Cyclic fatigue crack propagation of nanoparticle modified epoxy

Composites Science and Technology 72 (2012) 1530–1538

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Cyclic fatigue crack propagation of nanoparticle modified epoxy Hong-Yuan Liu ⇑, Gongtao Wang, Yiu-Wing Mai Centre for Advanced Materials Technology (CAMT), School of Aerospace, Mechanical & Mechatronic Engineering J07, The University of Sydney, Sydney, NSW 2006, Australia

a r t i c l e

i n f o

Article history: Received 8 December 2011 Received in revised form 9 May 2012 Accepted 31 May 2012 Available online 9 June 2012 Keywords: B. Fracture toughness B. Fatigue A. Polymer–matrix composites (PMCs) A. Nano-particles

a b s t r a c t An experimental study on the fatigue performance of nanoparticle modified epoxy was conducted. Seven material systems were examined which were: neat epoxy (E), 6 and 12 weight percent (wt.%) silica nanoparticle modified epoxy (S6, S12), 6 and 12 wt.% rubber nanoparticle modified epoxy (R6, R12), 3 wt.% each of silica and rubber nanoparticle modified epoxy (S3R3) and 6 wt.% each of silica and rubber nanoparticle modified epoxy (S6R6). Effects of those nanoparticles on the fatigue threshold (DGth and DKth) and fatigue crack propagation rates (da/dN) were studied. It was found that, compared to neat epoxy (E), nanosilica (S6, S12) increased DGth (and DKth) but nanorubber (R6 and R12) did not. However, a synergistic effect was observed on the fatigue threshold when both silica and rubber nanoparticles were added into epoxy. All these nanoparticles, individually or conjointly, decreased da/dN with silica the most effective. Morphology of the fracture surface was examined to understand the role of nanoparticles on toughening mechanisms under cyclic loading, which depended on the applied DG levels. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Since the introduction of nanotechnology, nanoparticles have been extensively used in epoxy matrix composites as reinforcements. Compared to micro-fillers, composites with nanoparticles open up a wide range of new potential applications due to their much enhanced engineering properties, such as stiffness and hardness, and other beneficial functions like moisture barrier and fire retardancy. Thus, research on the mechanical performance of nanocomposites has continuously attracted great attention within both the scientific and engineering communities. In recent years, the effects of silica nanoparticles and rubber nanoparticles on the static fracture toughness of bulk epoxies have been rigorously investigated in [1–5]. Although there is no consensus yet on how to estimate quantitatively the toughness increase due to these added nanoparticles, the dramatic effect of those nanoparticles on toughening epoxy is unanimously reported. Recently, we presented a systematic study on nanoparticle toughening of epoxy [6]. Effects of silica nanoparticle, rubber nanoparticle and their hybrids on the toughness of epoxies were discussed in detail. It was found that rubber/epoxy composites have high toughness and rubber/silica/epoxy hybrid composites possess well-balanced elastic stiffness and fracture toughness. As engineering materials, epoxy-based composites are often subjected to cyclic loading conditions. Besides their static mechanical properties, their fatigue properties, such as fatigue ⇑ Corresponding author. Tel.: +61 2 93517148; fax: +61 2 93513760. E-mail address: [email protected] (H.-Y. Liu). 0266-3538/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compscitech.2012.05.025

lifetime (S–N curve), fatigue threshold (DKth or DGth) and fatigue crack propagation rate (da/dN), are also of great importance. Using otherwise smooth un-notched samples, Wang et al. [7] reported that silica nanoparticles increased the fatigue life of epoxies. However, at the same stress amplitude, the fatigue life of silica/rubber/ epoxy composites was less than that of neat epoxy, which showed a negative hybrid effect. Manjunatha et al. [8] presented their (S–N) results on nanosilica particle and microrubber particle modified epoxies. They found that adding either 9 wt.% microrubber particles or 10 wt.% nanosilica particles into epoxy gave almost identical fatigue life improvements. Hybridizing 9 wt.% microrubber and 10 wt.% nanosilica lead to further increase in fatigue life. Close examination of the test data suggests that a positive hybrid effect exists, especially at low applied stress amplitudes. Other fatigue studies were also performed on samples containing sharp cracks to examine the effect of nanoparticles on fatigue crack growth [5,9–12]. Wetzel et al. [5] reported that the addition of Al2O3 nanoparticles significantly reduced da/dN of epoxy and that crack deflection, matrix plastic deformation and crack pinning were the main toughening mechanisms. But, particle debonding processes were unlikely to have taken place in the process zone. Zhao et al. [9] also used Al2O3 nanoparticles with and without surface treatment to increase the fatigue growth resistance of epoxies. Their results showed that there is a transition point, DKT, above which the fatigue crack growth rate da/dN of the nanofiller modified epoxies was reduced. However, different to Wetzel et al. [5], they observed that particle debonding, plastic void growth and matrix plastic shear deformation are the dominant mechanisms responsible for the improvement of the fatigue crack growth resistance. Especially,

