Epoxy Composite Under Static And Fatigue Loads

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Procedia 00 (2008) 000–000 PhysicsPhysics Procedia 2 (2009) 1195–1203 www.elsevier.com/locate/XXX www.elsevier.com/locate/procedia

Proceedings of the JMSM 2008 Conference

Delamination Growth In Unidirectional Glass/Epoxy Composite Under Static And Fatigue Loads M. Kenane * USTHB, Faculté GM-GP, Laboratoire LSGM, BP32 El Alia, 16111 Bab Ezzouar, Alger, Algerie

Received 1 January received in revised 31 date Julyhere; 2009; accepted Elsevier2009; use only: Received date here;form revised accepted date 31 hereAugust 2009

Abstract Both static growth of cracking and delamination fatigue-crack growth experiments have been carried out on unidirectional glass/epoxy laminates. Three specimen types were tested: double cantilever beam (DCB), mixed-mode bending (MMB) and endloaded split (ELS), for mode I, mixed-mode (I+II), and mode II loading, respectively. They have been expressed in terms of the total fracture resistance, GTR , in static loading, and the measured delamination growth rates, da/dN, versus the total strain energy release rate ΔGI, in fatigue loading. A large number of GH/GI mode ratios have been studied. For each modal ratio, several specimens were tested. Experimental results were correlated through the plotting of the total fracture resistance, GTR , versus the GH/GI modal ratio, and of the parameters d and B versus the GH/GI modal ratio. Good agreement was obtained between theses experimental results and calculations from a semi-empirical relationship. © 2009 Elsevier B.V. All rights reserved PACS: Type pacs here, separated by semicolons ; Key words: glass/epoxy; interlaminar fracture; mixed-mode; total fracture resistance fatigue; delamination growth rate; semi- empirical criterion.

1. 1. Introduction Organic matrix composites reinforced by continuous fibers have gained a wide use as structural materials. A major problem encountered by these materials concerns their exposure to delamination damage which may significantly reduce the stiffness and the strength of the material. The delamination can appear under applied both static and cyclic loads. However, the mechanical fatigue and the resultant degradation of the material are responsible for most of the failures. It is now widely recognized that the ability to anticipate and quantify delamination failure using linear elastic fracture mechanics (LEFM) analysis plays an important role in the understanding of composite behaviour. In fact, LEFM can used to characterize delamination initiation and growth [1,2]. For that, several test configurations have been proposed under various kinds of loading which give good results for unidirectional laminates. However, these configurations and methods must be optimized for multidirectional laminates [3].

* Corresponding author. Tel.: +213-770-379-634; fax: +213-21-247-182 E-mail address: [email protected]

doi:10.1016/j.phpro.2009.11.082

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Delamination growth can be predicted by use of experimental data or by applying the criteria. Data are limited in their usefulness in that they only apply to the conditions under which they were obtained. For design purposes, criteria are preferable since, in principle, they can predict delamination growth over a wide range of conditions. Criteria of delamination growth under static loads, have been proposed by several authors [4,5]. However, a little attention has paid to the study of delamination growth under cyclic loading. The present study concerns the characterization of delamination growth on the basis of a strain energy release rate concept under static loading. And in fatigue case, the measured delamination growth rates, da/dN, were related to the total strain energy release rate, ΔGT. However, experimental results obtained in static and fatigue tests are correlated with a semi-empirical criterion proposed in previous study [6]. It was demonstrated that this semi-empirical criterion was checked for several materials [7,8] and it was found to accurately predict the delamination length. 2. Experimental procedure

2.1. Material and specimen Unidirectional laminates with a nominal thickness of 6 mm were fabricated from prepreg of 52 vol % of E-glass fiber with M10 epoxy resin by compression moulding. Teflon films of 0.06 mm in thickness were inserted during molding at the mid plane as initial cracks for these laminates. Five percent of fibers were woven perpendiculary to hold the parallel fibres together. Double cantilever beam (DCB) specimen (width k = 20 mm, length L = 150 mm and nominal thickness 2h = 6 mm) was used for tests under mode I loading (Fig.1). The mode II delamination test specimen used in this study is the end loaded split (ELS) specimen (width B = 20 mm, length L = 65 mm and nominal thickness 2h = 6 mm). Fig.2 shows the ELS specimen. The mixed-mode fracture tests were conducted by means of the Mixed Mode Bending (MMB) method (width B = 20 mm, length 2L = 130 mm and nominal thickness 2h = 6 mm) developed by Reeder J.R. and Crews J.H. [9, 10]. Actually, the MMB (Fig.3) is included in the ASTM standards [11].

