INITIAL SKIN BUCKLING AND MODE-JUMPING IN INTEGRALLY
STIFFENED METALLIC PANELS
A. Murphy, D. Quinn and M. Price
School of Mechanical and Aerospace Engineering
Queen's University Belfast, Northern Ireland
a.murphy@qub.ac.uk, dquinn14@qub.ac.uk and m.price@qub.ac.uk
ABSTRACT
To increase structural efficiency of integrally machined stiffened panels it is plausible to vary the skin thickness between
stiffeners to increase the skin stability without increasing material volume. As potential static strength performance gains are
strongly linked to the form and magnitude of skin buckle waves, experimental capture of skin deformation behaviour under test
is required to validate skin profiling philosophies and analysis tools. The work presented in this paper documents the
experimental element of a research programme undertaken to validate strength analysis tools of panels with skin profiling. The
paper demonstrates that a full-field, non-contact measurement system can greatly assist in determining stiffened panel skin
buckling behaviour. For the examined specimen geometries various buckling behaviour is captured, including the evolution of
skin post-buckling deformation patterns.
Introduction
Stiffened panels dominate aircraft structure with their design potential for high strength with low weight. This characteristic is
due to the use of high strength materials and the stable post-buckling response of stiffened panels to compression and shear
loading. By permitting the skin between stiffeners to buckle in service at defined percentages of the panel ultimate load, panel
strength-to-weight ratio is maximised. Advances in strength and damage tolerant characteristics of available aerospace
materials offers opportunities for increased working and limit stresses. To fully exploit material improvements as weight
savings on aircraft primary structures, it is desirable to enhance the buckling stability of stiffened panels. To further increase
the structural efficiency of integrally machined stiffened panels it is plausible to vary the skin thickness between stiffeners to
increase the skin stability without increasing material volume, Murphy et al. [1]. Additionally, considering the issues
surrounding the damage tolerance of integral structures, skin profiling may be designed to retard fatigue crack growth,
improving the damage tolerance characteristics of the structure, Farley et al. [2] and Ehrström et al. [3].
Focusing on potential static strength performance gains, it is believed that the ability to improve initial skin buckling and
ultimate panel collapse behaviour is strongly linked to the form and magnitude of skin bay deformation. To fully define and
validate the linkage between static strength performance gains and skin behaviour experimental capture of skin deformation
under test is required. This paper documents an experimental programme undertaken to capture skin buckling behaviour, both
initial and post-buckling, of integrally machined stiffened panels with skin profiling. The paper documents the experimental
methods applied to capture the skin behaviour along with captured experimental data.
The following section introduces the design of the experimental specimens. This is followed with details on the applied
experimental test procedures. The experimental results are then presented along with discussion. The paper concludes with a
summary of the measured experimental behaviour and assessment of the applied experimental methods.
Test Specimen Design and Manufacture
Specimen design was constrained to representative aerospace material, machining technology, panel loading intensities and
buckling to post-buckling strength ratios. A number of initial configurations were studied and a general test specimen layout
defined with three blade section longitudinal stringers and a flat skin base, machined from a single 50 mm thick billet of 2024T351 material. This configuration results in two central skin bays and two edge skin bays separated by the stiffeners. The edge
skin bay width was defined such that initial skin buckling for the edge bays would occur at a marginally higher stress level than
that required for the central bays. Experimentally this arrangement stops the premature failure of the specimen edge stiffeners.
The selected skin profiling philosophy introduced multiple, geometrically equivalent, skin steps, designed to act as integrated
crack retarders, improving the damage tolerant characteristics of the total panel structure as well as influence the static
strength. Based on damage tolerance analysis and manufacturing machining constraints a simple rectangular step profile was
defined. Given the designed skin profiling and the selected specimen layout four specimens were designed, Figure 1. Each
specimen was designed to have an equal length, breadth and a cross-sectional area within 1.25% of the baseline profile,
Profile B. Due to machining tolerances and applied damage tolerance design constraints equal cross-sectional areas were not
possible. The baseline specimen, was designed without skin profiling, having a constant skin thickness of 1.6 mm. Profile 1
was configured with three skin profile steps between each primary blade stiffener and with no skin step reinforcement at the
primary stiffener base. Profile 2 was configured with two skin profile steps between each primary blade stiffener and a half a
step on either side of the primary stiffeners. Profile 3 was designed with a single centrally located skin step and a full step on
either side of the primary stiffeners.
