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Composites Science and Technology 142 (2017) 20e29
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Experimental characterization of the interlaminar fracture toughness of a woven and a unidirectional carbon/epoxy composite D. Fanteria a, L. Lazzeri a, *, E. Panettieri a, U. Mariani b, M. Rigamonti b a b
Department of Civil and Industrial Engineering, University of Pisa, Via G. Caruso 8, 56122, Pisa, Italy Leonardo Helicopter Division, Via Giovanni Agusta 520, 21017, Cascina Costa di Samarate, Varese, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 December 2016 Received in revised form 27 January 2017 Accepted 28 January 2017 Available online 2 February 2017
An experimental program has been carried out at the University of Pisa, in collaboration with Leonardo Helicopter Division, to investigate the differences in interlaminar fracture toughness properties of a graphite/epoxy composite material, available in two forms: unidirectional tape and five harness satin fabric. To this end, tests have been carried out in mode I, mode II and mixed I þ II mode on specimens manufactured with the two material systems by Leonardo HD, following their industrial standards. The results show a considerably higher toughness of the fabric, as a consequence of the peculiar features at the delamination interface and of the other local mechanisms, capable of absorbing energy, that are present only in fabric composites. Some fractographic observations confirm these mechanisms. Finally, numerical analyses have been carried out, modelling with Finite Element the various tests, to complement and evaluate the data reduction methods used to derive the toughness values. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Polymer-matrix composites (PMCs) Fabrics/textiles Fracture toughness Delamination Fractography
1. Introduction Application of advanced composite materials to aircraft primary structures is continuously growing, and projects like the Boeing 787 and the Airbus A350 XWB in the field of commercial aeroplanes are striking examples of how far current technology can extend. Further developments are in progress in the areas of low cost processes or inclusion of sensors to obtain multifunctional materials, so that predictions are in favour of a wide increase in applications in future aeronautical programs. At present, the main design requirements that must be accomplished by most composite structural applications are relevant to either stiffness, static strength or resistance to low energy impact damage. Similar considerations also hold for the helicopter world, where composite parts must account for challenging loading spectra. In order to avoid structural problems in service, current design procedures have led to the adoption of rather low allowable strain levels. In the certification process, durability and damage tolerance criteria
* Corresponding author. E-mail addresses: [email protected] (D. Fanteria), [email protected] (L. Lazzeri), [email protected] (E. Panettieri), ugo.mariani@ leonardocompany.com (U. Mariani), [email protected] (M. Rigamonti). http://dx.doi.org/10.1016/j.compscitech.2017.01.028 0266-3538/© 2017 Elsevier Ltd. All rights reserved.
require composite structures containing undetected damage to be acceptable to fly. Comparing different types of damage, inadvertently introduced during manufacturing or induced in service, delamination growth is considered one of the most important failure mechanisms that can be detrimental for flight safety and consequently, delaminations must be considered not only in the design process, but also in structural verification testing. Delamination growth can occur as a consequence of interlaminar stresses and possible situations that may induce such undesired stresses are quite numerous: local buckling, free edges and notches such as holes, ply drops, impact damage or, in complex structures, unanticipated outof-plane loading. It is important therefore to improve the knowledge of delamination growth both theoretically and experimentally. The helicopter community pioneered investigations about how to approach the delamination problem; early works by O'Brien, related to free edge delamination in tension loaded structures date back to the 80-ies [1], and the use of fracture mechanics was fostered, with the strain energy release rate identified as the parameter most suitable for strength and stability analysis. Since then, a flood of papers have been published on delamination experiments and analysis, but nevertheless the certification process remains very expensive and time consuming, because it is
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based on the so-called building block approach [2] or test pyramid [3]. Therefore, currently there is a great interest in the development and refinement of prediction methods for reducing time and costs of assessments and for evaluating, on a rational basis, problems like: second/alternative material supplier, manufacturing discrepancies, transfer of production from a plant to another, etc. This paper stems from a collaboration between the University of Pisa (UP) and Leonardo Helicopter Division (formerly AgustaWestland), a helicopter manufacturer that is involved in research activities in this field since the early times [4,5]. The interest is in the study of rotor area materials, and is focused on the characterization of interlaminar fracture resistance of a carbon/epoxy system, available in two forms: 5 harness satin fabric and unidirectional tape. Experiments have been carried out for the assessment of interlaminar fracture toughness in various conditions (mode I on DCB specimens, mode II on 3ENF coupons and mixed I þ II conditions using the MMB procedure). The carbon/epoxy materials, provided by Leonardo HD, are commonly used in the helicopter rotor area and are manufactured from Hexcel prepregs: they are a 8552S/AGP280 woven fabric in the 5-harness satin style and a unidirectional 8552/AS4 tape. This choice was not unintentional, as the two materials share essentially the same constituents: the AGP280 fabric is made out of AS4-3K rows and according to Hexcel literature no practical differences exist between 8552 and 8552S resins. There is a strong interest in comparing the two systems, since recently there have been substantial efforts towards the introduction of fabrics in composite structures because of easier handling and lay-up processing than for unidirectional tape laminates. In addition, woven fabric composites are more damage tolerant in the presence of a delamination. The reasons for this better behaviour are in the nonplanar interply structure of woven fabric composites, so that a delamination, if present, will interact with matrix rich regions and the weave structure during its propagation; this interaction will increase material toughness significantly. 2. Literature review about interlaminar fracture toughness differences between unidirectional and fabric composite materials In the literature about fracture toughness of fabric composites, a number of papers discuss the influence of the style at the delamination interface on the interlaminar toughness. Indeed, Funk and Deaton make a systematic analysis on the mode I fracture toughness of DCB coupons, made in 4 different styles [6] and show how the different structure at the interface (in particular presence of cooriented fibers on opposite faces) strongly influences the toughness. Their work moves from the results of the many studies carried out on multidirectional DCB specimens, where the interface may change from the 0/0 of the standard ASTM coupons [7] to other combinations (e.g. q/0 or q/-q or others). This is a more realistic situation, while the 0/0 interface of the standard specimens is rather unusual to be critical in real structures. It was noted that the 90/90 interface resulted in a delamination path that strongly interacted with other damage mechanisms, such as matrix cracks, giving rise to continuous jumps from the upper interface with a non-90 ply to the lower one, and vice versa, absorbing substantially higher energy (see also [8,9]). Ref. [6] discusses the cases of symmetric and asymmetric yarn disposition at the interface, considering anyhow also situations that are not common in engineering practice. For instance, a 5H satin shows a different appearance if seen from one side or from the other: in one case, 80% of yarns are oriented in one direction and 20% in the other, while on the opposite face the ratio is reciprocal, 20% and 80%. It is evident that
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the interface plays a fundamental role: the situation of two mirror plies interface is evidently quite different from the situation of two equi-oriented plies stacked one on the other. A number of papers available in the literature are relevant to studies on fabric DCB specimens that refer to very specific interfaces, sometimes deliberately particular, that are anyhow unusual as well, in the same measure of the 0/0 interface [10,11]. In this experimental activity, it was decided to address the most frequent case, commonly used in the engineering practice, i.e. the one of a lay-up made of equally oriented plies stacked one over the other. Therefore the fabric specimens were manufactured by stacking 16 plies, equally oriented: this is the most realistic sequence. Therefore, at the delamination interface, the two neighbouring plies offered faces with different characteristics (one with prevailing longitudinal yarns and the other with prevailing transversal yarns), so that the probability of matching equally oriented bundles was intermediate between the extreme cases studied in the literature: the too optimistic, and therefore unconservative, case of complete overlap of the transversally oriented yarns is thus avoided. Too optimistic means that, according to fractographic observations [10,11], there are many failure mechanisms active during the delamination growth in a fabric DCB, and among others the debonding of 90-degrees oriented bundles is particularly helpful in absorbing energy, but also fiber failure, fiber pull-out, fracture of matrix resin, matrix plastic deformation and delamination front deflection are active mechanisms. Significant examples of test data publication, supported by fractography and failure analysis, can be found in papers by Alif, Carlsson and Boogh [12], Alif, Carlsson and Gillespie [13], Pereira and others [14] and Martin [15]. Recently (2016) Czabaj and Davidson [16] have published an experimental work on the influence of temperature on the interlaminar fracture properties of a fabric carbon/polyimide system; obviously, with such a matrix, the objective of the paper was the study of the influence of the temperature (up to 300 C) on the interlaminar fracture toughness expressed by that material, but an interesting literature review on fabric interlaminar toughness peculiar behaviour, substantially very similar to the one performed in the present work, completes the paper. On the contrary, the main fracture mechanisms in unidirectional laminated composites are fibre debonding and matrix plastic deformation. The observation of other failure modes supports the general finding that 2-D woven fabric laminates show substantially higher interlaminar fracture resistance than unidirectional laminates. 3. Experimental program The experimental program comprised different kinds of tests, i.e. Mode I on DCB specimens, Mode II on ENF specimens tested in three point bending and mixed mode I þ II using the Mixed Mode Bending procedure. All of these are covered by ASTM standards, with the mode II procedure that has been published very recently, after the beginning of the experimental activity of this paper. The available ASTM standards [7,17,18] anyhow refer to unidirectional composite systems; in the case of the fabric system, the same approach has been used, even if some adjustments are necessary (e.g. requirement on the specimen thickness, to maintain the applicability of small deformation theory). A representation of the three tests is shown in Fig. 1. Moreover, the characterization of the same material system at different fracture modes (Mode I, Mode II and Mixed I þ II modes) points out the problem of having uniformity among the data reduction methods which are different between Mode I, Mode II and Mixed I þ II mode fracture tests.
