ENGINEERING FRACTURE MECHANICS 2016COMPUTING THE GROWTH OF NATURALLY-OCCURING DISBONDS IN

ADHESIVELY-BONDED PATCHES TO METALLIC STRUCTURES

W. Hu1, R. Jones1 and A. J. Kinloch2

1Centre of Expertise for Structural Mechanics, Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria, 3800, Australia.

2Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK

Abstract: In 2009 the US Federal Aviation Administration (FAA) introduced a slow growth approach for certifying composite and adhesively-bonded structures. This approach requires that delamination or disbond is slow, stable and predictable under cyclic-fatigue loads. The present paper addresses the challenge of developing a methodology capable of enabling this approach to certification to be implemented. To this end we have examined the growth of disbonds from small naturally-occurring material discontinuities in adhesively-bonded structures. It is shown that, for the examples studied, the disbond growth histories can be accurately computed using a form of the Hartman and Schijve variant of the NASGRO crack-growth equation. It is also shown that the scatter in the disbond growth histories can be captured by allowing for small changes in the fracture-mechanics threshold term. These findings suggest that the Hartman and Schijve variant of the NASGRO crack-growth equation has the potential to address the ‘slow growth’ approach to certifying composite/bonded structures and bonded repairs outlined in the US FAA Airworthiness Advisory Circular No: 20-107B.

Keywords: Adhesives, fatigue crack growth, NASGRO, joints, scatter.

Corresponding authors: rhys.jones@monash.edu, a.kinloch@imperial.ac.uk

1. INTRODUCTION

Adhesively-bonded joints are commonly used in the aerospace industry both in the fabrication of new aircraft and in the repair of both metallic and composite structures [1, 2]. The adhesives used are typically based upon thermosetting epoxy polymers which are highly crosslinked and amorphous in nature. As with all materials, such epoxy polymers undergo failure under cyclic fatigue loading more rapidly than under the equivalent loads applied statically. However, little work has been reported on gaining a fundamental understanding of the mechanisms involved [3]. Nevertheless, it is clear that the fatigue mechanisms which are operative in epoxy polymers at relatively low frequencies below about 10 to 20 Hz are broadly similar to those in other materials [4]. They involve the creation of a plastic damage zone at the crack tip, which typically is in the form of localised or diffuse shear bands in the case of epoxy polymers, which is repeatedly subjected to tensile and then compressive stress fields as the polymer is subjected to repeated loading-unloading cycles. This causes disruption of the plastic zone and rupture of the polymeric molecular chains, and thus more readily enables crack advance under such applied fatigue loads. Nevertheless, significant advances have been made in measuring accurately the fatigue crack behaviour of epoxy polymers, especially via applying a fracture mechanics approach [3].

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Until recently certification of adhesively-bonded aircraft structures was based on a ‘no growth’ design philosophy. However, there have been a number of in-service instances and full scale fatigue tests where there has been extensive delamination/disbonding [5, 6]. In each case the disbonds grew from small naturally occurring sub mm material defects. To address this problem the US Federal Aviation Administration (FAA) introduced a slow growth approach to certify composite and adhesively-bonded structures and adhesively-bonded repairs [7]. The precise wording given in FAA Advisory Circular 20-107B [7] is:

“The traditional slow growth approach may be appropriate for certain damage types found in composites if the growth rate can be shown to be slow, stable and predictable. Slow growth characterization should yield conservative and reliable results. As part of the slow growth approach, an inspection program should be developed consisting of the frequency, extent, and methods of inspection for inclusion in the maintenance plan.”

Unfortunately a lack of understanding of, and an inability to predict, disbond growth, especially for disbonds that arise from small naturally-occurring material discontinuities, is an obstacle that hampers the use of this approach to certification. It also means that to ensure against growth the design limit strains are kept low. As such the present paper reveals how the approach presented in [8], which dealt with disbond growth associated with large artificial initial disbonds, can be used to compute the growth of disbonds that grow from small naturally occurring sub mm material defects. It is also shown that the constants needed for this approach can be determined from tests on specimens containing large artificial initial disbonds.

