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Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations
International Journal of Fatigue xxx (2015) xxx–xxx
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations q A.J. Brunner a,⇑, S. Stelzer b, G. Pinter b, G.P. Terrasi a a b
Laboratory for Mechanical Systems Engineering, Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600 Dübendorf, Switzerland Chair of Material Science and Testing of Polymers, Montanuniversity Leoben, Otto Glöckel-Strasse 2, A-8700 Leoben, Austria
a r t i c l e
i n f o
Article history: Received 25 December 2014 Received in revised form 21 October 2015 Accepted 27 October 2015 Available online xxxx Keywords: Carbon fiber reinforced polymer-matrix composites Cyclic delamination fatigue Test development Data analysis Composite structural design
a b s t r a c t Activities toward standardization of fracture mechanics tests on carbon fiber-reinforced polymer-matrix (CFRP) composites have recently focused on cyclic fatigue under mode I (tensile opening), mode II (in-plane shear) and mixed-mode I/II loading. Data from recent round robins performed by Technical Committee 4 (TC4) of the European Structural Integrity Society (ESIS) and from preliminary testing of additional CFRP epoxy laminates at the authors’ laboratories are analyzed with different approaches in attempts to reduce scatter and to identify parameters for CFRP structural design. Selected test data comparing load and displacement control for the cyclic fatigue tests are also discussed. Specifically, threshold values from Paris-law data fitting are compared with values from fitting with a modified Hartman–Schijve approach. Independent of the approach used for the analysis, mode I threshold values of selected CFRP seem to be in the range between about 30 and 100 J/m2, i.e., roughly around the range of critical mode I energy release rate values (denoted by GIC) obtained from fracture testing of neat commercial epoxy resins, but clearly below quasi-static initiation GIC-values for unidirectional CFRP composites. Implications for CFRP structural design based on mode I fatigue fracture mechanics test data are briefly discussed. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Fatigue delamination propagation in CFRP composite laminates is an important failure mechanism limiting the service life of composite structures and elements. There have been significant research efforts for characterizing delamination resistance or critical fracture toughness of CFRP laminates under quasi-static and cyclic fatigue load conditions [1,2]. However, these efforts so far only resulted in one standard test method, aiming at the determination of mode I delamination onset [3]. Test development for a standard procedure for determination of mode I fatigue delamination propagation is pursued by ESIS TC4 [4–6] and Committee D30.06 of the American Society for Materials and Testing (ASTM) [6,7]. ESIS TC4 also explores mode II and mixed mode I/II fatigue delamination propagation test development [2,8–10]. The development of standard test procedures involves technical aspects (e.g., defining test rig types and test parameter ranges) as well as scope and applicability (e.g., use of the test data). The q This paper was submitted for the special issue Fatigue at all Scales (ECF20 Fatigue). ⇑ Corresponding author. Tel.: +41 58 765 44 93; fax: +41 58 765 69 11. E-mail address: [email protected] (A.J. Brunner).
present contribution discusses a number of technical issues that are likely to be implemented in a future standard fatigue test procedure, but also highlights some issues relating to data analysis and to applying the test data in structural design with CFRP composites. 2. Experimental The materials used in this research were all CFRP composite laminates obtained from different suppliers (see acknowledgment). Carbon fiber types comprise G30-500 and IM7, the epoxy matrix types were R5276, 977-2 and 8552. Fatigue delamination propagation and reference values from quasi-static delamination tests for comparison with the cyclic fatigue data were obtained for mode I according to [11,12], i.e., the so-called Double Cantilever Beam (DCB) test, for mode II according to [13], i.e., the so-called Clamp-Calibrated End-Loaded Split (C-ELS) test, and for mixed mode I/II (GI/IIC) according to a draft procedure under development within ESIS TC4. This latter procedure, the so-called Fixed-Ratio Mixed mode I/II (FRMM) test is essentially based on the C-ELS test rig [13], but with the specimen and load application point, respectively, inverted. This test rig then yields a constant ratio of the mode I to the mode II component of 4:3, see, e.g., [1,14] for details.
http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025 0142-1123/Ó 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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Tests were performed on either servo-hydraulic test machines (from Material Testing Systems type MTS 858 with a 15 kN load cell calibrated to a load range from 0 to 400 N, or from Instron type 1273 with a 1 kN load cell calibrated in the range of 0–200 N) or on an electro-mechanical test machine (type Instron ElectroPuls E3000 with a load cell range of 250 N) with cross-head speeds of 2 mm/min for the quasi-static test and at a frequencies of 3, 5 or 10 Hz with a R-value of 0.1 for the cyclic delamination fatigue tests. Machine data comprising maximum load and displacement were recorded every 500 or 1000 cycles in the cyclic delamination fatigue tests and for selected tests, these data were recorded for every cycle. Nevertheless, cyclic tests were stopped from time to time for visual determination of the delamination lengths (using a traveling microscope with magnification of 10 or 16), in order to correlate visual observation with compliance based delamination length. 3. Results and discussion 3.1. Overview The data and test results shown and discussed below were chosen with the intention to highlight selected issues in the analysis of cyclic fatigue delamination tests on CFRP epoxy composites and to point out potential problems when using the delamination fatigue data for design of composite structures. The first example discusses difficulties encountered when using load control rather than displacement control under mode I cyclic fatigue loading. This complements the data and discussion presented in [10]. The second example then compares Paris type data obtained from cyclic mode I, mode II and FRMM I/II with an alternative data analysis based on a modified Hartman–Schijve approach recently developed by Jones et al. [15,16]. The third example finally looks at cyclic delamination fatigue under mode I loading where data analysis and fitting is based on recording every load cycle rather than on selected data points (typically every 500 or 1000 cycles) as in the two previous examples. 3.2. Load control of delamination fatigue under mode I Ref. [10] had presented and discussed cyclic delamination fatigue tests and their analysis under mode I loading performed either under displacement or load control on a servo-hydraulic test machine (type MTS 858) both with R-values of 0.1. Fig. 1 shows the respective load and displacement values (selected data points recorded every 1000 cycles) as a function of cycle number for G30-500/R5267 CFRP laminates. From Fig. 1, it is obvious that in
the case presented here, displacement control is stable and results in a continuously decreasing load with increasing delamination length. There is clearly some scatter in the measured load data which requires smoothing or fitting for data analysis. In the case of load control, the load values are less stable (relative to the set value around 50 N) and the scatter tends to increase with increasing displacement. The corresponding displacement values seem to increase without much scatter, but if the scale of the plot is reduced, there is a behavior analogous to that observed for the load signal under displacement control. It has to be noted that the machine load control in this specific example (machine type MTS 858) may not have been optimal yet. However, there is another issue with load control that, from a practical point of view, deserves attention. Independent of whether the test is started from a film insert in the specimen or from a mode I precrack, an initial load value has to be chosen. If this value is chosen too high, the displacement will rapidly increase and the specimen may fail after a relatively low number of fatigue cycles. This will result in few data points for the analysis and the determination of the Paris-type plot. Specifically, analyzing the low load and delamination length increment per cycle range (i.e., in the near threshold regime) will not be possible. On the other hand, if the value is chosen too low, it may take many cycles (and hence test time) for the delamination to start propagating. This is the main problem in a cyclic fatigue test for the determination of delamination onset, e.g., according to [3]. One example for a load value below the delamination onset regime is shown in Fig. 2. For determining the appropriate value of displacement for displacement controlled fatigue delamination tests, it suffices to perform a quasi-static test, stop after a short precrack length and then use the last displacement value for machine control. Load controlled fatigue delamination, even if run at an appropriate load level, has also indicated a problem in data analysis. A previous study [6] on fatigue delamination analysis of round robin data on three different CFRP laminates using displacement control had indicated that using a power law fit for the load data points yielded reasonably smooth data. This approach resulted in less scatter than interpolating approaches, such as e.g., the (2n + 1)point polynomial method (n any integer between 2 and 4) described in [17]. For the load control data, however, the power law fitting approach (in this case applied to the crack length data) did not yield a reasonable fit to the experimental data as shown in Fig. 3. Fig. 4 shows another example of a load control mode I cyclic fatigue delamination test. The load signal clearly indicates significant scatter (about ±1 N at typical loads of about 40 N). The respective displacement is increasing roughly linearly, resulting in a roughly linear increase in calculated crack length
Fig. 1. Load and displacement values from cyclic delamination fatigue testing of a carbon–fiber epoxy composite (G30-500/R5276) under mode I tensile opening load; (left) displacement control, (right) load control.
