Advances in the Bonded Composite Repair o f Metallic Aircraft Structure phần 5 pdf

Chapter 8. Recent expansions in the capabilities of Rose’s closed-form una1ysi.s 20 1 A l!? ADHESIVE SHEAR STRESS (?e + ?P) * 0 ?e 7 ADHESIVE SHEAR STRAIN y Fig. 8.21. Elastic-plastic representation of adhesive non-linear behavior in shear mean that the adhesive actually behaves like a ductile metal. If it did, it would unload with a permanent offset; actually, it unloads with hysteresis but almost to the origin.) The results of the new elastic-plastic analysis, documented in reference [7], are depicted in Figure 8.22, in the same non-dimensionalized form as for Rose’s elastic solution in Figure 8.3. The value 1 on the ordinate of Figure 8.22 represents the elastic solution. It is clear that the added strain energy of ductile adhesives, with respect to brittle ones with no non-linear capacity, is to reduce the stiffness of the load over the 4 3 RATIO OF PLASTIC TO ELASTIC STRESS INTENSITY FACTORS 16. ELASTIC- 1 TRANSITIONAL CRACK LENGTH WHEN COD REACHES LIMIT SET BY THE ADHESIVE BOND, ADHESIVE ELASTIC //- -/ CHARCTERISTlCS OF UNPATCHED SKIN CRACK AT INCREASING LOAD LEVELS ELASTIC ADHESIVE I I I I I I I I I I* 2 3 4 5 6 7 8 9 10 OI’ 01 NONDIMENSIONALIZED HALF-CRACK LENGTH, &A Fig. 8.22. Effect of elastic-plastic adhesive behavior on crack-tip stress intensity factors underneath bonded patches. 202 Advances in the bonded composite repair of metallic aircrafi structure crack, for sufficiently high loads. This, of course, is undesirable, since it increases the stress intensity K. On the other hand, the same added flexibility goes hand-in- hand with increased joint strength, enabling bonded patches to be applied to thicker cracked structure than can be repaired with elastic adhesives - unless one is willing to employ stepped patches to decrease the load transferred per step and, at the same time, decrease the eccentricity in load patch for one-sided patches. The new, longer, effective half-crack tips and higher stress-intensity factors have been derived in [7] as (8.12) where the elastic values are defined in Eqs. (8.4) and (8.6). Reference [7] also contains an assessment of the effects of disbonds adjacent to the crack. It is predicted there that these disbonds cannot initiate until the crack has grown sufficiently and that, thereafter, any shear-dominated disbonds will grow in a stable manner, in concert with further crack extension. In other words, the width of any disbond is limited by, and eventually proportional to, the length of the crack. (The behavior of peel-induced disbonds has yet to be examined by closed-form analysis.) Disbonds render bonded patches far less effective; avoiding them justifies the use of more complex stepped patches let into stepped recesses cut into the skin around the crack. The choice between nominally uniform (or linearly tapered) patches on a uniform substrate or stepped patches bonded into a stepped recess cut from the structure seems to be difficult to establish, because so many factors have been omitted from older analyses that the patches have often out-performed the predictions. Nevertheless, the distinction is exceedingly simple to grasp; patches with complex geometries are needed whenever the structure is so thick and so highly loaded that the simple patches cannot do the job. 8.12. Out-of-plane bending effects with one-sided patches Rose’s original analysis includes the necessary geometrically non-linear bending analyses for the effects of the eccentricity in load patch inherent in one-sided bonded patches. He correctly established that the so-called Stage I correction factor is very small. Analyses under the CRAS program, reported in reference [I6], have confirmed this need. Indeed, the tendency for the centroid of the skin/patch combination to align itself with the plane of action of the remote load is so great that, in the worked example in reference [16], a linear bending analysis would have Chapter 8. Recent expansions in the capabilities of RoseS closed-form analysis 203 over-estimated the deflection in the patch, over the crack, by a factor of 18-to-1. Linear analyses are totally inappropriate for this class of problem. The author’s analyses in reference [16] include an improvement with respect to the model used by Goland and Reissner in their classical analysis of bonded single- lap joints. This model assumes that plane sections remain plane, even though the overlap area is treated as a single layer twice as thick as the individual adherends. Such an approximation is obviously unrealistic immediately adjacent to the ends of the overlap or, in the present context, immediately adjacent to the skin crack. The author removed this constraint by adding a flexible adhesive layer only