A detailed review of the current approaches for predicting crack (i.e. disbond or delamination) growth in both adhesively-bonded and composite structures was presented in the recent paper by Pascoe et al. [9]. Reference [9] noted that it is now accepted that the strain-energy release-rate (SERR), G, has a strong correlation with the delamination/disbond growth and, therefore, several authors have presented variants of the Paris crack-growth equation to represent delamination/disbond growth. Initial formulations tended to express the crack-growth rate per cycle, da/dN, as a function of either Gmax or ∆G [10, 9]; where Gmax is the maximum SERR applied in the fatigue cycle and ∆G is the range of the applied SERR and ∆G = Gmax - Gmin, where Gmin is the minimum SERR applied in the fatigue cycle. However, Martin and Murri [12] found that the exponents relating da/dN to Gmax or ∆G were relatively high and, as a result, correctly concluded that:

“For composites, the exponents for relating propagation rate to strain energy release rate have been shown to be high especially in Mode I. With large exponents, small uncertainties in the applied loads will lead to large uncertainties (at least one order of magnitude) in the predicted delamination growth rate. This makes the derived power law relationships unsuitable for design purposes1.”

To overcome this shortcoming researchers [5, 8, 13] have subsequently built on the work of Alderliesten et al. [14, 15] and the Hartman-Schijve variant [16, 17] of the NASGRO equation [18], which was originally developed to represent fatigue cracking in metals. This work led to a formulation of a delamination/disbond growth equation in terms of both √Gmax

and ∆√G, viz:1 Hence, it also makes the derived power law relationships unsuitable for the purpose of certifying composite and adhesively-bonded structures, and bonded repairs to either metallic or composite structures.

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dadN

=D [ ∆√G−∆√Gthr

√{1−√ Gmax

A } ]n

(1)

Here ∆ √G=√Gmax−√Gmin and D and n are experimental fitting constants. The value of A is best interpreted as a parameter chosen so as to fit the experimentally-measured da/dN versus G (or Gmax) data [8]. Now, for some structural adhesives and composites, it is often found from experimental tests that a clearly defined threshold value exists, below which little fatigue crack growth occurs. In this case the value of the threshold, ∆ √Gthr, is taken to be the experimentally-determined value [8]. If this is not the case, then the concepts described in the ASTM E647-13 standard, which are widely used by the metals community, may be employed. This standard defines a threshold value which, in the above terminology, may be taken to be the value of ∆ √G at a value of da/dN of 10-10 m/cycle [8].

Advantages of the formulation stated in Equation (1) are that a ‘master’ linear representation has been observed for the structural adhesives and composites studied when the experimental data are replotted according to this formulation [8]. Further, the slope, n, of this linear relationship has a relatively low value of about two [5, 4, 13]. As discussed above, this will greatly assist a designer to allow for some fatigue crack growth to occur but still provide a safe-life for the structure. Further, it has been found that the exponent, n, and the associated constant of proportionality, D, both appear to be independent of the mode mix [5, 8]. A related formulation has also been presented in [19].

Whilst this approach has been shown to be able to accurately represent both delamination and disbond growth [5, 4, 13] associated with large initial defects, the present paper focuses on small sub-millimetre initial disbonds. To this end two examples are studied where naturally-occurring disbonds have been allowed to initiate and grow in: i) a symmetrical double over-lap adhesively-bonded specimen [20] and ii) an asymmetrical adhesively-bonded doubler joint, typical of a bonded repair [1]. The present paper reveals that, in both cases, the Hartman-Schijve variant of the NASGRO equation gives rise to computed disbond-length versus number of fatigue cycle histories that are in very good agreement with the experimental measurements. This finding highlights the potential of the Hartman-Schijve variant of the NASGRO crack growth equation to be used to determine disbond growth histories, and hence to estimate the necessary inspection intervals needed to certify composite and adhesively-bonded structures and bonded repairs, see Appendix. It also raises the possibility of overcoming the artificially imposed strain limits, which are there to ensure no growth, mentioned above. This (in turn) has the potential to enable more highly strained and therefore lighter and more fuel efficient designs. To the best of the authors knowledge this is one of the first papers to show how to use long crack disbond growth data to accurately compute the growth of small naturally occurring disbonds.

2. THEORETICAL BACKGROUND

2.1 Introduction

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It is of interest to first consider the established ability of the Hartman-Schijve variant of the NASGRO equation to represent the growth of cracks from small naturally-occurring material discontinuities in metals [16, 21, 22]. Here it has been shown that one additional advantage of this formulation is its ability to also capture the scatter seen in fatigue tests under both constant amplitude and representative flight-load spectra [21, 22]. Indeed, it has been shown that this is true for both large cracks and for cracks that initiate and grow from small naturally occurring material discontinuities [21, 22]. For metals, the Hartman-Schijve variant of the NASGRO equation can be written in the form:

dadN

=D( ∆ K−∆ K thr

√1−Kmax

A )n

(2)

where ∆ K (= Kmax – Kmin) is the range of the stress-intensity factor (SIF), Kmax and Kmin are the maximum and minimum values of the SIF in a cycle, respectively The parameter A is a constant and ∆ K thr is a threshold value, see [16] for more details. The constant n has been found to be approximately two for several metallic materials [16, 17, 21, 22].