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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An extrapolation of the visual data for G30-500/R5276 (Fig. 5 right hand side) from a displacement controlled test does not indicate a clear threshold, but at a value of da/dN of about 107 mm/cycle (0.1 nm/cycle, i.e., close to molecular dimensions) which could be taken as a physical limit of crack extension, GImax amounts to about 35 J/m2. This can be taken as an experimental estimate of a threshold value, Gthr. Similar values of GImax or Gthr for G30-500/ R5276 CFRP laminates are obtained from another extrapolation approach discussed in the next section. It is hence hypothesized that threshold values for CFRP epoxy laminates without toughening additives are rather low and possibly amount to a few tens of J/m2 at best. With similar extrapolation, toughened epoxy matrix resins (e.g., epoxy resin type 977-2) tend to yield somewhat higher values of Gthr (around 100 J/m2) as discussed below. In any case, this example illustrates some of the pitfalls and problems encountered with mode I fatigue delamination testing under load control and the related data analysis and evaluation. Fig. 2. Displacement versus load control, data have been analyzed with the sevenpoint averaging procedure according to [17]. The test results shown for specimens 1 and 2 under load control show indications of delamination arrest, since the da/dNrange is limited to about one decade for full range of GImax.
(from compliance calibration). At the end of the test, however, the compliance of the specimen increases rapidly. This can cause problems in load control and lead to inaccurately applied loads (see Fig. 4, load data around 44 and 46 N). With an appropriate choice of the machine load control settings, this problem can be solved. However, this may require trial tests for evaluating the machine settings before performing the fatigue delamination tests. In a trial and error approach, a combination of two exponential functions with different exponents seemed to fit the crack length for load controlled mode I delamination fatigue tests as a function of cycle number best [10]. The resulting Paris law type graphs derived from the power law fit of the load curve and from the two exponential fits is shown in Fig. 5 (left hand side). The solid line representing the data calculated from the power law fit, if assessed without considering the quality of the fitting and the visual data, seems to suggest a threshold value around 150 J/m2 setting in at relatively high delamination length increments da/dN around 104 mm/cycle. The data calculated from fitting crack length with two exponential curves, however, do not yield any indication of a threshold within the range tested in the experiment in agreement with the data points from visual observation.
Fig. 3. Power law fitting of displacement for the epoxy CFRP (G30-500 fiber, epoxy Rigidite 5276 matrix) tested under mode I cyclic fatigue fracture using load control indicating deviations between compliance data and power law fit at low and high crack lengths.
3.3. Fatigue delamination propagation under mode II and mixed mode I/II Fig. 6 summarizes results from quasi-static and fatigue delamination tests under different loading modes (mode I, mode II and FRMM I/II) for IM7/977-2 CFRP laminates. The graph on the left hand side in Fig. 6 shows the Paris-law type plot, whereas that on the right hand side shows the data represented by a modified Hartman–Schijve fitting [15], see Eq. (1):
2
3b
pffiffiffiffiffiffiffiffi7 6 pffiffiffiffiffi 6D GI D Gthr 7 da ffi7 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ D6 6 qffiffiffiffiffiffiffiffi 7 dN 4 GImax 5 1 A
ð1Þ
pffiffiffiffiffi where D, b and A are constants and D GI is defined in Eq. (2)
pffiffiffiffi pffiffiffiffi pffiffiffiffi GI ¼ GImax GImin
ð2Þ
The Paris-law type plot (Fig. 6 left) indicates that mode I is conservative in the sense that it yields the highest Gmax value (compared with mode II and FRMM I/II) at any given value of delamination length increment da/dN. The extrapolation indicates a threshold around 100 J/m2 setting in around 1–5 times 107 mm/cycle. However, the data for mode II (C-ELS) and the FRMM I/II also seem to converge to a similar threshold value in this presentation (even though the extrapolations are not shown). When discussing ‘‘conservative” values the example of AS4/poly-etherether-ketone (PEEK), a thermoplastic CFRP laminate where mode I is lower than mode II in delamination fatigue for all Gmax values in the Paris-type plot (and hence not conservative) should be pointed out. However, there is no evidence so far that this could also be the case for CFRP with thermoset matrix. On the other hand, the quasistatic fracture toughness values for AS4/PEEK under mode I are lower than those for mode II, please see, e.g., [9,18,19] for details on this. At this stage, it can only be speculated that the different behavior of more ductile thermoplastic versus more brittle thermoset matrix materials in CFRP (that has been shown to have a significant effect on damage accumulation in tensile fatigue tests, see, e.g., [20]) contributes to or results in this difference between quasi-static and fatigue fracture. Testing other thermoplastic CFRP laminates beside CF-PEEK in mode I and mode II fatigue fracture should yield more insight. Analyzing the data for G30-500/R5276 specimens tested under mode I delamination fatigue with displacement control (R-value = 0.1) at five laboratories [6] with the Hartman–Schijve fitting [15], the threshold values (Gthr) shown in Table 1 are
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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Fig. 4. (left) Load and displacement values from mode I delamination fatigue under load control and (right) corresponding delamination length increase.
Fig. 5. (left) Comparison of Paris-type plot for load control and fitting of the resulting displacement with a power law and with two exponential curves (see [10] for details) and (right) extrapolation of a power law fit of visually observed data (from a test under displacement control) to lower values of delamination length increment da/dN.
