Design and Fatigue Analysis of a Typical Aircraft Wing fuselage Lug attachmen...
Effect of Overload on Fatigue Crack Growth Behavior of Air Frame Structure
1. Effect of overload on fatigue crack
growth behavior of air frame structure
(fuselage)
2. Effect of overload on fatigue crack
growth behavior of air frame structure
GUIDE
Dr. P.K. DASH
BANGALORE AIRCRAFT INDUSTRY LTD.
PRESENTED BY
MR. SHISHIR SHETTY
USN NO: 3KB08AE013
PROJECT CARRIED OUT AT
BANGALORE AIRCRAFT INDUSTRY (PVT) Ltd.
3. Abstract
• Catastrophic structural failures in many engineering fields
like aircraft, automobile and ships are primarily due to
fatigue, where any structure experiences fluctuating
loading during service. Its load carrying capacity decreases
due to a process known as fatigue. Fatigue damage
accumulates during every cycle of loading
• Designing an airframe against fatigue failure under the
above assumption requires the “damage tolerance design
concept”. In this design concept, a structure is made to
tolerate the presence of damage. In other words, presence
of a fatigue crack, the airframe retains a certain specified
load carrying capability. This load carrying capacity is
specified by certifying authorities and is normally taken as
the design limit load.
4. Abstract continued…
• Airframe will experience the variable loading during the
service. If a damage is present in the structure in the form
of a crack (or one assumes a small crack present in the
structure in the damage tolerance design process), then one
needs to calculate the fatigue crack growth life. This is
essential to properly schedule the inspection intervals to
ensure the safety of the structure during its service.
5. Abstract continued…
• In the current project work a segment of fuselage is
considered for the analysis.
• Local analysis is carried out at the location of maximum
tensile stress to initiate a crack at the critical location.
• Pressurization of the fuselage is one of the critical load cases
considered in the design process.
• In the current project work internal pressurization is
considered for the analysis.
• The overload in the load spectrum will affect the crack
growth rate in the material. The crack growth rate before and
after an over load is calculated.
• Finite element analysis approach is used for the stress
analysis.
6. Problem definition
Effect of overload on fatigue crack growth behavior of a
air frame structure considering the segment of fuselage.
Objective
• Stress analysis of segment of fuselage.
• Identifying maximum stress location in the fuselage
segment.
• Local analysis of stiffened panel at the highest stress
location.
• Crack growth calculation in the stiffened panel.
• Study of overload on the fatigue crack growth.
7. Introduction to aircraft
structure
• An aircraft is a complex structure, but a very
efficient man-made flying machine.
• Aircrafts are generally built-up from the basic
components of wings, fuselage, tail
8.
9. Fuselage
• The main body structure is the fuselage to
which all other components are attached. The
fuselage contains the cockpit,passenger
compartment and cargo compartment.
• The fuselage structure consisting of a thin shell
stiffened by longitudinal axial elements
(stringers and Longerons) supported by many
traverse frames are rings (Bulkheads) along the
length.
• The fuselage skin carries the shear stresses
produced by torques and transverse forces. It
also bears the hoop stresses produced by
internal pressures.
10. Fuselage Loads
The fuselage will experience a wide range of loads
from a number of sources.
The weight of the fuselage structure and payload
will cause the fuselage to bend downwards from its
support at the wing, putting the top in tension and
the bottom in compression
The larger part of passenger and freighter aircraft is
usually pressurized for safety.
Internal pressure will generate large bending loads
in fuselage frames.
The structure in these areas must be reinforced to
withstand these loads.
11. • The most common metals used in aircraft
construction are aluminum, magnesium, titanium,
steel, and their alloys.
• Traditional metallic materials used in aircraft
structures are Aluminum, Titanium and steel
alloys.
• In the past three decades applications of advanced
fiber composites have rapidly gained momentum.
• To date, some modern military jet fighters already
contain composite materials up to 50% of their
structural weight.
Aircraft Materials
12. Selection of aircraft materials depends on initial
material cost, manufacturing cost and maintenance cost
and structural performance are
• Density (weight)
• Stiffness (young’s modulus)
• Strength (ultimate and yield strengths)
• Durability (fatigue)
• Damage tolerance (fracture toughness and crack
growth)
• Corrosion
14. INTRODUCTION TO FATIGUE
CRACK GROWTH
If the airframe does not have any fatigue cracks, the
load carrying capacity is the design ultimate load.
15. • During service this critical location must be
regularly inspected so that the presence of a crack
can be detected before it reaches the size acr.
Repair or replacement action can be taken to
remove the crack from the structure.
• In order to carry out safety this repair or
replacement action the time taken for a crack to
grow to its authorities Crack size must be
established this is schematically shown in finger
16. • Hear ‘ai’ is the initial crack length and ‘acr’ is the
critical crack length as obtained from figure ,‘H’
is the number of flight hours during which the
crack will grow to its critical size.
17. • Determination of ‘H’ requires a fatigue crack
growth analysis under service load spectrum.
• Such an analysis needs fatigue crack growth rate
data property under constant amplitude loading
in the form of
da
dN
and∆K curve as shown in
figure.
• where da/dN is the crack extension per cycle of
loading and ∆K is the stress intensity factor
range expressed as.
∆K= ∆σ ∏a f(a w)
18. Hear
• ∆σ= σmax- σmin is the stress range under
constant amplitude loading.
• a= half crack length for a center crack .full
crack length for an edge crack
• f (a/w) = geometry correction factor.
