Damage Tolerance Evaluation of Antenna Installations
By Patrick Safarian Spring 2012
Damage Tolerance Analysis DTA
Damage tolerance analysis (DTA) is the application of Fracture Mechanics to assess how a structure, assumed to be cracked, will respond to loads (cyclic and static) over time DTA assesses:
How a crack(s) will grow over time How the strength of the structure is affected by the crack(s)
Fatigue analysis is the proper approach to assess the structural durability and identify the critical details for DTA and set inspection thresholds.
Damage Tolerance Analysis DTA
Damage tolerance analysis (DTA) is the application of Fracture Mechanics to assess how a structure, assumed to be cracked, will respond to loads (cyclic and static) over time DTA assesses:
How a crack(s) will grow over time How the strength of the structure is affected by the crack(s)
Fatigue analysis is the proper approach to assess the structural durability and identify the critical details for DTA and set inspection thresholds.
General Requirements FAR Requirements
FAR 25.1529 requires preparation of Instructions for Continued Airworthiness (ICA) in Accordance with Part P art 25 Appendix H Part 25 Appendix H gives specific requirements for ICA preparation. requires inclusion of structural inspection procedures approved under FAR 25.571 25.571 requires:
Damage tolerance evaluation Establishment of inspections or other procedures necessary to prevent catastrophic failure Inclusion of appropriate inspections or other procedures in Airworthiness Limitations Section of the ICA
Part 26 Requirement and Applicability CFR Requirements
Despite all the requirements previous repairs and modifications were not evaluated for DT New Code of Federal Regulation Part 26.45 and 26.47 mandate the TC and STC holders, respectively, to develop DT based inspections for alterations and repairs to alteration in fatigue critical structures for Part 121 and 129 airplanes having:
A maximum type-certificated passenger capacity of 30 or more OR A maximum payload capacity of 7,500 pounds or more
This rule is known as Aging Aircraft Safety Rule (AASR)
Part 26 Requirement and Applicability AASR Requirements
So what are the AASR requirements?
To perform a damage tolerance evaluation on the structure that could contribute to catastrophic failure due to fatigue. This includes baselines structures and repairs and alteration The analysis requirements are similar to requirements of CFR 25.571 Amendment 24-45, or their TC amendment, which ever one is grater.
Specific Tasks Overview
The specific tasks: 1. Identify the most critical detail(s) of the installation 2. Perform crack growth and residual strength analyses 3. Determine inspection threshold and intervals 4. Develop an ICAW Include illustrations and clearly specify the inspection detail areas and direction
Physical Characteristics Through the AC Skin
Skin penetration for antenna cable Doubler attached to skin with mounting provisions for antenna (e.g. nut plates) To enhance the durability of the doubler to skin attachments it is best to pick up the stringer fasteners and stabilize the stringers using connecting intercostals New fatigue critical details are introduced
Open Holes Filled Loaded Holes
General Assumptions Skin Installation
Installation located in skin bounded by frames and stringers (i.e. longerons) Installation located away from discontinuities (e.g. doors, windows) and other repairs by at least one frame bay and 2 stringer bays Biaxial loading due to pressure plus vertical inertia fuselage bending only (internal shear neglected)
Calculation of the detail stress at the peripheral fasteners should include the contributions from membrane and bending stress components due to eccentricity caused by the doubler
Gross Loading Skin Stresses
Fuselage subjected to:
Internal pressure Overall bending and shear associated with gusts, maneuvers and ground conditions Loads introduced by gear, t wing and empennage
p0 L
pcabin H
R
Calculation of skin stresses Hoop = pR/t due to pressure away from Longitudinal = pR/2t discontinuities may conservatively where, p = pcabin - po be given as: Ignoring beneficial effects of frames and stringers is conservative
Gross Loading Skin Stresses
Major percentage of hoop stress for majority of fuselage skin is due to pressure; neglecting other loading may be reasonable
Use minimum skin gauge and standard radius
Contribution of fuselage bending to longitudinal stress may be significant and should NOT be ignored. This is especially true for installations located on the top and aft of the wing.