Fig. 6. (left) Mode I, mode II and FRMM I/II delamination fatigue data for IM//977-2 plotted as Paris-law type graph, and (right) the same data analyzed with a modified Hartman Schijve equation [15].
obtained. These range from 20 to 70 J/m2 with an average (of all specimens tested) of 56.8 J/m2 and a standard deviation of 13.9 J/ m2 if the slope b is set at 2.3 and the fitting value D is 4.0 107 mm[(J1/2/m)]b. Table 1 also shows the average values of Gthr and the standard deviation per laboratory (labeled A–E), with three to five specimens tested per laboratory. The standard deviation per laboratory amounts to 10–48% of the average Gthr with an average standard deviation for all data of 24%. The same type of analysis for the IM7/977-2 CFRP laminates yields a threshold value Gthr of 105 J/m2 (for D = 2.0, D = 3.0 106 mm[(J/m1/2)]b and A = 195 J/m2). The Gthr values
(average around 29 J/m2 for G30-500/R5276 and 105 J/m2 for IM7/977-2) are roughly in the range of Gthr obtained from fatigue fracture testing of unmodified epoxy resins (around 44 J/m2 [21]) or of a toughened epoxy adhesive (type EA 9628 with an average around 60 J/m2 and a standard deviation of 8.8 J/m2 [22]). Yet, they are clearly below quasi-static initiation values for CFRP composites comparable to the A value around 200 J/m2 for IM7/977-2 and an average of 365 J/m2 with a standard deviation of 108 J/m2 (30%) for R30-500/R5276 (see Table 1) or an average of 330 J/m2 with a standard deviation of 150 J/m2 (45%) for a standard diglycidyl ether of bis-phenol A [23]. It can be noted that the relative scatter of
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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Table 1 Threshold values Gthr used to obtain computed response of G30-500/R5276 laminates tested at different laboratories (labeled A–E) reported in [6], b was fixed to 2.3 and D was fixed to 4.0 107 mm[(J1/2/m)]b. Specimen no.
Fitting value A (J/m2)
Calculated Gthr (J/m2)
Average Gthr (J/m2)
Standard deviation Gthr (J/m2)
Design limit Gdesigna (J/m2)
95% Confidence interval Gthr (J/m2)
A.1 A.2 A.3 A.4
350 350 280 320
70 70 50 55
61.25
10.31
40.63
10.1
B.1 B.2 B.3
700 280 320
20 60 55
45.00
21.79
1.41
24.7
C.1 C.2 C.3 C.4 C.5
350 350 280 280 320
65 65 50 30 55
53.00
14.40
24.19
12.6
D.1 D.2
500 500
60 70
65.00
7.07
50.86
9.8
E.1 E.2 E.3
350 350 320
65 70 55
63.33
7.64
48.06
8.7
56.76
13.91
28.94
6.6
All specimens a
The design limit Gdesign was calculated by deducting twice the standard deviation from the average Gthr (in an empirical attempt to determine a lower limit of Gthr to be used in design).
average Gthr for the average of all specimens tested at five laboratories (24%) is somewhat larger than that observed in the average Gthr of a structural epoxy adhesive (14%) tested at one laboratory [22]. The relative scatter for individual laboratories (which can be considered a comparable measure of in-laboratory variation) for G30-500/R5276 ranges from 11% to 48%, but no round robin data are available for evaluating the inter-laboratory scatter for other types of epoxy cited here. This indicates that both approaches, i.e., an extrapolation of Paris-type data to a defined limit of da/dN (if measured with a load cell with sufficient resolution) and the alternative Hartman–Schijve data fitting yield consistent values of fatigue delamination thresholds for CFRP epoxy composite laminates. These values, derived from testing unidirectionally fiber-reinforced laminates, however, seem to be low, and that may pose problems for using them in fracture mechanics based structural design. 3.4. Fatigue delamination under mode I loading In the last example, recent delamination fatigue data obtained from IM7/8552 CFRP laminates under cyclic mode I loading again with R = 0.1 are presented and discussed. This time, maximum machine load and displacement values (machine type Instron ElectroPuls E3000 with a load cell range of 250 N) have been recorded for each cycle instead of every 500 or 1000 cycles, as in previous data sets. This has two advantages: First the full extent of scatter in load and displacement values can be assessed, and second, effects from averaging selected data ranges can be investigated. Fig. 7 shows the load signal obtained from two IM7/8552 CFRP laminate specimens tested under mode I fatigue delamination with displacement control using two different load cell ranges (5 kN and 250 N, respectively) for the two specimens. Clearly, the scatter in load signal is less for the 250 N load cell range over the number of cycles tested. This again shows that load signal resolution is a major source of scatter in the data, and that translates onto both axes of the Paris-law type graph, if compliance is used to determine the delamination length (and hence the delamination length increment) as discussed in detail by [6]. The graph further shows a comparison between a power law fit (dotted lines) and a moving average fit (solid lines) taking N/2 data points around each value
(N = 100 was chosen for Fig. 7). Displacement as a function of cycle number yields a graph (Fig. 7 right) indicating the scatter (resolution) in displacement measurement. The combined effect of scatter in load and displacement resulting from the compliance based data analysis is then shown in Fig. 8. The graph on the left shows the Paris-law type analysis with crack length increment per cycle (da/dN) versus applied GImax. The graph on the right shows the same data, this time analyzed with a modified Hartman–Schijve equation (see [16] for details). The extrapolation of the Paris-type data plot indicates a threshold (with some scatter) for the mode I loading in the range between 100 and 130 J/m2, slightly higher than that obtained for IM7/9772. If the scatter in predicted threshold for the different specimens is taken into account and a design threshold is estimated using a lower bound of twice the standard deviation, the design threshold may be as low as 80–90 J/m2. The quasi-static mode I critical fracture toughness GIC for IM7/8552 determined in the tests reported here is significantly higher (208 J/m2) and roughly agrees with values reported in the literature for a plain weave IM7/8552 of 263 ± 38 J/m2 [24]. Even though the estimated design threshold for IM7/8552 is a factor of two to three higher than the design threshold for G30-500/R5276, the problems for structural CFRP design are the same as those noted in the section above. If maximum machine load and displacement values are recorded for every cycle in fatigue delamination tests this will generate large data sets that typically cannot be handled with the available spreadsheets for data analysis. On the other hand, the data provide a basis for looking into the effects of averaging arbitrary numbers of cycles for obtaining selected data points with less scatter for compliance based analysis. Of course, such averaging could be applied on-line during the test and these averaged data could be recorded. The determination of the optimal number of cycles to be averaged, however, has not been investigated in detail yet (to the best knowledge of the authors). In subsequent analysis, different increasing sliding averages will be applied to the data and compared with the analysis of the full data set. Based on this evaluation, recommendations on averaging machine data on-line will then be implemented into the next version of the test procedures for delamination fatigue round robin testing of ESIS TC4 in order to keep data files sufficiently small.
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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Fig. 7. (left) Load and (right) displacement as a function of the number of load cycles for two specimens using different load cell ranges (5 kN and 250 N) and presenting the load signals as moving average (over 100 points) and power law fits from data recording the maximum load and displacement of every cycle.
Fig. 8. Mode I quasi-static and cyclic fatigue delamination data for IM7/8552 CFRP are plotted (left) in the Paris-law type graph and (right) with the modified Hartman Schijve fitting.