When analysing delamination/disbond growth in composites and adhesively bond structures the SERR approach, rather a SIF approach, is generally used [5, 8-15], for the reasons explained in [8]. The present authors [8] have previously demonstrated that, for large disbonds (i.e. large through-thickness disbonds) Equation (1) is applicable to Mode I, Mode II and Mixed-Mode I/II disbond growth. Further, different R-ratio, temperature and humidity tests may also be described by a single ‘master’ curve, when the experimental data are plotted according to Equation (1). This concept was validated for a number of structural adhesives [8]. As noted above, the present paper will investigate the ability of this approach, as embodied in Equation (1), to predict the disbond histories associated with disbonds that grow from relatively small, naturally-occurring discontinuities.

2.2 Accounting for the variability seen in crack growth

The seminal work on the variability in fatigue crack growth (FCG) rates by Virkler et al. [23] examined the variability in FCG by eliminating the variations in initial discontinuity size and loading. In this work Virkler et al. carefully prepared sixty-eight, nominally identical, 2.54 mm thick aluminium-alloy 2024-T3 centre-notched specimens and tested them under constant amplitude loading. The number of cycles it took for the centre-cracks to reach pre-specified lengths was determined. Care was specifically taken to ensure that the initial crack length, 2a, was 18.0 mm. This study revealed the degree of scatter in the FCG of such long cracks, even when the initial crack length was held constant, see Figure 1. Reference [16] illustrated that, with the values of A = 70 MPa√m, D = 1.2 10-9 m/cycle and n = 2 (taken from [17]), the variability in the measured FCG rates was captured to a relatively high degree of accuracy by merely allowing for changes in the value of Kthr, i.e. using vales of 2.9, 3.2, 3.4, 3.6, 3.8, 4 and 4.2 MPa√m in Equation (2). Also shown in Figure 1 is the conservative nature of the computed crack growth curve for the case when ΔKthr = 0.0 MPa√m. Reference [22] subsequently revealed that this finding, i.e. that variability in crack growth seen in crack growth under both constant amplitude and variable amplitude loading could be captured by allowing for small changes in the term Kthr, held for both large cracks and for cracks that initiated and grew from small naturally occurring material discontinuities.

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Reference [8] extended this finding, i.e. that the variability in crack growth could be captured by allowing for variability in the threshold, to the growth of relatively large, through-thickness, initial disbonds in adhesively-bonded joints. One such example involved FCG data measured for an epoxy-film aerospace structural adhesive [19], namely ‘EA9628’ adhesive (Hysol Dexter, USA). The fracture-mechanics tests were performed under Mode I loading conditions at a displacement ratio, R, of 0.5 and at 23±1°C and a relative humidity of 55±5%RH. A plot of the experimentally obtained log da/dN versus log G Imax data is given in Figure 2. Now, the data in Figure 2 is replotted in Figure 3 according to Equation (1). Here it may be seen that the test data, when plotted using log-log axes, can be represented by a linear ‘master’ curve with a slope of n = 2.55. The values of the constants employed in the Hartman and Schijve variant of the NASGRO crack-growth equation, i.e. Equation (1), to obtain the ‘master’ curve for the growth of disbonds in the ‘EA9628’ epoxy adhesive are given in Table 1 [8].

The log da/dN versus log G Imax relationships may now be computed using Equation (1) with the values of D, A and n fixed and allowing Δ√G thr to vary between 7.16 to 8.58 √(J/m2), see Table 1. (In this case, the values of Δ√Gthr were determined experimentally from replicate tests.) These computed relationships are compared to the experimental results in Figure 2. As may be seen, for each replicate test, there is excellent agreement between the experimental data and the computed representation. Thus, the cyclic-fatigue behaviour of the ‘EA9628’ structural adhesive may indeed be very well and conveniently represented using the Hartman and Schijve variant of the NASGRO crack-growth equation, see [8] for more details. Of special note is the observation that the variability in the fatigue results may be taken into account by this approach from employing the different values of ∆ √G Ithr, which do vary somewhat for the replicate test specimens, as shown in Table 1. At this stage it should be noted that the values of the parameters D, A and n are dependent on the material and the test environment.

3. EXPERIMENTAL: THE FATIGUE FRACTURE-MECHANICS DATA  

The papers by Pascoe et al. [1] and Cheuk et al. [20] have presented the delamination histories associated with tests employing an asymmetrical adhesively-bonded joint and a symmetrical double overlap adhesively-bonded joint, respectively, when they are subjected to cyclic fatigue tests. For each type of specimen the substrates were bonded using an aerospace epoxy-film adhesive (i.e. ‘FM73’ from Cytec, UK). Further, in both cases, the crack growth, which was through the adhesive layer, that was recorded under the fatigue loading initiated from relatively small, naturally-occurring, disbonds.