L = 150 mm

P

P a 2h 2h P

a Fig.1. DCB specimen

L =75 mm Fig. 2. ELS specimen

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Fig.3. MMB apparatus

2.2. Fracture mechanics parameter Using Irwin-Kies approach to determine the strain energy release rate : P 2 dC (1) G= 2k da where k is the specimen width, P is the applied load and C is the compliance. The compliance of the DCB was that proposed by Berry and defined as: δ an (2) C= = P m where n and m are the experimental constants (n = 1.89, m = 24.78x 105 N. mm n-1). A similar analysis applied to mode I, was adopted for mode II and mixed-mode (I+II), for which the compliance can be expressed as C=α+βa3. The constants α and β were estimated by plotting experimental values of C versus a3 under variable

GII modal ratio and the results are displayed in table 1. The critical energy release rates, GIC and GT

GIIC , respectively from mode I and mode II tests, and the total critical strain-energy release rate, GTC , from mixed mode considered in this work can be calculated and published in previous study [6].

Table 1. Constants for compliance fits

GII (%) GT -3 -1 α (10 mm.N ) -7 -1 -2 β(10 N .mm )

28

43

53

72

82

91

Mode II

33.86

20.74

15.38

12.41

11.48

8.94

1.85

3.52

1.47

1.11

0.75

1.05

0.99

1.06

2.3. Static testing All tests were conducted with an Instron machine at 2 mm/mn constant displacement rate. Each specimen was instrumented by a receptor of acoustic emissions. With the help of a computer system, the values of the applied load (P) and the crosshead displacement (δ) were obtained from the continuous recording.

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2.4. Fatigue testing The experiments were carried out in an Instron servo-hydraulic testing machine model 1341 with a 1KN load cell. Fatigue-induced delamination growth was characterized by conducting constant-amplitude fatigue tests at a cyclic load ratio (R) of 0.1 and frequency of 4 Hz. During tests, the maximum and the minimum strain-energy release rates G max and G min , and the delamination growth rate, da/dN, were monitored. 3. Results and analysis

GTR

3.1. Total fracture resistance,

The different compliance laws corresponding to

GII modal ratio values, allows us to plot the R-curve. The GT

generated curve presents the variation in total fracture resistance, GTR , as the delamination extends. For mode I, the values of aeff can be computed for Eq.3 from the compliance, C :

C=

δ IR PIR

=

n § δ a eff Ÿ a eff = ¨¨ m IR m © PIR

1

·n ¸ ¸ ¹

(3)

For mode II and mixed mode : 1

3 § δ TR − α ·¸ ¨ δ TR PTR 3 ¸ C= = α + βa eff Ÿ aeff = ¨ PTR β ¨¨ ¸¸ © ¹ Thus, the total fracture resistance during crack growth is expressed as [12]: na n−1 P 2 GIR = eff IR Mode I: 2km

(4)

(5)

3PTR2 βaeff2 (6) 2k The R-curve method allows the strain energy release rate to increase with crack length, reaching a plateau for aeff•50 GTR =

Mode II and mixed mode:

mm (Fig.4) corresponding to

G IR , G IIR and GTR as appropriate. We note that four specimens of each

ratio, with crack length a=25mm were tested.

Fig.4.

GTR

versus effective crack length, aeff

GII modal GT

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G II =28%) obtained from equations (3)GT (6). We notice the appearance of the propagation instability phenomenon when the contribution of mode II increases Figure 4 shows an example of R-curve generated from a MMB specimen (

(

GII • 50%). In these cases, if we consider GTR = GTC (total strain energy release rate corresponding to initiation GT

of cracking), an underestimate of the total fracture resistance was noticed. Nevertheless, some R-curves present a plateau permitting the measurement of the total fracture resistance for which the value is acceptable. Table 2 lists the experimentally obtained results for G IR , G IIR and GTR . Table 2. Experimental results of the total fracture resistances

GII (%) GT GTR (J/m2)

Mode I

28

53

72

82

Mode II

429 ± 42

1118 ± 111

1753 ± 130

2067 ± 177

2625 ± 0

2906 ± 245

3.2. Cyclic delamination growth The delamination crack growth rate, da/dN, may be related to the total strain-energy release, ΔG T , by a relationship of the form: da (7) = B(ΔG T ) d dN where ΔG T = G max − G min , and B and d are constants depending on the material, temperature, stress ratio, R, and frequency [13]. G max and G min correspond, respectively to Pmax and Pmin . As can be seen from Fig.5, the crack growth rate increases progressively from a=35mm to a=40 mm, beyond which the increase is more marked.

Fig. 5. Representative plots of crack length versus number of cycles.

