In this paper we show how the published literature reveals that the analytical solution for a composite repair to a cracked metallic plate is inconsistent with experimental data, and that the fibre bridging effect is often a second order effect. The result is that prediction of the effect of a composite repair on the structural integrity of cracked components repaired by an externally bonded composite repair is dramatically simplified

Cairns, K.

Jones, R.

Peng, D.

Pitt, S.

University of Queensland eSpace

5th Australasian Congress on Applied Mechanics, ACAM 2007  
10-12 December 2007, Brisbane, Australia 
Composite Repairs To Cracked Metallic Components- Experiment and Theory  
 
R. Jones, D. Peng, K. Cairns, and S. Pitt  
 
Monash-DSTO Centre of Expertise in Structural Mechanics, PO Box 31, Monash University, VIC 3800  
Abstract: In this paper we show how the published literature reveals that the analytical solution for a 
composite repair to a cracked metallic plate is inconsistent with experimental data, and that the fibre 
bridging effect is often a second order effect.  The result is that prediction of the effect of a composite 
repair on the structural integrity of cracked components repaired by an externally bonded composite 
repair is dramatically simplified.  
Keywords: Frost-Dugdale, fatigue crack growth, fatigue testing, composite repairs.  
1 Introduction 
The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and 
of error. But science is one of the very few human activities- perhaps the only one in which errors are 
systematically criticised and fairly often in time, corrected. This is why we can say that, in science, we often learn 
from our mistakes, and why we can speak clearly and sensibly about making progress there. Popper 1963 [1].  
With this in mind let us now reflect on the science of composite repairs to cracked metallic structures.  
There are several methods used to design 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 [2], and has 
been used to design several complex repair schemes, such as the repair of fatigue cracks in the lower 
skin of Mirage aircraft [3], and cracks on the upper surface of the wing pivot fitting of F111C aircraft in 
service with the Royal Australian Air Force (RAAF), see [4]. Following the development of this 
approach Rose [5] proposed that the stress intensity factor for a patched crack approached a constant 
value as the crack length increased. 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, i.e. the central section of the patch that lies over the crack, behaves like an adhesively bonded 
overlap joint.  Variants of this idealised solution are discussed in [6]. 
In recent years the validity of the assumptions underpinning this approximation have been questioned 
[7-9]. Jones, Barter, Molent and Pitt [7] and Jones and Pitt [9] revealed that the growth of cracks under 
composite repairs often conforms to the Frost-Dugdale law, and that for small to medium crack 
lengths, i.e. from ~ 0.1 to 20 mm, the effect of the patch appeared to be dominantly due to the 
reduction in the stress field in the metallic component. Jones, Krishnapillai, and Pitt [8] subsequently 
revealed how the crack growth rate in a plate repaired with a composite patch could be predicted 
using the generalised Frost-Dugdale crack growth law. In this paper we will show that the assumptions 
inherent in the approximate solutions presented in [5, 6] for crack growth under a bonded composite 
repair are inconsistent with experimental measurements.  
2 Composite Repairs to cracked metallic components 
Composite repairs to cracked metallic structures are believed to act in two fashions: 
 
1) They reduce the net section stresses in the (cracked) structure. 
2) The fibres bridging the crack restrict the opening of the crack faces. 
 
It is widely accepted that for small cracks the reduction in the net section stresses is the primary 
mechanism reducing the stress intensity factor, and thereby crack growth.  
 