• w=width of the plate.
19.
20. Effect of overload on fatigue crack
growth behavior
The crack growth characteristics depend to a large
extent on this plastically deformed material at the
crack tip. The size of crack tip plastic zone
depends on the magnitude of external loading of
given by the expression.
rp =α
K
Fty
2
Where
rp =radius of the plastic zone.
21. α = a constant depending upon the state of stress
(plane stress or plane strain) at the crack tip.
Fty= yield strength of the material.
• The fatigue crack growth is influenced by the
crack tip plastic zone under constant amplitude
loading.
• The crack tip plastic zone size at any crack
length depends on the Kmax value.
22. Constant amplitude loading plastic zone.
Let us compare two load sequences given below to
understand the load interaction effects.
23. single overload cycle. is applied after n- load
cycles
Constant amplitude loading plastic zone
and over load plastic zone.
24. • One can see that the current plastic zone size is
embedded in a large plastic zone created due to the
over load.
• In the case of a load cycle after an overload cycles
the current plastic zone remains under the influence
of the over load plastic zone.
• As consequences the crack growth rate after the
overload cycle is seen to be significantly different
than that under constant amplitude loading (without
overload effect).
25. current plastic zone size touches the boundary of the
overload plastic zone.
• This difference is crack growth rate is due to a
condition known as “load-interaction effect”. This
load interaction effect will affect the fatigue crack
grow till the current plastic zone size touches the
boundary of the overload plastic zone as shown in
figure
26. FINITE ELEMENT ANALYSIS
The finite element method (FEM), sometimes
referred to as finite element analysis (FEA), is a
computational technique used to obtain
approximate solutions.
Finite Element Analysis software programs
The stress analysis of Fuselage of the Transport
aircraft has been carried out using
MSC NASTRAN
MSC PATRAN
MSC PATRAN
Meshing is done in MSC Patran (pre-post
processor)is by using various meshing options.
27. Element Quality Criteria
Once required mesh pattern is got, it is
necessary to check the quality of mesh generated,
this can be done using quality checks available in
MSC Patran.
Elements are checked for quality parameters like
war page, aspect ratio, skew and Jacobean.
- Check the maximum and minimum interior
angles of all elements, Checking for shell normals,
Check for free edges, Check for connectivity,
Check for duplicates.
MSC NASTRAN
MSC NASTRAN (solver ) is one of the most
popular general purpose finite element packages
available for structural analysis.
28. Validation of FEA approach
• In this section validation of FEA approach can be
down by the considering the rectangular plate with
center hole.
• By varying the hole diameter keeping the plate
dimension’s constant for various a/w ratio different
scf are obtained from the Eq,
σnominal =′𝑃′ 𝑙𝑜𝑎𝑑
𝐴𝑟𝑒𝑎′𝐴′
SCF = σnominal
σmax
29. • Below fig shows the internal force lines are denser
near the hole.
• The boundary conditions are one end is
constrained and other end is uniformly distributed
load is applied. The boundary conditions are same
for all iterations.
• these results are comparing with the standard
experimental results (scf vs. a/w) graph shown in
below.
32. Geometric configuration and Finite element model
of the plate with hole
Geometric modeling is carried out by using
PATRAN software .Geometric dimensions of plate
with hole fig. All dimensions are in mm.
33. The finite element mesh generated on each part
of the structure using MSC PATRAN.
Fig shows the finite element mesh on plate with
hole.
Finite element
meshing of plate
with hole.
34. Close up view of mesh near the hole
Finite element meshing is carried out near the hole
fine meshing is done in this sections where stresses
are expected to be more to get good results shown
below fig
35. Loads and boundary conditions
All the edge nodes of plate are constrained in all five
degree of freedom (i.e13456) shown in figure. Except
loading direction which is Y direction (i.e. 2). At the
loading direction(Y direction) UDL (uniformly
distributed load) is applied. All the elements along
the thickness direction are constrained to avoid the
eccentricity due to stiffening members.
36. Close up view of UDL load
along y
Close up view of
constrained boundary
Loads and boundary conditions on plate
37. For iteration 5
Consider hole diameter a=60 mm
σnominal =′𝑃′ 𝑙𝑜𝑎𝑑
𝐴𝑟𝑒𝑎′𝐴′
Where
P is applied load= 1000kg
For udl 1000/width of the plate in mm
=1000/200=5Kg/mm
A is area of load applied
= (width of the plate-hole diameter)*thickness of
the plate
= (200-60)*2=280 mm2
σnominal = 1000
200−60 ∗2= 3.5714Kg/mm2
σmax= 8.42Kg/mm2 from the FEA results
SCF = σnominal
σmax = 3.5714
8.42 = 2.36
38. Results obtained from the finite element
analysis of the plate with hole.
• Pre-processing and post-processing is
carried out by using MSC Patran software
and Solved by using MSC Nastran (solver)
software.
• The response of the plate with hole in
terms of stresses due to loads and
boundary conditions described in the
previous sections are explained in the
following sections.
40. Similarly the fallowing tabulated results are
obtained for different a/w ratio
Comparison of obtain SCF values with SCF
value plate with hole.