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The measured crack growth rate data are correlated with the corresponding strain-energy release rate for each over GII/GTmode ratio (Fig.6), and the results may be fitted by equation (7).

(a)

(b)

(c)

(d)

Fig. 6. Delamination growth rate, da/dN, versus ΔGT

The coefficients d and B, obtained from the fit of the fatigue-crack growth rate curves, are presented in table 3. Table 3. Experimental values of d and B parameters

GII/GT(%) d B

Mode I 1.9 2.16 10-11

28 2.13 1.02 10-12

53 2.62 2.97 10-14

72 3.21 1.11 10-15

82 3.33 1.04 10-16

Mode II 4.24 1.73 10-23

The results published in the literature show that the d exponent for graphite/epoxy composites is generally much higher than that for glass/epoxy composites [14,15,16]. For glass/epoxy composite, the d value found by Prel et al.[15] is closer to our results. However Bathias C. and Laksimi A.[17] have studied glass-cloth-reinforced epoxy under similar loading conditions, and obtained a high d values for mode I (d=3.71) and mode II (d=7). In this case a crack can be confronted locally with several rigidities, unlike in unidirectional composites where the crack propagates in the plane in which the rigidity is relatively homogeneous. However, contrarily to graphite/epoxy composite, results obtained for glass /epoxy in this study show that the d exponent increases with GII/GT.

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4. Semi-empirical mixed-mode criterion Criteria of delamination growth under static loads have been proposed by several authors [4,5]. However, under cyclic loads, resulting in mixed-mode fracture conditions, few models have only been proposed [18-20]. They differ by their mathematical formulation and frequently yield different results. Nevertheless, to have good accuracy of G results predicted by any criterion, it is necessary to include several II ratios in the study in order to cover the GT maximum number of cases in the range from 0 to 100%. In our study, the semi-empirical criterion is then suggested:

§G G TR = G IR + (G IIR − G IR )¨¨ II © GT

· ¸¸ ¹

mR

(8)

GTR and the semi-empirical calculations are obtained and good m R = 1, this is the classical criterion widely used in the literature:

The correlation between the experimental values of results are deduced for

§G G TR = 419.21 + 2408.34¨¨ II © GT

· ¸¸ ¹

1

(9)

G IR =428.75 J/m2 ; G IIR = 2905.76 J/m2 ; G IIR - G IR = 2477.01 J/m2 . GII modal ratio. In fig.7 are plotted values of GTR versus GT From experiments:

G II modal ratio. GT In cyclic loading, The exponent d and the coefficient B data obey to the relationships of the form: Fig.7.

GTR

versus

§G · d = d I + (d II − d I )¨¨ II ¸¸ © GT ¹

md

(10) mB

§ G · (11) ln(B) = ln(BII ) + (ln(BI ) − ln(BII ) )¨¨1 − II ¸¸ © GT ¹ The experimental measurements of d and B have been plotted as function of GII/GT in Figs.8 and 9. The criterion provides good results for

md =1.85 and m B =0.35. It able to describe mixed-mode interaction under cyclic loading: §G d = 1.885 + 2.255¨¨ II © GT

1.85

· ¸¸ ¹

§ G · ln(B) = −52.616 + 28.058¨¨1 − II ¸¸ © GT ¹

(12) 0.35

(13)

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Fig. 8. Exponent d versus

GII GT

modal ratio.

Fig. 9. Parameter B versus

GII GT

modal ratio.

Table 4 presents a comparison between results from experiment and by using the criterion. Nevertheless, in order to verify the validity of the d and B relationships, it would be interesting to study composites with several different matrices and interfaces. Table 4. Comparison between results from experiment and criterion

dI dII -dI ln(BII) ln(BI) - ln(BII)

From experiment 1.9 2.34

From criterion 1,88 2.25

Error (%) 0.79 3.63

- 52.42 27.86

- 52.616 28.06

0.37 0.69

5. Conclusion Based on the experimental results, the following conclusions concerning the interlaminar static and fatigue crack growth behaviour of the test material, are drawn : 1. For each GII/GT mode ratio considered in this study, results are presented in the form of ΔG T versus da/dN plots which fit the Paris law.

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2. Good agreement was found between the experimental results of GTR , d and B and the results taken from the predicted semi-empirical criterion. It was noted that the variation of total fracture resistance GTR versus GII/GT modal ratio is found to be linear ( m R =1). The parameter d increases as function of GII/GT with m d =1.85, whereas the coefficient, ln(B), versus GII/GT mode ratio decreases with m B =0.35. 3. From the present results, mR , md , and mB can be considered as characteristic parameters of the material. This concluding point should be verified for other composite materials.

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