There are very few experimental studies where the stress intensity factor for a patched crack has been 
directly measured. Most work has attempted to infer the stress intensity factor from crack growth 
measurements. To the best of the authors knowledge the work by Baker et al [10, 11] and Aktepe and 
Baker [12] are the only studies that have attempted to directly measure the stress intensity factor. In 
  
[10, 11] X ray back reflection was used to determine the stress intensity factors in 1.5 mm thick 7075 
T6 aluminium alloy specimens patched on both surfaces with a 0.49 mm thick graphite epoxy 
laminate. Both uncracked and centre cracked panels, with total crack lengths (2a) of 10, 30 and 40 
mm, were examined. As a result of this study it was found [10, 11] that the experimentally determined 
stress intensity factor for a patched plate was given by 
 
K =   T  Ö(pa)             (1) 
 
where T is the stress field in the skin under the patch, and hence that crack bridging effects were 
negligible.  Unfortunately, the results presented by Aktepe and Baker [12] are questionable since the 
analysis used in [12] may contain an error, see [7]. 
This finding was echoed in the recent papers [7-9] which concluded that:  For composite repairs to 
small to medium length through cracks in thin sheets, that have low to mid range DKs, where bending 
effects are negligible the effect of  the patch is primarily due to the reduction of the net section stress. 
To illustrate this we will consider the following test cases. 
Case 1: Baker [11] presented the results for crack growth from an initial 5 mm long edge crack in a 
160 mm wide and 3.14 mm thick 2024-T3 aluminium alloy specimen patched with a seven ply (0.889 
mm thick) semi-circular uni-directional composite patch which had a radius of 80 mm. The specimen 
was subjected to constant amplitude fatigue testing with a remote uniaxial stress with max = 138 MPa 
and R= 0.1, see Baker [11], Figure 6.23 page 155.  The fibres were perpendicular to the crack and as 
such lay in the direction of the load. Bending, due to neutral axis offset effects, was eliminated by 
testing two specimens joined back to back. The resultant crack growth data, from [11], is shown in 
Figure 1. This figure reveals a (near) linear relationship between the log of the crack length and the 
number of cycles. The initial flaw size used in this test was 5 mm, and the size predicted from the log-
linear fit was 4.88 mm. 
y = 4.88 e9.0.00000994x
R2 = 0.997
1
10
100
0 50000 100000 150000 200000
Cycles
 C
ra
ck
 le
ng
th
 a
 (m
m
)
 
Figure 1 Crack length versus number of cycles, from Baker [11] 
 
Case 2: Baker [13] also presented the test results, in Figure 13.7 on page 385, for the seven ply boron 
epoxy repair described in Case (1), with the exception that the initial flaw size was 10mm, subjected to 
constant amplitude loading with D of 76 MPa, but with the R values that were successively increased 
from 0.1 to 0.55, 0.64 and finally 0.75 as the test continued. The resultant crack growth data is plotted 
in Figure 2, where it can be seen that as postulated in [13] crack growth was relatively insensitive to 
the R ratio and that the data is essentially log-linear, i.e. there was a near linear relationship between 
the log of the crack length and the number of cycles . 
  
y = 8.34 e0.00000184x
R2 = 0.999
10
100
100000 300000 500000 700000 900000
Cycles
C
ra
ck
 le
ng
th
 a
 (m
m
)
Increasing R ratio
 
Figure 2 Crack length versus number of cycles for the edge cracked 2024 T3 aluminium plate, 
repaired with a seven ply boron epoxy patch, under variable R ratio from Baker [13]. 
y = 8.35 e0.00000184x
R2 = 1.00
y = 10.8 e0.0000131x
R2 = 0.997
1
10
100
0 200000 400000 600000 800000
Cycles
C
rc
k 
le
ng
th
 a
 (m
m
)
Baker 160 MPa
Baker 80 MPa
 