3.5. Implications for design of composite structures The data presented here for a range of CFRP epoxy laminates (for which mode I seems to be conservative both in quasi-static and fatigue delamination tests) indicate very low threshold values for mode I delamination fatigue, typically between a few tens to about 100 J/m2. If threshold values determined from a Hartman– Schijve type fit to the fatigue delamination data are averaged and if an arbitrary value of twice the standard deviation is taken as a design threshold limit, G30-500/R5276 CFRP yields a Gdesign limit value around 29 J/m2. Quite likely, such low thresholds would constitute severe design limitations. It could be argued, however, that the data have been determined on essentially unidirectional fiber reinforced material (in accordance with the standard procedures, i.e., [11,12] which is rarely used in structural CFRP design. In multidirectional CFRP laminates, the loading modes may change due to the fiber lay-up either resulting in mixed mode conditions [25], partial or full intralaminar delamination [26], or multiple delamination paths [27], all yielding higher delamination resistance than the unidirectional case. This is one reason why investigating mixed mode I/II delamination fatigue is important.
4. Conclusions and outlook Until recently, design approaches for CFRP composite structures and elements essentially represented a so-called ‘‘no growth”
philosophy, i.e., delaminations and cracks shall not propagate under the applied service loads during the structure’s life-time. For this approach, determination of safe delamination threshold values for the different loading modes is essential. If mode I fatigue delamination testing of unidirectionally fiber-reinforced CFRP composites is considered to provide a lower limit to fatigue delamination propagation and thresholds compared with other modes or mode mixes, then test standard development could be limited to mode I. An alternative would be to use a different design methodology, i.e., a damage tolerant design in which a certain amount of delamination or crack propagation is allowed. Since recently, this may be considered for aircraft design, see, e.g., [16]. This design methodology also requires fatigue delamination data and thresholds, see, e.g., [28] for details. Safe operation, however, then requires either structural monitoring during service or detailed simulations for defining appropriate inspection intervals. If non-unidirectional or multidirectional fiber orientation proves to contribute significantly to the fatigue delamination propagation resistance and/or to higher thresholds than in the unidirectional lay-up, fatigue delamination propagation test development will have to be extended to non-unidirectional or multidirectional laminates. Therefore, development of test methodology for delamination fatigue of CFRP composites and data analysis yielding rates or thresholds that can be transferred to engineering design are essential for increasing use of CFRP structures in a wide range of engineering applications. Beside mode I, also mode II and mixed
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mode I/II will have to be considered for determining the conservative mode yielding the lowest, i.e., safe design values. Fatigue delamination test development and standardization is hence an important area for future research. Acknowledgments Supply of laminates by BASF (G30-500/R5276), Cytec (IM7/9772) and by Hexcel (IM7/8552) and discussions with members of Technical Committee 4 of ESIS, especially Prof. J.G. Williams and Prof. A.J. Kinloch (Imperial College London), and with Prof. Rhys Jones (Monash University, Australia) are gratefully acknowledged. References [1] Brunner AJ, Blackman BRK, Davies P. A status report on delamination resistance testing of polymer–matrix composites. Eng Fract Mech 2008;75 (9):2779–94. [2] Brunner AJ. Fracture mechanics of polymer composites for aerospace applications. In: Irving PE, Soutis C, editors. Polymer composites in the aerospace industry. vol. 50. Woodhead Publishing, Series in Composites Science and Engineering; 2014. p. 191–230 [Chapter 8]. [3] ASTM Standard D6115 1997. Standard test method for mode I fatigue delamination growth onset of unidirectional fiber-reinforced polymer matrix composites. West Conshohocken (PA): ASTM International; 2011. [4] Brunner AJ, Pinter G, Murphy N. Development of a standardized procedure for the characterization of interlaminar crack growth in advanced composites under fatigue mode I loading conditions. Eng Fract Mech 2009;76 (18):2678–89. [5] Stelzer S, Brunner AJ, Argüelles A, Murphy N, Pinter G. Mode I delamination fatigue crack growth in unidirectional fibre reinforced composites: development of a standardized test procedure. Compos Sci Technol 2012;72 (10):1102–7. [6] Stelzer S, Brunner AJ, Argüelles A, Murphy N, Cano GM, Pinter G. Mode I delamination fatigue crack growth in unidirectional fibre reinforced composites: results from ESIS TC4 round robins. Eng Fract Mech 2014;116:92–107. [7] Brunner AJ, Paris I, Pinter G. Fatigue propagation test development for polymer-matrix fibre-reinforced laminates. In: Proceedings 12th international conference on fracture, ICF-12, paper No. 00371, 2009. 8p. [8] Brunner AJ, Stelzer S, Pinter G, Terrasi GP. Mode II fatigue delamination resistance of advanced fiber-reinforced polymer-matrix laminates: towards the development of a standardized test procedure. Int J Fatigue 2013;50:57–62. [9] Stelzer S, Jones R, Brunner AJ. Interlaminar fatigue crack growth in carbon fiber reinforced composites. In: Eds. Hoa SV, Hubert P, editors. Proceedings 19th international conference on composites, ICCM-19. Canadian Association for Composite Structures and Materials/Association Canadienne pour les Structures et Matériaux Composites; 2013. p. 1689–97.
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[10] Stelzer S, Pinter G, Brunner AJ. Comparison of quasi-static and cyclic fatigue delamination resistance of carbon fiber reinforced polymer-matrix laminates under different mode loading. Proc Mater Sci (Proc ECF-20) 2014;3:1087–92. [11] ISO Standard 15024 fibre-reinforced plastic composites – determination of mode I interlaminar fracture toughness, GIC, for unidirectionally reinforced materials. International Organization for Standardization; 2000. [12] ASTM Standard D5228. Standard test method for mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. West Conshohocken (PA): ASTM International; 2013. [13] ISO 15114. Fibre-reinforced plastic composites — determination of the mode II fracture resistance for unidirectionally reinforced materials using the calibrated end-loaded split (C-ELS) test and an effective crack length approach. International Organization for Standardization; 2014. [14] Blackman BRK, Brunner AJ, Williams JG. Mode II fracture testing of composites: a new look at an old problem. Eng Fract Mech 2006;73(16):2443–55. [15] Jones R, Pitt S, Brunner AJ, Hui D. Application of the Hartman–Schijve equation to representing mode I and mode II fatigue delamination growth in composites. Compos Struct 2012;94(4):1343–51. [16] Jones R, Stelzer S, Brunner AJ. Mode I, II and mixed mode I/II delamination growth in composites. Compos Struct 2014;110:317–24. [17] ASTM E 647. Standard test method for measurement of fatigue crack growth rates. West Conshohocken (PA): ASTM International; 2013. [18] Martin RH, Murri GB. Characterization of mode I and mode II delamination growth and thresholds in AS4/PEEK composites. In: Garbo S, editor. Composite materials: testing and design: ASTM STP 1059. West Conshohocken (PA): American Society for Testing and Materials; 1990. p. 251–70. [19] Hojo M, Matsuda S, Ochiai S. Fracture mechanism for mode II propagation of delamination fatigue cracks in CF/PEEK laminates. J Soc Mater Sci Jpn 1997;46 (4):366–73. [20] Albouy W, Vieille B, Taleb L. Influence of matrix ductility on the hightemperature fatigue behavior of quasi-isotropic woven-ply thermoplastic and thermoset laminates. Composites Part A 2015;67:22–36. [21] Sprenger S. Epoxy resins modified with elastomers and surface-modified silica nanoparticles. Polymer 2013;54:4790–7. [22] Jones R, Hu W, Kinloch AJ. A convenient way to represent fatigue crack growth in structural adhesives. Fatigue Fract Eng Mater Struct 2015;38(4):379–91. [23] Kinloch AJ, Masania K, Taylor AC, Sprenger S, Egan D. The fracture of glass-fibre reinforced epoxy composites using nanoparticle-modified matrices. J Mater Sci 2008;43:1151–4. [24] Paris I, Minguet PJ, O’Brien TK. Comparison of delamination characterization for IM7/8552 composite woven and tape laminates. In: Bakis CE, editor. Composite materials: testing and design, fourteenth vol.. ASTM STP 1436; 2003. p. 372–90. [25] Andersons J, König M. Dependence of fracture toughness of composite laminates on interface ply orientations and delamination growth direction. Compos Sci Technol 2004;64(13–14):2139–52. [26] Macedo FS, Pereira AB, de Morais AB. Mixed bending-tension (MBT) test for mode I interlaminar and intralaminar fracture. Compos Sci Technol 2012;72:1049–55. [27] Choi NS, Kinloch AJ, Williams JG. Delamination fracture of multidirectional carbon-fiber/epoxy composites under mode I, mode II and mixed-mode I/II loading. J Compos Mater 1999;33:73–100. [28] Martin RH. Incorporating interlaminar fracture mechanics into design. Proc Inst Mech Eng Part L: J Mater Des Appl 2000;214(2):91–7.