in narrow zones adjacent to the ends of the patch and on each side of the crack. The analyses were made more accurate because of this refinement, but it was shown that, numerically, the Goland and Reissner level of model is sufficiently accurate. Rose relied upon these same phenomena when he modeled the load transfer between skin and patch as being instantaneous. It really isn’t - but a more precise derivation often does not change the answer significantly. Such simplifications are not always valid, however. No matter how precise the Stage I bending analysis, it is going to predict almost zero bending moment in the patch over the crack, provided that the lengths are long enough to allow the transverse deflections to occur. Nevertheless, both Rose’s original analysis, and the more recent one in reference [17], have included Stage 11 bending analyses in the immediate vicinity of the crack. The reason for this is that there is a local abrupt eccentricity in load path too short to effect the global bending. The same phenomenon is described in reference [ 161. It would be fair to say that this aspect of the problem is not yet adequately characterized. It is clearly not a classical plane- sections-remain plane linear bending analysis, because finite-element analyses performed as part of the CRAS program have confirmed the absence of curvature in that region, even with five elements through the thickness. So most of the eccentricity must be accommodated by shear-lag, as Wang, Rose, and Callinan recognized in preparing their reference [ 171 based on Reissner’s plate-bending analysis. However, it seems to the present author that the whole issue might be moot. The only interest in this particular bending moment is possible unequal crack opening across the thickness of the skin. But, surely this is more dominated, at the crack tips, by the uncracked and unbent very stiff laminate of skin and patch just ahead of the crack tips. It is obvious that the crack opening will vary from the patch side to the unrepaired side of the skin in the “bonded joint” zone of Figure 8.2, and that this might impart a slightly greater displacement than developed in the adhesive alone, but this seems to be far from the dominant effect at the crack tip. It must be remembered that only those portions of the crack within the very short length A are important here. Curiously, shear lag is known to be important in the patch, directly over the crack in the skin. Composite patches have very little transverse shear stiffness, in comparison with that of aluminum alloy skins, because a11 such load must be transmitted through the resin matrix. Consequently, those layers of fibers closest to the skin are locally loaded far more highly than those located far away on the outside of a thick patch. (The same phenomenon was observed at Douglas Aircraft 204 Advances in the bonded composite repair of metallic aircraft structure during the PABST program, where the splice plates in double-strap metal-to-metal joints were far more prone to fatigue failures, where the skins butted together, than the nominally equally stressed portions of the skins.) 8.13. Remaining challenges involving closed-form analyses Despite the abundance of Rose’s work, and that of the whole team led by Alan Baker, as well as the more recent contributions by the CRAS team, there are still challenges waiting to be addressed. Some may never be solved in this manner because it will be found that finite-element analyses are absolutely necessary. Nevertheless, some of the remaining tasks that will be attempted by the CRAS team include the following. 1. Adhesive stresses associated with patches with very long tapers. 2. Load transfer between the skin and the patch for thick structures (and patches 3. Further studies of disbonds, particularly those associated with adhesive peel Other investigations will continue with ways to improve or facilitate finite-element analyses, and these are no less important than the closed-form solutions discussed here. However, they lie beyond the scope of this article. to match). stresses. 