Number of Iterations 1 2 3 4 5
Radius of hole “r” In mm 10 15 20 25 30
Diameter of hole “a” In mm 20 30 40 50 60
Width of the plate “w” 200 200 200 200 200
aw ratio 0.1 0.15 0.2 0.25 0.3
Length of the plate “L” in mm 400 400 400 400 400
Thickness “t” In mm 2 2 2 2 2
Stress concentration factor “SCF” 2.72 2.61 2.51 2.43 2.36
σmax 7.50 7.64 7.80 8.09 8.42
σnominal 2.77 2.94 3.12 3.33 3.57
Stress concentration factor obtain“SCF” 2.71 2.60 2.5 2.43 2.36
41. Comparison of obtain SCF values with SCF values of plate with hole.
By plotting the obtained scf and standard scf
results shown in figure we conclude that the Fem
approach is valid
42. STRESS ANALYSIS OF FUSELAGE SEGMENT
As the aircraft reaches higher altitude the
atmospheric pressure will keep decreasing.
Therefore as the aircraft fly at higher altitudes,
fuselage (passenger cabin) will be pressurized for
the passenger comfort.
Then pressure inside the fuselage will be equivalent
to the sea level pressure.
For the current analysis the internal pressure is the
differential pressure introduced inside the fuselage
cabin which is considered as one of the critical load
case.
44. Geometric configuration of the fuselage
• A segment of the fuselage is considered in
the current study. The structural components
of the fuselage are skin, bulkhead and
longerons.
• Geometric modeling is carried out by using
CATIA V5 software .
• Geometric dimensions and CAD model of
fuselage figure and individual component
of the fuselage shown below. All
dimensions are in mm
47. The above figure shows the skin dimensions. Skin has
the thickness of 2 mm.
The skin houses rest of the components like
Bulkheads, Longerons, it is clear that the rivets which
are along the fuselage holds the skin with longeron and
the rivets which are in circumference to the fuselage
holds the bulkhead,
Distance between the longeron rivets are maintained
by the 15 degree angle along the fuselage
circumference and distance between the
circumference rivets are 450 mm, diameter of the rivet
used is 5mm, pitch of the rivet is 30mm.
48. Geometric configuration of the
fuselage Bulkhead
Bulkhead is also known as frame. Bulkhead is a
stiffening member in circumferential direction in the
fuselage structure. There are seven bulkheads in the
fuselage segment considered. All the dimensions of
the bulkheads are shown in fig
50. Geometric configuration of the fuselage
Longeron (stringer)
Longerons are also known as stringers which run
in longitudinal direction in the fuselage structure.
There are 24 longerons in the fuselage segment,
which are 15 degree angle along the fuselage
circumference to the each other.
52. Finite element model of the fuselage
Finite element meshing is carried out for all the
components of the fuselage such that there is a
node present at the point where riveting need to
be simulated and fine meshing is carried out at
the critical sections where stresses are expected
to be more.
The following figures show the details about the
finite element mesh generated on each part of the
structure using MSC PATRAN. Figure shows the
finite element mesh on fuselage.
55. Close up view of mesh on the skin with beam elements as rivets
Riveting is simulated by selecting the node on the
skin and the corresponding node on the other
component and created a beam element between
them.
56. Finite Element model of the Longeron
(Stringers)
Finite element mesh on Longeron
60. Fastening (riveting) Using Beam
Elements in the FEM of the Fuselage.
The rivets are used as the fasteners in the assembly of
the component of the fuselage structure such as skin,
tear strap, longeron and bulkhead. The meshing on
these structural components is carefully generated
such that there is a node present at the point where
riveting is to be carried out. The riveting process is
completed by creating beam element between the
nodes by selecting the node on the skin and the
corresponding node on the other component. The
pitch of the rivet is 25mm. Diameter of the rivet is
5mm.
61. Rivets used to assemble all components of fuselage
The figure shows the beam elements which are
indicated in red color connects all the components
of the stiffened panel and acts as the rivets.
62.
63. stress analysis of segment of fuselage.
The stress analysis of the fuselage segment is
carried out by applying a differential pressure of
0.0413826 MPa (6 psi). This differential pressure
is introduced as internal pressure in the fuselage
segment.
Loads and boundary conditions of fuselage
All the edge nodes of fuselage segment at both the
ends are constrained in all six degree of freedom
(i.e123456) and 0.0413826 MPa pressure is applied
to the internal pressure shown in figure below.
66. Results obtained from the finite element analysis
of the fuselage.
Displacement contour of the fuselage.
67. where white color showing minimum magnitude
of displacement while red color showing maximum
magnitude of displacement. In fuselage section
displacement is maximum at the skin because of
the stiffener members like stringers and bulkheads
present in longitudinal and transfer direction of the
fuselage. Unstiffened area present in between the
stringer and bulkhead gets maximum
displacement.
For this problem maximum magnitude of
displacement is 0.924 mm.
68. Close up view of Displacement contour of the fuselage
displacement contour of the stiffened fuselage.
69. Stress contour of the stiffened fuselage.
Stress contour for fuselage
70. shows the stress contour on fuselage from global
analysis results. It is clear that the maximum stress
on bulkhead is at stringer cut-out (mouse cut-out)
and this maximum stress is uniform in all the
stringer cut-outs. The magnitude of maximum
tensile stress is 68.4738MPa. In the bulkhead the
maximum stress will be at the bulkhead cut-out
(mouse hole) which is shown in figure and the
maximum stress locations are the probable locations
for crack initiation. Invariably these locations will be
at stringer cut-out locations in the bulkhead.
72. Similarly the fallowing tabulated results are
obtained for different pressurization loads
maximum magnitude of Displacement and
Stress contour in the fuselage for different
load cases.