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations q A.J. Brunner a,⇑, S. Stelzer b, G. Pinter b, G.P. Terrasi a a b
Laboratory for Mechanical Systems Engineering, Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600 Dübendorf, Switzerland Chair of Material Science and Testing of Polymers, Montanuniversity Leoben, Otto Glöckel-Strasse 2, A-8700 Leoben, Austria
a r t i c l e
i n f o
Article history: Received 25 December 2014 Received in revised form 21 October 2015 Accepted 27 October 2015 Available online xxxx Keywords: Carbon fiber reinforced polymer-matrix composites Cyclic delamination fatigue Test development Data analysis Composite structural design
a b s t r a c t Activities toward standardization of fracture mechanics tests on carbon fiber-reinforced polymer-matrix (CFRP) composites have recently focused on cyclic fatigue under mode I (tensile opening), mode II (in-plane shear) and mixed-mode I/II loading. Data from recent round robins performed by Technical Committee 4 (TC4) of the European Structural Integrity Society (ESIS) and from preliminary testing of additional CFRP epoxy laminates at the authors’ laboratories are analyzed with different approaches in attempts to reduce scatter and to identify parameters for CFRP structural design. Selected test data comparing load and displacement control for the cyclic fatigue tests are also discussed. Specifically, threshold values from Paris-law data fitting are compared with values from fitting with a modified Hartman–Schijve approach. Independent of the approach used for the analysis, mode I threshold values of selected CFRP seem to be in the range between about 30 and 100 J/m2, i.e., roughly around the range of critical mode I energy release rate values (denoted by GIC) obtained from fracture testing of neat commercial epoxy resins, but clearly below quasi-static initiation GIC-values for unidirectional CFRP composites. Implications for CFRP structural design based on mode I fatigue fracture mechanics test data are briefly discussed. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Fatigue delamination propagation in CFRP composite laminates is an important failure mechanism limiting the service life of composite structures and elements. There have been significant research efforts for characterizing delamination resistance or critical fracture toughness of CFRP laminates under quasi-static and cyclic fatigue load conditions [1,2]. However, these efforts so far only resulted in one standard test method, aiming at the determination of mode I delamination onset [3]. Test development for a standard procedure for determination of mode I fatigue delamination propagation is pursued by ESIS TC4 [4–6] and Committee D30.06 of the American Society for Materials and Testing (ASTM) [6,7]. ESIS TC4 also explores mode II and mixed mode I/II fatigue delamination propagation test development [2,8–10]. The development of standard test procedures involves technical aspects (e.g., defining test rig types and test parameter ranges) as well as scope and applicability (e.g., use of the test data). The q This paper was submitted for the special issue Fatigue at all Scales (ECF20 Fatigue). ⇑ Corresponding author. Tel.: +41 58 765 44 93; fax: +41 58 765 69 11. E-mail address: [email protected] (A.J. Brunner).
present contribution discusses a number of technical issues that are likely to be implemented in a future standard fatigue test procedure, but also highlights some issues relating to data analysis and to applying the test data in structural design with CFRP composites. 2. Experimental The materials used in this research were all CFRP composite laminates obtained from different suppliers (see acknowledgment). Carbon fiber types comprise G30-500 and IM7, the epoxy matrix types were R5276, 977-2 and 8552. Fatigue delamination propagation and reference values from quasi-static delamination tests for comparison with the cyclic fatigue data were obtained for mode I according to [11,12], i.e., the so-called Double Cantilever Beam (DCB) test, for mode II according to [13], i.e., the so-called Clamp-Calibrated End-Loaded Split (C-ELS) test, and for mixed mode I/II (GI/IIC) according to a draft procedure under development within ESIS TC4. This latter procedure, the so-called Fixed-Ratio Mixed mode I/II (FRMM) test is essentially based on the C-ELS test rig [13], but with the specimen and load application point, respectively, inverted. This test rig then yields a constant ratio of the mode I to the mode II component of 4:3, see, e.g., [1,14] for details.