Gross Loading Skin Stresses
Avoid installing antennas in fuselage locations where the primary loading consists of more than the basic pressure plus overall fuselage bending.
Stabilize the skin structure by installing intercostals . This reduces extra bending stresses in the skin.
In smaller radius fuselage add intercostals b/w frames
Gross Loading Skin Stresses
Vertical fuselage inertia bending adds to longitudinal skin stress is assumed to vary as shown: Lift
ANTENNA LOCATION
Front Spar
N O L
D U T I G
A N I
nzW
L
L
R T S
S S E
L = pR/2t + nz1G,max
S
L = pR/2t + nz (L/S) 1G,max
FUSELAGE LOCATION
1g, max Estimate
Assumed to occur at maximum bending location at top of fuselage over the wing Assume zero margin design and conservatively neglect aerosuction, relief valve setting, Nz > 2.5, etc. unless specifically known Based on the above and Nz = 2.5, FTU, B = 1.5 (PR/2t + 2.5g) 1g,max
=
(FTU, B/1.5 - PR/2t)/2.5
P = normal operating pressure at max design altitude, psi
FTU, B = B-basis ultimate tension allowable (ref. MMPDS)
Local Loads/Stresses Doubler Attachment 1) Skin holes used for doubler attachment will get induced fastener bearing loading in addition to basic stress.
0
0 BP
BR
Local Loads/Stresses Doubler Attachment
First row of fasteners in multi row design will have most critical combination of bearing and bypass stress D A O L
Calculate the fastener loads by a various method available, such as 1D FEA tool, Tom Swift or Huth method
Local Loads/Stresses Doubler Attachment 2) In addition to induced fastener bearing, bending stresses due to eccentricity cause by doubler thickness should be taken into account. Doubler Skin
Notice the skin bending due to eccentricity caused by the doubler. Max skin stress is at the faying surface in the first row of fasteners.
Fatigue Evaluation
Critical Locations Identify critical locations using fatigue evaluation
High stress concentrations in the structure and high load transfer points in the joint should be identified.
Fatigue lives be determined Location for crack growth analysis be determined
Crack Growth Scenarios - Threshold Inspection Threshold
Crack growth scenarios to be considered should be described and supporting rationale being given:
Fatigue analysis Consider factors such as:
Installation design, Detail being considered, Inspection method/procedures to be used for hidden parts
Inspection threshold should be the least of:
¼ of the unfactored fatigue life of the details ½ the life of rogue flaw size to critical length Threshold of the SSID or ALI ¾ the design service goal (DSG) of the airplane
Crack Growth Scenarios - Threshold Inspection Threshold
Ref. SACO Damage Tolerance Guidelines The threshold is calculated as the airplane total cycles unless:
The Doubler picks up new holes, or Uses existing holes that are zero-timed (After confirmation of no detectable cracks the hole is oversized)
For Setting Threshold Initial (Rogue) Flaw Assumptions
No longer 0.005,” but 0.010” 0.05”
Perform a crack growth analysis of a 0.05” single crack at a hole in a row of holes to failure, which is considered as a link-up to adjacent hole- End of Stage 1. Perform a similar crack growth analysis of an 0.010” single crack with the same scenario as above. This size of a1 at the end of stage 1 is the growth of 0.010” crack during the cycles that it took the 0.05” crack to grow to failure.
For Setting Threshold Initial (Rogue) Flaw Assumptions No longer 0.005,” but 0.010” 0.05”
The linked up holes plus 2*(0.010+a1) grow to the adjacent holes- End of Stage 2. The a2 is defined similar to a1 as growth of 0.010+ a1 at the end of stage 2.
