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.