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Fig. 2 shows the force vs displacement curves obtained for the UD and fabric DCB specimens. The curves of the UD specimens show that a good replicability exists in the linear part of the curve while, after the beginning of the crack propagation, two distinct levels at which the propagation occurs can be observed. The DCB results from the fabric material system show a small dispersion of the data in the linear part of the curves while the propagation curves are affected by failure phenomena that produce alternating growth and drop of the load during the crack propagation. This failure behaviour is typical of fabric material systems since the presence of both a non-uniform inter-laminar layer and bridging phenomena modify the crack propagation patterns. 3.3. Mode II tests
Fig. 1. Schemes of the DCB, ENF and MMB tests.
3.1. Materials A 5 harness satin fabric was used, Hexcel 8552S/37%/AGP280, to manufacture coupons, made of 16 layers for a typical thickness of about 4.5 mm (nominal ply thickness: 0.28 mm). The fibres were AS4 3K, with equal dimension of yarns in both directions, weft and fill. The other material system investigated was unidirectional graphite/epoxy, Hexcel 8552/34%/AS4, with each layer having a nominal thickness of 0.125 mm; the relevant coupons were manufactured stacking 24 plies, for a specimen thickness of around 3 mm. 3.2. Mode I tests These tests were carried out following the ASTM standard [7], even if it clearly states that it is applicable only to UD materials. The specimens were 150 mm long and 25 mm wide, and were tested in a servo-hydraulic machine built by A.I.P. Studio (Varese, Italy) interfaced with a digital controller. The load cell had a capacity of 200 N and the tests were carried out in displacement control, with a rate of 1 mm/min. The load cell and the displacement transducer of the machine allowed the measurement of load and displacement (twenty data per second) while an industrial camera (by The Imaging Source GmbH, resolution 960 1280 pixels) took pictures of the side of the specimen at regular intervals (one per second). Thus, the correlation between the crack length and the values of load and displacement allowed the estimation of Gc. The method used for data reduction will be discussed later.
A three point ENF test was used, with a 100 mm total span length. After years of discussions, ASTM has issued only recently a standard procedure, [17]. It is based on the use of the Compliance Calibration method to define the compliance derivative with respect to delamination length, a method that does not rely on an artificial correction to the delamination length, but makes use of a dC/da derivative determined from experimental measurements carried out on the same ENF specimen (and not in a DCB specimen, obviously of the same batch). Moreover, a debate has been active for a long time about the opportunity of initial precracking ([19,20]), because toughness values evaluated from a natural delamination are significantly lower than those generated by tests without precracking, i.e. with delamination starting directly from the insert. Another advantage of the procedure [17] is that it allows the possibility to assess the fracture toughness from the insert and from a natural delamination. Therefore, since the data generated was also used for design purposes, before the test all the ENF specimens were subjected to a precracking operation, performed in three point bending but with a total distance between the supports of 50 mm. The specimens were positioned on the loading frame in such a way to leave a distance of about 3e4 mm between the end of the insert and the central load application point; then the specimens were loaded, similarly to a test. The growth of the natural delamination from the insert typically stopped under the load application point. In the subsequent real tests, carried out with total distance between the supports of 100 mm, the specimens exhibited mainly an unstable growth (delamination growth is stable for a/L > 0.7), characterized by a linear behaviour followed by a sudden load drop; therefore, no picture acquisitions were performed. The force vs displacement curves are shown in Fig. 3 for the two material systems. In both cases, the crack propagation is essentially unstable. All the plots exhibit a linear initial loading phase until slight non-linearities are observed, just before the load drops down. These non-linearities are more pronounced in the fabric
Fig. 2. Force vs displacement of the DCB tests.
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Fig. 3. Force vs displacement of the ENF tests.
material system, due to intrinsic reasons (the fibre yarns have a curved path, and so a natural tendency towards non linear behaviour, particularly under compression loads) and maybe also to friction effects. 3.4. Mixed mode tests Mixed mode tests, in I þ II combined modes, were carried out according to the Mixed Mode Bending (MMB) procedure, defined originally by Reeder and Crews [21] and later adopted by ASTM [18]. The test apparatus used for the tests has been manufactured and assembled in Pisa, on the basis of the recommendations suggested in the ASTM standard. The great advantage of this procedure is that the desired mode partition can be obtained easily, simply modifying the distance c between the force application axis and the intermediate 3 point bending fulcrum, as depicted schematically in Fig. 1. The mode ratios ðGI =GII Þ examined were 2:1 and 1:2 (or, alternatively, B ¼ GII =GTOT equal to 0.33 and 0.67), which corresponded to a lever length c of 59 mm and 33 mm, respectively. The tests were carried out with not-precracked specimens and the same data (load, displacement and crack length pictures) acquisition system of the DCB tests was used. Eventually, the ASTM standard suggests also to evaluate the compliance of the test setup, for those cases in which the displacement of the load application point is not measured directly, but by means of the actuator displacement transducer, that has the merit of being easily available; for this purpose, a very stiff false specimen, made of steel, 6 mm thick, was built and used in a simulated test, to evaluate the contribution (very small, indeed) of the test rig to the measured compliance. The results of the MMB tests of the UD and fabric specimens carried out at B ¼ 0.33 and B ¼ 0.67 are shown in Figs. 4 and 5, respectively, in terms of force vs. displacement plots. The two material systems show profound differences in the delamination
propagation phase. The tests on the UD specimens show that the crack growth phase is associated with a load decrease that, for B ¼ 0.33 (prevailing mode I), is basically stable while, for prevailing mode II conditions (B ¼ 0.67), is unstable with a sudden load drop followed by a stable propagation. Conversely, the MMB tests carried out on the fabric material system exhibit a linear curve, for both values of B, followed by a stable propagation phase where the load keeps on increasing even when the delamination grows. This unexpected behaviour can be attributed to a combination of bridging phenomena and friction effects which stabilize the crack propagation. 4. Data reduction methodology Among the possible reduction methods [22], in this paper the data reduction methods based on the crack length correction, developed by Williams et al. [23,24] and adopted in the ASTM standard of the MMB tests [18], has been used for mode I and mode II data analysis. This choice ensures that the same data reduction method is used when pure modes and mixed modes are compared. The crack length correction, which modifies the measured physical length in order to take into account local crack tip constraints that reduce the laminate stiffness, involves the factor c which is computed according to Equation (1).
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " pffiffiffiffiffiffiffiffiffiffiffiffiffiffi u # u E11 E11 E22 G 2 t where G ¼ 1:18 c¼ ; 32 11G13 1þG G13
(1)
and E11 and E22 are the Young moduli in the longitudinal and transverse direction and G13 is the shear modulus in 1e3 out-ofplane direction. The relationships between geometric data, material properties and crack length required for computing the critical fracture toughness values, GI (mode I), GII (mode II) and GMM (mixed modes),
Fig. 4. Force vs displacement of the MMB (B ¼ 0.33) tests.
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Fig. 5. Force vs displacement of the MMB (B ¼ 0.67) tests.
are reported in Equations (2)e(4), respectively.
2 96P 2 a þ c 2t ; W 2 t 3 E1f
GI ¼
GII ¼
GI ¼
9P
2
(2)
5. Data reduction results: flexural modulus
t 2
a þ 0:42c 2 2W 2 t 3 E1f
;
(3)
2 2 9 P 2 ð3 c LÞ2 a þ c 2t 9P 2 ðc þ LÞ2 a þ 0:42c 2t ; G ¼ ; GMM II 2 W 2 t 3 E1f 2W 2 t 3 E1f
¼ GI þ GII ; (4) where a is the crack length, P is the critical load value, t is the thickness of the specimen, W is the specimen width, c is the lever length, L is the half-span length of the MMB test and E1f is the flexural modulus. The values of the flexural modulus, E1f , can be computed, for each type of test, using Equations (5)e(7).
Mode I : E1f ¼
3 64m a þ c 2t ; Wt 3
Mode II : E1f ¼
3 m 2L3 þ 3 a þ 0:42c 2t
Mixed mode : E1f
intersection between the experimental curve and a linear curve with a 5% reduced slope or the point in which the maximum force is attained (the event, between the two, that occurs first is selected).
