The present paper addresses the problem of fatigue crack growth in composite structures, with special relevance to composite airframes. Assessment of their in-service life can be based on either a ‘no-growth’ or a ‘slow-growth’ design philosophy. Whilst the most widely used approach is to adopt a ‘no-growth’ approach, it is accepted that this can result in an overly conservative design. Furthermore, even for ‘no-growth’ designs, delamination growth under cyclic fatigue loads can still arise in-service. Thus, the immediate challenge facing the composites community is to extend the ‘no-growth’ design philosophy to allow for the nucleation and growth of small, naturally-occurring delaminations in composite structures. The main aim of the present paper is, therefore, to investigate the robustness of the Hartman-Schijve methodology to meet this challenge when the effects of test temperature, together with the R-ratio, on the fatigue behaviour are considered.
Research Article
Fatigue Crack Growth Curves for Material Selection, Design and Service-Life Studies of Carbon-Fibre Reinforced-Plastic Composites: Effect of Test Temperature and R-ratio
https://doi.org/10.21203/rs.3.rs-8180128/v1
This work is licensed under a CC BY 4.0 License
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CFRP
composites
fatigue
fracture mechanics
modelling
service-life
test temperature
The third volume of the Composite Materials Handbook [2] provides methodologies and lessons learned for the design, analysis, manufacture and field support of fibre-reinforced, polymeric-matrix composite structures. It notes that the assessment of cyclic fatigue crack growth in such composite structures, with special relevance to airframes, can be based on either a ‘no-growth’ or a ‘slow-growth’ design philosophy. Whilst the most widely used approach is to adopt a ‘no-growth’ approach, it is accepted that this can result in an overly conservative design. Furthermore, it is now known [3,4] that, even for such ‘no-growth’ designs, delamination growth arising from cyclic fatigue loads can still arise in-service. As such two of the immediate challenges facing the composites community are:
To extend the ‘no-growth’ design philosophy to allow for the nucleation and growth of small naturally-occurring delaminations in composite structures.
To develop the tools needed to provide a conservative estimate for the remaining life, and hence the inspection intervals, for delamination damage found in an operational airframe. (These the tools are needed for aircraft sustainment.)
The principle of ‘slow-growth’ in fibre-reinforced polymeric-matrix composites is applicable to delamination growth under cyclic fatigue loads which is slow and stable. It is recommended [5, 6] that this be analysed using linear-elastic fracture-mechanics (LEFM). This requires a knowledge of the da/dN versus \(\:\varDelta\:\sqrt{G}\:\)curves, where da/dN is the fatigue crack (i.e. delamination) growth (FCG) per cycle and \(\:\varDelta\:\sqrt{G}\) is the\(\:\:\)range of the applied energy release-rate in the fatigue cycle, as defined by\(\:\:\sqrt{{G}_{max}}-\:\sqrt{{G}_{min}}\); where \(\:{G}_{max}\:\)and \(\:{G}_{min}\:\)are the maximum and minimum values of the applied energy release-rate in the fatigue cycle, respectively [7, 8]. Furthermore, the NASA Fracture Design Handbook NASA-HDBK-5010 [6] mandates the use of a ‘worst-case upper-bound’ FCG curve for material selection, design and service-life (sustainment) studies.
This worst-case upper-bound FCG curve for a carbon-fibre reinforced-plastic (CFRP) should:
Exhibit no, or only minimal, retardation, arising from fibre bridging. Since the fastest growing, i.e. lead, delaminations that arise under cyclic-fatigue loading of real composite structures or components from mis-drilled holes, ply drop-offs and impact damage show no, or only little, retardation from fibre-bridging developing across the faces of the delamination as the fatigue crack advances [8].
Allow for scatter in the test data [9, 10].
Encompass, and bound, all the experimental results.