8.14. Concluding remarks It is hoped that, more than a decade after the publication of Rose’s classical treatise on this subject, and the thousands of bonded patches that have been successfully applied by the RAAF and USAF, in particular, that it is now clear what a vital analysis it was. Also, as this paper shows, the techniques used have spawned a large number of refinements and expansions that retain the original simplicity while enabling the effects of far more parameters to be assessed parametrically. One must wonder whether or not Rose knew, at the time, that the precise transverse stiffness of composite patches was not to have a dominant influence on his Stage I analysis for the load attraction at the ends of the patch and the stress in the skin under the patch, where the crack existed. Certainly, it is now apparent that orthotropic composite patches designed with his analysis for isotropic patches would not be all that different if the composite patch analysis had been derived earlier. Rose’s foresight in recognizing the importance of a uniform stress surrounding the crack under the patch means that the restriction he accepted to elliptical patches to achieve that goal was sensible. Although octagonal patches are easier to make, it is important that the trimming of their corners lead to a patch that is equivalent to some elliptical patch. Otherwise, there will be regions of higher-than-average stress Chapter 8. Recent e.upansions in the capabilities of Rose’s closed-form analysis 205 for the crack to grow into. Again, what others have mistaken for a restriction on applicability is now revealed as good design advice. It is known that Rose had not anticipated the direct application his analysis to corrosion damage, simply by using a negative patch thickness. Nevertheless, once the idea had been suggested he was able to help the present author complete that task, so that Rose’s original analysis can be applied to a whole further class of problems. It should also be noted that the original analysis, intended for the analysis of repairs to structures damaged in service, can also be applied to yet another task - that of designing optimally sized local integral reinforcement to be left n place when the parts are first machined, so that they will not develop fatigue cracks in service. These very same tools can also be applied to prevent further instances of poorly designed stringer run-outs, which have been a chronic source of fatigue cracks in the past. Now there are simple closed-form analyses available to quantify potential hot pots before the designs are frozen. It is also now known that the idea of being able to directly apply Rose’s model to integrally stiffened structures is sound, and that, henceforth, they need not always be limited to the simple flat-plate geometries that formed the basis of the idealized model Rose first analyzed. It would take remarkable insight to predict where all of the extensions of Rose’s work will end. The author will make no such attempt. However, he will state the obvious, that much of the CRAS closed-form analysis work would not have been possible had Rose not taken that first giant step so many years ago. References 1. Baker, A.A. and Jones, R. (1988). Bonded Repairs of Aircraft Structures (A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers. 2. Rose, L.R.F. (1988). Theoretical analysis of crack patching. In Bonded Repairs of Aircrgfi Structures (A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers, pp. 77-106. 3. Baker, A.A. (1988). Crack patching: experimental studies, practical applications. In Bonded Repairs of Aircrafr Strucfures. (A.A. Baker and R. Jones, eds.). Martinus Nijhoff Publishers, pp. 107 173. 4. Hart-Smith, L.J. and Rose, L.R.F. Characterizing the Effects of Corrosion Damage Using Analytical Tools Developed for Bonded Composite Crack Patching. Boeing Paper MDC 00K00100, in preparation. 5. Hart-Smith, L.J. (1 973) Adhesive-Bonded Double-Lap Joints. NASA Langley Contract Report NASA CR-112235, January. 6. Rose, L.R.F. (1981). An application of the inclusion analogy for bonded reinforcements. Int’l. J. Solids and Structures, 17, pp. 827-838. 7. Hart-Smith, L.J. (1999). On the relative effectiveness of bonded composite and riveted patches over cracks in metallic structures. Boeing Paper MDC 99K0097, Proc. 1999 USAF Aircraft Structural Integrity Program Corzf., San Antonio, Texas, 30 November-2 December. 8. Wang. C.H., Rose, L.R.F., Callinan, R., et ul. Thermal stresses in a plate with a circular reinforcement. Int. J. Soli& and Structures, 37, pp. 4577-4599. 9. Hart-Smith, L.J. (2000). Analyses of bending deformations in adhesively bonded one-sided doublers and patches over skin cracks, Boeing Paper MDC 00K0024, Proc. of’the 4th Joint DoDIFAAINASA Conf. on Aging Aircrufi, St. Louis. Missouri, 15-18 May. 206 Advances in the bonded composite repair of metallic aircraft structure 10. Duong, C.N., Wang, J.J. and Yu, J. An approximate algorithmic solution for the elastic fields in bonded patched sheets. Int. J. of Solids and Structures, Vol. 38, 2001, pp. 46854699. 11. Hart-Smith, L.J. (1999). Nonlinear closed-form analyses of stresses and deflections in bonded on- sided splices and patches. Boeing Paper MDC 99K0069, Proc. of the 3rd Joint FAAIDoDINASA Conf. on Aging Aircraft, Albuquerque, New Mexico, 20-23 September. 