http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025 0142-1123/Ó 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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Tests were performed on either servo-hydraulic test machines (from Material Testing Systems type MTS 858 with a 15 kN load cell calibrated to a load range from 0 to 400 N, or from Instron type 1273 with a 1 kN load cell calibrated in the range of 0–200 N) or on an electro-mechanical test machine (type Instron ElectroPuls E3000 with a load cell range of 250 N) with cross-head speeds of 2 mm/min for the quasi-static test and at a frequencies of 3, 5 or 10 Hz with a R-value of 0.1 for the cyclic delamination fatigue tests. Machine data comprising maximum load and displacement were recorded every 500 or 1000 cycles in the cyclic delamination fatigue tests and for selected tests, these data were recorded for every cycle. Nevertheless, cyclic tests were stopped from time to time for visual determination of the delamination lengths (using a traveling microscope with magnification of 10 or 16), in order to correlate visual observation with compliance based delamination length. 3. Results and discussion 3.1. Overview The data and test results shown and discussed below were chosen with the intention to highlight selected issues in the analysis of cyclic fatigue delamination tests on CFRP epoxy composites and to point out potential problems when using the delamination fatigue data for design of composite structures. The first example discusses difficulties encountered when using load control rather than displacement control under mode I cyclic fatigue loading. This complements the data and discussion presented in [10]. The second example then compares Paris type data obtained from cyclic mode I, mode II and FRMM I/II with an alternative data analysis based on a modified Hartman–Schijve approach recently developed by Jones et al. [15,16]. The third example finally looks at cyclic delamination fatigue under mode I loading where data analysis and fitting is based on recording every load cycle rather than on selected data points (typically every 500 or 1000 cycles) as in the two previous examples. 3.2. Load control of delamination fatigue under mode I Ref. [10] had presented and discussed cyclic delamination fatigue tests and their analysis under mode I loading performed either under displacement or load control on a servo-hydraulic test machine (type MTS 858) both with R-values of 0.1. Fig. 1 shows the respective load and displacement values (selected data points recorded every 1000 cycles) as a function of cycle number for G30-500/R5267 CFRP laminates. From Fig. 1, it is obvious that in
the case presented here, displacement control is stable and results in a continuously decreasing load with increasing delamination length. There is clearly some scatter in the measured load data which requires smoothing or fitting for data analysis. In the case of load control, the load values are less stable (relative to the set value around 50 N) and the scatter tends to increase with increasing displacement. The corresponding displacement values seem to increase without much scatter, but if the scale of the plot is reduced, there is a behavior analogous to that observed for the load signal under displacement control. It has to be noted that the machine load control in this specific example (machine type MTS 858) may not have been optimal yet. However, there is another issue with load control that, from a practical point of view, deserves attention. Independent of whether the test is started from a film insert in the specimen or from a mode I precrack, an initial load value has to be chosen. If this value is chosen too high, the displacement will rapidly increase and the specimen may fail after a relatively low number of fatigue cycles. This will result in few data points for the analysis and the determination of the Paris-type plot. Specifically, analyzing the low load and delamination length increment per cycle range (i.e., in the near threshold regime) will not be possible. On the other hand, if the value is chosen too low, it may take many cycles (and hence test time) for the delamination to start propagating. This is the main problem in a cyclic fatigue test for the determination of delamination onset, e.g., according to [3]. One example for a load value below the delamination onset regime is shown in Fig. 2. For determining the appropriate value of displacement for displacement controlled fatigue delamination tests, it suffices to perform a quasi-static test, stop after a short precrack length and then use the last displacement value for machine control. Load controlled fatigue delamination, even if run at an appropriate load level, has also indicated a problem in data analysis. A previous study [6] on fatigue delamination analysis of round robin data on three different CFRP laminates using displacement control had indicated that using a power law fit for the load data points yielded reasonably smooth data. This approach resulted in less scatter than interpolating approaches, such as e.g., the (2n + 1)point polynomial method (n any integer between 2 and 4) described in [17]. For the load control data, however, the power law fitting approach (in this case applied to the crack length data) did not yield a reasonable fit to the experimental data as shown in Fig. 3. Fig. 4 shows another example of a load control mode I cyclic fatigue delamination test. The load signal clearly indicates significant scatter (about ±1 N at typical loads of about 40 N). The respective displacement is increasing roughly linearly, resulting in a roughly linear increase in calculated crack length
Fig. 1. Load and displacement values from cyclic delamination fatigue testing of a carbon–fiber epoxy composite (G30-500/R5276) under mode I tensile opening load; (left) displacement control, (right) load control.
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An extrapolation of the visual data for G30-500/R5276 (Fig. 5 right hand side) from a displacement controlled test does not indicate a clear threshold, but at a value of da/dN of about 107 mm/cycle (0.1 nm/cycle, i.e., close to molecular dimensions) which could be taken as a physical limit of crack extension, GImax amounts to about 35 J/m2. This can be taken as an experimental estimate of a threshold value, Gthr. Similar values of GImax or Gthr for G30-500/ R5276 CFRP laminates are obtained from another extrapolation approach discussed in the next section. It is hence hypothesized that threshold values for CFRP epoxy laminates without toughening additives are rather low and possibly amount to a few tens of J/m2 at best. With similar extrapolation, toughened epoxy matrix resins (e.g., epoxy resin type 977-2) tend to yield somewhat higher values of Gthr (around 100 J/m2) as discussed below. In any case, this example illustrates some of the pitfalls and problems encountered with mode I fatigue delamination testing under load control and the related data analysis and evaluation. Fig. 2. Displacement versus load control, data have been analyzed with the sevenpoint averaging procedure according to [17]. The test results shown for specimens 1 and 2 under load control show indications of delamination arrest, since the da/dNrange is limited to about one decade for full range of GImax.
(from compliance calibration). At the end of the test, however, the compliance of the specimen increases rapidly. This can cause problems in load control and lead to inaccurately applied loads (see Fig. 4, load data around 44 and 46 N). With an appropriate choice of the machine load control settings, this problem can be solved. However, this may require trial tests for evaluating the machine settings before performing the fatigue delamination tests. In a trial and error approach, a combination of two exponential functions with different exponents seemed to fit the crack length for load controlled mode I delamination fatigue tests as a function of cycle number best [10]. The resulting Paris law type graphs derived from the power law fit of the load curve and from the two exponential fits is shown in Fig. 5 (left hand side). The solid line representing the data calculated from the power law fit, if assessed without considering the quality of the fitting and the visual data, seems to suggest a threshold value around 150 J/m2 setting in at relatively high delamination length increments da/dN around 104 mm/cycle. The data calculated from fitting crack length with two exponential curves, however, do not yield any indication of a threshold within the range tested in the experiment in agreement with the data points from visual observation.
Fig. 3. Power law fitting of displacement for the epoxy CFRP (G30-500 fiber, epoxy Rigidite 5276 matrix) tested under mode I cyclic fatigue fracture using load control indicating deviations between compliance data and power law fit at low and high crack lengths.
3.3. Fatigue delamination propagation under mode II and mixed mode I/II Fig. 6 summarizes results from quasi-static and fatigue delamination tests under different loading modes (mode I, mode II and FRMM I/II) for IM7/977-2 CFRP laminates. The graph on the left hand side in Fig. 6 shows the Paris-law type plot, whereas that on the right hand side shows the data represented by a modified Hartman–Schijve fitting [15], see Eq. (1):
2
3b
pffiffiffiffiffiffiffiffi7 6 pffiffiffiffiffi 6D GI D Gthr 7 da ffi7 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ D6 6 qffiffiffiffiffiffiffiffi 7 dN 4 GImax 5 1 A
ð1Þ
pffiffiffiffiffi where D, b and A are constants and D GI is defined in Eq. (2)
pffiffiffiffi pffiffiffiffi pffiffiffiffi GI ¼ GImax GImin
ð2Þ
The Paris-law type plot (Fig. 6 left) indicates that mode I is conservative in the sense that it yields the highest Gmax value (compared with mode II and FRMM I/II) at any given value of delamination length increment da/dN. The extrapolation indicates a threshold around 100 J/m2 setting in around 1–5 times 107 mm/cycle. However, the data for mode II (C-ELS) and the FRMM I/II also seem to converge to a similar threshold value in this presentation (even though the extrapolations are not shown). When discussing ‘‘conservative” values the example of AS4/poly-etherether-ketone (PEEK), a thermoplastic CFRP laminate where mode I is lower than mode II in delamination fatigue for all Gmax values in the Paris-type plot (and hence not conservative) should be pointed out. However, there is no evidence so far that this could also be the case for CFRP with thermoset matrix. On the other hand, the quasistatic fracture toughness values for AS4/PEEK under mode I are lower than those for mode II, please see, e.g., [9,18,19] for details on this. At this stage, it can only be speculated that the different behavior of more ductile thermoplastic versus more brittle thermoset matrix materials in CFRP (that has been shown to have a significant effect on damage accumulation in tensile fatigue tests, see, e.g., [20]) contributes to or results in this difference between quasi-static and fatigue fracture. Testing other thermoplastic CFRP laminates beside CF-PEEK in mode I and mode II fatigue fracture should yield more insight. Analyzing the data for G30-500/R5276 specimens tested under mode I delamination fatigue with displacement control (R-value = 0.1) at five laboratories [6] with the Hartman–Schijve fitting [15], the threshold values (Gthr) shown in Table 1 are
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Fig. 4. (left) Load and displacement values from mode I delamination fatigue under load control and (right) corresponding delamination length increase.