Be representative of, and applicable to, small, naturally-occurring delaminations [11, 12]
However, the experimental determination of valid and relevant da/dN versus \(\:\varDelta\:\sqrt{G}\:\)FCG curves is where major problems have been encountered, which have only relatively recently been identified and resolved. These problems arise from the use of the double-cantilever beam (DCB) test specimen, see Fig. 1, to experimentally measure the Mode I (i.e. opening tensile) da/dN versus \(\:\varDelta\:\sqrt{G}\:\)FCG curves [13]. This test specimen contains a through-thickness crack and has an inserted polymer film to act as a starter crack of length, ao, for the crack from which the FCG measurements will be subsequently taken. However, this polymer film, although typically only about 10 to 13 µm in thickness, acts as relatively blunt crack and must be extended to a length ap so as to give a naturally-sharp crack tip for the subsequent actual measurements. Unfortunately, this requirement for some pre-test crack extension leads to fibre bridging developing across the crack faces, prior to the start of the fatigue test, which subsequently retards the propagation of the delamination under the cyclic fatigue loads. Indeed, the experimental data reveals that such retardation effects cannot be avoided. The experimental data also reveals that the DCB fatigue test results may show a great deal of scatter [9, 10], which in-part arises from fibre-bridging developing during the test. It is, therefore, very difficult to experimentally determine a worst-case upper-bound FCG curve. The same comments are true with respect to determining a valid value of the fatigue threshold, \(\:\varDelta\:\sqrt{{G}_{thr}}\), below which no significant FCG occurs. Finally, in the FCG of metallic structures it is well established that small, embedded, naturally-occurring defects do not behave in the same manner as relatively large through-thickness cracks as used in a typical test specimen [11, 12]. The problem being that such small, naturally-occurring, cracks grow faster than expected from observations of the latter type of through-thickness cracks. In the DCB test only though-thickness cracks can be employed. Consequently, the FCG curves developed using DCB tests are not applicable to a sustainment assessment.
To examine in detail these problems of measuring the FCG rate curves from DCB tests using CFRPs, the European Structural Integrity Society (ESIS), Technical Committee (TC) 4 (on Polymers, Composites and Adhesives) has launched a round-robin study, using Mode I DCB tests, into (a) the effect of the pre-crack length, ap-ao, prior to the start of the measurements from the laboratory cyclic-fatigue test, on the measured FCG rate, da/dN, data and (b) the reproducibility of the FCG rate curves under cyclic-fatigue loads. The first paper from this study [14] confirmed that a key experimental parameter is the value of the pre-crack (i.e. pre-delamination) extension length, ap-ao, in the DCB test specimen prior to any cyclic-fatigue measurements being undertaken. As mentioned above, this phenomenon arises since varying the value of ap-ao typically leads to a varying degree of fibre bridging developing behind the tip of the fatigue delamination, prior to the start of the actual fatigue test. The presence of such fibre bridging may retard the FCG rate and so lead to an impression of enhanced fatigue behaviour that is not present when no, or very, little fibre bridging occurs, as is typically the case in a real composite component. In this study [14], the FCG results were measured by the two independent laboratories and the results were in good agreement. In a second paper [15] it was shown that the Hartman-Schijve equation [7, 8, 16, 17], determined with test data generated [14] under an R-ratio of R = 0.1, could also be used to compute the FCG curves associated with tests performed at R = 0.3, 0.5 and 0.7, where R is the load ratio (= Pmin/Pmax). More importantly, the Hartman-Schijve methodology (a) can be used to determine a worst-case upper-bound da/dN versus \(\:\varDelta\:\sqrt{G\:}\:\)FCG curve which exhibits no retardation, (b) takes into account the experimental scatter, (c) encompasses and bounds all the experimental results and (d) can represent the fatigue growth of small, naturally-occurring delaminations in the CFRP. (The latter curves are needed for a sustainment analysis, i.e. to determine the remaining life of the airframe and hence the inspection intervals.) The main aim of the present paper is to investigate the robustness of this Hartman-Schijve methodology from [14, 15] when the effects of test temperature together with varying the R-ratio [18, 19] are studied.