H.-Y. Liu et al. / Composites Science and Technology 72 (2012) 1530–1538

significant plastic deformation can occur in epoxy when the interface between the particles and epoxy is strong. Blackman et al. investigated the fatigue behavior of nanosilica modified epoxy [10]. They showed that silica nanoparticles improved the fatigue performance of epoxy and the fatigue threshold increased with particle loading. The fatigue behaviors of fumed silica/epoxy nano-composites were also studied by Battistella et al. [11] who found that improvements in fatigue threshold and fatigue crack growth rate were insignificant compared to the increase in static toughness. Hence, they suggested that different toughening mechanisms could operate in these two different fatigue crack growth regimes. In all the above investigations, rigid nanoparticles are shown to increase the resistance to da/dN but there is no general agreement on the fatigue threshold. More importantly, the toughening mechanisms under cyclic loading need further detailed examination. There have been few studies on the effect of nano-sized rubber on the fatigue behavior of epoxies. Wang et al. [7] obtained S–N curves for un-notched smooth samples and showed that the fatigue strength near the endurance limit (106 cycles) for nanorubber (100 nm) filled epoxy was lower than neat epoxy. Azimi et al. [12], however, demonstrated that nanorubber (200 nm) did reduce da/ dN of epoxy, especially near the threshold region. The latter observation differs from Wang et al. [7] whose results imply that adding nanorubber to epoxy lowers the fatigue threshold value. In summing up the above, we believe two factors might have complicated the comparisons of test data leading to sometimes opposite conclusions: (a) Difference in apparently similar epoxies (e.g., same resin but different hardener, different nanoparticle surface treatment) and processing conditions (e.g., curing and post-curing schedules). (b) Inconsistent fatigue crack growth rate measurements owing to different data acquisition and analysis techniques. This is particularly true in the near-threshold region where the da/dN data are seldom obtained. In this study, the above-mentioned difficulties have been overcome by processing consistent materials for the fatigue experiments and obtaining the complete range of crack growth rates down to the nearthreshold regime. Following previous systematic studies on the effects of nanoparticles on epoxy fracture toughness [6], carbon fiber/epoxy interlaminar toughness [13] and fatigue lifetime (S–N curve) of epoxy [7], this paper presents recent work on the fatigue crack growth behaviors of nanoparticle modified epoxy composites. Fatigue threshold, in terms of stress intensity factor (DKth) and fracture energy (DGth), and fatigue crack growth rates (da/dN) will be evaluated and the toughening mechanisms due to the nanoparticles (that is, nanosilica and nanorubber) will be discussed with the aid of microstructure examinations. The influence of hybridization of rubber/silica nanoparticles on fatigue crack growth will also be studied.

despite the high loading. Spherical rubber particles averaged 100 nm with similarly excellent dispersion were supplied at 25 wt.% concentration in bisphenol A resin by Kaneka Corporation, Japan. The particles had a rubber core of 90 nm covered by an epoxy-compatible random copolymer shell with thickness about 10–20 nm. The curing agent used was a cycloaliphatic secondary amine, Piperidine, from Sigma–Aldrich. Material formulations were prepared by mixing plain DGEBA resin with the required amounts of nano-SiO2 or nano-rubber master batch. The amount of pre-mixing materials, the EEW of the blend and the corresponding stoichiometric amount of curing agent were calculated by an iterative program using Newton’s method, ensuring 0.01% precision for all component concentrations. Pure epoxy resin, nanoparticle master batches were heated up to 80 °C for 1 h to reduce the viscosity and remove traces of humidity and then were mixed using a laboratory stirrer for 0.5 h at 60 °C, degassed in vacuum at 100 kPa for 2 h at 80 °C. The curing agent was added while stirring slowly after the vacuum was removed and the mixture was poured into a pre-heated mold for curing at 120 °C for 16–22 h, as appropriate. Before testing, a 2 h post-cure at 100 °C was applied to remove any residual stress introduced during the fabrication process. This preparation procedure was identical to that used in the quasi-static fracture toughness (GIC or KIC) [6] and fatigue life (S–N) [7] tests. Seven material systems were examined, which were: (1) neat epoxy (E); (2) 6 wt.% silica nanoparticle modified epoxy (S6); (3) 12 wt.% silica nanoparticle modified epoxy (S12); (4) 6 wt.% rubber nanoparticle modified epoxy (R6); (5) 12 wt.% rubber nanoparticle modified epoxy (R12); (6) 3 wt.% silica nanoparticle/3 wt.% rubber nanoparticle modified epoxy (S3R3); and (7) 6 wt.% silica nanoparticle/6 wt.% rubber nanoparticle modified epoxy (S6R6). Compact tension (CT) samples, same as those used for quasistatic fracture toughness experiments [6], were used for the fatigue crack propagation tests as shown in Fig. 1 according to ASTM D5045-99 [14]. Cyclic loading was applied by an Instron 8800 servo hydraulic fatigue tester. 1 Hz sinusoidal frequency, same as that used for our previous work on the S–N tests [7], was applied. The load ratio, FImin/FImax, was kept at 0.1 in tension–tension mode under load control. Load range mapping was performed so that the 2 kN load cell could apply forces of <100 N without losing accuracy. A starting maximum load FImax was chosen at DK = KIC/2 initially with stepwise reductions to locate exactly DKth. Specifically, if crack growth higher than 0.002 mm occurred within 3 days (259,200 cycles), then DK was decreased to 90% the previous value. Several samples were dedicated for this purpose until DKth was