Wt 3
(5)
;
(6)
The crack length correction, c, introduced in the beam theory to include the effect of a more compliant constraint in correspondence of the crack front, and the experimental slope, m, of the force vs displacement curve, influence, as reported in Equations (5)e(7), the value of the flexural modulus, necessary to evaluate the critical fracture toughness in pure and mixed modes. The DCB test allows for an interesting comparison of the effects of the relevant correction on the computation of the flexural modulus. In fact the DCB test is performed in two phases: preliminarily, a natural crack is created in the DCB specimen starting from the initial Teflon insert front; subsequently, the real test is carried out, with the specimen containing a natural delamination. In both phases, data regarding force, displacement and initial crack length is collected: hence, the bending modulus can be estimated in both conditions: the one of an artificial straight crack front (determined by the Teflon insert) and in the other case of the naturallydeveloped front. A comparison of the flexural moduli obtained in the two conditions is shown in Fig. 6, relevant to the DCB tests performed on the UD and fabric material systems. The results highlight that the difference between the flexural modulus computed in the pristine (No-Precrack, NPC) and precracked (Precrack, PC) condition is not negligible for both material systems. This difference can be explained by pointing out the fact
i h 3 3 8 a þ c 2t ð3c LÞ2 þ 6 a þ 0:42c 2t þ 4L3 ðc þ LÞ2 1 ; ¼ 2L2 Wt 3 m Csys
where m is the slope of the linear part of the force vs displacement curve obtained in the test and Csys is the compliance of the test apparatus (measured through an ad-hoc test). The ASTM standard [7] suggests three criteria to choose the critical point, characterized by a combination of delamination length, actuator displacement and applied force, P; in particular, this last parameter can be: non-linear (PNL ), visual (PVIS ) and 5%/ MAX (P5%=MAX ). The NL criterion involves the first point of the force vs. displacement curve that deviates substantially from linearity; the VIS criterion is based on the first advancement of the crack tip visually observed, while the 5%/MAX criterion evaluates the
(7)
that the initial NPC condition is characterized by a straight crack front and by lack of any type of damage or material degradation induced in the material. Yet, the values of E1f obtained with the PC specimens for both the material systems are smaller than those obtained in the NPC tests. To understand these discrepancies, a numerical 3D FE model of the DCB tests has been developed within the commercial FE software Abaqus, for both material systems, to reproduce both tests: the NPC and the PC test. The dimensions used to create the specimen models (UD and fabric) as well as the crack lengths were the average of the ones measured on the real specimens.
D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
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Fig. 6. Average flexural moduli (error bars indicate standard deviations) obtained in DCB tests in the case of straight crack front (No-Precrack) and with a naturally developed crack (Precrack).
Fig. 7. Slope of the force vs displacement curves in No-Precrack tests: experimental average compared to numerical results.
To limit the computational costs of the FE analyses, only half of the specimen (in the longitudinal direction) was modeled and symmetric boundary conditions were applied. The specimen arms were modeled by means of solid elements (C3D8 elements): 12 elements along the thickness of each DCB arm were used, the width direction was discretized with 17 elements and, lastly, in the longitudinal direction a variable mesh size was assigned so that the mesh sizes were between 0.25 mm, around the crack tip, and 3 mm in the far ends of the specimen arms. To reproduce the hinges of the test, multi-point constraints were created between 2 reference points (one for each specimen arm) and the nodes of the corresponding specimen edges. The simulations were performed with the implicit solver of the FE code (Abaqus/Standard) and, in particular, since only the initial elastic part of the force vs displacement was to be reproduced, static analyses have been carried out. A first comparison of the experimental data and the numerical results is presented in Fig. 7 for the NPC test. The average experimental slope of the force vs displacement curves (i.e. the sublaminate stiffness) is compared with the result of the FE model of the corresponding average specimen (average dimensions and
average initial crack length) characterized with an elastic modulusE11 ¼ E1f . The value of E1f is the one obtained in case of a straight insert front (the insert, NPC) reported in Fig. 6. The comparison in Fig. 7 shows that the results of the numerical simulations reproduce exactly the experimental stiffness values for both material systems. Conversely, if the same E11 value is assumed when the simulation of the PC test is performed, the results shown in Fig. 8 are obtained, which suggest that something is not perfectly reproduced. The difference between the numerical and the experimental results can be attributed to two different causes: the assumption of a straight crack front (whose length is the one measured at the end of the NPC test, on the side of the specimen) and the hypothesis that the material around the crack front has not undergone any constitutive degradation. It is well-known [25] that the strain energy release rate distribution along the delamination front in a DCB specimen is not constant, but has a minimum on the sides and a maximum in the center of the specimen (half-width). So, the measurement based on the tip position on the specimen side is underestimating the length,
Fig. 8. Slope of the force vs displacement curves in Precrack tests: experimental average compared to numerical results.
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Fig. 9. Critical fracture toughness evaluated with the NL and 5%/MAX criteria.
Fig. 10. Critical fracture toughness evaluated with the NL and 5%/MAX criteria.
because the “effective” length is a little longer. Moreover, the start of the delamination growth is associated with some damage in the areas close to the front which has the effect of a further reduction of the specimen stiffness, i.e., the constraint, ideally conceived at the crack tip, becomes more compliant. So, the experimental slopes have two good reasons for being lower than expected. 6. Data reduction results: critical fracture toughness According to the data reduction methodology summarized in Equations (2)e(4), the values of the interlaminar fracture toughness depend on the critical point that has been selected in the test. Figs. 9 and 10 compare the critical fracture toughness obtained for both material systems in pure modes and mixed modes, respectively, evaluated for the NL and for the 5%/MAX critical point. In both pure modes, the UD specimens exhibit similar Gc values, independently of the criterion used to define the critical condition, either the NL or the 5%/MAX. A similar comment is also valid in pure mode I for the fabric material system, which anyhow shows
much higher GIc values, due to the complex damage mechanisms that are active in the fabric material [10e12]. Some fractographic observations, giving evidence of these phenomena, will be shown later. Conversely, for pure mode II tests, the fabric material system (Fig. 9, right) shows that the 5%/MAX criterion leads to values of GIIc that are remarkably higher than those obtained by using the NL criterion. This difference is explained by noting that the force vs displacement curves obtained for pure. Mode II tests (see Fig. 3) exhibit a relatively short linear part, the plot deviates early from linearity, while the critical load level (associated with unstable crack propagation) is still far away. So, the two critical load P values differ significantly, and consequently also the GIIc values. Fig. 10 shows the results obtained in the tests carried out with mode mix ratios B equal to 0.33 and 0.67. Also for these load conditions, the two critical point criteria (NL and 5%/MAX) produce almost identical results in the UD specimens, in terms of critical fracture toughness. The results of the fabric specimens point out completely
Fig. 11. Critical fracture toughness vs mode mix according to different criteria.
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pure mode I the fabric material system presents values of Gc that are relevantly greater than those obtained for B ¼ 0.33. This result could appear as a surprising one but, in literature, similar results have already been reported on fabric materials. For instance, Czabaj and Davidson [16] have found a similar drop in mixed-mode fracture toughness data in carbon/polyimide fabric. In the same work, fractographic analyses did now show any damage mechanisms that could be considered responsible for this phenomenon. Further investigations are currently in progress on this issue. 7. Fractographic examination
Fig. 12. Evidence of fibre failure due to bridging occurrence in the horizontal yarn (upper side) and also fiber failure in the vertical direction.
different mechanical behaviours (see Figs. 4 and 5) compared to the UD specimens. The force is initially linear up to a point where the delamination starts to grow, then the load keeps on increasing with reduced slope together with a slow propagation of the crack until the maximum load is reached (then, the loading phase is interrupted and the specimen is unloaded). The significant differences between the NL and the 5%/MAX forces cause similar differences in the critical fracture toughness, as reported in Fig. 10. Eventually, the results of the Gc values obtained for pure and mixed modes are plotted in Fig. 11 for the two material systems. The results obtained with the VIS criterion have been added: such values have been determined by examining the specimen lateral side pictures, and identifying the first crack growth increment, typically between 0.5 and 1.0 mm. In general, for the tests on the UD specimens, the VIS criterion produces load values intermediate between the other two criteria or, in any case, values that are close to each other. Differently, the tests carried out on the fabric specimens show that the VIS criterion leads to load values that, in case of presence of mode II, are greater than the ones obtained with the other criteria. The analysis of the relationship between Gc and mode mix ratio highlights that for the UD specimens the value of Gc is monotonically growing between pure mode I and pure mode II. The trend is consistent with literature results and is well approximated by the Benzeggagh-Kenane law [26], also shown by the dotted curve in Fig. 11 (left). The results obtained on the fabric specimens point out that for
A few pictures have been taken at a SEM (Jeol JSM 5600 LV), available at the Department of Civil and Industrial Engineering of the University of Pisa, for evidencing the peculiarities of damage accumulation in DCB fabric coupons. To this end, two DCB samples have been fully opened, after completion of the test, and prepared for low magnification observation. In all the figures, the delamination grew from the lower part to the upper part of the figure. Fig. 12 shows a region characterized by a number of failure modes, with evidence in detail of broken transversal fibres, due to bridging; the two halves of the coupons were juxtaposed side-byside, each one giving a mirror image of the other. Two higher magnification images from Fig. 12 are shown in Fig. 13, one from the left side (a) and the other from the right side (b): the energy absorption phenomenon of fibre failure is clearly evidenced, together with debonding of fibre bundles from the opposite surface. Another example of a picture with a general view of the fracture surface is shown in Fig. 14, with again a number of broken fibres in both directions, plus evidences of matrix rich areas, that offer a reservoir for energy during fracture. 8. Conclusions The same carbon/epoxy composite material system was available in the form of unidirectional tape and of 5-harness satin; it was considered interesting to evaluate the differences in the interlaminar fracture toughness. According to the literature on the subject, the damage mechanisms are quite different and consequently also interlaminar fracture toughness. The purpose of this paper was to assess quantitatively these differences and provide some deeper insight on the behaviour of the fabric material, e.g. by means of some simple fractographic analysis. To this end, an experimental program has been carried out with DCB, ENF and MMB specimens and the results have confirmed the significantly different behaviour between the two forms of the same material. To make a more meaningful comparison of the
Fig. 13. Magnifications of SEM image in Fig. 12, with evidence of fractured fibres and debonded vertical bundles.
