Skin Stiffener Panel Configuration
Cross-Section, Ast (inch2)
Bay Width (w)
= 1.0, Fastener diameter D = 0.5 inch, 2D edge distance, 3D spacing
Material Property Data
The following material strength, fracture and
fatigue-crack-propagation data are given as follows:
2024-T3 sheet or plate
Kc = 90 ksi Öin (t = 0.2
- 0.3 inch)
Ftu = 77 ksi
Fty = 67 ksi
Selection of “Optimum” Geometry
configurations defined in the table were analyzed
for residual strength and crack arrest capability. The results were determined for rigid
fasteners. Complete residual strength
diagrams were developed for each structural geometry: (a) stiffener failure due to skin crack, (b) skin failure with
crack, and (c) fastener shear failure
based on allowable per 1,000 pounds.
The three critical structural cracking conditions analyzed were
A skin crack located symmetrically about a stiffener
A skin crack located symmetrically about a broken stiffener
A skin crack located symmetrically at mid-bay between
The next figure shows the critical
stress or residual strength as a function of crack aspect ratios (a/w) for a skin crack across the
stiffener. The residual strength of the
skin, stiffener, and first fastener adjacent to the crack are shown. The skin critical stress is based on Kc and the stiffener critical
stress is based on Ftu. The fastener parameter is scr/Qcr
is the critical stress per Qcr
(Qcr = 1000 lb). The
curves shown are for 60% stiffening and were generated using methods described
in Section 4.5. Similar curves would be
generated for 40% and 50% stiffening.
The results demonstrate an increase of residual strength with increasing
percent stiffening. Residual strength
decreases with increased stiffener spacing.
Strength Diagram – Skin Crack Across Stiffener
The following figure shows the residual strength diagram for
the skin stiffener panel for a crack located across a broken stiffener. The variation of residual strength with
crack size is shown for the skin and the adjacent stiffeners at 40, 50 and 60
percent stiffening. The critical stress
for the skin is based on Kc
and the adjacent stiffener critical stress is based on Ftu. This
structural crack condition is the most critical of the three cases. Since the stiffener is failed, the load
transfer carrying capability of the stiffener is lost and actually causes the
crack to open more and increase the skin stress intensity level. This case should be considered primary in
Fail Safe Crack Arrest structural design.
Strength Diagram – Broken Stringer
The residual strength of the skin stiffened panels for a
structural crack located at mid-bay are shown in the next figure. The structural geometries analyzed are the
same as for a skin crack located across a stiffener. Again only the 60% stiffening curves are shown. The effect of increasing percent stiffening
on increasing residual strength can be seen in the figures for each bay
width. For a given percent stiffening,
the residual strength of the structural panel decreases with increased bay
Strength Diagram – Mid–Bay Skin Crack
In comparing the three cases analyzed and presented in the
previous figures, the following conditions of structural instability are
For a skin crack located symmetrically across a stiffener, the
critical structural element is either the stiffener or skin.
For a skin crack located symmetrically across a failed
stiffener, the critical structural element is the skin.
For a skin crack located symmetrically between stiffeners, the
critical structural element is the skin.
The skin stiffener geometry results in crack-arrest
capability. A skin crack that grows
critical will be arrested provided the adjacent stiffeners are intact. Examination of the results of the trade
study shows that the requirement to contain damage hinges on the ability of the
stiffener to remain intact with a crack.
Therefore, it was required to conduct fatigue-crack-propagation analysis
of the skin stiffened panel for the following crack conditions:
A skin crack located symmetrically about a stiffener.
A crack in the stiffener with a crack in the skin.
The results of the trade study are summarized below in terms of
crack arrest capability. The maximum
allowable stress that can be applied to the structure for crack containment is
presented as a function of bay width and percent stiffening. The “near-optimum” structural configuration
selected for further analysis was:
Percent Stiffening = 60 percent
Bay Width = 7.0 inches
Fastener Diameter = 0.50 inch
2D edge distance
Arrest Capability of Structure (Results of Trade
The selection of 60 percent stiffening was also enhanced by the
crack arrest capability of the structure for a broken central stiffener
Since the results of the trade study considered rigid fastener
connections, the effect of fastener flexibility or deformation has to be
evaluated. Using techniques described
in Section 11.2 and Section 4.5, a model was developed to obtain the
stress-intensity factor for this configuration. The stiffeners were simulated by a lumped stiffness
finite-element mesh system. This system
was over-layed on the finite-element mesh system of the skin. The mesh systems were connected through
discrete nodes that simulated the fastener flexibility by “soft-springs”. Crack progression was simulated by unzipping
The variation of stress-intensity factor with
through-the-thickness crack size is shown in the next figure. Comparison with the
behavior of an unstiffened panel shows the decrease in stress-intensity
level due to the load transfer at a given crack size. The stiffener stress concentration factor due to load transfer (sg
+ Dsg)/sg and the first fastener loads are shown
in the following figure.
Intensity Variation with Crack Length
Symmetric about Stringer)
Stress Concentration and Fastener Load Due to Load Stiffener
Damage Tolerance Analysis
In an effort to demonstrate the interrelationships between all
the elements in the damage tolerance analysis, the results of all the analyses
have been collected on a single figure.