12. Hart-Smith, L.J. (1983). Adhesive bonding of aircraft primary structures, Douglas Paper 6979, presented to SAE Aerospace Congress and Exhibition, Los Angeles, California, 13-16 October, 1980; SAE Trans. 801209; reprinted in High Performance Adhesive Bonding, (L. De Frayne, ed.). Society of Manufacturing Engineers, Dearborn, Michigan, pp. 99-1 13. 13. Hart-Smith, L.J. and Duong, C.N. Use of bonded crack-patching analysis tools to design repairs for non-crack-like (Corrosion) damage, Boeing Paper MDC OOKOOlOl, in preparation. 14. Hart-Smith, L.J. (2001). A demonstration of the versatility of Rose’s closed-form analyses for bonded crack-patching, Boeing Paper MDC 00K0104, presented to 46th International SAMPE Symposium and Exhibition, Long Beach, California, 6-10 May. 15. Hart-Smith, L.J. (2001). Extension of the Rose bonded crack-patching analysis to orthotropic composite patches, also accounting for residual thermal stresses, Boeing Paper MDC 00K0102, to be presented to 5th Aging Aircrufi Conference, Kissimmee, Florida, 10-13 September, 2001. 16. Hart-Smith, L.J. and Wilkins, K.E. (2000). Analyses of bending deformations in adhesively bonded one-sided doublers and patches over skin cracks, Boeing Paper MDC 00K0024, presented to the Fourth Joint DoDIFAAINASA Con$ on Aging Aircraft, St. Louis, Missouri, 15-18 May. 17. Wang, C.H., Rose, L.R.F. and Callinan, R. (1998). Analysis of out-of-plane bending in one-sided bonded repair, Int. J. of Solids and Structures, 35, pp. 1653-1675. Chapter 9 NUMERICAL ANALYSIS AND DESIGN R. JONES Department of Mechanical Engineering, Monash University, Wellington Rd, Clayton, Victoria 3168, Australia 9.1. Analysis and design This chapter describes a number of complementary approaches to the analysis and design of bonded repairs. First, an approach based on the two dimensional finite element method is presented and illustrated by an application to an actual repair. An analytical approach for the design parameters for repairs to rib stiffened panels is then presented. Section 4 subsequently compares the predictions with both experimental and numerical results. Design studies for repairs to thick sections are described in Sections 9.5-9.8. Section 9.9 presents a methodology for allowing for adhesive non-linearities and visco-plasticity. Section 9.10 discusses how to extend existing design methodologies to allow for variable adhesive thickness. Section 1 1 presents the solution for composite repairs t'o cracked fastener holes or corrosion damage under bi-axial loading. Section 9.12 summarises the findings for repairs to primary structures, and also discusses the applicability of a range of commercially available finite element programs. There are several methods available for designing composite repairs to cracks in thin metallic skins, i.e. typical thickness less than 3 mm. The finite element method was the first to be developed [l], and has been used to design several complex repair schemes, such as the repair of fatigue cracks in the lower skin of Mirage aircraft [2], and cracks on the upper surface of the wing pivot fitting of FlllC aircraft in service with the Royal Australian AirForce (RAAF), see [3]. Following the development of this approach the work presented in [4] revealed that the stress intensity factor for a patched crack approached a constant value as the crack length increased, thus simplifying the initial design process. This approach was based on the premise that, for a sufficiently long crack in a structure which is subjected to a remote uniform stress field, the central region of the patch, over the 207 Baker, A.A Rose, L.R.F. and Jones, R. (ed.s.), Advances in ihe Bonded Composiie Repaim of Metallic Aircraft Structure 2002 Elsevier Science Ltd. All rights reserved. 208 Advances in itre bonded composiie repair of metallic uircrafi structure crack, behaves like an overlap joint. From this premise it follows that the stress distribution in this central region should be independent of crack length, see Chapter 7 for more details. As a result of this analogy the problem of a bonded symmetric lap joint can be used in the initial design process. The analytical formulae are particular easy to use and provide a first estimate for the patch design. In some cases, this first estimate is sufficient. However, there are situations in which the repair is critical and a long life is required. In these cases, a full finite element analysis is necessary. As a result, the finite element approach will be discussed first and illustrated by considering the design of a repair to the lower wing skin of a Mirage I11 aircraft. At this stage it should be noted that whilst much of the initial impetus for composite repairs arose from the need to maintain the structural integrity of military aircraft [ 1-41 the concepts, analysis and design tools are also applicable to repairs to civilian aircraft [5-lo]. 