Figure 3 Crack length versus number of cycles for the edge cracked 2024 T3 aluminium plate, 
repaired with a seven ply boron epoxy patch, with max equal to 160 and 80 MPa , from Baker [13]. 
Case 3:  Baker [13] also presented crack growth data for this test specimen geometry with R = 0.1 and 
various max levels , see Figure 13.6 on page 383. The crack growth data for the cases max= 160 and 
80 MPa, and where there were no inbuilt disbonds, are presented in Figure 3.  Here we again see that 
the measured data was essentially log linear, i.e. there is a near linear relationship between the log of 
the crack length and the number of cycles. 
The above examples show that for small to medium length cracks repaired with an externally bonded 
composite repair there is a near linear relationship between the log of the crack length and the number 
of cycles and that this relationship holds for crack lengths (a) in the range 5 mm< a < 40 mm. (In the 
  
field of fatigue crack growth the term small crack is used somewhat flexibly. However, it is generally 
taken to mean less than ~ 1 mm. In this paper we use the term medium length cracks to mean length 
of the order of 10 mm.) As a result it follows that, as first shown in the extensive USAF test programs 
outlined in Naboulsi and Mall [14] and Schubbe [15], the increment in the crack length per cycle (da/dN) 
is essentially proportional to the crack length.  
For small cracks it is accepted that the dominant effect of  the patch is due to the reduction in the net 
section stress. The log-linear relationship shown in Figures 1-3, over the range 5 mm< a < 40 mm, 
which corresponds to a (near) linear relationship between da/dN and the crack length (a), reveals that 
over this range of crack lengths the dominant mechanism is essentially unchanged. This in turn means 
that the dominant mechanism is essentially that seen for a composite repair to a small crack, i.e. it is 
(essentially) due to the reduction in the net section stress beneath the patch. This finding when taken 
together with the results presented in [10, 11], the experimental results presented above and in [7-9, 
14, 15] reveals crack bridging effects to be a secondary effect over this range of crack lengths and 
hence invalidate the theoretical model presented by Rose and c o-workers [5, 6].   
When developing this model Rose and co-workers [5, 6] assumed over the crack the stresses in the 
patch were constant through the thickness of the patch, and that the maximum stresses in the patch 
occurred over the crack. The experimental and numerical results presented in [16-19] invalidates 
these assumptions. In [16, 17, 18] it was found that over the crack the stress field in the patch is highly 
three dimensional, i.e. the maximum principal stress varies through the thickness, and that there is a 
dramatic reduction in the (surface) stresses in the patch directly over the crack. This conclusion, i.e. 
that the stress field over the crack in the patched structure is highly three dimensional and that there is 
a dramatic reduction in the (surface) stresses in the patch directly over the crack, has been confirmed 
via three dimensional finite element analysis [17, 18] and by strain gauge measurements [19]. In [19] a 
series of strain gauges were located along a line on the surface of the patch that lay at a distance of 
32 mm from the edge of the specimen, see Figure 4, which in this study was as described in Case (1). 
The gauges, which as mentioned above lay on a line that was perpendicular to the line of the crack, 
were located at distances of  0, ± 2, ± 4, ± 6, ± 8 and 10 mm from the centre line of the specimen. (As 
shown in Figure 4 the line of the crack was nominally along the centre line of the specimen.) In this 
study it was found that the surface fibre strain directly over the crack dropped dramatically as the crack 
grew underneath the central gauge and that the surface fibre strain in the patch directly above the 
crack was significantly lower than that on either side of the crack, see Figure 4. As such the 
assumption adopted in [5, 6] that the stress distribution in the patch resembles the 2D lap joint solution 
is invalid. Furthermore, the assumption adopted in [5, 6] that over the crack the stress in the patch is 
constant through the thickness of the patch is also invalid. 
To further evaluate that the hypothesis that the stresses in the central region looked like that 
associated with a lap joint tests were performed on the specimen geometry tested in [11] which 
contained a 32 mm long edge crack repaire d with a seven ply uni-directional boron epoxy patch. This 
specimen geometry is identical to the edge cracked specimen outlined in Case (1) above except that 
the (seven ply) uni-directional boron epoxy patch was on the inner surface so that the cracked panel 
could be monitored during testing. A picture of the bulk stress field in the plate, obtained using lock-in 
infra-red thermography, for a cyclic remote stress Ds = 100 MPa and R= 0.1, near the crack is shown 
in Figure 5.  Here we see that the stress field does not resemble that of a lap joint, i.e. the iso-stress 
lines are not parallel to the crack. Hence the Rose assumption that the region behaves like a lap joint 
is invalid. 
Noting that the near tip cyclic stress bulk stress (Dsx + Dsy  + Dsz ) can be written as  
Dsx + Dsy  + Dsz = {DK1 /Ö(pr/2) }cos(q/2) + A +BÖr cos(q/2)   (2) 
where A and B are constants and r is the distance from the crack tip, it is possible to use the bulk 
stress data to determine the stress intensity factor. Analyzing the data at an angle  = 0°, i.e. directly 
ahead of the crack, we obtained a value of DK1  = 17.9 MPa Öm, whilst a value of DK1  = 16.0 MPa Öm 
was obtained when analyzing the data along the line perpendicular to the crack plane, i.e.  = 90°.  
These values compare reasonably well with the corresponding solution of DK1 = 21.2 MPa Öm 
obtained assuming that the reduction in the stress intensity factor was only due to the reduction in the 
net section stress. In contrast Aktepe and Baker [12] reported that for this repair configuration to a 
30 mm long crack subjected to a remote stress amplitude of 78.6 MPa the Rose solution for this test is 
approximately DK1  = 6.8 MPa Öm so that for a stress amplitude of 100 MPa the Rose solution yields a 
  