Table 1 presents the designed cross-sectional areas and variations between the designed and manufactured specimens due
to machining radii and machining tolerances. Given the specimen unequal cross-sectional areas the following experimental
results are not only presented in terms of specimen load but also in terms of normalised loading intensity based on
manufactured cross-sectional areas.
Figure 1. Test specimen geometry.
Specimen manufactured
cross-sectional area
(mm2)
Specimen design
cross-sectional area
2
(mm )
Design
Profile B
963.8
970.6
[100.7%]
Profile 1
960.6
976.5
[101.7%]
Profile 2a
968.6
1016.8 [105.0%]
Profile 2b
968.6
1029.3 [106.3%]
Profile 3
975.6
993.1 [101.8%]
1
1
– Values in brackets are specimen manufactured cross-sectional area as
percentage of specimen designed cross-sectional area.
Table 1. Test specimen design and manufactured cross-sectional areas.
Specimen Test
The specimens were tested in a 250 kN capacity hydraulic testing machine. A 42 mm thick Cerrobend (low melting point alloy)
base was cast on to the specimens, producing fully clamped boundary conditions at each end. Keying holes were drilled
through the ends of the specimens prior to casting to hold the Cerrobend in position and to help prevent specimen-Cerrobend
separation. The ends were subsequently machined flat and perpendicular to the skin to ensure that uniform axial loads were
applied. Once machined each specimen was marked and strain gauged in preparation for test. Gauges were located to assist
in the determination of skin buckling and post-buckling collapse behaviour. Two calibrated displacement transducers, one
either side of the specimen, were used to measure specimen end-shortening. The specimens were loaded monotonically at a
rate of approximately 10 kN/min until failure occurred, deflection and strain data were recorded automatically at 4-second
intervals. Finally, two Profile 2s were tested (Profile 2a, Profile 2b) to allow assessment of experimental repeatability.
Experimental Results and Discussion
The measured initial skin buckling loads for the specimens are presented in Table 2. Within the test series specimen initial skin
buckling occurred between 36.8% (Profile 3) and 40.9% (Profile 2b) of specimen ultimate collapse loads. Profile 1 initially
buckled at a lower load than the baseline constant plate thickness design – Profile B, however both Profile 2 and Profile 3
buckled at higher loads than the baseline specimen. Considering the normalized loading intensity based on manufactured
cross-sectional areas, Profile 2b, the specimen with the highest initial buckling performance, buckled at a normalized loading
intensity of 117% that of Profile B.
Design
Initial skin
buckling load
(kN)
Profile B
69.3 [71.4 MPa]
Profile 1
62.7 [64.2 MPa]
Profile 2a
82.5 [81.1 MPa]
Profile 2b
86.3 [83.8 MPa]
Profile 3
77.7 [78.2 MPa]
1
1
– Values in brackets are normalised loading
intensities based on manufactured
cross-sectional areas.
Table 2. Test specimen initial buckling loads.
To determine the initial skin buckling load the average strain method [4] was used. The method plots compression load versus
mid-plane strain, with buckling defined to have occurred at the inflection point. The strain data used for each calculation was
taken from back-to-back strain gauges placed at the centre of the RHS central skin bay. Figure 2 presents the measured back-
to-back strain data used to determine skin buckling load. The method only considers a single point on the skin and considering
the non-localised behaviour of skin buckling the analysis results are dependent on the gauge location and the initial buckling
wave formation, particularly the relative locations of the measuring gauge and initial buckling wave crests.
Figure 2. Strain gauge data used to determine initial skin buckling loads.
Given the importance of the skin buckling behaviour within this project a 3D Digital Image Correlation system was also used to
measure specimen skin out-of-plane deformation during the tests (VIC-3D, Correlated Solutions, LIMESS GmbH). This
method allows the determination of the specimen deformation by cross correlating successive images of the specimen skin
acquired during the test. The specimen is viewed by a pair of high resolution, digital CCD cameras and a random pattern with
good contrast applied to the surface of the test specimen, Figure 3. The deformation of the specimen is recorded at set time
intervals during the test by the cameras and the data post processed once the test is completed to evaluate specimen
deformation behaviour. Strain data may also be obtained from the image correlation analysis.