Prior to predicting the disbond growth histories associated with these test specimens, information on the fatigue performance of the ‘FM73’ adhesive is needed. The paper by Johnson and Butkus [25] has presented the results of fracture-mechanics tests using the ‘FM73’ adhesive to bond aluminium-alloy 7075-T651 substrates to form double-cantilever beam specimens. In all cases the locus of joint failure was via cohesive crack growth through the adhesive layer, which is the same type of failure as observed by Pascoe et al. [1] and Cheuk et al. [20] in their test specimens. Johnson and Butkus [25] plotted their results in the form of a log da/dN versus log ΔGI relationship, as shown in Figure 4.

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The experimental data given in Figure 4 is shown replotted in Figure 5 according to the Hartman and Schijve variant of the NASGRO crack-growth equation embodied in Equation

(1). Hence, log da/dN is plotted against log [ ∆√GI−∆√GIthr

√ {1−√G Imax/√ A } ] and the values of the various

parameters employed are given in Table 2. The plot in Figure 5 is indeed linear with a low degree of scatter, as revealed by the relatively high value of the correlation coefficient that has been deduced. This linear plot has a slope, n, of value of 2.7. Equation (1), with the values given in Table 2, was then used to compute the da/dN versus ΔGI relationship and these results are also plotted in Figure 4. Again, there is excellent agreement between the measured and the computed relationships.

These results from relatively short-term fracture-mechanics tests are next employed to predict the long-term crack-growth histories from naturally-occurring disbonds in the test specimens studied by Pascoe et al. [1] and Cheuk et al. [20]. The Hartman and Schijve variant of the NASGRO crack-growth equation is employed, as represented in Equation (1), with the necessary values based upon those given in Table 2.

4. PREDICTING THE FATIGUE BEHAVIOUR ADHESIVELY-BONDED PATCH REPAIR JOINTS  

4.1 The Bonded-Joint Configuration from Cheuk et al. 

4.1.1 Introduction

Cheuk et al. [20] have presented disbond length versus number of fatigue cycles data for a symmetrical double over-lap adhesively-bonded specimen, see Figure 6. The inner and outer substrates were 2024-T3 aluminium-alloy and the adhesive was ‘FM73’. The fatigue crack was observed to grow cohesively through the adhesive layer from naturally-occurring defects which were present in the adhesive layer. The modulus and Poisson’s ratio associated with the aluminium-alloy substrates and the ‘FM73’ adhesive are shown in Table 3.

The inner aluminium-alloy substrate was 400 mm long and 6.4 mm thick. The outer aluminium-alloy substrate was 200 mm long and 3.05 mm thick. The ‘FM73’ adhesive layer was 0.4 mm thick. The specimen was symmetrical with a width of 20 mm. The right-hand side of the specimen is shown in Figure 6.

The specimen was subjected to variable amplitude loading. As explained in [20] the test spectrum consisted of a series of constant amplitude (sub) spectra, i.e.:

(i) Sub-spectra 1: 18,000 cycles, at a frequency of 3Hz, of constant amplitude loading where the load was varied from 0 to 25 kN.

(ii) Sub-spectra 2: 62,000 cycles, at a frequency of 3Hz, of constant amplitude loading where the load was varied from 0 to -25 kN.

(iii) Sub-spectra 3: 25,000 cycles, at a frequency of 3Hz, of constant amplitude loading where the load was varied from 0 to 25 kN.

(iv) Sub-spectra 4: 26,000 cycles, at a frequency of 3Hz, of constant amplitude loading where the load was varied from 0 to -25 kN.

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(v) Sub spectra 5: 50,000 cycles, at a frequency of 3Hz, of constant amplitude loading where the load was varied from 0 to 25 kN.

(However, it should be noted that Cheuk et al. [20] observed that the disbond did not propagate under compression, i.e. sub-spectra (ii) and (iv). Therefore, these two sub-spectra were ignored in the analyses below.)