value of 8.6 MPa Öm. Even if we allow for the fact that the crack in this test was approximately 32 mm 
long we see that the measured values are significantly greater than the value of approximately 8.6 
MPa Öm obtained using the Rose theory. This is due to the fact that the stress field in the patch over 
the crack is very three dimensional, i.e. it varies through the thickness of the patch, and the two 
dimensional approximation used by Rose, which assumes that all of the plies over the crack are 
equally effective in restraining the opening of the crack, is invalid. 
 
-500
-250
0
250
500
-12 -8 -4 0 4 8 12
Distance from centre line (mm)
m
ic
ro
 s
tra
in
 
45 mm crack
40.5 mm crack
35 mm crack
 
Figure 4 Patch surface strains for a 35, 40.5 and 45 mm long crack, from Galea [19]. 
  
Figure 5 Geometry of the test specimen and the stress field around the crack 
This example supports the findings presented in [7-9] that, as a first approximation, crack bridging 
effects can often be ignored. One advantage of this approach is that the solution will always be 
conservative. A less conservative approach would be to assume that only the first few plies over the 
crack play a role in preventing its opening. 
   
honeycomb   
core   
460 
  280   
2024-T3 -   
t = 3.18 mm   
grips   
160 2024-T3 plate 
-   
7 layer boron/epoxy patch    
(inside)   
75   
boron/epoxy   
patch   
Patch 
 
 
 Strip gauge 
crack 
centreline  
1 mm sensing length  
2 mm pitch 
32 mm 
   crack 
   