Fig. 5. (left) Comparison of Paris-type plot for load control and fitting of the resulting displacement with a power law and with two exponential curves (see [10] for details) and (right) extrapolation of a power law fit of visually observed data (from a test under displacement control) to lower values of delamination length increment da/dN.
Fig. 6. (left) Mode I, mode II and FRMM I/II delamination fatigue data for IM//977-2 plotted as Paris-law type graph, and (right) the same data analyzed with a modified Hartman Schijve equation [15].
obtained. These range from 20 to 70 J/m2 with an average (of all specimens tested) of 56.8 J/m2 and a standard deviation of 13.9 J/ m2 if the slope b is set at 2.3 and the fitting value D is 4.0 107 mm[(J1/2/m)]b. Table 1 also shows the average values of Gthr and the standard deviation per laboratory (labeled A–E), with three to five specimens tested per laboratory. The standard deviation per laboratory amounts to 10–48% of the average Gthr with an average standard deviation for all data of 24%. The same type of analysis for the IM7/977-2 CFRP laminates yields a threshold value Gthr of 105 J/m2 (for D = 2.0, D = 3.0 106 mm[(J/m1/2)]b and A = 195 J/m2). The Gthr values
(average around 29 J/m2 for G30-500/R5276 and 105 J/m2 for IM7/977-2) are roughly in the range of Gthr obtained from fatigue fracture testing of unmodified epoxy resins (around 44 J/m2 [21]) or of a toughened epoxy adhesive (type EA 9628 with an average around 60 J/m2 and a standard deviation of 8.8 J/m2 [22]). Yet, they are clearly below quasi-static initiation values for CFRP composites comparable to the A value around 200 J/m2 for IM7/977-2 and an average of 365 J/m2 with a standard deviation of 108 J/m2 (30%) for R30-500/R5276 (see Table 1) or an average of 330 J/m2 with a standard deviation of 150 J/m2 (45%) for a standard diglycidyl ether of bis-phenol A [23]. It can be noted that the relative scatter of
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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Table 1 Threshold values Gthr used to obtain computed response of G30-500/R5276 laminates tested at different laboratories (labeled A–E) reported in [6], b was fixed to 2.3 and D was fixed to 4.0 107 mm[(J1/2/m)]b. Specimen no.
Fitting value A (J/m2)
Calculated Gthr (J/m2)
Average Gthr (J/m2)
Standard deviation Gthr (J/m2)
Design limit Gdesigna (J/m2)
95% Confidence interval Gthr (J/m2)
A.1 A.2 A.3 A.4
350 350 280 320
70 70 50 55
61.25
10.31
40.63
10.1
B.1 B.2 B.3
700 280 320
20 60 55
45.00
21.79
1.41
24.7
C.1 C.2 C.3 C.4 C.5
350 350 280 280 320
65 65 50 30 55
53.00
14.40
24.19
12.6
D.1 D.2
500 500
60 70
65.00
7.07
50.86
9.8
E.1 E.2 E.3
350 350 320
65 70 55
63.33
7.64
48.06
8.7
56.76
13.91
28.94
6.6
All specimens a
The design limit Gdesign was calculated by deducting twice the standard deviation from the average Gthr (in an empirical attempt to determine a lower limit of Gthr to be used in design).
average Gthr for the average of all specimens tested at five laboratories (24%) is somewhat larger than that observed in the average Gthr of a structural epoxy adhesive (14%) tested at one laboratory [22]. The relative scatter for individual laboratories (which can be considered a comparable measure of in-laboratory variation) for G30-500/R5276 ranges from 11% to 48%, but no round robin data are available for evaluating the inter-laboratory scatter for other types of epoxy cited here. This indicates that both approaches, i.e., an extrapolation of Paris-type data to a defined limit of da/dN (if measured with a load cell with sufficient resolution) and the alternative Hartman–Schijve data fitting yield consistent values of fatigue delamination thresholds for CFRP epoxy composite laminates. These values, derived from testing unidirectionally fiber-reinforced laminates, however, seem to be low, and that may pose problems for using them in fracture mechanics based structural design. 3.4. Fatigue delamination under mode I loading In the last example, recent delamination fatigue data obtained from IM7/8552 CFRP laminates under cyclic mode I loading again with R = 0.1 are presented and discussed. This time, maximum machine load and displacement values (machine type Instron ElectroPuls E3000 with a load cell range of 250 N) have been recorded for each cycle instead of every 500 or 1000 cycles, as in previous data sets. This has two advantages: First the full extent of scatter in load and displacement values can be assessed, and second, effects from averaging selected data ranges can be investigated. Fig. 7 shows the load signal obtained from two IM7/8552 CFRP laminate specimens tested under mode I fatigue delamination with displacement control using two different load cell ranges (5 kN and 250 N, respectively) for the two specimens. Clearly, the scatter in load signal is less for the 250 N load cell range over the number of cycles tested. This again shows that load signal resolution is a major source of scatter in the data, and that translates onto both axes of the Paris-law type graph, if compliance is used to determine the delamination length (and hence the delamination length increment) as discussed in detail by [6]. The graph further shows a comparison between a power law fit (dotted lines) and a moving average fit (solid lines) taking N/2 data points around each value
(N = 100 was chosen for Fig. 7). Displacement as a function of cycle number yields a graph (Fig. 7 right) indicating the scatter (resolution) in displacement measurement. The combined effect of scatter in load and displacement resulting from the compliance based data analysis is then shown in Fig. 8. The graph on the left shows the Paris-law type analysis with crack length increment per cycle (da/dN) versus applied GImax. The graph on the right shows the same data, this time analyzed with a modified Hartman–Schijve equation (see [16] for details). The extrapolation of the Paris-type data plot indicates a threshold (with some scatter) for the mode I loading in the range between 100 and 130 J/m2, slightly higher than that obtained for IM7/9772. If the scatter in predicted threshold for the different specimens is taken into account and a design threshold is estimated using a lower bound of twice the standard deviation, the design threshold may be as low as 80–90 J/m2. The quasi-static mode I critical fracture toughness GIC for IM7/8552 determined in the tests reported here is significantly higher (208 J/m2) and roughly agrees with values reported in the literature for a plain weave IM7/8552 of 263 ± 38 J/m2 [24]. Even though the estimated design threshold for IM7/8552 is a factor of two to three higher than the design threshold for G30-500/R5276, the problems for structural CFRP design are the same as those noted in the section above. If maximum machine load and displacement values are recorded for every cycle in fatigue delamination tests this will generate large data sets that typically cannot be handled with the available spreadsheets for data analysis. On the other hand, the data provide a basis for looking into the effects of averaging arbitrary numbers of cycles for obtaining selected data points with less scatter for compliance based analysis. Of course, such averaging could be applied on-line during the test and these averaged data could be recorded. The determination of the optimal number of cycles to be averaged, however, has not been investigated in detail yet (to the best knowledge of the authors). In subsequent analysis, different increasing sliding averages will be applied to the data and compared with the analysis of the full data set. Based on this evaluation, recommendations on averaging machine data on-line will then be implemented into the next version of the test procedures for delamination fatigue round robin testing of ESIS TC4 in order to keep data files sufficiently small.