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D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
Fig. 14. On the left side, resin rich areas in correspondence with crossing of fabric weft and fill with evidence of fibre failure in the horizontal bundle (left) and detail (right) with evidence of resin volumes and fibre failure.
various G values, it has been necessary to define a data reduction method that could be unique for the various tests. The choice has fallen on the Williams formulation, that has the merit of being fully numerical, and independent on measured parameters in the test; this is important, because the mode I ASTM standard proposes three methods for assessing the toughness but each one depends on a different experimental correction parameter, to be measured during the test. The test results from DCB allow also some deeper insight, by means of focused numerical activities: the first part of the test consists in a pre-cracking operation, to introduce a natural delamination in the specimen. The material is pristine and the delamination front is straight, namely the end of the insert: a simple case to analyse and a very good agreement is obtained between the numerical and the experimental tests. On the contrary, the second part of the test is performed on a “natural” delamination, with a curved front and in presence of some damage introduced at the tip, for “crack initiation”. The real situation is not easy to model and the experimental stiffness remains a bit lower than expected on the numerical model based on the bending modulus evaluated in the NPC test. This means that while for the NPC test the flexural modulus can be correctly assumed as the average elastic modulus of the material, when a natural crack growth occurs it is fundamental to reproduce correctly the front shape as well as the degradation of the material ahead of the delamination front. The results show clearly the higher interlaminar fracture toughness exhibited by the fabric system; the reasons for such behaviour are not only the larger resin volume present in the interface (due to the non-flat interfaces) but also a number of other damage mechanisms that are active in fabric and not in unidirectional materials. For instance, for mode I tests and with reference to the NL point, the Williams relationship provides an average value of GIc equal to 267.0 J/m2 for the unidirectional material, and of 673.3 J/m2 for the 5H satin style. A low magnification analysis at SEM of the fracture surfaces of fabric DCB specimens has easily shown a number of debonded and/or fractured fibres and presence of bridging of transversal bundles, all mechanisms absent or rare in unidirectional materials and capable of absorbing a substantial quantity of energy. Very good fractographic documentation in fabric materials can be found in Refs. [6,10,11]. In the ENF and MMB tests, the fabric system shows a peculiar behaviour, due to the early onset of the non-linearity condition, rather anticipated with respect to the maximum force values. This makes the use of the NL values (a conservative procedure) too pessimistic. Finally, the Benzeggagh-Kenane relationship, highly diffused for unidirectional systems, seems questionable for fabric, because the mode I critical value remains higher than the one relevant to the
2:1 mixed mode condition, and almost equal to the one corresponding to the 1:2 condition. Further investigations on the failed specimens are in progress. References [1] T.K. O'Brien, Characterization of delamination onset and growth in a composite laminate, in: K.L. Reifsnider (Ed.), Damage in Composite Materials, ASTM, 1982, pp. 140e167. STP 775. [2] R.S. Whitehead, Certification of primary composite aircraft structures, in: D.L. Simpson (Ed.), New Materials and Fatigue Resistant Aircraft Design, Proceedings of the 14th Symposium of the International Committee on Aeronautical Fatigue, EMAS publ., 1987, pp. 585e617. [3] MIL-HDBK-17-3F, Composite material handbook, in: Polymer Matrix Composite Materials, 3, U.S. Department of Defence, 2002. [4] T.K. O'Brien, M. Rigamonti, C. Zanotti, Tension Fatigue Analysis and Life Prediction for Composite Laminates, NASA, 1988. TM100549. [5] M. Caslini, C. Zanotti, T.K. O'Brien, Fracture Mechanics of Matrix Cracking and Delamination in Glass Epoxy Laminates, NASA, 1986. TM 89007. [6] J.G. Funk, J.W. Deaton, The Interlaminar Fracture Toughness of Woven Graphite/Epoxy Composites, NASA, 1989. TP2950. [7] ASTM 5528-01, Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-reinforced Polymer Matrix Composites, ASTM annual book of Standards, 2001. [8] A.B. de Morais, M.F. de Moura, A.T. Marques, P.T. de Castro, Mode-I interlaminar fracture of carbon/epoxy cross-ply composites, Compos. Sci. Technol. 62 (2002) 679e686. [9] A.B. Pereira, A.B. de Morais, Mode-I interlaminar fracture of carbon/epoxy multidirectional laminates, Compos. Sci. Technol. 64 (2004) 2261e2270. [10] Y. Wang, D. Zhao, Characterization of interlaminar fracture behaviour of woven fabric reinforced polymeric composites, Composites 26 (1995) 115e124. [11] P. Suppakul, S. Bandyopadhyay, The effect of weave pattern on the mode-I interlaminar fracture energy of E-glass/vinyl ester composites, Compos. Sci. Technol. 62 (2002) 709e717. [12] N. Alif, L.A. Carlsson, L. Boogh, The effect of weave pattern and crack propagation direction on mode I delamination resistance of woven glass and carbon composites, Compos. Part B 29B (1998) 603e611. [13] N. Alif, L.A. Carlsson, J.W. Gillespie Jr., Mode I, mode II, and mixed mode interlaminar fracture of woven fabric carbon/epoxy, in: S.J. Hooper (Ed.), Composite Materials: Testing and Design, Thirteenth Volume, ASTM, 1997, pp. 82e106. STP 1242. [14] A.B. Pereira, A.B. de Morais, M.F.S.F. de Moura, A.G. Magalhaes, Mode I interlaminar fracture of woven glass/epoxy multidirectional laminates, Compos. Part A 36 (2005) 1119e1127. [15] R.H. Martin, Delamination characterization of woven glass/polyester composites, J. Compos. Tech. Res. 19 (1997) 20e28. [16] M.W. Czabaj, B.D. Davidson, Determination of the mode I, mode II, and mixedmode I-II delamination toughness of a graphite/polyimide composite at room and elevated temperatures, J. Compos. Mater. 50 (2016) 2235e2253. [17] ASTM D 7905e14, Standard Test Method Determination of the Mode II Interlaminar Fracture Toughness of Uni-directional Fiber Reinforced Polymer Matrix Composites, ASTM annual book of Standards, 2014. [18] ASTM D 6671e04, Standard Test Method for Mixed Mode I - Mode II Interlaminar Fracture Toughness of Uni-directional Fiber Reinforced Polymer Matrix Composites, ASTM annual book of Standards, 2004. [19] T.K. O'Brien, G.B. Murri, S.S. Salpekar, Interlaminar Shear Fracture Toughness and Fatigue Thresholds for Composite Materials, NASA, 1987. TM89157. [20] T.K. O'Brien, W.M. Johnston, G.J. Toland, Mode II Interlaminar Fracture Toughness and Fatigue Characterization of a Graphite Epoxy Composite Material, NASA, 2010. TM-2010e216838.
D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29 [21] J.R. Reeder, J.H.J. Crews, Redesign of the Mixed-Mode bending delamination test to reduce nonlinear effects, J. Compos. Tech. Res. 14 (1992) 12e19. [22] S. Bhashyan, B.D. Davidson, Evaluation of data reduction methods for the mixed-mode bending test, AIAA J. 35 (1997) 546e552. [23] J.G. Williams, End corrections for orthotropic DCB specimens, Compos. Sci. Technol. 35 (1989) 367e376. [24] Y. Wang, J.G. Williams, Corrections for Mode II fracture toughness specimens
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of composite materials, Compos. Sci. Technol. 43 (1992) 251e256. [25] J. Schon, T. Nyman, A. Blom, H. Ansell, A numerical and experimental investigation of delamination behaviour in the DCB specimen, Compos. Sci. Technol. 60 (2000) 173e184. [26] M.L. Benzeggagh, M. Kenane, Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixedmode bending apparatus, Compos. Sci. Technol. 56 (1996) 439e449.