Due to the inhomogeneity and anisotropy of continuous-fibre composites, the energy release-rate, G, approach, rather than the stress-intensity factor approach, is generally used to study delamination growth in such materials. Now, following the work of Paris et al. [20–22] on metals, where the range, \(\:\varDelta\:K\), of the applied stress-intensity factor is invariably employed to analyse the data, then at first sight the most obvious and corresponding parameter against which to plot the measured rate of the FCG, da/dN, for composites is the range of the applied energy release-rate, \(\:\varDelta\:G\), where \(\:\varDelta\:G={G}_{max}-{G}_{min}\). However, theoretical work by Sih, Paris and Irwin [23] and recent work, for example by Jones et al. [7, 8, 24], Yao et al. [25] and Simon et al. [26], has revealed that the logical extension of the Paris FCG equation for metals to delamination growth in CFRPs is, in fact, to express da/dN as a function of \(\:\varDelta\:\sqrt{G}\) rather than ∆G. Where \(\:\varDelta\:\sqrt{G}\:\)is given by:
$$\:\varDelta\:\sqrt{G}=\sqrt{{G}_{max}}-\sqrt{{G}_{min}}$$
1
Following these ideas, a novel empirical methodology based on using a variant of the Hartman-Schijve [15, 16] equation has been proposed to access the ‘worst-case upper-bound’ FCG rate curve, which may be thought of as a material-allowable property. The form proposed [e.g. 7,8,14,15,25,26] for the Hartman-Schijve equation, which is a variant of the NASGRO equation, in terms of \(\:\varDelta\:\sqrt{G}\) is:
$$\:\frac{da}{dN}=D.\:{}^{n}=\:D.{\left[\frac{\varDelta\:\sqrt{G}-\:\varDelta\:\sqrt{{G}_{thr}}}{\surd\:\left\{1-\:\sqrt{{G}_{max}}/\sqrt{A}\right\}}\right]}^{n}\:$$
2
where \(\:\:\) is the crack driving force (CDF) [17] in terms of energy release-rate, i.e. the ‘similitude parameter’, and where D and n are constants and A is the cyclic fracture toughness. The term \(\:\varDelta\:\sqrt{{G}_{thr}}\) is defined by:
$$\:\:\varDelta\:\sqrt{{G}_{thr}}=\:\sqrt{{G}_{max.thr}}-\:\sqrt{{G}_{min.thr}}$$
3
and the subscript ‘thr’ in Equations (2) and (3) refers to the values at threshold, below which no significant FCG occurs. As noted above, using the Hartman-Schjive methodology it has been found possible (a) to determine a worst-case upper-bound da/dN versus \(\:\varDelta\:\sqrt{G\:}\:\)FCG curve which exhibits no FCG retardation and (b) to take into account the experimental scatter. This worst-case curve (a) encompasses and bounds all the experimental results and (b) can be formulated to be representative of small naturally-occurring delaminations in the CFRP [15]. It should be noted that, since the DCB test cannot yield a directly measured ‘worst-case upper-bound’ FCG curve which is free from fibre-bridging, other methods of analysing the experimentally results have also been by proposed [e.g. 27]. However none of these have also considered the additional detrimental effect of small, naturally-occurring delaminations, as opposed to through-thickness delaminations, as might be found in an operational composite component or structure. This is a major aim of the present work.
In the present study the cyclic fatigue test results for the unidirectional CFRP material are taken at test temperatures of -40oC, 50oC and 80oC from Yao et al. [18, 19] and are compared to those reported for room temperature tests at 22oC reported by Michel et al. [14, 15]. It will be shown that delamination growth in these tests can be captured using the same equation as given in Michel et al. [14, 15] for room temperature tests at R-ratios of 0.1, 0.3. 0.5 and 0.7, viz:
$$\:\frac{da}{dN}=1.23.{10}^{-10}\:{\left[\frac{\varDelta\:\sqrt{G}-\:\varDelta\:\sqrt{{G}_{thr}}}{\surd\:\left\{1-\sqrt{{G}_{max}}/\sqrt{A}\right\}}\right]}^{4.49}$$
4
The CFRP was a continuous carbon-fibre epoxy-matrix polymer composite which was fabricated using a prepreg of unidirectional, continuous carbon fibres in a thermosetting epoxy polymer matrix, ‘M30SC/DT120′ supplied by Delta-Tech S.p.A., Altopascio, Italy. (A unidirectional, continuous fibre CFRP was chosen since this is the orientation of the fibres given in the ISO Standard test method [1] and this fibre orientation typically results in a severe degree of fibre-bridging occurring.) In all cases, a thin film of poly(tetrafluoroethylene), 12.7 µm in thickness, was inserted at one end of the DCB test specimen between the plies in the mid-plane of the CFRP panel during the hand lay-up process to act as an initial delamination, or ‘starter crack’, see Fig. 1; where the nominal length, ao, is about 50 mm. The laid-up panels were placed in an autoclave and cured for 90 minutes at a temperature of 120°C under a pressure of 6 bar. The glass transition temperature of the resulting thermosetting epoxy polymer matrix was 120°C.