Figure 3. Experimental setup including 3D DIC system.
Figure 4 presents the specimen initial skin buckling modes found using the 3D DIC system. The central skin bays of each
specimen initially buckled, with either four half-waves (Profile 1, Profile 2) or five half-waves (Profile B, Profile 3) along the
specimen length, with an asymmetry pattern between the two central skin bays.
Figure 4. Initial modes.
Figure 5 depicts the skin post-buckling behaviour of Profile B illustrating the specimen load versus end-shortening curve along
with selected specimen skin out-of-plane deformation data (front view). The figure also illustrates selected section out-of-plane
deformation data for the RHS skin bay. The initial five half-wave skin buckles (asymmetry between bays) altered at 175.4 kN
(94.9% of the specimen maximum load) with an additional half-wave forming at the bottom of the RHS skin bay (large arrow in
Figure 5). The additional half-wave grow steadily from its detection at 175.4 kN until specimen collapse, causing the original
lower two half-waves in the RHS bay to reduce in length.
Figure 5. Profile B skin post-buckling behaviour.
Figure 6 depicts the skin post-buckling behaviour of Profile 1, again illustrating the specimen load versus end-shortening curve
and selected out-of-plane deformation data. In this case the specimen skin buckles evolve individually in each bay. First at
142.3 kN (84.2% of the specimen maximum load) in the LHS skin bay, with the half-wave pattern increasing from four to five
half-waves. Then at 161.5 kN (95.5% of the specimen maximum load) in the RHS skin bay, again with the pattern increasing
from four to five half-waves. As with the Profile B results, the additional half-waves grow steadily until specimen collapse.
LHS skin bay out-of-plane deflection
RHS skin bay out-of-plane deflection
Figure 6. Profile 1 skin post-buckling behaviour.
Figure 7 presents the skin post-buckling behaviour of Profile 2b. For this specimen both skin bay wave patterns alter between
117 kN and 127 kN (55.5% to 60.2% of the specimen maximum load).
Figure 7. Profile 2b skin post-buckling behaviour.
Considering Profile 3, Figure 8 presents the skin post-buckling behaviour, as before. For this specimen there is no postbuckling mode changes between initial skin buckling and final specimen collapse. The specimen half-waves simply grow in
out-of-plane magnitude, Figure 8.
Figure 8. Profile 3 skin post-buckling behaviour.
Conclusions
The aim of this paper was to document the experimental element of a research programme undertaken to validate strength
analysis tools for panels with skin profiling. The paper outlines the experimental work undertaken to capture initial skin buckling
behaviour, both initial buckling load and mode, along with the skin post-buckling behaviour. Back-to-back strain gauge data
along with the average strain method is used to determine the initial skin buckling load. A 3D Digital Image Correlation system
is used to determine the initial skin buckling modes and the post-buckling deformation behaviour.
Reviewing the experimental data a number of obvious observations can be made:
•
•
•
•
In each test were the skin mode pattern changed, the number of skin bay half-waves increased.
When additional half-waves develop within the specimen skin bays, they initiate at either the top or bottom of the bay.
The additional half-waves start small and grow in size with additional loading. The additional half-waves appear to grow
steadily from their initiation, reducing the length of original bay half-waves.
Finally, changes in local skin bay behaviour are evident in global specimen behaviour as reductions in post-buckling
stiffness.
The work demonstrates that a full-field, non-contact measurement system can greatly assist in determining buckling behaviour.
For the examined specimen geometries various initial buckling and post-buckling behaviour was captured, including the
evolution of skin post-buckling patterns.
Acknowledgments
The authors gratefully acknowledge the technical support of ALCAN (ALCAN Centre de Recherches de Voreppe, France) and
the financial support of the European Union (European Social Fund).
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Island, AIAA-2006-1944.
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Structural Dynamics & Materials Conference, 19-22 April 2004, Palm Springs, California, AIAA 2004-1924.
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