaminar) and toughened CFRP (intralaminar). There was no significant difference in the averaged initial values of fracture toughness amongst these laminates. On the other hand, the initial value of fracture toughness of toughened CFRP (interlaminar) was more than twice higher than those of the others due to interlayer toughening. The GIR at propagation of toughened CFRP (interlaminar) was almost constant; however, those of the others increased with increasing Da owing to fibre bridging effect. In addition, the Rcurve of toughened CFRP (intralaminar) approximately corresponded to that of non-toughened CFRP (intralaminar). That is, the R-curve of intralaminar fracture toughness was not influenced by interlayer toughening. Details of the static tests were described in a separate paper [32]. 3.2. Fatigue DCB test for non-toughened CFRP Fig. 6 shows representative da/dN-Da curves for non-toughened CFRP (intralaminar) and non-toughened CFRP (interlaminar) obtained by the fatigue DCB test under a constant Gmax. For both non-toughened CFRP (intralaminar) and non-toughened CFRP (interlaminar), da/dN decreased linearly with increasing Da, except at the initial stage of crack growth. This tendency was also observed in previous studies of CF/epoxy and CF/PEEK laminates, and a decrease in da/dN was found to be caused by the fibre bridging effect [39–41]. The negative gradients of non-toughened CFRP (intralaminar) of the da/dN-Da curves were larger than those of non-toughened CFRP (interlaminar). This was explained quantitatively using the parameter b of Eq. (1), which controls the gradient of the da/dN-Da relationship. The average b for all the specimens of non-toughened CFRP (intralaminar) was 2.12 ± 0.19 [1/m]; on the other hand, that of non-toughened CFRP (interlaminar) was 0.91 ± 0.05 [1/m]. This indicated that the fibre bridging effect of non-toughened CFRP (intralaminar) was more significant than that

(Fatigue DCB test) 800

Fracture toughness GIR [J/m2]

(1) Fatigue DCB test under a constant Gmax was once carried out using a1 and a0, which were obtained in the static DCB test. During the fatigue test, load, displacement, compliance, and number of cycle data were collected every 20 cycles. In parallel, crack extension was also visually measured (about 10 data points for each fatigue test). (2) After the individual fatigue test, a1 and a0 in Eq. (2) were recalculated from the compliance and crack length measurement during the fatigue test. Here, a1 and a0 (fatigue) are slightly different from a1 and a0 (static). (3) Applied Gmax values were recalculated using a1 and a0, which were obtained in the fatigue DCB test, since a1 and a0 (fatigue) are slightly different from a1 and a0 (static), Gmax slightly changes during fatigue test. Since this change is less than 5 J/m2, this change is negligible. (4) Each crack length a in every 20 cycle was calculated by using Eq. (2), a1 and a0 (fatigue).

600

400

Intralaminar

200

Interlaminar

Non-toughened CFRP Toughened CFRP 0

0

10

20

30

40

Crack extension Δa [mm] Fig. 5. R-curves of non-toughened and toughened CFRPs.

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the figure shows a fitting curve (power function) obtained using the plots of non-toughened CFRP (interlaminar). As shown in this figure, there is no significant difference between non-toughened CFRP (interlaminar) and non-toughened CFRP (intralaminar) in terms of the relationship between da/dN at Da = 0 and Gmax. This is in agreement with the results of the DCB static fracture toughness values, where the initial value of non-toughened CFRP (intralaminar) was the same as that of non-toughened CFRP (interlaminar) shown in Fig.4. Therefore, the relationships between da/dN at Da = 0 and Gmax is not affected by fibre bridging and is most conservative for interlaminar and intralaminar crack growth under fatigue loading.

3.3. Fatigue DCB test for interlayer toughened CFRP laminate

Fig. 6. Relationship between crack growth rate da/dN and crack extension Da for non-toughened CFRPs.