The cyclic-fatigue tests were undertaken according to the test protocol outlined in [13]. This protocol involved first growing the crack under quasi-static loading until a clearly visible stable crack extension has been observed, which should be a relatively short distance, i.e. less than 3.0 mm, from the initial delamination, ao. This new pre-crack extension length, was termed ap-ao. Fatigue cycling was then started, under displacement control, with a deformation range where the maximum deformation was equal to the value reached in the preceding quasi-static loading test. (It should be noted that, if a pre-crack extension length of ap-ao is not used in the fracture mechanics test, then optimistically high values of the quasi-static toughness and fatigue resistance will be measured. This is because the starter crack film of length ao represents a relatively blunt crack tip compared to that of a pre-crack of length ap, which is naturally-grown ahead of the starter film prior to the commencement of the test.) For any given DCB specimen, the test method that was employed involved growing the crack under cyclic-fatigue loading, at a relatively low frequency of 5 Hz, to avoid heating effects, for a relatively short distance from the initial value of the pre-crack extension length, ap-ao, whilst taking readings of the number of cycles, N, crack length, a, load, P, and displacement, δ. This fatigue test was then halted and the fatigue testing was repeated, but now with respect to the new, longer crack that was present in the DCB specimen, i.e. the crack length ap-ao that was now present was taken to be the relevant initial value for this repeated fatigue test. Thus, a key variable when testing a given DCB test is the value of the pre-crack extension length, ap-ao, prior to measurements being taken for any cyclic-fatigue test. For these fatigue tests [18, 19], the test temperature was − 40o, 50o or 80o C and the value of the \(\:R\)-ratio used was 0.1 or 0.5. The measured data were employed to calculate, for a given DCB test at a given value of the crack extension length, ap-ao, the FCG rate, da/dN, using the ‘incremental polynomial method’ [11, 13]. Also, the values of the maximum and minimum energy release-rate, \(\:{G}_{max}\:\)and \(\:{G}_{min}\), applied in a fatigue cycle were deduced from the maximum and minimum applied measured loads,\(\:\:{P}_{max}\) and \(\:{P}_{min},\) respectively, using the ‘modified compliance method’ as described in detail in the ISO Standard [1].
Finally, it should be noted that experimental results reveal that the DCB fatigue test may show a great deal of scatter [9, 10], which in-part arises from fibre-bridging developing during the test, as noted above. Another source of possible scatter in the experimental data arises from the fact that changes in the fracture or fatigue delamination resistance of fibre-reinforced polymer-matrix composites may occur from the absorption of moisture from the respective ambient humidity [28–31]. Thus, tests results obtained outside of a controlled laboratory climate, e.g. 23 ± 2°C and 50 ± 5% relative humidity [32], at different temperatures without controlling the ambient humidity may therefore be affected by the level of moisture. In the present tests [18, 19] the relative humidity in the temperature chamber was not reported.
4.1 Overview
In the present section, the experimental results from the tests conducted [18, 19] at -40o, 50o and 80oC and at the R-ratios of 0.1 and 0.5, and reinterpreted according to the theoretical scheme discussed above, for the CFRP are first considered, see Figs. 2 to 7. The use of the Hartman-Schijve Eq. (2), to replot all these data to obtain a unique, linear, master relationship is then presented and these data are compared to the previous results [14, 15] for the same type of CFRP obtained at 22oC, see Fig. 8. The parameters deduced from this approach are then used to compute the experimentally measured results that are shown in Figs. 2 to 7. Finally, the ‘worst-case upper-bound FCG curves’, for a small, naturally-occurring delamination present in a structure or component using this type of CFRP, are calculated using the Hartman-Schijve methodology and are compared to the experimentally measured results, see Figs. 9 and 10.