4.1.2 Computation of the SERR as a function of crack length

Before we can predict the delamination growth, the SERR, G, versus disbond (crack) length, a, relationship is needed. In [20] this relationship was obtained using finite element analysis (FEA). However, for convenience, the geometry of the FEA model used in [20] to determine this relationship differed somewhat from the actual geometry used in the experimental tests. Namely, the width and thickness of the specimen remained the same as in the experimental test, but the inner and outer substrates were somewhat shortened to 240 mm and 120 mm, respectively. Therefore it was decided to undertake an independent analysis of the double over-lap adhesively-bonded specimen used in [20], using the properties given in Table 3. In this two-dimensional, elastic, FEA model the length of the crack was placed within the adhesive layer and its length was varied from 0.25 mm to 10 mm and the virtual crack-closure technique (VCCT) was implemented. The calculated values of the total SERR, G, as a function of the crack length, a, from the two FEA studies are shown in Figure 7. The two independent sets of results are in excellent agreement. The empirical relationships between the SERR, G, and the disbond (crack) length, a, from Figure 7 is given in Equation (3):

G={ ( 11.12√ πaa0.377 )

2

,∧a<1

(11.014 √πaa0.453 )

2

,∧a≥1

(3)

4.1.3 Comparison of theoretical predictions and measured debonding histories

The disbond length history versus number of fatigue cycles was now computed using the procedure outlined in Figure 8. In this procedure the values of the constants A and D used in Equation (1) were as given in Table 1, i.e. A = 2000 J/m2, D = 1.9 10-10 m/cycle, n = 2.7 and Δ√Gthr = 7.1 √(J/m2). Equation (1) was integrated using the simple forward integration procedure outlined in Figure 8 and the Gmax versus a relationship shown in Figure 7.

The measured and predicted delamination histories for the naturally-occurring defects in the double over-lap adhesively-bonded specimens growing under the cyclic fatigue loads are shown in Figure 9. There is excellent agreement between the measured and predicted results.Next, it was considered to be a valuable exercise to try and also predict the typical scatter observed in the crack growth histories of the adhesively-bonded double over-lap joints. As discussed above in Section 2.2, it is considered that the variability in the observed crack growth may be captured by allowing for variability in the threshold value, Δ√Gthr. Now, unfortunately, Johnson and Butkus [25] did not undertake sufficient replicate fracture-mechanics tests to enable the scatter on their reported data to be accurately assessed. However, the epoxy-film adhesive ‘FM73’ is very similar in chemical and mechanical properties to the ‘EA9628’ epoxy-film adhesive discussed above. Thus, it is not unreasonable

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to apply the degree of scatter observed for this adhesive to the values of the threshold for the ‘FM73’ adhesive. This proposal leads to lower- and upper-bound values of Δ√GIthr of 6.6 and 7.6 √(J/m2), respectively, for the ‘FM73’ adhesive. Using these values of Δ√GIthr to account for the variability in the predicted crack growth, then from Figure 9 it may be seen that there is not only very good agreement between the measured and predicted disbond histories with Δ√GIthr = 7.1 √(J/m2), but that the measured data are also essentially bounded by these two computed predictions where Δ√GIthr = 6.6 and Δ√GIthr = 7.6 √(J/m2). Thus, Figure 9 reveals that in these bonded joints the growth, and associated variability, of a disbond from small naturally-occurring material discontinuities in the ‘FM73’ adhesive may be accurately captured using the Hartman-Schijve variant of the NASGRO equation, i.e. Equation (1).

4.2 The Bonded Joint Configurations from Pascoe et al. 

4.2.1 Introduction

The second problem studied involved disbond growth in the adhesive layer of an asymmetric joint consisting of an adhesively-bonded doubler as shown in Figure 10, where the adhesive was again the epoxy-film ‘FM73’ adhesive [1]. The test specimens consisted of a tapered aluminium-alloy 7175 adhesively-bonded to a 0.4 mm thick aluminium-alloy 7475 plate, which was bonded to a high static-strength (HSS) ‘Glare’ plate. The aluminium-alloy 7475 plate extended beyond the edge of the patch. Two tests were performed under load control with an R-ratio of 0.1. The initial, naturally-occurring, disbond grew in the adhesive layer which bonded the aluminium-alloy 7475 plate to the ‘Glare’ substrate and the length of the growing disbond was measured from the edge of the lower aluminium-alloy 7475 plate. For each test the length of the growing disbond was independently measured from both sides of the test specimen, so resulting in two sets of crack growth histories for any one test. The maximum applied stress in the ‘Glare’ plate employed for the cyclic fatigue tests was either 150 or 170 MPa.

Pascoe et al. [1, 26] used FEA with a remote stress on the ‘Glare’ substrate plate of 150 MPa or 170 MPa to obtain the total SERR, G, versus disbond length, a, relationship The results are given in Figure 11.