of non-toughened CFRP (interlaminar), which is in good agreement with the static DCB test results. In Fig. 7, all da/dN data in Fig. 6 were plotted against Gmax for non-toughened CFRP. Each symbol corresponds to a different specimen. Open symbols indicate experimental values and solid symbols indicate the estimated values of da/dN at Da = 0 determined by extrapolating these experimental data described in Section 2.2.3. Almost all estimated values of da/dN at Da = 0 showed a higher crack growth rate than the experimental results. Hence, they provide a conservative relationship between da/dN and Gmax. In addition, the relationship between da/dN at Da = 0 and Gmax in log–log plots was roughly linear for both non-toughened CFRP (intralaminar) and non-toughened CFRP (interlaminar). It is well known that this power law relationship is for interlaminar crack growth [39– 41]. The present results revealed that this power law relationship is also applicable for intralaminar crack growth. The relationships between da/dN at Da = 0 and Gmax for both non-toughened CFRP (intralaminar) and non-toughened CFRP (interlaminar) were simultaneously plotted in Fig. 8. The line in

Fig. 9 shows representative da/dN-Da curves for the interlayer toughened CFRP laminates obtained by the fatigue DCB test under a constant Gmax. The da/dN-Da curve of toughened CFRP (intralaminar) was completely different from that of toughened CFRP (interlaminar). Except at the initial stage of crack growth, the da/dN of toughened CFRP (intralaminar) decreased with increasing Da, for all the specimens. The fracture surface observation of toughened CFRP (intralaminar) revealed that a crack always propagated within the fibre-rich region; thus, bridging fibres possibly reduced da/dN. On the other hand, the da/dN of toughened CFRP (interlaminar) increased at initial stage of crack growth, and saturated at Da = 2–4 mm. One of the reasons for this behaviour is that the crack growth is not uniform in the width direction owing to the distribution of the energy release rate as shown in the initial part of Fig. 4. Thus the da/dN at Da = 0 mm for toughened CFRP (intralaminar) was estimated by extrapolating the relationship between da/dN and Da in the range in which the relationship was linear. The same approach was conducted in the same approach for the non-toughened CFRP (intralaminar) and non-toughened CFRP (interlaminar) as shown in Fig. 6. On the other hand, da/dN at Da > 4 mm was constant (and the crack also propagated almost within the particle layer, as shown later in Fig. 10). Then the averaged value of the range of Da = 4–10 mm is substituted as the da/dN at Da = 0 mm of toughened CFRP (interlaminar). Macroscopic fracture surface images of toughened CFRP (interlaminar) after the static and fatigue DCB tests are shown in Fig. 10. In these images, black regions on the left-hand side correspond to the location of the inserted PTFE film. As a representative SEM

Fig. 7. Relationship between crack growth rate da/dN at Da = 0 and maximum energy release rate for non-toughened CFRP.

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Fig. 8. Relationship between crack growth rate da/dN estimated at Da = 0 and maximum energy release rate for non-toughened CFRP.

Fig. 9. Relationship between crack growth rate da/dN and crack extension Da for interlayer toughened CFRP.

image of fracture surface of toughened CFRP (interlaminar) after the fatigue DCB test, the SEM image corresponding to the region pointed by the white arrow in Fig. 10b is shown in Fig. 11. Fracture surface of the upper and lower left-hand side shows the fracture of

PA12 particles and debondings between matrix resin and PA12 particles. Debondings between carbon fibre and matrix resin were also observed in the right-hand side of Fig. 11. By comparison between the SEM image and the optical microscopic image, it was revealed that the white region in the images indicates that the crack path was within the layer with PA12 particles, whereas the black region indicates that the crack path was within the fibre rich region (i.e., intraply delamination) or between the interlayer and the fibre-rich region [29,32]. As shown in Fig. 10, over 90% of the region of fracture surfaces after the static and fatigue DCB tests is white. This indicates that the main failure mode of toughened CFRP (interlaminar) was the fracture within the interlayer region. For the interlayer toughened CFRP (interlaminar), previous studies showed that the fracture toughness decreases when the crack path shifts from the interlayer region to the intralayer region with increasing crack extension [24,25,28,29]. For the present material system, the crack always propagated within the interlayer region, as shown in Fig. 10, and this enabled to keep da/dN constant. Note that the crack path shifted from the interlayer region to the intralayer fibre-rich region with a shorter crack extension under fatigue loading than under static loading in a previous study [29]. On the other hand, in the present study, there was no significant difference between the static and fatigue crack growths for the crack path location. In the present material system, debondings between the epoxy resin and the PA12 particles occurred more easily than those in the previous study. This is one of the reasons why the crack always propagated within particle layers under both static and fatigue loadings. Fig. 12 shows representative da/dN-Da curves of toughened CFRP (intralaminar) and non-toughened CFRP (intralaminar), which is reproduced from Fig. 6. For simplicity, only one fitting curve for each specimen is shown in this figure. The gradients of the curves for toughened CFRP (intralaminar) were similar to those for non-toughened CFRP (intralaminar). The gradient parameter b of toughened CFRP (intralaminar) was 2.05 ± 0.17 [1/m], and that of non-toughened CFRP (intralaminar) was 2.12 ± 0.19 [1/m]. This agreement indicates that the fibre bridging effect of toughened CFRP (intralaminar) was equivalent to the non-toughened CFRP (intralaminar) not only for static loading but also under fatigue loading. In Fig. 13, all da/dN data in Fig. 9 were plotted against Gmax for interlayer toughened CFRP (intralaminar) and interlayer toughened CFRP (interlaminar) (Fig. 9). Each symbol corresponds to a different specimen. Open symbols indicate the experimental values. Solid symbols for toughened CFRP (intralaminar) indicate estimated values of da/dN at Da = 0, determined by extrapolating the relationship between da/dN and Da. Solid symbols for toughened CFRP (interlaminar) also indicate estimated values of da/dN at Da = 0 determined by the da/dN-Da relationship at saturation (Da = 5–10 mm). For toughened CFRP (intralaminar), all the