For Setting Threshold Continuing Damage 0.005” 0.010”++a a1 1
0.005” 0.010”+ + a a1 D
A e + D + 2(.005 +a A =e+D+2(0.010”+ a1)1) 11=
e
End of Stage 1 0.005” 0.010”++a a1 1+ +a a2 2
0.010”+ a11 + a22 0.005” + a +a
D
e
A22=3e+D+2(0.010”+ = 3e + D + 2(.005 +a1+ a1 + A a2)a2)
End of Stage 2
For Setting Inspection Threshold NThreshold acrit a
, H T G N E L K C A R C
Inspection Threshold (Nthreshold) Nthreshold = Ncr /2
0.05”
CYCLES, N
Ncr/2
Ncr
DTA of Repair Inspection Technique
Most common inspection techniques are:
General Visual (Surveillance) Detail Inspection Special Inspection
High frequency eddy current (HFEC) Low frequency eddy current (LFEC) Medium frequency eddy current (MFEC) Ultrasound (UT)
In Table 1 of SACO Damage Tolerance Guidelines guidance for detectable crack size for most of these techniques are provided
Use OEM NDI procedure manual to specify the technique procedure
Detectable Crack Sizes Inspection Techniques and adetectable TABLE 2. Detectable Crack Sizes Associated with Inspection Techniques (Reference [4])
Reference: SACO Damage Tolerance Guidelines, Table 1
Method Visual
Penetrant
Magnetic Particle
X-RAY Radiography Ultrasonic Shear-Wave (Angle Beam)
Ultrasonic Longitudinal Wave (Straight Beam)
Bolt Hole Eddy Current (Faster Removed)
Description
Detectable Crack Length (inch)
Unpainted Surface*: 3 to 5x Magnification Painted Surface
None
Unpainted Surface: 3 to 5x Magnification Without Magnification Painted Surface
0.125 0.250 None
Unpainted Surface: 3 to 5x Magnification Without Magnification Painted Surface: Without Magnification Uncovered length of crack in aluminum (not covered by a steel member) Crack at fastener hole using mini probe (0.25 x 0.25 inch element) at 5 to 10 Mhz
1.0 or Hole-to-Edge
0.0625 0.125 0.250 0.75 or Hole-to-Hole or Hole-to-Edge 0.125 Long x .0625 Deep
Crack in Clevis or Lug
0.125 Long x 0.0625 Deep
Bolts
¼ to 1/3 Diameter
Crack at Fastener Hole
0.125
Edge Corner Crack
0.030 x 0.030
Inside Diameter Surface
0.060 Long x .030 Deep
Eddy Current Surface Probe Crack at Fastener Crack away from fastener
* Only primer is allowed on unpainted surfaces.
0.0625 Uncovered Length 0.125
DTA of Repair Inspection Technique
Examples from Boeing NDT procedure manual to specify the technique (use approved spec’s):
727 NDT manual Part 6
LFEC: 53-30-00 Figure 5 HFEC: Surface and around fastener 51-00-00 Fig 4 or Fig 23 HFEC: Open Hole 51-00-00 Fig 16 or Fig 11 (only for t>0.062”, needs less space than fig 16)
Recommended Minimum detectable crack lengths:
HFEC: 0.20” Gen Area, 0.10” + fastener head diameter MFEC: 0.50” Gen Area, 0.25” @ fastener shank
0.15” @ fastener (727 NDT Part 6 53-30-27 Fig 17)
LFEC: 0.20” C’snk & 0.25” Button-head (0.04
(727 NDT Part 6 53-30-27 Fig 13 refers to 53-30-00 Fig9)
Crack Growth Scenarios Setting Inspection Intervals
Determine the detectable crack size based on the inspection technique
An acceptable way to model MSD is to assume detectable cracks exist at every equally critical detail growing to failure; e.g. both sides of each hole in a row of equally critical holes Detectable crack at every equally critical hole (Total of 10 in this schematic)
Another acceptable way to model MSD is to assume detectable cracks at a single hole growth to a 1 ” tip-to-tip
(Reference Damage Tolerance Facts and Fictions by Ulf Goranson, figure 16)
1.0”
Crack Growth Scenarios Setting Inspection Intervals
Determine the fatigue loads and develop spectrum
In absence of OEM data use conservative approach
Using residual strength analysis compute the critical crack length
Choose the shorter length of the net section yield and LEFM results
For MSD situations most often the critical crack length is based on net section yield If p=8.9 psi, R=128”, pitch=1.2”, D=0.188”, t=0.062”, KA= 130 Ksi*in**0.5, FTU=62 Ksi and FTY=42 Ksi show that the critical crack length is 0.24”?