Analytical approximations for the G versus disbond length, a, relationships shown in Figure 11 are given below in Equations (4) and (5):

For an applied maximum stress of 150 MPa:

G=0.0019 a3−0.2122 a2+4.9287 a+238.12(4)

and, for an applied maximum stress of 170 MPa:

G=0.0023 a3−0.2744 a2+6.6657 a+312.79(5)

As may be seen from Figure 11, these analytical approximations in Equations (4) and (5) provide an excellent fit to the results obtained from the FEA methods for both the 150 MPa and the 170 MPa maximum fatigue stress levels that were employed.

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4.2.2 Comparison of theoretical predictions and measured debonding histories

Equation (1), together with the relationship between G and a given in Equations (4), and (5), and the associated constants given in Table 2 (i.e. A = 2000 J/m2, D = 1.9 10-10 m/cycle, n = 2.7 and Δ√GIthr = 7.1 √(J/m2)) were used to compute the disbond growth histories associated with each of the tests, as explained in the procedure outlined above and in Figure 8. The measured and the predicted histories of the disbond length versus the number of fatigue cycles are shown in Figure 12. As may be seen, the agreement between the measured and predicted crack growth histories, for both levels of applied maximum load, are in excellent agreement. Indeed, for the applied maximum load of 150 MPa, the predicted relationship is approximately the average of the histories for the two crack measurements, taken from either side of the joint.

As above, it was considered to be a valuable exercise to try and also predict the typical scatter observed in the crack growth histories of the asymmetrical adhesively-bonded doubler joints. As discussed above in Section 2.2, it is considered that the variability in the observed crack growth may be captured by allowing for variability in the threshold value, Δ√GIthr. Thus, as above, lower- and upper-bound values of Δ√GIthr of 6.6 and 7.6 √(J/m2), respectively, for the ‘FM73’ adhesive were employed. Using these values of Δ√GIthr to account for the variability in the predicted crack growth, then from Figure 12 it may be seen that there is very good agreement between the measured and predicted disbond histories with Δ√GIthr = 7.1 √(J/m2) an, furthermore, the measured data are also essentially bounded by these two computed predictions where Δ√GIthr = 6.6 and Δ√GIthr = 7.6 √(J/m2). Thus, Figure 12 also reveals that in these bonded joints the growth, and associated variability, of a disbond from small naturally-occurring material discontinuities in the ‘FM73’ adhesive may be accurately captured using the Hartman-Schijve variant of the NASGRO equation, i.e. Equation (1).

5 CONCLUSIONS

The present paper has shown that the Hartman-Schijve variant of the NASGRO equation can be used to accurately represent the growth of disbonds under cyclic fatigue loading that initiate from small naturally-occurring discontinuities in adhesively-bonded joints. It is also shown that, as for metals and tests involving large artificial initial cracks, the scatter in the disbond growth histories may be captured by allowing for small changes in the threshold term, Δ√Gthr. These findings suggest that the Hartman-Schijve variant of the NASGRO crack growth equation has the potential2 to address the ‘slow growth’ approach to certify adhesively-bonded structures and adhesively-bond bonded repairs outlined in the US FAA Airworthiness Advisory Circular No: 20-107B.

These findings also raise the possibility of designing bonded composite repairs to metallic airframes to ensure that they meet the current damage tolerant design criteria.

6. REFERENCES 

2 See Appendix

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1. Pascoe, J.A., Rans, C.D. and Alderliesten, R.C. and Benedictus, R. (2013) Fatigue disbonding of bonded repairs – an application of the strain energy approach. 27th ICAF Symposium, Jerusalem, 5-7 June.

2. Baker AA. and Jones R., Bonded Repair of Aircraft Structure. 1988, The Hague: Martinus Nijhoff Publishers. pp 107- 173.

3. Kinloch, A.J. (1987) ‘Adhesion and Adhesives: Science and Technology’, Springer Science, New York.

4. Ritchie, R.O. (1999) Mechanisms of fatigue-crack propagation in ductile and brittle solids. Intern. J. Fracture, 100, 55-83.

5. Jones, R., Steltzer, S. and Brunner, A.J. (2014) Mode I, II and mixed mode I/II delamination growth in composites. Composite Structures, 110, 317-324.

6. Baker AA., Structural health monitoring of a bonded composite patch repair on a fatigue-cracked F-111C Wing, DSTO-RR-0335, March 2008.

7. Federal Aviation Authority, (2009) Airworthiness Advisory Circular No: 20-107B. Composite Aircraft Structure, 09/08/2009.

8. Jones, R., Hu, W. and Kinloch, A.J. (2015) A convenient way to represent fatigue crack growth in structural adhesives. Fatigue and Fracture of Engineering Materials and Structure , 38, 379-391.

9. Pascoe, J.A., Alderliesten, R.C. and Benedictus, R. (2013) Methods for the prediction of fatigue delamination growth in composites and adhesive bonds - a critical review. Engineering Fracture Mechanics, 112-113, 72-96.