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Fig. 7. (left) Load and (right) displacement as a function of the number of load cycles for two specimens using different load cell ranges (5 kN and 250 N) and presenting the load signals as moving average (over 100 points) and power law fits from data recording the maximum load and displacement of every cycle.
Fig. 8. Mode I quasi-static and cyclic fatigue delamination data for IM7/8552 CFRP are plotted (left) in the Paris-law type graph and (right) with the modified Hartman Schijve fitting.
3.5. Implications for design of composite structures The data presented here for a range of CFRP epoxy laminates (for which mode I seems to be conservative both in quasi-static and fatigue delamination tests) indicate very low threshold values for mode I delamination fatigue, typically between a few tens to about 100 J/m2. If threshold values determined from a Hartman– Schijve type fit to the fatigue delamination data are averaged and if an arbitrary value of twice the standard deviation is taken as a design threshold limit, G30-500/R5276 CFRP yields a Gdesign limit value around 29 J/m2. Quite likely, such low thresholds would constitute severe design limitations. It could be argued, however, that the data have been determined on essentially unidirectional fiber reinforced material (in accordance with the standard procedures, i.e., [11,12] which is rarely used in structural CFRP design. In multidirectional CFRP laminates, the loading modes may change due to the fiber lay-up either resulting in mixed mode conditions [25], partial or full intralaminar delamination [26], or multiple delamination paths [27], all yielding higher delamination resistance than the unidirectional case. This is one reason why investigating mixed mode I/II delamination fatigue is important.
4. Conclusions and outlook Until recently, design approaches for CFRP composite structures and elements essentially represented a so-called ‘‘no growth”
philosophy, i.e., delaminations and cracks shall not propagate under the applied service loads during the structure’s life-time. For this approach, determination of safe delamination threshold values for the different loading modes is essential. If mode I fatigue delamination testing of unidirectionally fiber-reinforced CFRP composites is considered to provide a lower limit to fatigue delamination propagation and thresholds compared with other modes or mode mixes, then test standard development could be limited to mode I. An alternative would be to use a different design methodology, i.e., a damage tolerant design in which a certain amount of delamination or crack propagation is allowed. Since recently, this may be considered for aircraft design, see, e.g., [16]. This design methodology also requires fatigue delamination data and thresholds, see, e.g., [28] for details. Safe operation, however, then requires either structural monitoring during service or detailed simulations for defining appropriate inspection intervals. If non-unidirectional or multidirectional fiber orientation proves to contribute significantly to the fatigue delamination propagation resistance and/or to higher thresholds than in the unidirectional lay-up, fatigue delamination propagation test development will have to be extended to non-unidirectional or multidirectional laminates. Therefore, development of test methodology for delamination fatigue of CFRP composites and data analysis yielding rates or thresholds that can be transferred to engineering design are essential for increasing use of CFRP structures in a wide range of engineering applications. Beside mode I, also mode II and mixed
Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025
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mode I/II will have to be considered for determining the conservative mode yielding the lowest, i.e., safe design values. Fatigue delamination test development and standardization is hence an important area for future research. Acknowledgments Supply of laminates by BASF (G30-500/R5276), Cytec (IM7/9772) and by Hexcel (IM7/8552) and discussions with members of Technical Committee 4 of ESIS, especially Prof. J.G. Williams and Prof. A.J. Kinloch (Imperial College London), and with Prof. Rhys Jones (Monash University, Australia) are gratefully acknowledged. References [1] Brunner AJ, Blackman BRK, Davies P. A status report on delamination resistance testing of polymer–matrix composites. Eng Fract Mech 2008;75 (9):2779–94. [2] Brunner AJ. Fracture mechanics of polymer composites for aerospace applications. In: Irving PE, Soutis C, editors. Polymer composites in the aerospace industry. vol. 50. Woodhead Publishing, Series in Composites Science and Engineering; 2014. p. 191–230 [Chapter 8]. [3] ASTM Standard D6115 1997. Standard test method for mode I fatigue delamination growth onset of unidirectional fiber-reinforced polymer matrix composites. West Conshohocken (PA): ASTM International; 2011. [4] Brunner AJ, Pinter G, Murphy N. Development of a standardized procedure for the characterization of interlaminar crack growth in advanced composites under fatigue mode I loading conditions. Eng Fract Mech 2009;76 (18):2678–89. [5] Stelzer S, Brunner AJ, Argüelles A, Murphy N, Pinter G. Mode I delamination fatigue crack growth in unidirectional fibre reinforced composites: development of a standardized test procedure. Compos Sci Technol 2012;72 (10):1102–7. [6] Stelzer S, Brunner AJ, Argüelles A, Murphy N, Cano GM, Pinter G. Mode I delamination fatigue crack growth in unidirectional fibre reinforced composites: results from ESIS TC4 round robins. Eng Fract Mech 2014;116:92–107. [7] Brunner AJ, Paris I, Pinter G. Fatigue propagation test development for polymer-matrix fibre-reinforced laminates. In: Proceedings 12th international conference on fracture, ICF-12, paper No. 00371, 2009. 8p. [8] Brunner AJ, Stelzer S, Pinter G, Terrasi GP. Mode II fatigue delamination resistance of advanced fiber-reinforced polymer-matrix laminates: towards the development of a standardized test procedure. Int J Fatigue 2013;50:57–62. [9] Stelzer S, Jones R, Brunner AJ. Interlaminar fatigue crack growth in carbon fiber reinforced composites. In: Eds. Hoa SV, Hubert P, editors. Proceedings 19th international conference on composites, ICCM-19. Canadian Association for Composite Structures and Materials/Association Canadienne pour les Structures et Matériaux Composites; 2013. p. 1689–97.
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Please cite this article in press as: Brunner AJ et al. Cyclic fatigue delamination of carbon fiber-reinforced polymer-matrix composites: Data analysis and design considerations. Int J Fatigue (2015), http://dx.doi.org/10.1016/j.ijfatigue.2015.10.025