9.2. The 2D finite element formulation A variety of numerical techniques are now available for analysing composite repairs. These include 2D finite element techniques [I], boundary element formulations [ 113, finite element techniques using of Mindlin plate bending elements [12], 2D and 3D finite element alternating techniques [13] and fully 3D finite element analysis [3]. Of the various techniques the 2D finite element and 2D alternating finite element techniques are the simplest to apply. When a more detailed analysis is required or it is necessary to determine the interlaminar stresses in the repair then it is best to use 3D finite element analysis since Mindlin plate bending elements cannot capture the true ‘three dimensional stress states at the patch adhesive interface. The current 3D finite element alternating technique has a similar shortcoming. However, recent, as yet unpublished, work has shown that it is possible to use the 3D alternating technique to obtain a sub-structure like model of the cracked region and combine this with a standard finite element model for the remaining region and the repair. A detailed discussion of the relative applicability of a range of commercial finite element analysis programs is given in Section 9.12. In general the best results are obtained using 21 nodded hex elements or cubic iso- parametric elements. Variants of these elements are available in a range of commercial finite element programs, viz: PATRAN, NE-NASTRAN and PAFEC. Standard quadratic iso-parametric elements can also be used but care must be taken to avoid ill conditioning. When analysing bonded repairs to cracked metallic sheets it is first necessary to develop a realistic mathematical model for the behaviour of the adhesive layer bonding the patch to the sheet. Under in plane or transverse loading, shear stresses are developed in the adhesive. If we define the x and y axes to lie in the plane of the sheet with the z axis in the thickness direction, then these shear-stresses can be Chapter 9. Numerical analysis and design 209 expressed in terms of the displacements in the sheet and the patch, viz: Here z,~, and t,Ty are the values of the shear stresses in the adhesive KI, K2, K3, &, K5 and K6 are spring constants whose values depend on the material properties and thickness of the adhesive, skin and composite patch. The terms UR, UR and up> up are the displacements at the mid-surface of the patch and the skin respectively while IV is the vertical deflection. It is often a reasonable assumption that for the composite patch, which from here on will be considered to be unidirectional with the fibres perpendicular to the crack, G13 = G23 = GIZ(GR), i.e. the interlaminar shear moduli are equal. This assumption is unnecessary and the full form for the Kl’s is contained in [l]. However, it dramatically simplifies the analysis and has little effect on any quantities of interest. With these assumptions we obtain, in the case of a patch on one side of the skin: where tA, tR and tp are the thicknesses of the adhesive, patch (composite overlay) and skin respectively and GA, GR and Gp are the shear modulii of the adhesive, patch and skin. These formulae were presented in [l] and make full allowance for the shear deformation which occurs throughout the composite patch and skin. With this approach, the u and v displacements through the patch, adhesive and skin are given by: 210 Advances in the bonded composite repair of metallic aircraft structure and a similar expression for v. If the patch is placed on both sides of the skin, then the term 3tp/8Gp appearing in the above equations is replaced by tp/4Gp. These assumptions result in a shear stress profile which is piece wise linear. 9.2.1. Element stiffness matrix Having obtained the nature of the stress field in the adhesive we can now derive the stiffness matrix for the adhesive layer. When there is no bending, the sheet is assumed to be in a state of plane stress and it is usually modelled by isoparametric membrane elements while the patch is modelled by isoparametric membrane elements with an orthotropic stress strain law. The adhesive is also assumed to only carry the shear stresses zxz and zyz. As a result, the total strain energy of an element of the repaired structure is: (9.4) where Kp and KR are the stiffness matrices of the skin and patch respectively. The last term in this expression is the contribution due to shear deformation. To be completely accurate, the z integration should be over the total thickness of the skin, adhesive and patch, whilst the x, y, integration is over the surface area of the element. We first define a vector f such that: where the components of N are generalised functions of position and TT aT = (6, ,6' sf) Here the element is considered to be an arbitrary shape with m nodes and The strain vector may be expressed as: [...]