Fig. 10. Fracture surfaces of toughened CFRP after static and fatigue loadings.

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Fig. 11. SEM image of fracture surfaces of toughened CFRP (interlaminar) after fatigue loading (Gmax = 290 J/m2).

R=0.5, 10Hz

Crack propagation rate [m/cycle]

1.E-5

Toughened CFRP Non-toughened CFRP 1.E-6

1.E-7 Gmax 140 J/m2 130 J/m2

1.E-8 105 J/m2 100 J/m2

1.E-9 0

2

4

105 J/m2

115 J/m2

6

Crack extension Δa [mm]

8

Fig. 12. Linear trend lines showing the relationships between da/dN and Da for intralaminar crack growth of non-toughened and toughened CFRPs.

Fig. 13. Relationship between crack growth rate da/dN and maximum energy release rate Gmax.

estimated values of da/dN at Da = 0 showed higher crack growth rate than experimental values. Thus, they provide a conservative relationship between da/dN and Gmax. For toughened CFRP (interlaminar), the estimated values of da/dN at Da = 0 indicate essentially the highest values amongst the obtained experimental results. Fig. 14 shows the relationships between da/dN at Da = 0 and Gmax for all the laminates evaluated. In addition, the maximum values of da/dN for toughened CFRP (interlaminar) are also shown with open squares using a dashed line. The plots of the da/dN-Gmax relationship for toughened CFRP (intralaminar) were in good agreement with those for non-toughened CFRP (intralaminar). This indicated that the da/dN-Gmax relationship at Da = 0 was not affected by interlayer toughening as well as the initial fracture toughness of the static DCB test. The small difference in the gradient parameter b between non-toughened CFRP (intralaminar) and toughened CFRP (intralaminar) also supported this behaviour. For toughened CFRP (interlaminar), da/dN at Da = 0 was 106– 108 m/cycle when the applied Gmax range was 200–300 J/m2. This Gmax range was much higher than that for toughened CFRP (intralaminar) (80–110 J/m2), and a more than twice higher Gmax was required to reach this crack growth rate (106–108 m/cycle). Interlaminar fatigue crack growth tests for interlayer toughened CFRP (interlaminar) were also carried out in our previous studies

Fig. 14. Relationship between crack growth rate da/dN at zero crack extension and maximum energy release rate Gmax.