 
x 
y 
  
  
3 Conclusions and recommendations 
In this paper we have shown how the published literature reveals that the Rose solution for a 
composite repair to a cracked metallic plate is inconsistent with experimental data, and that for the 
problems examined in this paper the fibre bridging effect is a second order effect that for practical 
purposes can be effectively ignored.  As a result the prediction of the effect of a composite repair on 
the structural integrity of cracked components repaired by an externally bonded composite repair is 
dramatically simplified.  
References 
1. Popper KM., Conjectures and reflections: The growth of scientific knowledge (1963), pp 50. 
2. Jones R.  and Callinan RJ., A design study in crack patching, Journal of Structural Mechanics, 1, 7, pp107-
130, 1979. 
3. Baker AA. , Callinan RJ. , Davis  M.J., Jones R. and Williams  JG., Repair of Mirage iii aircraft using BFRP 
crack patching technology, Theoretical and Applied Fracture Mechanics, 2, 1, 1-16, 1984. 
4. Molent L., Callinan RJ. and Jones R., Structural aspects of the design of an all boron/epoxy reinforcement 
for the F-111C wing pivot fitting- Final report, Aeronautical Research Laboratory, Research Report 1, 
ARL-RR-1, November 1992. See also Composite Structures 11, 1, 57-83, 1989. 
5. Rose LRF., A cracked plate repaired with bonded reinforcements, Int. Journal of Fracture, 18, pp135-
144, 1982. 
6. Rose LRF. and  Wang CH., Analytical Methods fo r Designing Composite Repairs, Chapter 18,  Advances 
in the Bonded Composite Repair of Metallic Aircraft Structure, A. Baker, L. R. F. Rose and R. Jones, 
Elsevier Applied Science Publishers, 2002. ISBN 0-08-042699-9.  
7. Jones R., Barter SA., Molent L. and Pitt S., Crack patching: An experimental evaluation of fatigue crack 
growth, Journal of Composite Structures, 67/2, (2004) 229-238. 
8. Jones R., Krishnapilla K., and Pitt S., Crack Patching: Predicting Fatigue Crack Growth, Theoretical and 
Applied Fracture Mechjanics, 45, 79  91, 2006.  
9. Jones R, Pitt S. Crack patching revisited, Composite  Structures, 2006; 76: 218-223.  
10. Baker AA., Hawkes GA., and Lumley E., Proceedings 2nd International Conference on Composite 
Materials, Toronto, Metallurigcal Society of AIME, 1978.  
11. Baker AA., Crack patching: experimental studies, practical applications, Chapter 6, Bonded Repair of 
Aircraft Structure,  A. Baker and R. Jones, Martinus Nijhoff Publishers, The Hague, 1988. (Book), pp 107- 
173.  
12. Bayram Aktepe and Baker AA., Validation of stress intensity estimations in patched panels, Chapter 18,  
Advances in the Bonded Composite Repair of Metallic Aircraft Structure, A. Baker, L. R. F. Rose and R. 
Jones, Elsevier Applied Science Publishers, 2002. ISBN 0-08-042699-9.  
13. Baker AA., Boron epoxy patching efficiency studies, Chapter13, Advances in the Bonded Composite 
Repair of Metallic Aircraft Structure, A. Baker, L. R. F. Rose and R. Jones, Elsevier Applied Science 
Publishers, 2002. ISBN 0-08-042699-9.  
14.  Naboulsi S. & Mall S., Fatigue crack growth analysis of adhesively repaired panel using perfectly and 
imperfectly composite patches, Theoretical and Applied Fracture Mechanics 28 (1997) 13-28. 
15. Schubbe,  JJ., Thickness effects on a cracked aluminium plate with a composite repair, Phd Tehsis, Air 
Force Institute of Technology, Wright Patterson Ai rForce Base, 1997. 
16. Jones R., Heller M.  Lombardo D., Dunn S., Paul J.  and Saunders  D., "Damage growth in composites", 
Composites Structures 12, pp. 291-314, 1989. 
17. McKenzie I., Jones R., Marshall IH. and  Galea S.,Optical Fibre Sensors For Health Monitoring of Bonded 
Repair Systems, Composite Structures, 50, 5, pp 405-416,  2000.  
18. Heller M, Dunn S., Williams JF. and Jones R., "Thermo-mechanical analysis of metallic and composite 
specimens, J. Composite structures 11, pp. 309-324, 1989. 
19. Galea SC., Smart Patch Systems, Chapter 20, Advances in the Bonded Composite Repair of Metallic 
Aircraft Structure, A. Baker, L. R. F. Rose and R. Jones, Elsevier Applied Science P ublishers, 2002. ISBN 
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Composite Repairs To Cracked Metallic Components- Experiment and Theory

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Composite Repairs To Cracked Metallic Components- Experiment and Theory

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