Contents lists available at ScienceDirect
Composites Science and Technology journal homepage: http://www.elsevier.com/locate/compscitech
Experimental characterization of the interlaminar fracture toughness of a woven and a unidirectional carbon/epoxy composite D. Fanteria a, L. Lazzeri a, *, E. Panettieri a, U. Mariani b, M. Rigamonti b a b
Department of Civil and Industrial Engineering, University of Pisa, Via G. Caruso 8, 56122, Pisa, Italy Leonardo Helicopter Division, Via Giovanni Agusta 520, 21017, Cascina Costa di Samarate, Varese, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 December 2016 Received in revised form 27 January 2017 Accepted 28 January 2017 Available online 2 February 2017
An experimental program has been carried out at the University of Pisa, in collaboration with Leonardo Helicopter Division, to investigate the differences in interlaminar fracture toughness properties of a graphite/epoxy composite material, available in two forms: unidirectional tape and five harness satin fabric. To this end, tests have been carried out in mode I, mode II and mixed I þ II mode on specimens manufactured with the two material systems by Leonardo HD, following their industrial standards. The results show a considerably higher toughness of the fabric, as a consequence of the peculiar features at the delamination interface and of the other local mechanisms, capable of absorbing energy, that are present only in fabric composites. Some fractographic observations confirm these mechanisms. Finally, numerical analyses have been carried out, modelling with Finite Element the various tests, to complement and evaluate the data reduction methods used to derive the toughness values. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Polymer-matrix composites (PMCs) Fabrics/textiles Fracture toughness Delamination Fractography
1. Introduction Application of advanced composite materials to aircraft primary structures is continuously growing, and projects like the Boeing 787 and the Airbus A350 XWB in the field of commercial aeroplanes are striking examples of how far current technology can extend. Further developments are in progress in the areas of low cost processes or inclusion of sensors to obtain multifunctional materials, so that predictions are in favour of a wide increase in applications in future aeronautical programs. At present, the main design requirements that must be accomplished by most composite structural applications are relevant to either stiffness, static strength or resistance to low energy impact damage. Similar considerations also hold for the helicopter world, where composite parts must account for challenging loading spectra. In order to avoid structural problems in service, current design procedures have led to the adoption of rather low allowable strain levels. In the certification process, durability and damage tolerance criteria
* Corresponding author. E-mail addresses: [email protected] (D. Fanteria), [email protected] (L. Lazzeri), [email protected] (E. Panettieri), ugo.mariani@ leonardocompany.com (U. Mariani), [email protected] (M. Rigamonti). http://dx.doi.org/10.1016/j.compscitech.2017.01.028 0266-3538/© 2017 Elsevier Ltd. All rights reserved.
require composite structures containing undetected damage to be acceptable to fly. Comparing different types of damage, inadvertently introduced during manufacturing or induced in service, delamination growth is considered one of the most important failure mechanisms that can be detrimental for flight safety and consequently, delaminations must be considered not only in the design process, but also in structural verification testing. Delamination growth can occur as a consequence of interlaminar stresses and possible situations that may induce such undesired stresses are quite numerous: local buckling, free edges and notches such as holes, ply drops, impact damage or, in complex structures, unanticipated outof-plane loading. It is important therefore to improve the knowledge of delamination growth both theoretically and experimentally. The helicopter community pioneered investigations about how to approach the delamination problem; early works by O'Brien, related to free edge delamination in tension loaded structures date back to the 80-ies [1], and the use of fracture mechanics was fostered, with the strain energy release rate identified as the parameter most suitable for strength and stability analysis. Since then, a flood of papers have been published on delamination experiments and analysis, but nevertheless the certification process remains very expensive and time consuming, because it is
D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
based on the so-called building block approach [2] or test pyramid [3]. Therefore, currently there is a great interest in the development and refinement of prediction methods for reducing time and costs of assessments and for evaluating, on a rational basis, problems like: second/alternative material supplier, manufacturing discrepancies, transfer of production from a plant to another, etc. This paper stems from a collaboration between the University of Pisa (UP) and Leonardo Helicopter Division (formerly AgustaWestland), a helicopter manufacturer that is involved in research activities in this field since the early times [4,5]. The interest is in the study of rotor area materials, and is focused on the characterization of interlaminar fracture resistance of a carbon/epoxy system, available in two forms: 5 harness satin fabric and unidirectional tape. Experiments have been carried out for the assessment of interlaminar fracture toughness in various conditions (mode I on DCB specimens, mode II on 3ENF coupons and mixed I þ II conditions using the MMB procedure). The carbon/epoxy materials, provided by Leonardo HD, are commonly used in the helicopter rotor area and are manufactured from Hexcel prepregs: they are a 8552S/AGP280 woven fabric in the 5-harness satin style and a unidirectional 8552/AS4 tape. This choice was not unintentional, as the two materials share essentially the same constituents: the AGP280 fabric is made out of AS4-3K rows and according to Hexcel literature no practical differences exist between 8552 and 8552S resins. There is a strong interest in comparing the two systems, since recently there have been substantial efforts towards the introduction of fabrics in composite structures because of easier handling and lay-up processing than for unidirectional tape laminates. In addition, woven fabric composites are more damage tolerant in the presence of a delamination. The reasons for this better behaviour are in the nonplanar interply structure of woven fabric composites, so that a delamination, if present, will interact with matrix rich regions and the weave structure during its propagation; this interaction will increase material toughness significantly. 2. Literature review about interlaminar fracture toughness differences between unidirectional and fabric composite materials In the literature about fracture toughness of fabric composites, a number of papers discuss the influence of the style at the delamination interface on the interlaminar toughness. Indeed, Funk and Deaton make a systematic analysis on the mode I fracture toughness of DCB coupons, made in 4 different styles [6] and show how the different structure at the interface (in particular presence of cooriented fibers on opposite faces) strongly influences the toughness. Their work moves from the results of the many studies carried out on multidirectional DCB specimens, where the interface may change from the 0/0 of the standard ASTM coupons [7] to other combinations (e.g. q/0 or q/-q or others). This is a more realistic situation, while the 0/0 interface of the standard specimens is rather unusual to be critical in real structures. It was noted that the 90/90 interface resulted in a delamination path that strongly interacted with other damage mechanisms, such as matrix cracks, giving rise to continuous jumps from the upper interface with a non-90 ply to the lower one, and vice versa, absorbing substantially higher energy (see also [8,9]). Ref. [6] discusses the cases of symmetric and asymmetric yarn disposition at the interface, considering anyhow also situations that are not common in engineering practice. For instance, a 5H satin shows a different appearance if seen from one side or from the other: in one case, 80% of yarns are oriented in one direction and 20% in the other, while on the opposite face the ratio is reciprocal, 20% and 80%. It is evident that
21
the interface plays a fundamental role: the situation of two mirror plies interface is evidently quite different from the situation of two equi-oriented plies stacked one on the other. A number of papers available in the literature are relevant to studies on fabric DCB specimens that refer to very specific interfaces, sometimes deliberately particular, that are anyhow unusual as well, in the same measure of the 0/0 interface [10,11]. In this experimental activity, it was decided to address the most frequent case, commonly used in the engineering practice, i.e. the one of a lay-up made of equally oriented plies stacked one over the other. Therefore the fabric specimens were manufactured by stacking 16 plies, equally oriented: this is the most realistic sequence. Therefore, at the delamination interface, the two neighbouring plies offered faces with different characteristics (one with prevailing longitudinal yarns and the other with prevailing transversal yarns), so that the probability of matching equally oriented bundles was intermediate between the extreme cases studied in the literature: the too optimistic, and therefore unconservative, case of complete overlap of the transversally oriented yarns is thus avoided. Too optimistic means that, according to fractographic observations [10,11], there are many failure mechanisms active during the delamination growth in a fabric DCB, and among others the debonding of 90-degrees oriented bundles is particularly helpful in absorbing energy, but also fiber failure, fiber pull-out, fracture of matrix resin, matrix plastic deformation and delamination front deflection are active mechanisms. Significant examples of test data publication, supported by fractography and failure analysis, can be found in papers by Alif, Carlsson and Boogh [12], Alif, Carlsson and Gillespie [13], Pereira and others [14] and Martin [15]. Recently (2016) Czabaj and Davidson [16] have published an experimental work on the influence of temperature on the interlaminar fracture properties of a fabric carbon/polyimide system; obviously, with such a matrix, the objective of the paper was the study of the influence of the temperature (up to 300 C) on the interlaminar fracture toughness expressed by that material, but an interesting literature review on fabric interlaminar toughness peculiar behaviour, substantially very similar to the one performed in the present work, completes the paper. On the contrary, the main fracture mechanisms in unidirectional laminated composites are fibre debonding and matrix plastic deformation. The observation of other failure modes supports the general finding that 2-D woven fabric laminates show substantially higher interlaminar fracture resistance than unidirectional laminates. 3. Experimental program The experimental program comprised different kinds of tests, i.e. Mode I on DCB specimens, Mode II on ENF specimens tested in three point bending and mixed mode I þ II using the Mixed Mode Bending procedure. All of these are covered by ASTM standards, with the mode II procedure that has been published very recently, after the beginning of the experimental activity of this paper. The available ASTM standards [7,17,18] anyhow refer to unidirectional composite systems; in the case of the fabric system, the same approach has been used, even if some adjustments are necessary (e.g. requirement on the specimen thickness, to maintain the applicability of small deformation theory). A representation of the three tests is shown in Fig. 1. Moreover, the characterization of the same material system at different fracture modes (Mode I, Mode II and Mixed I þ II modes) points out the problem of having uniformity among the data reduction methods which are different between Mode I, Mode II and Mixed I þ II mode fracture tests.