The most critical case is the crack in the skin with the central
stringer broken. This is the case
Tolerant of Fail Safe Structure
The figures shows the residual strength diagram, the crack
growth curve, the degradation of residual strength as a function of time, and
the assumed load spectrum. The residual
strength diagram and the crack growth curve are drawn in an unusual way, with
the crack axis to the left and the cycle axis to the bottom. This has been done to get all plot properly
Initially, when the crack is small, the center stringer is
still intact. Since the attachment
holes in skin and stringer are assembly drilled, both holes are assumed
initially flawed (0.05 flaw). This
means that the center stringer will fail at a certain moment in time. The occurrence is shown in the crack growth
curve, because it is important for the life.
The residual strength diagram is only for the case with the center
stringer failed, because that is the relevant situation. Corresponding points in the three diagrams
are indicated by A, B, C; A’, B’, C’; A”, B”, C”; and .
The assumed load spectrum is a gust exceedance spectrum for
30,000 flight hours, or 1 lifetime.
Average flight time is supposed to be 3 hours, so the life is 10,000
flights. The vertical axis shows
accelerations. It is assumed that the
conversion to stresses is properly made, so that a point in the exceedance
diagram corresponds with a point at the same level in the residual strength
diagram. Limit load is assumed to be as
the once-per-lifetime occurrence, which brings the design ultimate at the
indicated level. The techniques
described in Section 126.96.36.199 were used to develop the mission segment stress
history from the load spectrum. This
stress history was then used for the crack growth predictions.
The spectrum permits determination of the fail safe loads. It is assumed that the spectrum may be
linearly extrapolated. Only PLT, PDM, and PWV
are indicated. The load PLT is the highest load
occurring in 20 lives, i.e., it has a frequency of occurrence of 5 x 10-2
in one lifetime. The Depot Level fail
safe load occurs once in 5 lives, so it has a frequency of occurrence of 2 x 10-1
in one lifetime. Finally, PWV occurs once in 1000
The damage tolerance requirement for intact structure concerns
the growth of the initial flaw to instability, i.e., to the point at which an
instability would first be possible at the given fail safe load. For a non-inspectable, intact, fail-safe
structure, the initial 0.02-inch flaw may not cause instability at PLT in one lifetime. Instability at PLT is first possible at . This point is at
34,000 hours which is just over one lifetime.
Hence, the condition is satisfied.
The instability would extend the crack from B to C. In the crack growth curve there would be a
jump from B’
and crack growth would continue along C” D” parallel to C’ D’. Instability need not occur at , since PLT
may not be encountered (PLT
could occur once in 20 lives; it may not be met at all in less than 20
lives). In that case, crack growth will
continue along B’
The possibility that the
structure might qualify as Depot Level inspectable will now be considered. For Depot Level inspectability the crack
growth period should be a quarter lifetime to instability at PDM. The instability would first be possible at . The in-service
damage depends on inspection.
For normal NDI without removal of fasteners, the damage would be 0.25
inch through-the-thickness crack (a = 0.25 in.). The 0.25 inch crack is at E’, the residual strength is at
E. Thus, the period from to should be ¼
lifetime. Apparently, the structure
could qualify for this.
For a close-visual, Depot-Level inspection, the in-service
damage is a 2-inch crack (a = 1
inch). This crack occurs at H’, with
a residual strength at H. The period
from to should cover ¼
lifetime, or 7,500 hours. Since it
covers approximately 10,000 hours, the structure would still qualify as
Apparently, there would be no problems in satisfying any one of
the primary requirements for intact structure.
Next consider the requirements to be met at and after instability. The residual strength at instability should
be 1.15 PLT or 1.15 PDM, whichever is applicable.
The non-inspectable structure may show instability at . The crack will grow
to and be arrested. At that moment, the residual strength is
still at . Hence, the level of
should be 1.15 times
the level of . In reality, it is
only 10 percent higher. Consequently,
the structure does not qualify as non-inspectable after all.
The Depot-Level-inspectable structure may show instability at . The crack will be
arrested at , the residual strength still being at . The level of is 19 percent above , so that the structure would meet the requirement. Hence, the structure should be classified as
Depot Level inspectable. Inspections
should be called for either by NDI or close visual, since both are adequate as
The requirements for remaining structure damage call for
adequate crack growth life after instability.
A two-bay crack is assumed to be Walk-Around Visual detectable. In that case, the required residual strength
is PWV, the load occurring
once in 1,000 flights. The remaining
structure damage may not grow to critical at PWV within 5 times the inspection interval, i.e. 50
flights. At PWV, the skin crack would become critical at . However, the
stringer becomes critical already at . At that point the
skin crack extends to N’ (or ).
Instability may occur at with arrest at . Hence crack growth
from to should take at least
50 flights. According to the figure,
this crack growth covers approximately 5,000 hours of 1,700 flights, which
should be plentiful. However, at this
point, the figure is deceiving, because the possibility of stringer failure by
fatigue was ignored.