4.2 Experimental plots of the logarithmic da/dN versus the logarithmic \(\:\varDelta\:\sqrt{G}\)
In Fig. 2 values of the logarithmic da/dN versus the logarithmic \(\:\varDelta\:\sqrt{G}\) calculated from the tests reported in [18, 19] at -40oC for an R-ratio of 0.5 for the CFRP composites are given as a function of the pre-crack extension length, ap-ao, prior to the start of measurements from the DCB fatigue test.
As may be seen from the results shown in Fig. 2, the FCG curves move steadily to the right as the pre-crack extension length, ap-ao, prior to measurements being taken for the test is increased. This implies that there is a retardation of the FCG rate as the value of ap-ao is increased. That is, as the value of ap-ao increases, and for a given value of \(\:\varDelta\:\sqrt{G}\), the corresponding value of da/dN is lower; so, at a given value of\(\:\:\varDelta\:\sqrt{G}\), the fatigue crack grows slower as the value of ap-ao is increased. These observations arise from the extent of fibre bridging in the DCB test specimen being more extensive as the pre-crack extension length, ap-ao, is increased, since this retards the rate of delamination growth at a given value of\(\:\:\varDelta\:\sqrt{G}\). It is very important to note that such results as in Fig. 2 agree in general form with those from previous studies [e.g. 8,13–15,25,26] and clearly reveal that there is not one unique FCG rate curve. Instead, a number of such FCG rate curves may be obtained depending upon the chosen value of the pre-crack extension length, ap-ao, at the start of the test, prior to measurements being taken from that given cyclic-fatigue test. The results shown in Figs. 3 to 7 for the other test temperatures and R-ratios all reveal similar effects. Furthermore, by comparing Figs. 2 and 3 for − 40oC, Figs. 4 and 5 for 50oC and Figs. 6 and 7 for 80oC, it may be seen that for the DCB tests, at a given value of the pre-crack extension length, ap-ao, then when subjected to the higher R-ratio of 0.5, as opposed to 0.1, a somewhat higher value of da/dN is recorded for a given value of the \(\:\varDelta\:\sqrt{G}\). This is as expected [24], since an increase in the R-ratio increases the mean stress and therefore for a given value of \(\:\varDelta\:\sqrt{G}\), at a given value of ap-ao, a higher R-ratio leads to a higher FCG rate, da/dN. (The effect of test temperature on the FCG behaviour is discussed below.)
4.3 Use of the Hartman-Schijve Equation
To bring all the results shown in Figs. 2 to 7 together in one ‘master’ plot, the use of the Hartman-Schijve methodology, more specifically Eq. (2), is next examined to investigate whether the experimental results shown in Figs. 2 to 7 can be replotted to give a unique, linear, master curve so that the constants D and n may be ascertained. To achieve this, the values of A and \(\:\varDelta\:\sqrt{{G}_{thr}}\) are chosen so as to ensure that Eq. (2) best fits an experimental set of test data of logarithmic da/dN versus logarithmic \(\:\varDelta\:\sqrt{G}\:\)over the entire range of FCG rates. As in [14, 15], the values of A and \(\:\varDelta\:\sqrt{{G}_{thr}}\:\)were determined using the ‘Total Least Squares’ methodology described in [33], so that, for a given set of test data at a given value of ap-ao, the logarithmic da/dN versus logarithmic \(\:\left[\frac{\varDelta\:\sqrt{G}-\:\varDelta\:\sqrt{{G}_{thr}}}{\surd\:\left\{1-\:\sqrt{{G}_{max}}/\sqrt{A}\right\}}\right]\:\)plots became virtually linear. After the individual linear relationship for a given set of test data points had been determined, a combined plot of each of the different tests was assembled, as shown in Fig. 8. Here, it can be seen that, allowing for experimental error, all the resultant plots enable a single, linear, master relationship to be defined when using logarithmic axes. This unique, linear, master relationship, i.e. as in Eq. (2), holds for the over forty sets of data shown in Fig. 8. The value of the linear coefficient of determination, R2, for this linear plot is 0.93. This is somewhat lower than found previously [14, 15] due to the relatively high scatter observed in the test conducted at 80oC at an R ratio of 0.1 with ap-ao being 90.6 mm, see Fig. 7. Notwithstanding, the linear fit for the present set of test data is in very good agreement with that from previous work [14, 15], as may be seen from Fig. 8, and the values of D and n for the present and previous tests [14, 15] are 1.23 x 10− 10 and 4.49, respectively. These values are used below (a) to compute the logarithmic da/dN versus logarithmic \(\:\varDelta\:\sqrt{G}\) relationships as a function of ap-ao, together with the respective \(\:\varDelta\:{\sqrt{G}}_{thr}\) and \(\:\surd\:A\) values and (b) to predict the worst-case, upper-bound FCG rate curves for a small naturally-occurring delamination, together with the appropriate mean value of \(\:\varDelta\:{\sqrt{G}}_{thr}\) (taken to be zero) and the quasi-static value of the Mode I (tensile) interlaminar fracture energy, \(\:{G}_{co}\), at the onset of crack growth, as described below.