2. Experimental work 2.1. Sample preparation and cyclic fatigue test The materials were based on a single-part epoxy formulation. The resin was standard diglycidyl ether of bisphenol A (DGEBA) with an epoxide equivalent weight (EEW) of 185 g/mol, AralditeF was supplied by Sigma–Aldrich, Australia. Nano-silica particles were obtained at 40 wt.% concentration in DGEBA resin master batch, NanopoxÒ F400, from Nanoresins AG, Germany. Surface modified SiO2 particles were formed in situ through sol–gel processing with an average size 20 nm and would not change the dispersion during further blending. A low viscosity master batch was obtained via agglomerate-free colloidal dispersion of SiO2

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Fig. 1. Fatigue crack growth test set-up and CT sample.

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obtained. Then, the corresponding DGth was calculated based on the applied Kmax and Kmin from the relation:

GI ¼

ð1  m2 ÞK 2I E

m

(a)

da =C ' (Δ G )2 dN

ð1Þ

where E is Young’s modulus and m is Poisson’s ratio. Crack mouth opening displacement (COD) data were used to determine the crack length a during fatigue crack growth via the COD-load compliance technique. The COD was measured by a dynamic clip gauge (MTS 2620-602) attached to knife edges located at position Xv0 = 0.25W on the specimen front surface and the crack length, a, was obtained by [15,16]:

a ¼ C 0 þ C 1 U x þ C 2 U 2x þ C 3 U 3x þ C 4 U 4x þ C 5 U 5x ; ðfor 0:2 W 6 a=W 6 0:975Þ where

C 0 ¼ 1:001;

C 1 ¼ 4:6695; C 2 ¼ 18:46;

C 3 ¼ 236:82; C 4 ¼ 1214:9;

C 5 ¼ 2143:6

ΔGth

ð2Þ ð3Þ

and

Ux ¼

1þ

(b)

1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi BE  COD=F

m da =C (Δ K ) dN

ð4Þ

in which B is the sample thickness equal to 6 mm in this study. The crack lengths were measured every 100-cycle and confirmed optically with a travelling microscope in initial experiments on each material system [17]. da/dN was determined using an incremental polynomial method recommended by ASTM E647-08 [18]. Calculations of stress intensity factor K with measured normalized crack lengths a/W are the same as in [6], that is:

F K ¼ pffiffiffiffiffiffi f ða=WÞ B W

ð5Þ

ΔKth

and

2þa ð1  aÞ3=2

ð0:886 þ 4:64a  13:32a2

þ 14:72a3  5:6a4 Þ

ð6Þ

2.2. Results and discussion Fig. 2a and b show the log–log plots of da/dN versus applied DG and DK, respectively, for neat epoxy (E), nanosilica modified epoxy (S6, S12), nanorubber modified epoxy (R6, R12), hybrid silica/rubber modified epoxy (R3S3, R6S6) from the near-threshold region to the Paris law [19] regime. At least four samples were tested for each material. The Paris regime data are more clearly shown by seven straight lines in Fig. 3 for all tested materials and they can be described by:

da da ¼ C’ðDGÞm=2 or ¼ CðDKÞm dN dN

ð7Þ

Table 1 lists the respective values of C’, C and m for all materials, E, S6, S12, R6, R12, S3R3 and S6R6, for which da/dN is in mm/cycle, G in J/m2 and K in MPa m1/2. The fatigue threshold values, DGth and DKth, are also given. 2.2.1. Effect of nanoparticles on fatigue crack growth thresholds, DGth and DKth Fatigue crack growth thresholds in terms of the amplitudes of the strain energy release rate DGth and the stress intensity factor DKth are useful for fatigue design, since below which fatigue crack growth cannot occur. It can be seen from Table 1 that the epoxy filled with hybrid nanoparticles, S6R6, has the highest fatigue threshold. The values of DGth and DKth for the two hybrid systems,

Fig. 2. Log–Log plots of fatigue crack growth rate da/dN against (a) strain energy release rate range DG and (b) DK for neat epoxy (E), silica modified epoxy (S6, S12), rubber modified epoxy (R6, R12) and hybrid silica/rubber modified epoxy (S3R3, S6R6).