SR.No Pressure in psi Pressure in
MPa
Max Displacement in
mm
Max stress contour in
MPa
1 6 0.04138 0.924 68.4738
2 8 0.05517 1.23 91.3311
3 10 0.06896 1.54 113.796
4 16 0.11034 2.46 182.466
5 18 0.12413 2.77 205.029
6 20 0.13793 3.08 233.478
73. LOCAL ANALYSIS OF THE STIFFENED
PANEL
From the finite element analysis carried out on the
fuselage segment, the maximum stress location was
identified which is explained in the previous section.
Based on the maximum stress location a local
analysis is carried out by considering a stiffened
panel near the maximum stress location.
74. Stiffened panels are the most generic
structural elements in an airframe.
The stiffened panel consists of
Skin
Bulkhead
Longerons (stringer)and
Fasteners (rivets).
Introduction to stiffened panel
75.
76. Geometric configuration of the stiffened
panel
Geometric modeling is carried out by using CATIA
V5 software .Geometric dimensions and CAD model
of fuselage and individual component of the
stiffened panel are shown below. All dimensions are
in mm.
78. • The above shows the skin dimensions
considered for the local analysis.
• Skin has the thickness of 2 mm. The skin
houses rest of the components like Bulkheads,
Longerons, which are assembled by riveting
process,
• It is clear that the rivets which are in columns
holds the bulkhead, distance between the
rows is 450mm and the diameter of the rivet
used is 5mm pitch of the rivet is 25mm.The
below figure shows the CAD model of the
skin with rivet holes.
80. Geometric configuration of the stiffened
panel Bulkhead
Bulkhead is also known as frame. Bulkhead is a
stiffening member in circumferential direction in the
fuselage structure. There are three bulkheads in this
stiffened panel. All the dimensions of the bulkheads
are shown in figure.
Cross sectional view (Bottom view) of the bulkhead
82. Finite element model of the stiffened panel
shows the finite element mesh on skin. The skin
houses rest of the components like bulkheads.
Finite element Mesh on skin
83. Close up view of mesh on the skin with beam elements as rivets
84. Finite element mesh of the stiffened
panel Bulkhead (Frame)
Bulkhead is also known as Frame. The bulkhead
has Z cross-section. The bulkheads are placed on
top of the skin and riveted onto the skin.
Finite element mesh on Bulkhead
88. Finite element model summary
Fuselage
Total number of Grid points =211312
Total number of Beam elements=19508
Total number of Quad elements=121680
Total number of Tria elements=31104
Stiffened panel
Total number of Grid points = 232558
Total number of Beam elements= 214
Total number of Quad elements= 217564
Total number of Tria elements= 26708
89. Local analysis at maximum stress
location.
The maximum stress location and the
magnitude of maximum stress are identified
from the global analysis of the fuselage segment.
As described in the previous section the
maximum tensile stress is near the bulkhead cut
out region a local model representing the highest
stress location is considered for the local analysis.
Stiffened panels with three bulkheads are
considered for the local analysis.
90. Loads in the local model
A differential pressure of 9 psi (0.06206MPa) is
considered for the current case. Due to this
internal pressurization of fuselage (passenger
cabin) the hoop stress will be developed in the
fuselage structure. The tensile loads at the edge
of the panel corresponding to pressurization
will be considered for the linear static analysis of
the panel.
91. Hoop stress is given by
σ hoop =
𝑝∗𝑟
𝑡
---Eq 1
Where
Cabin pressure (p)=9 psi=0.06206 MPa
Radius of curvature of fuselage(r) = 1500 mm
Thickness of skin (t) = 2 mm
After substitution of these values in the above eq we will
get
σ hoop = 4.74525 Kg/mm2
=46.55 MPa
We know that
σ hoop =
𝑃
𝐴
Above equation can be written as
P = σ hoop *A ---Eq 2
92. Uniformly distributed tensile load is applied on either side
of the stiffened panel in Y axial direction.
Load on the skin
Here
Ps=Load on skin
σ hoop =4.74525 Kg/mm2
A=Cross sectional area of skin in mm2
i.e. Width *Thickness(1000*2)=2000
Substituting these values in the Eq 2 we get
Ps=9490.5 Kg
Ps=93101.805N
Uniformly distributed load on skin will be
Ps =9490.5 /1000
=9.4905Kg/mm
93. Load on Bulkhead
Here
Pb =load on Bulkhead in Kg
σ hoop =4.74525 Kg/mm2
A =Cross sectional area of each Bulkhead in mm2
i.e. Width *Thickness, (L1+L2+L3)*tb
i.e. (18.5+68.5+18)*1.5=232mm2
Substituting the values in (Eq 2) we get
Pb =1100.898 Kg
Pb =10799.8093N
Uniformly distributed load on Bulkhead will be
Pb = 1100.898 /116
=9.4905 Kg/mm
94. Similarly for the pressure 12 psi=0.082737154 MPa
Load on Bulkhead
Pb =1467.864 Kg
Pb =14399.746 N
Load on Skin
Ps =12654 Kg, Ps =124135.74 N
95. All the edge nodes of stiffened panel are constrained
in all five degree of freedom (i.e13456) except
loading direction which is Y direction (i.e. 2).
All the elements along the thickness direction are
constrained to avoid the eccentricity due to stiffening
members.