4.4 Computed plots of the logarithmic da/dN versus the logarithmic \(\:\varDelta\:\sqrt{G}\)
Equation (2) with the values of the parameters needed to fit the Hartman-Schijve relationship, see above, can now be used to compute the full experimental curve of logarithmic da/dN versus logarithmic \(\:\varDelta\:\sqrt{G}\). The computed relationships are shown in Figs. 2 to 7 and, as may be seen, there is excellent agreement between the experimental data and the computed curves from the Hartman-Schijve methodology. Indeed, the values of the coefficients of determination, R2, associated with a comparison of the measured and computed curves shown in Figs. 2 and 3 were determined and have a mean of about 0.90 and a standard deviation of 0.08. Therefore, despite the obvious and expected scatter in the experimental measurements, the values of R2 for the various computed curves are relatively high, thereby confirming the good agreement between the experimental and theoretical results.
4.5. The worst-case upper-bound FCG curve for sustainment
Let us next address the question of how to determine the worst-case upper-bound FCG curve of da/dN versus \(\:\varDelta\:\sqrt{G}\) that is needed to assess the FCG rate for a small naturally-occurring delamination that may arise in an operational airframe, i.e. for a sustainment assessment of the airframe. To undertake this calculation we use Eq. (2) and take from Fig. 8 the values of the constants D and n to be 1.23 x 10− 10 and 4.49, which are in agreement with previous work for this CFRP [15]. Next, we need the value \(\:\varDelta\:\sqrt{{G}_{thr}}\), and following previous convention [15] we set the value of \(\:\varDelta\:\sqrt{{G}_{thr}}\) to be zero.
This only leaves the question of what value to use as the worst-case value of the apparent cyclic fracture toughness, \(\:A\). However, since we are dealing with small, naturally-occurring cracks, and since as shown in [18, 19], the value of \(\:{G}_{co}\)appears to be essentially independent of the test temperature, the logical approach is to use the worst-case [8, 15, 34, 35] of the ‘mean-3σ’ value of the quasi-static initiation term, termed \(\:{G}_{co,3\sigma\:}\). Noting that the mean value of \(\:{G}_{co}\) given in [15, 18] is 250 J/m2 with a standard deviation, σ, of ± 45 J/m2, this yields a worst-case value of \(\:\sqrt{A}\:\)of 10.7 √(J/m2).
Now, in Figs. 9 and 10 the values of logarithmic da/dN versus logarithmic \(\:\varDelta\:\sqrt{G}\) are plotted again for the tests performed at -40o, 50o and 80oC for the CFRP for the two R-ratios of 0.1 and 0.5, respectively. Values are given in the legend for the pre-crack extension length, ap-ao, prior to the start of measurements from the DCB fatigue test specimen. It may be seen that the experimental data reveals that the FCG rate can accelerate with elevated temperatures but decrease at sub-zero temperatures. However, the dependence of the FCG curve at a given value of \(\:\varDelta\:\sqrt{G}\) on the pre-crack extension length, ap-ao, greatly complicates the interpretation and assessment of the overall effect of test temperature.