1.00E-01

Epoxy 1.00E-02

da/dN (mm/cycle)

f ða=WÞ ¼ f ðaÞ ¼

R6 R12 S6R6

1.00E-03

S3R3 S6 S12

1.00E-04

1.00E-05

1.00E-06

10

100

1000

ΔG (J/m 2) Fig. 3. Log–Log plots of da/dN versus DG in the Paris regime for all tested materials.

S3R3 and S6R6, are much higher than those predicted by the simple Rule of Mixtures (RoM) based on the DGth and DKth values of (S6, R6) and (S12, R12), respectively, having the same total wt.%

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(a)

Material code

E S6 S12 R6 R12 S3R3 S6R6

Fatigue crack growth threshold

Parameters for Paris law

DGth (J/m2)

DKth (MPa m1/2)

C0

C

m

43.7 65.4 61.8 47.0 43.3 63.0 102.0

0.342 0.425 0.429 0.330 0.308 0.398 0.503

7.49  1012 1.48  109 2.10  109 1.48  108 2.40  108 8.50  1010 6.72  109

4.59  102 5.03  104 2.96  104 1.33  103 1.24  103 9.86  104 1.32  103

7.6 4.33 4.08 3.75 3.52 4.66 4.06

2.2.2. Effect of nanoparticles on fatigue crack growth rate, da/dN The fatigue crack growth rates da/dN versus applied DG of all 7 materials (E, S5, S12, R6, R12, S3R3 and S6R6) in the Paris regime are already shown in Fig. 3 and their parameters C, C0 and m in Table 1. With increasing applied DG, the crack growth rates increase. Incorporation of nanoparticles into epoxy retards da/dN compared to neat epoxy (E) and this effect is most prominent for nanosilica (S6, S12), then nanorubber (R6, R12) and least for hybrid nanorubber/nanosilica (S6R6). The effect of the hybrid S3R3 is between the two groups of data for (R6, R12) and (S6 and S12). In general, a sample fails from the initiation and propagation of an existing flaw to a critical size. When DG > DGth, the flaw grows under cyclic loading according to the Paris law (Eq. (7)) until its size increases to a critical value fracturing at GIC. Hence, DGth and da/dN are the two deciding factors that control the fatigue life of a material. Table 1 and Fig. 3 show that for nanosilica/epoxies DGth is highest but da/dN lowest compared to neat epoxy and nanorubber/epoxies. These results mean that nanosilica/epoxies have the longest fatigue lifetimes. Indeed, supporting evidence can be found in our recent S-N study [7] for these same materials. However, accurate quantitative predictions of fatigue lifetimes (N) at given

(b)

0.2

ΔG th /GIC

0.18

0.5

Δ Kth /KIC

0.4

0.16 0.14

0.3

0.12 0.1

0.2

0.08

Δ K th / K IC

of nanoparticles. This result indicates a ‘synergetic’’ or positive hybrid effect on the fatigue threshold due to the hybridization of two types of nanoparticles of silica and rubber. As shown in Fig. 2 and Table 1, silica nanoparticles, whether 6 wt.% or 12 wt.% in epoxy, make notable improvements in both DGth and DKth. However, 6 wt.% or 12 wt.% rubber nanoparticles have little effect on DGth or even slightly adverse effect on DKth compared to neat epoxy. In an earlier study [6], rubber nanoparticles are shown to improve dramatically the toughness of epoxy under static loading owing to rubber cavitation and matrix plastic deformation. It appears that these toughening mechanisms are inactive or much less active under cyclic loading near the fatigue threshold region, hence offering less resistance to crack initiation. (See Section 2.3 later). Interestingly, Battistella et al. [11] made similar comments in their fatigue study on fumed silica/epoxy nanocomposites. A different interpretation of the fatigue crack growth thresholds may be obtained by comparing the ratio of DGth/GIC (or DKth/KIC) shown in Fig. 4a and re-plotted as bar charts in Fig. 4b, where values of GIC (or KIC) measured in [6] and this study are given in Table 2. These results mean that fatigue crack growth starts at decreasing fractions of the static toughness GIC (or KIC) from E (0.158), S6 (0.141), S12 (0.078), R6 (0.050) to R12 (0.018). By hybridizing the two types of nanoparticles, this ratio for S3R3 and S6R6 is increased to 0.048 and 0.083, respectively. Hence, owing to the widely different GIC (or KIC) values of the nanoparticle modified epoxies, their absolute DGth (or DKth) threshold values for (S6, S12, S3R3 and S6R6) are higher than and for (R6 and R12) similar to neat epoxy (E) as given in Table 1.