Loads and boundary conditions of stiffened panel
100. . It is clear that the maximum stress on bulkhead is
at stringer cut-out (mouse cut-out) and this
maximum stress is uniform in all the stringer cut-
outs. The magnitude of maximum tensile stress is
1.29 kg/mm2
which is more than the stresses in all other
components of the stiffened panel. In the bulkhead
the maximum stress will be at the stringer cut-out
(mouse hole)
maximum stress locations are the probable
locations for crack initiation. Invariably these
locations will be at stringer cut-out locations in the
bulkhead
102. From the stress analysis of the stiffened panel it can be
observed that a crack will get initiated from the maximum
stress location. There are two structural elements at the rivet
location near the high stress location. Crack will either get
initiated from the bulkhead at stringer cut out or from the
nearby rivet location from the rivet hole. Figure shows the
rivet force near the high stress location is 84.1kg and 83.2kg.
Rivet force near the high stress location
103. Local analysis at maximum stress location
with considering the rivet hole.
There are two structural elements at the rivet
location near the high stress location, the rivet near
the high stress location are removed by creating the
hole on bulkhead and skin same as the rivet
dimensions and applying the rivet force near the
high stress location. All other loads and boundary
conditions stiffened panel is same as shown in the
above
104. Close up view of hole near the high stress
location on the skin
105. Results obtained from the finite element
analysis of the stiffened panel with
considering the rivet hole.
Displacement contour of the stiffened panel
106. Stress contour of the stiffened panel
Stress distribution on skin
. Stress contour for skin
107. • Above shows the stress contour on the skin from
local analysis results. It is clear that the maximum
stress on skin is at the rivet hole location. The
magnitude of maximum tensile stress is
38.4kg/mm2
• which is more than the stresses in all other
components of the stiffened panel. In the bulkhead
the maximum stress will be at the skin rivet hole
which is shown above
• The maximum stress locations are the probable
locations for crack initiation. Invariably these
locations will be at rivet locations in the skin. Skin
is the critical stress locations for the crack
initiation.
111. Validation of FEM approach for stress
intensity factor (SIF) calculation
Geometry, Loads and boundary conditions
of unstiffened panel
Geometry of the unstiffened panel
114. Close up view of fine mesh at the center of skin
near the crack
115. Consider crack length, 2a=10 mm
1. SIF calculation by Theoretical method
KI =𝜎 𝑅 𝜋 ∗ 𝑎 * f (𝛼) − −Eq (a)
Where
𝜎 𝑅=P/A=
1000
200∗2
=2.5Kg/mm2
𝑎 =5 mm
f (𝛼)= 1.001165 which is calculated by using Eq
f (𝛼) =
1+0.326( 𝑎 𝑏)2−0.5
𝑎
𝑏
1−
𝑎
𝑏
Where
𝑎 = Crack length in mm
f (𝛼) =Correction factor
b=Width of the plate (200 mm)
116. Substituting above values in Eq(a) .SIF value will be
KI theoretical =3.077334 MPa 𝑚
2. SIF calculation by Analytical method(FEM)
Nodes and Elements near the crack tip
117. Strain energy relies rate is calculated by Eq
G=
𝐹 𝑢
2 ∆𝑐 𝑡
For relative displacement 𝑢 adding the
displacement of nodes 8608 and 9211 in T2
direction. The displacement is obtained in the f06
file created by the MSC Nastran (solver) software
shown in table.
POINT ID. TYPE T1 T2 T3 R1 R2 R3
8608 G 6.075589E-04 1.981864E-03 0.0 0.0 0.0 7.221852E-04
9211 G 6.075589E-04 1.981864E-03 0.0 0.0 0.0 7.221852E-04
D I S P L A C E M E N T V E C T O R For
Unstiffened Panel
118. For the relative displacement
𝑢 (1.981864E-03+1.981864E-03) = 0.00396 mm
For Forces at the crack tip in kg or N, adding any one
side of elements (Elm 8395, 8396 or Elm8595, 8596)
forces acting on the crack tip in T2 direction. The
Forces at the crack tip is obtained in the f06 file
created by the MSC Nastran (solver) software shown
in table
POINT-ID ELEMENT-ID SOURCE T1 T2 T3
8808 8395 QUAD4 -2.395632E+00 -6.864131E+00 0.0
8808 8396 QUAD4 +2.395632E+00 +6.652291E+00 0.0
8808 8595 QUAD4 -2.395632E+00 +6.864131E+00 0.0
8808 8596 QUAD4 +2.395632E+00 -6.652291E+00 0.0
G R I D P O I N T F O R C E B A L A N C E For Unstiffened Panel
119. For Forces at the crack tip
F=(6.864131E+00+6.652291E+00)=13.51642 Kg.
Where
F = 13.51Kg =132.533N
U = 0.00396 mm
𝜟c= 1 mm
T = 2 mm
Substitute all values in above Eq then
G= 0.13120 MPa
Now Analytical SIF is calculated by Eq
KI fem= 𝐺𝐸
Where
E=7000kg/mm2=68670 MPa
Substituting G and E values in Eq
KI fem=3.0423 MPa 𝑚
120. The above calculation is carried for different
crack length considering a known load.
A stress intensity factor value calculated by
FEM and stress intensity values calculated by
theoretical method for un-stiffened panel is
tabulated.