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[29]. The results showed that the Gmax range for the fatigue crack growth of toughened CFRP with the same crack growth rate range (106–108 m/cycle) was 200–500 J/m2. This Gmax range was much higher than that for non-toughened CFRP (90–120 J/m2). Furthermore, fatigue crack growth resistance decreased, once the crack path shifted from the interlayer region to the intralayer fibre-rich region with increasing Da. Then, the resistance increased owing to the fibre bridging effect. These two factors overlapped, and no conservative da/dN-Gmax relationship was obtained in the previous study. Since the initial defect is located in the intralayer region for the proposed method in the present study, the fatigue crack growth properties of intralaminar fibre-rich region can be evaluated directly. In addition, the da/dN-Gmax relationship at Da = 0 was found to be not affected by bridging fibres. Thus, the most conservative data for toughened CFRP were obtained. Our conclusion is that this conservative da/dN-Gmax relationship for toughened CFRP was obtained for the first time by our proposed method, in which the intralaminar film insertion method and fatigue crack growth test under a constant Gmax are applied. From a perspective of the current no crack growth design, the most conservative evaluation of threshold values for fatigue crack growth is important. By using this proposed method, the da/dNGmax relationship can be obtained for the intralaminar crack growth. The exponents of the power function are rather large for typical CF/epoxy composites, and therefore the estimated values by extrapolation can be regarded as a good reference for the threshold value. In addition, the fatigue life prediction method had also been proposed by combining a delamination onset threshold approach and a modified damage tolerance approach recently [58]. In this method, not only the threshold value but also the da/dN-Gmax relationship at low crack growth region is required for fatigue life prediction. Thus the conservative da/dN-Gmax relationship obtained by the proposed method can contribute to a sophisticated fatigue life prediction. This proposed method is the only approach to evaluate the intralaminar crack growth behaviour of toughened CFRP laminates. Furthermore, since the da/dN-Gmax relationship of toughened CFRP (intralaminar) at Da = 0 is almost the same as that of non-toughened CFRP (interlaminar), the da/dN-Gmax relationship of non-toughened CFRP (interlaminar) at Da = 0 can be roughly substituted for that of toughened CFRP (intralaminar) when it would be difficult to use the intralaminar film insertion method because of limitations such as the wettability of fibres and the viscosity of the matrix resin. Here, it should be noted that this postulation can be applied only to a typical unidirectional CF/epoxy composite under mode I loading and when the intralaminar da/dN-Gmax relationship is the same as the interlaminar da/dN-Gmax relationship. If the matrix resin is ductile and the interlayer resin rich region is thick, the interlaminar da/dNGmax relationship can be higher than the intralaminar da/dN-Gmax relationship [29]. In addition, when the loading mode is different from mode I, the da/dN-Gmax relationship was strongly influenced by the thickness of interlayer resin rich region. It is well known that the thickness effect of interlayer resin rich region under mode II loading is more significant than that under mode I loading [29]. Furthermore, for multidirectional CFRP laminate, the residual stress effect is also significant for da/dN-Gmax relationship [13]. It is known that the crack growth properties was strongly influenced by the lamination pattern although the crack propagates along 0/0 interface of multidirectional CFRP laminate [59]. Thus the intralaminar da/dN-Gmax relationship is possibly influenced by the residual stress effect, although the crack propagated within a single layer, in which carbon fibres are aligned unidirectionally. In this study, intralaminar fatigue crack growth properties of typical unidirectional CFRP laminates were evaluated as a first step. Further research activities are desired to predict the intralaminar fatigue crack growth behaviour in real composite structures.

4. Conclusion A new fatigue crack growth test method that applies the intralaminar film insertion method to a fatigue DCB test under constant maximum energy release rate, Gmax, was proposed. By using this method, the intralaminar fatigue crack growth properties of conventional and interlayer toughened CFRP laminates were evaluated for the first time. The results are summarised as follows: (1) For the conventional CFRP laminates, the da/dN-Gmax relationship at a given crack length showed that the fatigue crack growth resistance was larger for intralaminar crack growth than for interlaminar crack growth. On the other hand, the da/dN-Gmax relationship at zero crack extension for intralaminar crack growth was almost identical to that for interlaminar crack growth. This relationship was not influenced by the fibre bridging effect, and provided a conservative evaluation for interlaminar and intralaminar crack growths. (2) For the interlayer toughened CFRP laminates, the da/dNGmax relationships at a given crack length showed that the fatigue crack growth resistance was smaller for intralaminar crack growth than for interlaminar crack growth. (3) Regarding intralaminar crack growth behaviour, there is no significant difference between the conventional CFRP laminates and the interlayer toughened CFRP laminates. That is, the intralaminar fatigue crack growth properties were not affected by interlayer toughening. In addition, for the interlayer toughened CFRP laminates, the da/dN-Gmax relationship at zero crack extension for intralaminar crack growth was also most conservative between interlaminar and intralaminar crack growths.

Acknowledgement The authors would like to acknowledge the many valuable discussions with Prof. Karl Schulte (Technische Universität Hamburg-Harburg).

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