ΔG th / G IC

Table 1 Fatigue crack growth properties of neat epoxy and its nanocomposites.

0.06 0.1

0.04 0.02 0

0 E

S6

S12

R6

R12

S3R3

S6R6

Fig. 4. Results showing (a) fatigue crack growth rate da/dN plotted against normalized strain energy release rate DG/GIC, and (b) DGth/GIC and DKth/KIC for all tested materials.

stress amplitudes (S) require further details on the initial flaw size distribution and a proper fatigue crack initiation criterion. An interesting finding in Fig. 3 is that the 3 materials with rubber particles, R6, R12 and S6R6 almost have identical da/dN curves, but DGth of S6R6 is much higher than those of R6 and R12 (see Table 1). A ‘‘transition’’ at DGT = 50 J/m2 was found for the two rubber modified epoxies, R6 and R12. When DG < 50 J/m2, their da/dN values are higher than neat epoxy; but when DG > 50 J/m2, the effect of the rubber particles begins to decrease da/dN. This fatigue behavior is similar to that observed by Zhao et al. [9] in alumina nanoparticle modified epoxy and also by Azimi et al. [12] in micro-rubber particle modified epoxy. This also confirms that the toughening mechanisms of those particles are different for different applied DG levels below and above DGT. However, Azimi et al. [12] did not observe this transition in their nano-rubber particle modified epoxies. 2.2.3. Some remarks on nanoparticle toughening mechanisms From the different effects of the nanoparticles on GIC [6], da/dN and DGth, which were measured under different applied DG levels, the toughening mechanisms of different types of nanoparticles could be clarified. For silica nanoparticles, crack deflection, particle debonding and plastic void growth are the main mechanisms. The first mechanism acts at high or low load (that is, G) levels but predominantly the latter; the last two mechanisms occur mainly at moderate to high loads (G). These observations explain generally the consistent improvements caused by silica nanoparticles on GIC [6], da/dN and DGth. It is commonly agreed that rubber particles improve the fracture toughness of epoxy by rubber cavitation, void growth and matrix plastic deformation. However, rubber

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Table 2 Mechanical properties (with ±1 standard deviation) of neat epoxy and its nanocomposites. Material Code

E [6]

S6 [6]

S12 [6]

R6 [6]

R12 [6]

S3R3 [6]

S6R6 [6]

E (GPa) GIC (J/m2) KIC (MPa m1/2)