121. SR.No Crack length
”2a” in mm
Kfem in MPa√m Kth without
considering the
C.F in MPa√m
Correction
factor
C.F
Kth with
considering the
C.F in MPa√m
%error
1 10 3.042304 3.073753 1.001165 3.077334 1.138
2 20 4.367924 4.346943 1.004824 4.367913 0
3 30 5.406574 5.323896 1.011259 5.383838 0.422
4 40 6.318190 6.147506 1.020810 6.275436 0.681
5 50 7.166964 6.873120 1.033890 7.106050 0.857
6 60 7.991123 7.529126 1.051012 70913202 0.984
7 70 8.816894 8.132386 1.072820 8.724586 1.056
8 80 9.668487 8.693886 1.100134 9.564440 1.080
9 90 10.572659 9.221259 1.134024 10.457129 1.104
10 100 11.545625 9.720060 1.175919 11.430003 1.010
Comparison of analytical (FEM) SIF values with theoretical SIF value for
un-stiffened panel for 1 mm element size.
122. SR.No Crack length
”2a” in mm
Kfem in MPa√m Kth without
considering the
C.F in MPa√m
Correction factor
C.F
Kth with
considering the
C.F in MPa√m
%error
1 10 3.076609 3.073753 1.001165 3.077334 0.023
2 20 4.391599 4.346943 1.004824 4.367913 0.542
3 30 5.426225 5.323896 1.011259 5.383838 0.787
4 40 6.335258 6.147506 1.020810 6.275436 0.953
5 50 7.183796 6.873120 1.033890 7.106050 1.094
6 60 8.007325 7.529126 1.051012 70913202 1.189
7 70 8.833447 8.132386 1.072820 8.724586 1.247
8 80 9.686039 8.693886 1.100134 9.564440 1.271
9 90 10.587531 9.221259 1.134024 10.457129 1.247
10 100 11.565942 9.720060 1.175919 11.430003 1.189
Comparison of analytical (FEM) SIF values with theoretical SIF value for
un-stiffened panel for 0.5 mm element size
123. Comparison of Theoretical SIF value with analytical SIF value
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0 10 20 30 40 50 60 70 80 90 100 110
SIFINMPa√m
CRACK LENGTH a in mm
SIF by theoretical in MPa√m
SIF by analytical in MPa√m for 1
mm element size
SIF by analytical in MPa√m for 0.5
mm element size
124. Methodology of finding SIF values for un-stiffened
panel using FEM was extended to get SIF values for
stiffened panel.
Where red fringes shows the maximum
displacement which is at the center of the panel.
Displacement contour for un-stiffened panel with center crack
125. FATIGUE CRACK GROWTH CALCULATIONS
Calculation of stress intensity factor (SIF)
for 100 mm crack in the stiffened panel for
constant amplitude loading.
Considering a crack length of 100 mm in the skin at
high stress region SIF is calculated.
The maximum load corresponding to 9 PSI which is
L=9490.5kg ≈ 9.4905kg/mm uniformly distributed load is
applied at the remote edge of the panel.
126. Loads and boundary conditions of
stiffened panel
All the edge nodes of stiffened panel are constrained
in all five degree of freedom (i.e13456) except
loading direction which is Y direction (i.e. 2). All the
elements along the thickness direction are
constrained to avoid the eccentricity due to stiffening
members. All loads and boundary conditions of
stiffened panel is shown in the below
fig
129. Close up view of Stress contour in the stiffened panel for 100 mm crack
Considering the maximum stress in Z1 direction
and max-principal failure theory, the max stress
occurred at the skin region is 51.00 Mpa.
130. SIF calculation by Analytical method (FEM)
Nodes and Elements near the crack tip
Nodes and elements ID shown in above figure are
near the crack tip at which maximum stress are
acting. Strain energy relies rate is calculated by
Equation G=
𝐹 𝑢
2 ∆𝑐 𝑡
−− −A
131. For relative displacement 𝑢 subtracting the
displacement of nodes 106071 and 233376 in T2
direction. The displacement is obtained in the f06 file
created by the MSC Nastran (solver) software shown
in table
D I S P L A C E M E N T V E C T O R
POINT ID. TYPE T2
106071 G 0.4655189
233376 G 0.4791793
For the relative displacement
𝑢 (0.4655189-0.4791793) = 0.0136604 mm
132. For Forces at the crack tip in kg or N, adding any
one side of elements (Elm 151247, 151248 or
Elm153247, 153248) forces acting on the crack tip in
T2 direction. The Forces at the crack tip is obtained
in the f06 file created by the MSC Nastran (solver)
software shown in table
G R I D P O I N T F O R C E B A L A N C E
POINT-ID ELEMENT-ID SOURCE T2
104444 151247 QUAD4 20.77951
104444 151248 QUAD4 23.20860
104444 153247 QUAD4 23.97819
104444 153248 QUAD4 20.00991
For Forces at the crack tip
F=(20.77951+23.20860)=43.98811 Kg.
133. Where
F = 43.988 Kg
U = 0.0136604 mm
𝜟c= 0.5 mm
T = 2 mm
Substitute all values in Eq ‘A’ then
G= 0.30044759 Kg/mm
Now Analytical SIF is calculated by equation.
KI fem= 𝐺𝐸
Where
E=7310kg/mm2
Substituting G and E values in above equation
KI fem=14.53824748 MPa 𝑚
134. Calculation of crack growth
𝐝𝐚
𝐝𝐍
rate for 100
mm crack in the stiffened panel
The crack growth rate is calculated or obtained
through
da
dN
vs 𝜟k curve from the respective
material.