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D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
Fig. 2 shows the force vs displacement curves obtained for the UD and fabric DCB specimens. The curves of the UD specimens show that a good replicability exists in the linear part of the curve while, after the beginning of the crack propagation, two distinct levels at which the propagation occurs can be observed. The DCB results from the fabric material system show a small dispersion of the data in the linear part of the curves while the propagation curves are affected by failure phenomena that produce alternating growth and drop of the load during the crack propagation. This failure behaviour is typical of fabric material systems since the presence of both a non-uniform inter-laminar layer and bridging phenomena modify the crack propagation patterns. 3.3. Mode II tests
Fig. 1. Schemes of the DCB, ENF and MMB tests.
3.1. Materials A 5 harness satin fabric was used, Hexcel 8552S/37%/AGP280, to manufacture coupons, made of 16 layers for a typical thickness of about 4.5 mm (nominal ply thickness: 0.28 mm). The fibres were AS4 3K, with equal dimension of yarns in both directions, weft and fill. The other material system investigated was unidirectional graphite/epoxy, Hexcel 8552/34%/AS4, with each layer having a nominal thickness of 0.125 mm; the relevant coupons were manufactured stacking 24 plies, for a specimen thickness of around 3 mm. 3.2. Mode I tests These tests were carried out following the ASTM standard [7], even if it clearly states that it is applicable only to UD materials. The specimens were 150 mm long and 25 mm wide, and were tested in a servo-hydraulic machine built by A.I.P. Studio (Varese, Italy) interfaced with a digital controller. The load cell had a capacity of 200 N and the tests were carried out in displacement control, with a rate of 1 mm/min. The load cell and the displacement transducer of the machine allowed the measurement of load and displacement (twenty data per second) while an industrial camera (by The Imaging Source GmbH, resolution 960 1280 pixels) took pictures of the side of the specimen at regular intervals (one per second). Thus, the correlation between the crack length and the values of load and displacement allowed the estimation of Gc. The method used for data reduction will be discussed later.
A three point ENF test was used, with a 100 mm total span length. After years of discussions, ASTM has issued only recently a standard procedure, [17]. It is based on the use of the Compliance Calibration method to define the compliance derivative with respect to delamination length, a method that does not rely on an artificial correction to the delamination length, but makes use of a dC/da derivative determined from experimental measurements carried out on the same ENF specimen (and not in a DCB specimen, obviously of the same batch). Moreover, a debate has been active for a long time about the opportunity of initial precracking ([19,20]), because toughness values evaluated from a natural delamination are significantly lower than those generated by tests without precracking, i.e. with delamination starting directly from the insert. Another advantage of the procedure [17] is that it allows the possibility to assess the fracture toughness from the insert and from a natural delamination. Therefore, since the data generated was also used for design purposes, before the test all the ENF specimens were subjected to a precracking operation, performed in three point bending but with a total distance between the supports of 50 mm. The specimens were positioned on the loading frame in such a way to leave a distance of about 3e4 mm between the end of the insert and the central load application point; then the specimens were loaded, similarly to a test. The growth of the natural delamination from the insert typically stopped under the load application point. In the subsequent real tests, carried out with total distance between the supports of 100 mm, the specimens exhibited mainly an unstable growth (delamination growth is stable for a/L > 0.7), characterized by a linear behaviour followed by a sudden load drop; therefore, no picture acquisitions were performed. The force vs displacement curves are shown in Fig. 3 for the two material systems. In both cases, the crack propagation is essentially unstable. All the plots exhibit a linear initial loading phase until slight non-linearities are observed, just before the load drops down. These non-linearities are more pronounced in the fabric
Fig. 2. Force vs displacement of the DCB tests.
D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
23
Fig. 3. Force vs displacement of the ENF tests.
material system, due to intrinsic reasons (the fibre yarns have a curved path, and so a natural tendency towards non linear behaviour, particularly under compression loads) and maybe also to friction effects. 3.4. Mixed mode tests Mixed mode tests, in I þ II combined modes, were carried out according to the Mixed Mode Bending (MMB) procedure, defined originally by Reeder and Crews [21] and later adopted by ASTM [18]. The test apparatus used for the tests has been manufactured and assembled in Pisa, on the basis of the recommendations suggested in the ASTM standard. The great advantage of this procedure is that the desired mode partition can be obtained easily, simply modifying the distance c between the force application axis and the intermediate 3 point bending fulcrum, as depicted schematically in Fig. 1. The mode ratios ðGI =GII Þ examined were 2:1 and 1:2 (or, alternatively, B ¼ GII =GTOT equal to 0.33 and 0.67), which corresponded to a lever length c of 59 mm and 33 mm, respectively. The tests were carried out with not-precracked specimens and the same data (load, displacement and crack length pictures) acquisition system of the DCB tests was used. Eventually, the ASTM standard suggests also to evaluate the compliance of the test setup, for those cases in which the displacement of the load application point is not measured directly, but by means of the actuator displacement transducer, that has the merit of being easily available; for this purpose, a very stiff false specimen, made of steel, 6 mm thick, was built and used in a simulated test, to evaluate the contribution (very small, indeed) of the test rig to the measured compliance. The results of the MMB tests of the UD and fabric specimens carried out at B ¼ 0.33 and B ¼ 0.67 are shown in Figs. 4 and 5, respectively, in terms of force vs. displacement plots. The two material systems show profound differences in the delamination
propagation phase. The tests on the UD specimens show that the crack growth phase is associated with a load decrease that, for B ¼ 0.33 (prevailing mode I), is basically stable while, for prevailing mode II conditions (B ¼ 0.67), is unstable with a sudden load drop followed by a stable propagation. Conversely, the MMB tests carried out on the fabric material system exhibit a linear curve, for both values of B, followed by a stable propagation phase where the load keeps on increasing even when the delamination grows. This unexpected behaviour can be attributed to a combination of bridging phenomena and friction effects which stabilize the crack propagation. 4. Data reduction methodology Among the possible reduction methods [22], in this paper the data reduction methods based on the crack length correction, developed by Williams et al. [23,24] and adopted in the ASTM standard of the MMB tests [18], has been used for mode I and mode II data analysis. This choice ensures that the same data reduction method is used when pure modes and mixed modes are compared. The crack length correction, which modifies the measured physical length in order to take into account local crack tip constraints that reduce the laminate stiffness, involves the factor c which is computed according to Equation (1).
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " pffiffiffiffiffiffiffiffiffiffiffiffiffiffi u # u E11 E11 E22 G 2 t where G ¼ 1:18 c¼ ; 32 11G13 1þG G13
(1)
and E11 and E22 are the Young moduli in the longitudinal and transverse direction and G13 is the shear modulus in 1e3 out-ofplane direction. The relationships between geometric data, material properties and crack length required for computing the critical fracture toughness values, GI (mode I), GII (mode II) and GMM (mixed modes),
Fig. 4. Force vs displacement of the MMB (B ¼ 0.33) tests.
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D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
Fig. 5. Force vs displacement of the MMB (B ¼ 0.67) tests.
are reported in Equations (2)e(4), respectively.
2 96P 2 a þ c 2t ; W 2 t 3 E1f
GI ¼
GII ¼
GI ¼
9P
2
(2)
5. Data reduction results: flexural modulus
t 2
a þ 0:42c 2 2W 2 t 3 E1f
;
(3)
2 2 9 P 2 ð3 c LÞ2 a þ c 2t 9P 2 ðc þ LÞ2 a þ 0:42c 2t ; G ¼ ; GMM II 2 W 2 t 3 E1f 2W 2 t 3 E1f
¼ GI þ GII ; (4) where a is the crack length, P is the critical load value, t is the thickness of the specimen, W is the specimen width, c is the lever length, L is the half-span length of the MMB test and E1f is the flexural modulus. The values of the flexural modulus, E1f , can be computed, for each type of test, using Equations (5)e(7).