2.86 ± 0.08 277 ± 25 0.951 ± 0.03

2.98 ± 0.10 465 ± 44 1.26 ± 0.04

3.2 ± 0.14 791 ± 62 1.70 ± 0.05

2.45 ± 0.02 946 ± 41 1.62 ± 0.03

2.25 ± 0.10 2380 ± 190 2.47 ± 0.04

2.69 ± 0.10 1310 ± 50 2.00 ± 0.04

2.67 ± 0.07 1250 ± 70 1.95 ± 0.03

cavitation cannot occur when the applied load level is insufficient. As shown in Fig. 4b, fatigue crack growth thresholds of nanorubber/epoxies, R6 and R12, are DGth/GIC = 0.05 and 0.018, respectively. At these low DG levels, rubber cavitation, void growth and matrix plastic deformation cannot occur or only occur partially. Hence, nanorubber particles do not increase DGth (see Table 1). But, with increasing applied DG, the effect of nanorubber particles becomes important, promoting rubber cavitation and matrix plastic deformation so that da/dN of R6 and R12 are lower than neat epoxy in the Paris regime (see Fig. 3). The hybrid system, S6R6, has the highest DGth, increases GIC and decreases da/dN. These beneficial effects of hybrid silica and rubber nano-particles are also seen in the hybrid system S3R3. They may come from the cooperative actions of rigid silica and soft rubber particles under different applied load (or G) levels. However, we cannot provide at this time quantitative explanations on the ‘‘synergetic’’ effect of S6R6 and S3R3 on DGth. But in terms of the S–N curves reported in [7], the fatigue life of the hybrid composite S6R6 is decreased (rather than increased) compared to neat epoxy at the same applied stress range. Further studies will be performed to identify the reasons for this apparent inconsistency. 2.3. Fatigue fracture surface analysis Fracture surfaces were examined by optical and scanning electron microscopy (OM and SEM) to further understand the deformation and failure mechanisms induced by the nanoparticles under cyclic loading. Typical of all the materials tested, Fig. 5a shows a stable fatigue crack growth region (in S6) following the razor sharp crack and before fast fracture. For all the rubber-containing epoxies (R6, R12, R3S3 and R6S6), this stable crack growth region also corresponds to the stress-whitened zone. In addition, fatigue striations can be found in this region such as demonstrated in Fig. 5b (in S12). The area ratio of the striated region to the stable fatigued region depends on the initial applied DG and the material system. Two comments may be made here. (a) The striations do not represent the crack growth per cycle but are larger than da/dN at given positions on the fatigue fracture surface. For example, in Fig. 5b, at DK = 0.68 (or Kmax = 0.76) MPa m1/2, the fatigue striations in S12 are 50 lm which can be compared to da/dN of 4  102 lm/cycle. (b) Consequent to (a), it may be inferred that fatigue crack growth in S12 assumes a ‘‘discontinuous’’ form. This means that a crack-tip damage zone is developed corresponding to the applied Kmax and damages are accumulated with each cycle at the given DK until a critical crack tip opening displacement is reached, whence the crack jumps forward to its next equilibrium damage zone length. The whole crack growth process repeats giving rise to ‘‘sticks-slips’’ or fatigue striations. Using Kmax = 0.76 MPa m1/2 and ry = 48 MPa [6], the damage zone lengths calculated by Dugdale’s yield strip model and Irwin’s plane strain model are 98 lm and 15 lm, respectively, which are 2–3times larger or smaller than 50 lm measured from Fig. 5b. Comments (a) and (b) also apply to fatigue striations seen in R6 at the final stage near fast fracture, Fig. 5c. In discussing the fatigue fracture surfaces for (S6, S12), (R6, R12) and (S3R3, S6R6) in the following paragraphs, it should be pointed out that the identified toughening mechanisms have occurred within the fatigue striations.

Fig. 6a and b show typical SEM images of the fracture surfaces of nanosilica/epoxy, S6, which has the highest DGth/GIC value of all the nanocomposites. The applied DG is 152 J/m2 (DK = 0.65 MPa m1/2) in Fig. 6a and 245 J/m2 (DK = 0.824 MPa m1/2) in Fig 6b, respectively. As shown in Fig. 4, the fatigue threshold DGth of S6 is 14% GIC. In Fig. 6a, DG is152 J/m2 and Gmax is 33% GIC. In the da/dN curve of S6 in Fig. 2a, this loading level is well within the Paris crack growth regime with da/dN = 7.6  105 mm/cycle. The SEM image, Fig. 6a, shows a slightly roughened surface owing to crack deflection caused by the nanosilica particles but also reveals a few debonded particles. In Fig. 6b, DG is 245 J/m2 and Gmax is 53% GIC, da/dN = 2.1  104 mm/cycle. Silica particle debonding and pullout and matrix plastic deformation are evident on the fracture surface. Some voids are larger than 20 nm, which is the original size of the silica particles. But the change in the average void size is insignificant, indicating little plastic void expansion has occurred. These observed failure mechanisms at low and high DG levels can also be found in Figs. 6c and d for S12 when the applied DG is 97 J/m2 (DK = 0.54 MPa m1/2) and 218 J/m2 (DK = 0.807 MPa m1/2), respectively, and the corresponding da/dN are 2.4  105 and 1.2  104 mm/cycle. At DG = 97 J/m2 (Gmax = 12.4% GIC), Fig. 6c shows a moderately rough surface, similar to Fig. 6a for S6, due to crack deflection but with no particle debonding since this is in the early stage of Paris crack growth regime. At DG = 218 J/m2 (Gmax = 28% GIC), Fig. 6d shows characteristic features of silica debonding pullout and matrix shear deformation similar to Fig. 6b for S6. As is expected, compared to the fracture surface of compact tension samples taken after the static toughness GIC test [6], the fatigue fracture surfaces in Fig. 6 are smoother with fewer debonded particles and holes and much less matrix deformation, since the applied DG and Gmax are much lower than GIC. Hence, in the Paris regime, there is a gradual change of toughening mechanisms owing to silica from crack deflection at low DG to particle debonding, limited void growth, pullout and matrix plastic deformation at high DG. Hence, silica particles increase DGth and decrease da/dN at high applied DG levels. It should be noted that crack pinning is not a toughening mechanism in these silica/epoxy composites studied since tail-like features around silica particles have not been found on the fracture surface. This observation is different to Wetzel et al. [5] who identified crack pinning in Al2O3/epoxy nanocomposite where the particle size is 13 nm. Fig. 7 show typical SEM images of the fracture surfaces of nanorubber/epoxy, R12, which has the lowest DGth/GIC value of all the nanocomposites, at two different positions in the Paris crack growth region. In Fig. 7a, the applied DG is 154 J/m2 (DK = 0.571 MPa m1/2) and da/dN = 1.7  104 mm/cycle. In Fig. 7b, the applied DG is 320 J/m2 (DK = 0.82 MPa m1/2) and da/ dN = 6.2  104 mm/cycle. As shown in Fig. 7a, when DG is low (=154 J/m2) and Gmax = 6.5% GIC, the fracture surface is relatively smooth and there is no evidence of rubber cavitation. The matrix plastic deformation is negligible compared to that observed in GIC test [6]. As shown in Fig 4b, the fatigue threshold, DGth, of R12 is only 2% GIC and even lower than the applied DG in Fig. 7a. It is thus reasonable to expect that rubber cavitation may not occur near the threshold region. This also explains why rubber nanoparticles do not increase DGth in this study. At high DG (=320 J/m2), and Gmax = 13.6% GIC, rubber cavitation becomes clearly visible in