Therefore to obtain the
da
dN
(crack growth rate) one
should first calculate the 𝜟keffective.
𝜟keffective is calculated by using the Eq B and Eq C
(Ref: “The practical use of fracture mechanics” by
David Broek).
𝜟Keffective= 𝜟Kmax-𝜟Kopening ---MPa 𝑚 Eq B
𝜟Kopening=𝜟Kmax(0.5×0.4R) R→0 ---MPa 𝑚 Eq C
135. Where
𝜟Kmax = maximum stress intensity factor
𝜟Kmax = minimum stress intensity factor
R =
𝜎 𝑚𝑖𝑛
𝜎 𝑚𝑎𝑥
= 0 because 𝝈minimum→0
We know that
Kmax =14.53 MPa 𝑚.
Kmin=0.0
Substituting the values in Eq ‘C’ we get
Kopening=7.27 MPa 𝑚
Substituting the values in Eq ‘B’ we get
Keffective= 7.26 MPa 𝑚
From graph shown in below Crack growth rate curve
we get the crack growth rate per cycle
136.
137. For Keffective =7.27 MPa 𝑚,
we get 5×10-5 mm/cycle
To growth a crack of 1mm it requires 20,000
cycles .
After 20,000 cycles the crack size will be 101mm
which is considered for the next analysis and
overload cycle is applied.
138. Calculation of stress intensity factor (SIF)
for 101 mm crack in the stiffened panel with
overload is applied.
Considering a crack length 0f 101 mm on the skin
and the overload corresponding to 12 PSI which
is L=12654kg ≈ 12.654kg/mm uniformly
distributed load is applied at the remote edge of
the panel.
Stress contour of the stiffened panel
The stress distribution is shown below in the fig
8.6 at a crack length of 2a=101mm
139. Stress counter in the stiffened panel for 100 crack
Considering the maximum stress in Z1 direction and
max-principal failure theory. The max stress
occurred at the skin region is 68.20 Mpa.
140. Similarly
F = 58.8225 Kg
U = 0.0182676 mm
𝜟c= 0.5 mm
T = 2 mm
G= 0.302213863 Kg/mm
E=7310kg/mm2
KI fem=19.44129471 MPa 𝑚
Kmax =19.44129471 MPa 𝑚.
Kmin=0.0
Kopening= 9.720647354 MPa 𝑚
Keffective= 9.720647354 MPa 𝑚
Crack growth rate
We get 5×10-4 mm/cycle
141. With 1 cycle of load the crack growth increment
is 0.0005mm.
After the application of one overload cycle with
crack increment of 0.0005 mm the total crack size
will be 101.0005mm.
With the crack length of 101mm another iteration
is carried out with the load of 9psi.
142. Calculation of stress intensity factor (SIF)
for 101 mm crack with 9psi load.
Considering a crack length of 101 mm in the
skin at high stress region SIF is calculated. The
maximum load corresponding to 9 PSI which
is L=9490.5kg ≈ 9.4905kg/mm uniformly
distributed load is applied at the remote edge
of the panel.
Stress contour of the stiffened panel
The stress distribution is shown in the below
fig 8.8 with the crack length of 2a=101mm
and 9psi load
143. Considering the maximum stress in Z1 direction
and max-principal failure theory, the max stress
occurred at the skin region is 68.20 Mpa.
Stress counter stiffened panel for 101 mm crack
144. Similarly
F = 44.11688 Kg
U = 0.0137006 mm
𝜟c= 0.5 mm
T = 2 mm
G= 0.302213863 Kg/mm
KI fem=14.58091865 MPa 𝑚
E=7310kg/mm2
Kmax =14.58091865MPa 𝑚.
Kmin=0.0
Kopening=7.290459325 MPa 𝑚
Keffective= 7.290459325 MPa 𝑚
we get 5×10-5 mm/cycle
145. Over load plastic zone size calculations
When one single high stress is interspersed in a
constant amplitude history, the crack growth
immediately after the “overload” is much slower
than before the overload.
After a period of very slow growth immediately
following the overload, gradually the original
growth rates are resumed. This phenomenon is
known as “retardation”.
The loading pattern used for the calculation of
overload effect is shown in the following figure.
147. The overload plastic zone size is given by the
following Equation
Rpc =Rpo=
1
2∏
×
Kmax
Fty
2
Where
Rpo= over load plastic zone size
Kmax= maximum SIF value
Fty= yield strength
Considering Fty=345 Mpa
And Kmax=19.44129471Mpa 𝑚
Substituting the values in Equation.
Rpo=
1
2∏
×
19.44129471
345
2
= 5.05396592×10-4mm.
148. Followed by the 101.0005mm crack and 9psi load
Kmax=14.58091865Mpa 𝑚
Rpc=
1
2∏
×
14
.
58091865
345
2
= 2.842835404×10-4mm.
Where
Rpc= current plastic zone size
149. Calculations for the Retardation factor
crack growth retardation because of the overload
plastic zone size the retardation factor is calculated
using the following equation.
ØR=
Rpc
𝑎𝑜+Rpo
−
ai
𝛾
here 𝛾 = 1.4
Where
ØR= Retardation factor
ai = current crack length
ao = after the overload crack length
𝛾 = wheeler parametric value =1.4
ØR=
2.842835404×10−4
101.0005+5.05396592×10−4
−
101
1.4
= 0.170600296.