... 9.4 From this we see that even without allowing for effect of the stiffener and the predicted values lie within 18% of the numerical values When allowing for the stiffeners using the stiffener correction factor (SCF), i.e Eq (9.29) the approximate formulae was accurate, for all (200+) test cases, to within 5% To confirm the accuracy of these formulae an experimental study into the composite repair of... the need to: 1 Allow for interlaminar failure in the composite repair 2 Allow for the visco-plastic behaviour of the epoxy At the moment this level of analysis can only be done using advanced finite element tools Hence for primary structures repairs need to be designed using 3D finite element analysis A methodology for allowing for material non-linearities without the need to perform a fully non-linear... at ninety degrees to the crack Initially, it was uncertain if carrying the fibres over the drain hole was necessary, or how frequently the drain hole was used in service As a result, in three of the patches considered a hole was left so as not to interfere with the draining of the wing In the other three patches, varying amounts of the hole were covered In one case, one third of the total area of the. .. designing bonded repairs to cracked metallic wing skins 9.2.2 Repair o cracks in aircraft wing skin f In the late 1970s a boron fibre patch was developed for cracks in the lower wing skin of a number of Mirage I11 aircraft These cracks were pre-dominantly found at an angle of 45" to the main spar To investigate the feasibility to a b/ep repair, a design study was undertaken into the repair of a crack whose... 0.1 651 mm thick and has a shear modulus of 700 MPa The aluminium alloy has a Youngs modulus E of 7.2.86 GPa and a Possoin’s ratio of 0.3, whilst the Fig 9.10 Geometry of edge cracked edge notch test specimen Advances in the bonded composite repair of metallic aircrajl structure 228 95 (.93) 51 (0.47) Fig 9.11 View of the repaired region showing the ratio of measured strains to the far field strain, finite... Advances in the bonded composite repair of metallic aircruft structure Fig 9.3 Schematic of three dimensional 1/4 finite element model of stiffened panel To illustrate the accuracy of this formulae a 3D finite element study for the composite repair of cracked rib stiffened panels was undertaken In this study the stiffeners were assumed to be riveted to the skin Symmetry considerations enabled only a 1/4 of... we now find that: (9.14) AN6dxdy As a result, we find that the stiffness matrix Ik" for the adhesive layer, plus the shear 212 Advances in the bonded composite repair of metallic aircraft structure coupling in the skin and patch, is given by: (9. 15) For a patch on both sides of the skin, the stiffness matrix for both layers of adhesive and the shear coupling in the skin and patch is: (9.16) A more... essentially growing as a mode 1 fracture and that of the two crack tips the tip closest to the spar was growing the faster Indeed, the tip closest to the spar was found to be very close to final failure Having thus obtained a reasonable model for the unpatched crack, we add to this a finite element representation of the repair Six boron epoxy patch configurations were considered, each with the same plan form,... of the neutral axis of the patch-adhesive-skin section will differ from the neutral axis of the wing skin itself Hence, forces applied to the skin will result in an out of plane bending which will reduce the efficiency of the repair There are several methods that can be used One approach, developed at Northrop see [I41 for more details, can be used to account for this out of plane bending Other more... case the use of a steel sleeve bonded into the hole Chapter 9 Numerical analysis and design 2 35 To obtain a first estimate of the worst (highest) value for K it is possible to use the solution for a through crack Table 9. 15 allows us to predict the effect of the patch on fatigue life For the case of a patch only with a = c = 3 mm we see that the ratio of the unpatched stress intensity factor to unpatched . Proc. of the 4th Joint DoDIFAAINASA Conf. on Aging Aircrufi, St. Louis. Missouri, 15- 18 May. 206 Advances in the bonded composite repair of metallic aircraft structure 10. Duong,. varying amounts of the hole were covered. In one case, one third of the total area of the hole was covered, while in the other cases virtually all of the hole was covered. For each of the. desirable to reduce K, to below the fatigue threshold limit of the wing skin. Let us now consider the effect that the difference between the coefficients of thermal expansion of the boron patch