H.-Y. Liu et al. / Composites Science and Technology 72 (2012) 1530–1538

(a)

1535

(b)

(c) Fig. 5. (a) Typical fatigue fracture surface (S6) showing a stable fatigue crack growth region before fast fracture. Fatigue striations are clearly revealed in the stable fatigue crack growth region in (b) S12 at DK = 0.68 MPa m1/2 and (c) R6 at DK = 0.93 MPa m1/2.

Fig. 6. SEM images of the fracture surfaces of S6 taken in the Paris fatigue crack growth region at: (a) DG = 152 J/m2 (DK = 0.65 MPa m1/2) and (b) DG = 245 J/m2 (DK = 0.824 MPa m1/2); and fracture surface of S12 at (c) DG = 97 J/m2 (DK = 0.54 MPa m1/2) and (d) DG = 218 J/m2 (DK = 0.807 MPa m1/2). Note that white arrows denote matrix plastic deformation and the circles indicate silica debonding with void growth.

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Fig. 7. SEM images of the fracture surface of R12 taken in the Paris fatigue crack growth region at: (a) DG = 154 J/m2 (DK = 0.571 MPa m1/2) and (b) DG = 320 J/m2 (DK = 0.82 MPa m1/2) with a higher magnification.

Fig. 7b; only some voids are larger than 100 nm (that is, the original average size of rubber particles), indicating limited void growth. At these sub-GIC levels, the matrix shear deformation on the fracture surface is much less than that found in the static GIC test [6]. The same toughening mechanisms at low and high DG are also found in R6. Despite their small magnitudes, these toughening mechanisms work cooperatively in reducing da/dN with applied DG as shown in Fig. 3. As we mentioned in Section 2.2.2, Azimi et al. reported [12] that nanorubber particles can reduce crack growth rates at the near-threshold region. Their SEM image (see Fig. 16 in [12]) shows cavitation of treated nanorubber particles (MBS-COOH) near the fatigue threshold (DK = 0.45 MPa m1/2) and voids grow at a higher DK (=1.571 MPa m1/2). This difference in toughening mechanisms may be due to the different properties of rubber particles and the different bonding conditions between rubber and epoxy in their composites. Figs. 8a and b show typical SEM images of the fracture surfaces of the hybrid nanocomposite, S6R6, at two different applied DG levels in the Paris fatigue crack growth regime, which are: (a) DG = 147 J/m2 (DK = 0.607 MPa m1/2), da/dN = 1.6  104 mm/ cycle; and (b) DG = 337 J/m2 (DK = 0.91 MPa m1/2), da/dN = 9.0  104 mm/cycle. At low DG = 147 J/m2 and Gmax = 11.9% GIC, as shown in Fig. 8a, silica particle debonding is rare but rubber cavitation can be easily found. But, in R12, at similar DG = 154 J/m2 and Gmax = 6.5% GIC, Fig. 6a shows no rubber cavitation. These obviously opposite results could be due to the higher Gmax/GIC ratio in