150. Calculating the crack growth rate with in
the overload region
As the crack grows within the overload plastic size
the effect of over load on the crack growth rate also
varies. Therefore the crack growth rate is calculated
by dividing the overload region by four parts each
one having region as 1.26349148×10-4mm.
152. 1st region.
To calculate crack growth rate in the 1st region
following data are considered
Load of 9psi with crack size now become
ai= 101+(1.26349148×10-4×1)
=101.0001263mm
And ao, Rpc ,Rpo will be as follows
ao= 101.0005+(1.26349148×10-4×1)
=101.0006263mm
Rpc=2.842835404×10-4 mm
Rpo=(1.26349148×10-4×3)
=3.79047444×10-4 mm
Retardation factor for first region from Equation
ØR1=
Rpc
𝑎𝑜+Rpo
−
ai
𝛾
here 𝛾 = 1.4
154. 2nd region.
To calculate crack growth rate in the 2nd region
considering the following data
Load of 9psi with crack size now become
ai= 101+(1.26349148×10-4×2)
=101.000252mm
And ao, Rpc ,Rpo will be
ao =101.0005+(1.26349148×10-4×2)
=101.000752mm
Rpc=2.842835404×10-4mm,
Rpo=(1.26349148×10-4×2)
=2.52698296×10-4mm,
Retardation factor for second region from Equation
ØR2=
Rpc
𝑎𝑜+Rpo
−
ai
𝛾
here 𝛾 = 1.4
156. 3rd region.
To calculate crack growth rate in the 3rd region we
taken fallowing data
Load 9psi with crack size now become
ai= 101+(1.26349148×10-4×3)
=101.000378mm,
And ao, Rpc ,Rpo become
ao =101.0005+(1.26349148×10-4×3)
=101.000878
Rpc=2.842835404×10-4mm,
Rpo=(1.26349148×10-4×1)
= 1.26349148×10-4,
157. The overload plastic
zone size after the
second region is
1.26×10-4 is less than the
current plastic zone
size. Therefore the
assumed 3rd region for
the calculation of
retardation factor need
not to be considered.
shown in table.
Crack growth calculations
SIF 𝒅𝒂
𝒅𝑵
Number of cycles required for
a crack growth increment of
1mm.
Constant amplitude loading
(9PSI) 9.4906Kg/mm2 for 100
mm crack
SIF= 14.5382
5𝖷10-5cycles 20,000
Overload (without
considering the overload
plastic zone size
applied)(12PSI)12.654Kg/mm2
SIF=19.4412 at 101mm crack
length
5𝖷10-4cycles 2000
After the overload plastic zone size effect
With considering the
retardation factor 0.170600296
0.170600296𝖷5𝖷10-5 =
8.5300148𝖷10-6cycles. 1,17,233
158. OBSERVATIONS AND DISCUSSIONS
• Damage tolerance design philosophy is generally
used in the aircraft structural design to reduce the
weight of the structure.
• Stiffened panel is a generic structural element of
the fuselage structure. Therefore it is considered for
the current study.
• A FEM approach is followed for the stress analysis
of the stiffened panel.
• The internal pressure is one of the main loads that
the fuselage needs to hold.
• Stress analysis is carried out to identify the
maximum tensile stress location in the stiffened
panel.
159. • A local analysis is carried out at the maximum
stress location with the rivet hole representation.
• The crack is initiated from the location of
maximum tensile stress.
• MVCCI method is used for calculation of stress
intensity factor
• A crack in the skin is initiated with the local
model to capture the stress intensity factor
• Stress intensity factor calculations are carried out
for various incremental cracks
• When the SIF at the crack tip reaches a value
equivalent to the fracture toughness of the
material, then the crack will propagate rapidly
leading to catastrophic failure of the structure
160. • A load spectrum consisting of constant load cycles
with a over load in-between is considered to study
the over load effect on the crack growth rate
• The crack growth rate for constant amplitude load
cycles is carried out by considering the crack
growth rate data curve (da/dN Vs 𝜟K)
• Plastic zone size due to constant amplitude load
cycles and over load cycle is calculated.
• The calculations have indicated that the over load
will reduce the rate of crack growth due to large
plastic zone size near the crack tip.
• The effect of large plastic zone due to over load is
estimated by calculating the crack growth
retardation factor
161. • The crack growth retardation factor with a over
load reduces the rate of crack growth to 17%
than compared to crack growth rate without a
over load.
162. SCOPE FOR FURTHER STUDIES
• The overload effect can be calculated for different
load spectrum using the similar approach
• Structural testing of the stiffened panel can be
carried out for validating the analytical
predictions.
• Crack growth analysis in the stiffened panel with
a different skin material can be carried out
• The bi-axial stress field can be considered for the
crack growth study in the stiffened panel
163. REFERENCES
1. F. Erdogan and M. Ratwani, International journal of fracture
mechanics, Vol. 6, No.4, December 1970.
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3. H. Vlieger, 1979, “ Application of fracture mechanics of built up
structures”, NLR MP79044U.
4. Thomas P. Rich, Mansoor M. Ghassem, David J. Cartwright,
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5. Pir M. Toor “On damage tolerance design of fuselage structure
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164. 7. Federal Aviation Administration technical center “ Damage
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8. T. Swift “Damage tolerance capability”, international journal of
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9. J. Schijve “Multiple –site damage in aircraft fuselage structure”
In 10 November 1994.
10. T. Swift, 1997, “Damage tolerances analysis of redundant
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16. Michael F. Ashby and David R. H. Jones “Engineering materials
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