The resultant worse-case FCG curves for a small naturally-occurring delamination that may arise in an operational airframe were calculated as described above and are shown in Figs. 9 and 10, where they are labelled the ‘Small delam curve’. Several interesting points arise concerning these worst-case curves. Firstly, these worst-case FCG curves shown in Figs. 9 and 10 are in very good agreement with that calculated for the previous tests conducted [15] at 22oC at R-ratios of 0.1, 0.3, 0.5 and 0.7. Secondly, as required, these predicted FCG worst-case curves shown in Figs. 9 and 10 encompass and bound all the experimental results. Thirdly, these (sustainment) FCG curves are independent of the test temperature and the R-ratio. Fourthly, the vertical lines shown in Figs. 9 and 10 are for the case when the value of \(\:{G}_{max}\:\)is taken to be equal to \(\:{G}_{co,3\sigma\:}\)= \(\:A\) in Eq. (2) and they represent the asymptotic values for the worst-case FCG curves for a naturally-occurring delamination. Finally, these predicted FCG curves might be considered by some to be ‘overly-conservative’ but they are as determined in accordance with standard airframe economic life-assessment procedures, as first delineated by Lincoln et al. [36]. (The paper by Lincoln [36] was the first to highlight that a sustainment analysis should use the crack growth curve associated with small naturally-occurring cracks.) Indeed, one reason, of course, for their apparent conservative appearance is that we have chosen to use the ‘mean-3σ’ value of the quasi-static initiation term, termed \(\:{G}_{co,3\sigma\:}\), which yields a worst-case value of \(\:A\). This is termed the ‘A’ basis approach [8, 34, 35]. In this case, the mechanical property value indicated is the value above which at least 99% of the population of values is expected to fall with a confidence of 95%. This value is used to design and predict the service-life of a member where the loading is such that its failure would result in a loss of structural integrity. This approach to ensuring structural integrity is mandated in the NASA Fracture Control Handbook NASA-HDBK-15-10 [6]. If a lower number of standard deviations, σ, is taken, e.g. taking minus two standard deviations as in the ‘B’ basis approach [8, 34, 35], then the statistical probability of failure increases and the design becomes less conservative.
The present paper addresses the problem of fatigue crack growth in composite structures, with special relevance to airframes. Assessment of their in-service life can be based on either a ‘no-growth’ or a ‘slow-growth’ design philosophy. Whilst the most widely used approach is to adopt a ‘no-growth’ approach, it is accepted that this can result in an overly conservative design. Furthermore, even for ‘no-growth’ designs, delamination growth arising from cyclic fatigue loads can still arise in-service. Thus, two of the immediate challenges facing the composites community are to extend the ‘no-growth’ design philosophy to allow for the nucleation and growth of small naturally-occurring delaminations and to develop the tools needed to determine the remaining life of a damaged airframe, and hence the necessary inspection intervals. The main aim of the present paper has been therefore to investigate the robustness of the Hartman-Schijve methodology to meet this challenge when the effects of test temperature, together with the R-ratio, on the fatigue behaviour are considered.
Studies have been published in the literature [18, 19] on the cyclic fatigue crack growth (FCG) behaviour, as a function of both test temperature and R-ratio, of a continuous carbon-fibre epoxy-matrix plastic (CFRP) composite which was fabricated using a prepreg of unidirectional, continuous carbon fibres in a thermosetting epoxy polymer matrix. We have re-interpreted these data such that a Hartmann-Schjive approach [7, 8, 15, 16] may be adopted. Hence, worse-case FCG curves for a small naturally-occurring delamination that may arise in an operational airframe have been deduced. These curves, which are obtained by following an approach that reflects the USAF-Boeing approach [36] and that mandated in NASA-HDBK-1510 [6], are in good agreement with previous results [15] for tests conducted at 22oC at R-ratios of 0.1, 0.3, 0.5 and 0.7. Further, as required, these predicted worst-case, small naturally-occurring delamination FCG curves encompass and bound all the experimental results; and they are independent of the test temperature and the R-ratio. Such curves provide the data needed for a ‘slow-growth’ design philosophy to be adopted and for the remaining life and inspection intervals to be determined. Otherwise the detection of delamination damage in an operational aircraft will lead to the need to either immediately repair or to replace the component.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding:
This work did not receive external funding.
Author Contribution
Andreas J. Brunner : Review & Editing. Anthony J. Kinloch : Validation, Writing, Review & Editing. Rhys Jones : Analysis and Methodology, Review & Editing.
Acknowledgements
The inputted experimental data has been previously published [18,19] and the authors would wish to thank Dr. L.Yao for making some of it available to Professor Jones in a spreadsheet format.
Data Availability
Data will be made available on request.
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No competing interests reported.