S6R6 compared to R12 and/or the different stress state in the rubber particles surrounded by smaller silica particles in the epoxy matrix. Further numerical studies following the approaches described in [20,21] will be adopted to include both types of nanoparticles to clarify the deformation and toughening behavior. At high applied DG = 337 J/m2 and Gmax = 27.2% GIC, slightly more debonded silica particles and intensive rubber cavitation occur, Fig. 8b, which are responsible for the much decreased da/dN compared to neat epoxy. Figs. 8c and d confirm that rubber cavitation has also occurred at both low and high applied DG levels in the hybrid nanocomposite, S3R3. But there seems to be no silica debonding at these DG levels. By comparing the fracture surfaces of binary silica/epoxy composites, S6 and S12 (Figs. 6b and d), and hybrid silica/rubber/epoxy composites, S6R6 (Fig. 8b) and S3R3 (Fig. 8d) at the same magnification and similar applied DG, it is seen that the hybrid composites are much smoother. In the hybrids, rubber cavitation is evident but matrix shear deformation is limited. This appears to support S3R3 and S6R6 are not as effective as S6 and S12 (in which both particle debonding, pullout and matrix plastic deformation are predominant) in retarding da/dN (see Fig. 3). Manjunatha et al. [8] have reported a positive hybrid effect of the ternary microrubber/nanosilica/epoxy composites. At the same applied stress range, their fatigue life is superior to neat epoxy and the binary composites. They showed that rubber cavitation/void growth and silica debond/void growth are the key operative toughening mechanisms in their ternary composites, albeit at quite high applied stress ranges. However, in our nanorubber/nanosilica/ epoxy hybrids, void growth around debonded nanosilica and/or cavitated nanorubber particles cannot be confirmed from SEM images in both the near-threshold DGth and high DG regimes which are still distant from GIC. Finally, Wu et al. [22] developed a fatigue crack growth model which considers Coffin-Mansion type of damage accumulation of material at the crack-tip and Dugdale yield strip model, and which is capable of accounting for the fatigue threshold and stress ratio effects on fatigue crack growth rates. Abou-Hamda et al. [23] successfully applied this model to predict the full range of da/dN versus DK data at different stress ratios for a micro-rubber/epoxy. Based on the fatigue fracture surface observations from Figs. 5–9, particularly those related to Figs. 5b and c, Wu et al.’s fatigue model may be applicable to predict the da/dN versus DK curves for all the polymer nanocomposites shown in Fig. 2a. Further work will be performed to assess the usefulness of this model.

3. Conclusions The effects of incorporating nano-sized silica and rubber particles into epoxy were studied in terms of their fatigue crack growth behaviors. The major findings are given below: (a) Nanosilica (S6, S12) and nanorubber (R6, R12) modified epoxies, as well as their hybrids (S3R3, S6R6), all displayed fatigue crack growth rates da/dN which obeyed Paris power law, Eq. (7), and the existence of fatigue thresholds DGth. Silica nanoparticles increased DGth of neat epoxy; but rubber nanoparticles did not. However, both nanoparticles decreased da/ dN at given DG in the Paris regime compared to neat epoxy, though nanosilica is more effective than nanorubber. (b) Epoxy modified by hybrids of nanosilica and nanorubber (S3R3, S6R6) showed a synergistic effect on DGth compared to epoxies with one type of nanoparticles of the same total weight fractions (S6 and R6, S12 and R12, respectively). But the retardation on da/dN was less significant than that achieved by having silica nanoparticles alone.

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Fig. 8. SEM images of the fracture surface of S6R6 taken in the Paris fatigue crack growth region at: (a) DG = 147 J/m2 (DK = 0.607 MPa m1/2) and (b) DG = 337 J/m2 (DK = 0.91 MPa m1/2). Note that the circles indicate silica debonding with void growth; and fracture surface of S3R3 taken in the Paris fatigue crack growth region at: (c) DG = 99.7 J/m2 (DK = 0.5 MPa m1/2) and (d) DG = 300 J/m2 (DK = 0.867 MPa m1/2).

(c) SEM examinations of fracture surfaces revealed different toughening mechanisms acting at different applied DG levels within the Paris crack growth regime. Rigid nanosilica particles toughened epoxy resins mainly by crack deflection under low applied DG, but particle debonding, pullout and matrix plastic deformation are predominant at high applied DG. Rubber nanoparticles did not cavitate when applied DG is low, especially near the fatigue threshold. However, rubber cavitation did occur at high applied DG. With hybrid particles, even though few or no silica debonded, rubber cavitation did happen at low applied DG. However, silica debonding and extensive rubber cavitation occurred in S6R6 at high applied DG.

Acknowledgements H.-Y. Liu wishes to thank the Australian Research Council (ARC) for the support of this project through a Future Fellowship awarded to her (FT0992081, 2009–2013) tenable at the University of Sydney. Y.-W. Mai also thanks the ARC for supporting his work on polymer nanocomposites. Finally, the authors wish to acknowledge Nanoresin AG, Germany for the supply of nanosilica particles for this study.

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