Mode I : E1f ¼
3 64m a þ c 2t ; Wt 3
Mode II : E1f ¼
3 m 2L3 þ 3 a þ 0:42c 2t
Mixed mode : E1f
intersection between the experimental curve and a linear curve with a 5% reduced slope or the point in which the maximum force is attained (the event, between the two, that occurs first is selected).
Wt 3
(5)
;
(6)
The crack length correction, c, introduced in the beam theory to include the effect of a more compliant constraint in correspondence of the crack front, and the experimental slope, m, of the force vs displacement curve, influence, as reported in Equations (5)e(7), the value of the flexural modulus, necessary to evaluate the critical fracture toughness in pure and mixed modes. The DCB test allows for an interesting comparison of the effects of the relevant correction on the computation of the flexural modulus. In fact the DCB test is performed in two phases: preliminarily, a natural crack is created in the DCB specimen starting from the initial Teflon insert front; subsequently, the real test is carried out, with the specimen containing a natural delamination. In both phases, data regarding force, displacement and initial crack length is collected: hence, the bending modulus can be estimated in both conditions: the one of an artificial straight crack front (determined by the Teflon insert) and in the other case of the naturallydeveloped front. A comparison of the flexural moduli obtained in the two conditions is shown in Fig. 6, relevant to the DCB tests performed on the UD and fabric material systems. The results highlight that the difference between the flexural modulus computed in the pristine (No-Precrack, NPC) and precracked (Precrack, PC) condition is not negligible for both material systems. This difference can be explained by pointing out the fact
i h 3 3 8 a þ c 2t ð3c LÞ2 þ 6 a þ 0:42c 2t þ 4L3 ðc þ LÞ2 1 ; ¼ 2L2 Wt 3 m Csys
where m is the slope of the linear part of the force vs displacement curve obtained in the test and Csys is the compliance of the test apparatus (measured through an ad-hoc test). The ASTM standard [7] suggests three criteria to choose the critical point, characterized by a combination of delamination length, actuator displacement and applied force, P; in particular, this last parameter can be: non-linear (PNL ), visual (PVIS ) and 5%/ MAX (P5%=MAX ). The NL criterion involves the first point of the force vs. displacement curve that deviates substantially from linearity; the VIS criterion is based on the first advancement of the crack tip visually observed, while the 5%/MAX criterion evaluates the
(7)
that the initial NPC condition is characterized by a straight crack front and by lack of any type of damage or material degradation induced in the material. Yet, the values of E1f obtained with the PC specimens for both the material systems are smaller than those obtained in the NPC tests. To understand these discrepancies, a numerical 3D FE model of the DCB tests has been developed within the commercial FE software Abaqus, for both material systems, to reproduce both tests: the NPC and the PC test. The dimensions used to create the specimen models (UD and fabric) as well as the crack lengths were the average of the ones measured on the real specimens.
D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
25
Fig. 6. Average flexural moduli (error bars indicate standard deviations) obtained in DCB tests in the case of straight crack front (No-Precrack) and with a naturally developed crack (Precrack).
Fig. 7. Slope of the force vs displacement curves in No-Precrack tests: experimental average compared to numerical results.
To limit the computational costs of the FE analyses, only half of the specimen (in the longitudinal direction) was modeled and symmetric boundary conditions were applied. The specimen arms were modeled by means of solid elements (C3D8 elements): 12 elements along the thickness of each DCB arm were used, the width direction was discretized with 17 elements and, lastly, in the longitudinal direction a variable mesh size was assigned so that the mesh sizes were between 0.25 mm, around the crack tip, and 3 mm in the far ends of the specimen arms. To reproduce the hinges of the test, multi-point constraints were created between 2 reference points (one for each specimen arm) and the nodes of the corresponding specimen edges. The simulations were performed with the implicit solver of the FE code (Abaqus/Standard) and, in particular, since only the initial elastic part of the force vs displacement was to be reproduced, static analyses have been carried out. A first comparison of the experimental data and the numerical results is presented in Fig. 7 for the NPC test. The average experimental slope of the force vs displacement curves (i.e. the sublaminate stiffness) is compared with the result of the FE model of the corresponding average specimen (average dimensions and
average initial crack length) characterized with an elastic modulusE11 ¼ E1f . The value of E1f is the one obtained in case of a straight insert front (the insert, NPC) reported in Fig. 6. The comparison in Fig. 7 shows that the results of the numerical simulations reproduce exactly the experimental stiffness values for both material systems. Conversely, if the same E11 value is assumed when the simulation of the PC test is performed, the results shown in Fig. 8 are obtained, which suggest that something is not perfectly reproduced. The difference between the numerical and the experimental results can be attributed to two different causes: the assumption of a straight crack front (whose length is the one measured at the end of the NPC test, on the side of the specimen) and the hypothesis that the material around the crack front has not undergone any constitutive degradation. It is well-known [25] that the strain energy release rate distribution along the delamination front in a DCB specimen is not constant, but has a minimum on the sides and a maximum in the center of the specimen (half-width). So, the measurement based on the tip position on the specimen side is underestimating the length,
Fig. 8. Slope of the force vs displacement curves in Precrack tests: experimental average compared to numerical results.
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Fig. 9. Critical fracture toughness evaluated with the NL and 5%/MAX criteria.
Fig. 10. Critical fracture toughness evaluated with the NL and 5%/MAX criteria.
because the “effective” length is a little longer. Moreover, the start of the delamination growth is associated with some damage in the areas close to the front which has the effect of a further reduction of the specimen stiffness, i.e., the constraint, ideally conceived at the crack tip, becomes more compliant. So, the experimental slopes have two good reasons for being lower than expected. 6. Data reduction results: critical fracture toughness According to the data reduction methodology summarized in Equations (2)e(4), the values of the interlaminar fracture toughness depend on the critical point that has been selected in the test. Figs. 9 and 10 compare the critical fracture toughness obtained for both material systems in pure modes and mixed modes, respectively, evaluated for the NL and for the 5%/MAX critical point. In both pure modes, the UD specimens exhibit similar Gc values, independently of the criterion used to define the critical condition, either the NL or the 5%/MAX. A similar comment is also valid in pure mode I for the fabric material system, which anyhow shows
much higher GIc values, due to the complex damage mechanisms that are active in the fabric material [10e12]. Some fractographic observations, giving evidence of these phenomena, will be shown later. Conversely, for pure mode II tests, the fabric material system (Fig. 9, right) shows that the 5%/MAX criterion leads to values of GIIc that are remarkably higher than those obtained by using the NL criterion. This difference is explained by noting that the force vs displacement curves obtained for pure. Mode II tests (see Fig. 3) exhibit a relatively short linear part, the plot deviates early from linearity, while the critical load level (associated with unstable crack propagation) is still far away. So, the two critical load P values differ significantly, and consequently also the GIIc values. Fig. 10 shows the results obtained in the tests carried out with mode mix ratios B equal to 0.33 and 0.67. Also for these load conditions, the two critical point criteria (NL and 5%/MAX) produce almost identical results in the UD specimens, in terms of critical fracture toughness. The results of the fabric specimens point out completely
Fig. 11. Critical fracture toughness vs mode mix according to different criteria.
D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
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pure mode I the fabric material system presents values of Gc that are relevantly greater than those obtained for B ¼ 0.33. This result could appear as a surprising one but, in literature, similar results have already been reported on fabric materials. For instance, Czabaj and Davidson [16] have found a similar drop in mixed-mode fracture toughness data in carbon/polyimide fabric. In the same work, fractographic analyses did now show any damage mechanisms that could be considered responsible for this phenomenon. Further investigations are currently in progress on this issue. 7. Fractographic examination
Fig. 12. Evidence of fibre failure due to bridging occurrence in the horizontal yarn (upper side) and also fiber failure in the vertical direction.