10. Roderick, G.L., Everett, R.A. and Crews, J.H. Jr. (1974) Debond propagation in composite reinforced metals. Technical Report NASA (USA), TM X-71948.

11. Bathias, C. and Laksimi, A. (1985) Delamination threshold and loading effect in fiber glass epoxy composite. ASTM STP, 876, 217-237.

12. Martin, R.H. and Murri, G.B. (1990) Characterization of Mode I and Mode II delamination growth and thresholds in AS4/PEEK composites. ASTM STP, 1059, 251-270.

13. Jones, R., Pitt, S., Brunner, A.J. and Hui, D. (2012) Application of the Hartman-Schijve equation to represent mode I and mode II fatigue delamination growth in composites. Composite Structures, 94, 1343-1351.

14. Alderliesten, R.C., Schijve, J. and Zwaag, S. (2006) Application of the energy release rate approach for delamination growth in ‘Glare’. Engineering Fracture Mechanics, 73, 697-709.

15. Alderliesten, R.C. (2009) Damage tolerance of bonded aircraft structures. International Journal of Fatigue, 31, 1024-1030.

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16. Jones, R. (2014) Fatigue crack growth and damage tolerance. Fatigue and Fracture of Engineering Materials and Structures, 37, 463-483.

17. Jones, R., Molent, L. and Walker, K. (2012) Fatigue crack growth in a diverse range of materials. International Journal of Fatigue, 40, 43-50.

18. Forman, R.G. and Mettu, S.R. (1992) Behavior of surface and corner cracks subjected to tensile and bending loads in Ti-6Al-4V alloy. ASTM STP, 1131, 519-546.

19. Xiang, Y., Liu, R., Peng, T. and Liu, Y. (2014) A novel sub-cycle composite delamination growth model under fatigue cyclic loadings. Composite Structures, 108, 31-40.

20. Cheuk, P.T., Tong, L., Rider, A.N. and Wang J. (2005) Analysis of energy release rate for fatigue cracked metal-to-metal double-lap shear joints. International Journal of Adhesion and Adhesives, 25, 181-191.

21. Jones, R., Molent, L. and Barter, S. (2013) Calculating crack growth from small discontinuities in 7050-T7451 under combat aircraft spectra. International Journal of Fatigue, 55, 178-182.

22. Molent L. and Jones R., (2015) The Influence of Cyclic Stress Intensity Threshold on Fatigue Life Scatter, http:/dx.doi.org/10.1016/j.ijfatigue.2015.10.0006

23. Virkler, D.A., Hillberry, B.M. and Goel, P.K. (1978) The statistical nature of fatigue crack propagation. Trans. ASME, 101, 148-153.

24. Kinloch, A.J., Little, M.S.G. and Watts, J.F. (2000) The role of the interphase in the environmental failure of adhesive joints. Acta Materialia, 48, 4543-4553.

25. Johnson, W.S. and Butkus, L.M. (1998) Considering environmental conditions in the design of bonded structures: a fracture mechanics approach. Fatigue and Fracture of Engineering Materials and Structures, 21, 465-478.

26. Pascoe, J.A. (2015) Delft University of Technology, The Netherlands, Private Communication.

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APPENDIX

In the design of metallic structures the USAF Joint Services Structural Guidelines JSSG2006 lists the initial (mandatory) crack sizes to be used in design. These sizes essentially correspond to the minimal detectable crack size. The size of the initial disbonds/delaminations to be used is not spelt out in the FAA ac 20-107b. (Note: FAA ac 20-107b uses the terminology intrinsic flaws and small delaminations.) The authors interpretation of FAA ac 20-107b is that in this instance the original equipment manufacturer (OEM) would need to propose and justify their choice of an initial delamination/disbond size.

The situation can be somewhat different for aircraft sustainment. To clarify this let us focus on sustainment issues related to military aircraft and, more specifically, Australian military aircraft. In this case when disbonds are found in-service aircraft, as was the case in the boron-fibre epoxy repairs to the F111 wing-pivot fitting and the F111 lower-wing skin repairs [5, 6], the question arises: What is the disbond growth rate and what are the associated inspection intervals for growth from the observed disbond sizes? As such, in this instance, the “initial” disbond size is set by the in-service measurement.