different mechanical behaviours (see Figs. 4 and 5) compared to the UD specimens. The force is initially linear up to a point where the delamination starts to grow, then the load keeps on increasing with reduced slope together with a slow propagation of the crack until the maximum load is reached (then, the loading phase is interrupted and the specimen is unloaded). The significant differences between the NL and the 5%/MAX forces cause similar differences in the critical fracture toughness, as reported in Fig. 10. Eventually, the results of the Gc values obtained for pure and mixed modes are plotted in Fig. 11 for the two material systems. The results obtained with the VIS criterion have been added: such values have been determined by examining the specimen lateral side pictures, and identifying the first crack growth increment, typically between 0.5 and 1.0 mm. In general, for the tests on the UD specimens, the VIS criterion produces load values intermediate between the other two criteria or, in any case, values that are close to each other. Differently, the tests carried out on the fabric specimens show that the VIS criterion leads to load values that, in case of presence of mode II, are greater than the ones obtained with the other criteria. The analysis of the relationship between Gc and mode mix ratio highlights that for the UD specimens the value of Gc is monotonically growing between pure mode I and pure mode II. The trend is consistent with literature results and is well approximated by the Benzeggagh-Kenane law [26], also shown by the dotted curve in Fig. 11 (left). The results obtained on the fabric specimens point out that for
A few pictures have been taken at a SEM (Jeol JSM 5600 LV), available at the Department of Civil and Industrial Engineering of the University of Pisa, for evidencing the peculiarities of damage accumulation in DCB fabric coupons. To this end, two DCB samples have been fully opened, after completion of the test, and prepared for low magnification observation. In all the figures, the delamination grew from the lower part to the upper part of the figure. Fig. 12 shows a region characterized by a number of failure modes, with evidence in detail of broken transversal fibres, due to bridging; the two halves of the coupons were juxtaposed side-byside, each one giving a mirror image of the other. Two higher magnification images from Fig. 12 are shown in Fig. 13, one from the left side (a) and the other from the right side (b): the energy absorption phenomenon of fibre failure is clearly evidenced, together with debonding of fibre bundles from the opposite surface. Another example of a picture with a general view of the fracture surface is shown in Fig. 14, with again a number of broken fibres in both directions, plus evidences of matrix rich areas, that offer a reservoir for energy during fracture. 8. Conclusions The same carbon/epoxy composite material system was available in the form of unidirectional tape and of 5-harness satin; it was considered interesting to evaluate the differences in the interlaminar fracture toughness. According to the literature on the subject, the damage mechanisms are quite different and consequently also interlaminar fracture toughness. The purpose of this paper was to assess quantitatively these differences and provide some deeper insight on the behaviour of the fabric material, e.g. by means of some simple fractographic analysis. To this end, an experimental program has been carried out with DCB, ENF and MMB specimens and the results have confirmed the significantly different behaviour between the two forms of the same material. To make a more meaningful comparison of the
Fig. 13. Magnifications of SEM image in Fig. 12, with evidence of fractured fibres and debonded vertical bundles.
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D. Fanteria et al. / Composites Science and Technology 142 (2017) 20e29
Fig. 14. On the left side, resin rich areas in correspondence with crossing of fabric weft and fill with evidence of fibre failure in the horizontal bundle (left) and detail (right) with evidence of resin volumes and fibre failure.
various G values, it has been necessary to define a data reduction method that could be unique for the various tests. The choice has fallen on the Williams formulation, that has the merit of being fully numerical, and independent on measured parameters in the test; this is important, because the mode I ASTM standard proposes three methods for assessing the toughness but each one depends on a different experimental correction parameter, to be measured during the test. The test results from DCB allow also some deeper insight, by means of focused numerical activities: the first part of the test consists in a pre-cracking operation, to introduce a natural delamination in the specimen. The material is pristine and the delamination front is straight, namely the end of the insert: a simple case to analyse and a very good agreement is obtained between the numerical and the experimental tests. On the contrary, the second part of the test is performed on a “natural” delamination, with a curved front and in presence of some damage introduced at the tip, for “crack initiation”. The real situation is not easy to model and the experimental stiffness remains a bit lower than expected on the numerical model based on the bending modulus evaluated in the NPC test. This means that while for the NPC test the flexural modulus can be correctly assumed as the average elastic modulus of the material, when a natural crack growth occurs it is fundamental to reproduce correctly the front shape as well as the degradation of the material ahead of the delamination front. The results show clearly the higher interlaminar fracture toughness exhibited by the fabric system; the reasons for such behaviour are not only the larger resin volume present in the interface (due to the non-flat interfaces) but also a number of other damage mechanisms that are active in fabric and not in unidirectional materials. For instance, for mode I tests and with reference to the NL point, the Williams relationship provides an average value of GIc equal to 267.0 J/m2 for the unidirectional material, and of 673.3 J/m2 for the 5H satin style. A low magnification analysis at SEM of the fracture surfaces of fabric DCB specimens has easily shown a number of debonded and/or fractured fibres and presence of bridging of transversal bundles, all mechanisms absent or rare in unidirectional materials and capable of absorbing a substantial quantity of energy. Very good fractographic documentation in fabric materials can be found in Refs. [6,10,11]. In the ENF and MMB tests, the fabric system shows a peculiar behaviour, due to the early onset of the non-linearity condition, rather anticipated with respect to the maximum force values. This makes the use of the NL values (a conservative procedure) too pessimistic. Finally, the Benzeggagh-Kenane relationship, highly diffused for unidirectional systems, seems questionable for fabric, because the mode I critical value remains higher than the one relevant to the
2:1 mixed mode condition, and almost equal to the one corresponding to the 1:2 condition. Further investigations on the failed specimens are in progress. References [1] T.K. O'Brien, Characterization of delamination onset and growth in a composite laminate, in: K.L. Reifsnider (Ed.), Damage in Composite Materials, ASTM, 1982, pp. 140e167. STP 775. [2] R.S. Whitehead, Certification of primary composite aircraft structures, in: D.L. Simpson (Ed.), New Materials and Fatigue Resistant Aircraft Design, Proceedings of the 14th Symposium of the International Committee on Aeronautical Fatigue, EMAS publ., 1987, pp. 585e617. [3] MIL-HDBK-17-3F, Composite material handbook, in: Polymer Matrix Composite Materials, 3, U.S. Department of Defence, 2002. [4] T.K. O'Brien, M. Rigamonti, C. Zanotti, Tension Fatigue Analysis and Life Prediction for Composite Laminates, NASA, 1988. TM100549. [5] M. Caslini, C. Zanotti, T.K. O'Brien, Fracture Mechanics of Matrix Cracking and Delamination in Glass Epoxy Laminates, NASA, 1986. TM 89007. [6] J.G. Funk, J.W. Deaton, The Interlaminar Fracture Toughness of Woven Graphite/Epoxy Composites, NASA, 1989. TP2950. [7] ASTM 5528-01, Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Fiber-reinforced Polymer Matrix Composites, ASTM annual book of Standards, 2001. [8] A.B. de Morais, M.F. de Moura, A.T. Marques, P.T. de Castro, Mode-I interlaminar fracture of carbon/epoxy cross-ply composites, Compos. Sci. Technol. 62 (2002) 679e686. [9] A.B. Pereira, A.B. de Morais, Mode-I interlaminar fracture of carbon/epoxy multidirectional laminates, Compos. Sci. Technol. 64 (2004) 2261e2270. [10] Y. Wang, D. Zhao, Characterization of interlaminar fracture behaviour of woven fabric reinforced polymeric composites, Composites 26 (1995) 115e124. [11] P. Suppakul, S. Bandyopadhyay, The effect of weave pattern on the mode-I interlaminar fracture energy of E-glass/vinyl ester composites, Compos. Sci. Technol. 62 (2002) 709e717. [12] N. Alif, L.A. Carlsson, L. Boogh, The effect of weave pattern and crack propagation direction on mode I delamination resistance of woven glass and carbon composites, Compos. Part B 29B (1998) 603e611. [13] N. Alif, L.A. Carlsson, J.W. Gillespie Jr., Mode I, mode II, and mixed mode interlaminar fracture of woven fabric carbon/epoxy, in: S.J. Hooper (Ed.), Composite Materials: Testing and Design, Thirteenth Volume, ASTM, 1997, pp. 82e106. STP 1242. [14] A.B. Pereira, A.B. de Morais, M.F.S.F. de Moura, A.G. Magalhaes, Mode I interlaminar fracture of woven glass/epoxy multidirectional laminates, Compos. Part A 36 (2005) 1119e1127. [15] R.H. Martin, Delamination characterization of woven glass/polyester composites, J. Compos. Tech. Res. 19 (1997) 20e28. [16] M.W. Czabaj, B.D. Davidson, Determination of the mode I, mode II, and mixedmode I-II delamination toughness of a graphite/polyimide composite at room and elevated temperatures, J. Compos. Mater. 50 (2016) 2235e2253. [17] ASTM D 7905e14, Standard Test Method Determination of the Mode II Interlaminar Fracture Toughness of Uni-directional Fiber Reinforced Polymer Matrix Composites, ASTM annual book of Standards, 2014. [18] ASTM D 6671e04, Standard Test Method for Mixed Mode I - Mode II Interlaminar Fracture Toughness of Uni-directional Fiber Reinforced Polymer Matrix Composites, ASTM annual book of Standards, 2004. [19] T.K. O'Brien, G.B. Murri, S.S. Salpekar, Interlaminar Shear Fracture Toughness and Fatigue Thresholds for Composite Materials, NASA, 1987. TM89157. [20] T.K. O'Brien, W.M. Johnston, G.J. Toland, Mode II Interlaminar Fracture Toughness and Fatigue Characterization of a Graphite Epoxy Composite Material, NASA, 2010. TM-2010e216838.
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of composite materials, Compos. Sci. Technol. 43 (1992) 251e256. [25] J. Schon, T. Nyman, A. Blom, H. Ansell, A numerical and experimental investigation of delamination behaviour in the DCB specimen, Compos. Sci. Technol. 60 (2000) 173e184. [26] M.L. Benzeggagh, M. Kenane, Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixedmode bending apparatus, Compos. Sci. Technol. 56 (1996) 439e449.