Thus, in both instances, i.e. in both design and in sustainment, the size of the initiating disbond will be set albeit by the OEM in concert with the relevant airworthiness authority or by in-service measurements. As per Section 3, the parameters to be used in the Harman-Schijve variant of the NASGRO equation could be determined from Mode I DCB tests. The Harman-Schijve variant of the NASGRO equation could then be used to compute the disbond history from this initial disbond size. However, it should be noted that this would require that as the disbond grew, and its computed shape/size changed, the values of the SERR, G, would be need to be continuously re-computed and then these new values of G used to compute the new size and shape of the disbond.

This is essentially the process described in the various examples presented in this paper.

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Figure 1. Crack growth data from Virkler et al. [23] and the computed variability [16] for an aluminium-alloy (2024-T3). Note that the (conservative) curve computed using ΔKthr = 0 is also shown.

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100 10001.0E-12

1.0E-11

1.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

f(x) = 9.51805835912093E-29 x^7.96513696508586R² = 0.97392885848921

Test 1Power (Test 1)Test 2Test 3Test 4Test 5Computed Test 1Computed Test 2Computed Test 3Computed Test 4Computed Test 5

GImax (J/m2)

da/d

N (m

/cyc

le)

Figure 2. The measured [24] and computed curves for the fatigue behaviour for a rubber-toughened epoxy-film adhesive (‘EA9628’), from [8].

y = 5.26E-07x2.55

R² = 0.946

1.0E-11

1.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

0.01 0.1 1 10 100 1000

da/d

N(m/cycle)

(√GI -√GIthr)/√(1-√(GImax/A)) (√(J/m2))

Test 1

Test 2

Test 3

Test 4

Test 5

Figure 3. The Hartman-Schijve representation of the fatigue behaviour for a rubber-toughened epoxy-film adhesive (‘EA9628’), from [8].

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10 100 1000 100001.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

f(x) = 2.66470196124502E-16 x^3.44097259099727R² = 0.948011891304897

Measured

ΔGI (J/m2)

da/d

N (m

/cyc

le)

Figure 4. The measured [25] data points and computed curve for the fatigue behaviour for the rubber-toughened epoxy-film adhesive (‘FM73’).

1 10 1001.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

f(x) = 1.93094537056669E-10 x^2.69530565146897R² = 0.942182472564793

(Δ√GI-Δ√GIthr)/√(1-√(GImax/A)) (√(J/m2))

da/d

N (m

/cyc

le)

Figure 5. The Hartman-Schijve representation of the fatigue behaviour for the rubber-toughened epoxy-film adhesive ‘FM73’.

15

Figure 6. Schematic of the right-hand side of the symmetrical double over-lap adhesively-bonded specimen [20].

0 2 4 6 8 10 120

100

200

300

400

500

600

Cheuk et al. FEA results

Present FEA results

a (mm)

G (J

/m2)

Figure 7. The calculated values of the SERR, G, as a function of the crack length, a. The FEA results from Cheuk et al. [20] and the present study are both shown.

16

Figure 8. The flowchart of the procedure to compute the disbond growth as a function of the number, N, of fatigue cycles.

0 20000 40000 600000

5

10

15

20

25

30

Measured data

Computed Δsqrt.Gthr = 7.6

Computed Δsqrt.Gthr = 7.1

Computed Δsqrt.Gthr =6.6

N (Cycles)

a (m

m)

Figure 9. The measured [20] and predicted delamination histories for the initial naturally-occurring defects growing under the cyclic fatigue loading in the double over-lap adhesively-

bonded specimens.

17

Figure 10. The asymmetric joint consisting of an adhesively-bonded doubler and the location of the disbond [1].

0 10 20 30 40 500

100

200

300

400

FEA 170 MPa

a (mm)

G (J/

m2)

Figure 11. The calculated values of the SERR, G, as a function of the crack length, a, for applied stresses of 150 MPa and 170 MPa for the asymmetrical adhesively-bonded doubler

joint (see Figure 10) [1, 26]. (The FEA results and the polynomial fits, see Equations (4) and (5), are both shown.)

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0 100 200 300 400 500 6000

5

10

15

20

25

30

35

40

45

50170 MPa Crack 1170 MPa Crack 2Computed 170 MPa, Δsqrt.Gthr = 6.6Computed 170 MPa, Δsqrt.Gthr = 7.1Computed 170 MPa, Δsqrt.Gthr = 7.6150 MPa Crack 1150 MPa Crack 2Computed 150 MPa, Δsqrt.Gthr = 6.6Computed 150 MPa, Δsqrt.Gthr = 7.1

N (kilo cycles)

a (mm

)

Figure 12 . The measured and predicted delamination histories for the initial naturally-occurring defects growing under cyclic fatigue loading in the asymmetric joint consisting of

an adhesively-bonded doubler. Results are shown for both the 150 MPa and the 170 MPa maximum fatigue stress levels that were employed.

19