Fastener Pitch
aCritical (Typical 10 locations)
Crack Growth Scenario for DTA of Repair Operational Stresses
Use the following residual stress levels to determine the critical crack length (acritical)
Longitudinal cracks,
Hoop, Res = (1.1 p + 0.5)R/t (Up to Amendment 25-86) Hoop, Res = 1.15 (p + 0.5)R/t (Amendment 25-96 and higher)
Circumferential cracks
Long, Res = PR/2t + Nz 1g,MAX (aft of front spar) Long, Res = PR/2t + Nz(L/S)1g,MAX (fwd of front spar) p = normal operating pressure at maximum design altitude P = normal operating pressure at maximum design altitude plus 0. 5 psi for
aerosuction Nz = maximum design limit load factor (at least 2.5 but not greater that 3.8)
Crack Growth Scenarios Setting Inspection Intervals
Using LEFM principals grow the cracks from detectable length to the critical length.
Cycle by cycle crack growth or simplified equivalent stress crack growth methods can be employed
Programs available include NASGRO, AFGROW, FractureResearch, CRACKS9x, user-developed programs, or combinations of features from the listed programs.
Find the most critical cracking scenario(s) using S-N curves & analyze different crack sequence scenarios The most critical inspection program should be applied to ALL fatigue critical details,
e.g. inspect the most critical (outer) row in longitudinal and circumfrential directions of a rectangular doubler.
Crack Growth Stresses Cycles
Equivalent once per flight cycle used:
TYPICAL
EQUIVALENT CYCLE
Most OEM’s have their approach to calculate the equivalent cycles .
Boeing uses a modified Miner’s rule approach
Crack Growth Scenario for DTA of Repair Setting Inspection Intervals
Vertical fuselage inertia bending adds to longitudinal skin stress is assumed to vary as shown: ANTENNA LOCATION
Lift
Front Spar
nzW
L L A N I D U T I G N O L
S S E R T S
S
L = pR/2t + nz1G,max
L = pR/2t + nz (L/S) 1G,max FUSELAGE LOCATION
Crack Growth Scenario for DTA of Repair Operational Stresses
Longitudinal cracks,
Hoop,min = 0 Hoop,max = PR/t
Circumferential cracks,
Use 1.5 for large transports, e.g. Boeing, and 1.3 for small transports, e.g. Gulfsteam, airplane models
Long,min = 0
Long,max
Long,max = 0.4 (FTU, B + PR/2t) (aft of front spar)
Long,max = 0.4 ((L/S)FTU, B + PR/2t) (fwd of front spar)
P = normal operating pressure at max design altitude + 0.5psi
1.5g,max 1.5 g,max
= 1.5
1.0g,max
+ PR/2t
For p=8.9 psi, R=128”, t=0.062”, and FTU=62 Ksi what are the hoop and longitudinal stresses?
(aerosuction)
Use the bending stresses provided in the next few slides to adjust for the joint eccentricity created due to installing the repair doubler
Crack Growth Stresses Hoop and Longitudinal Loading
Finite element analysis of a 6 ” tall antenna on a 0.04”t skin & a 0.056”t doubler subject to hoop and longitudinal loading.
Fasteners do pick up the adjacent stringers Antenna Skin
Antenna Base Doubler Stringer
Model includes skin, stringer, doubler, antenna, 8.6 psi internal pressure and 5 psi side pressure load on the antenna
Note the difference in the skin out of plane displacements caused by presence of the doubler.
Crack Growth Stresses Principal Stress
Max principal stress contour indicates membrane stress of 17.2 Ksi and Max fiber stress of 25.3 Ksi
Membrane + bending principal stress contour
Membrane principal stress contour
Similar analysis indicates that the increased stresses for antennas less than 6” tall are mainly due to the eccentricity caused by the doubler. In this case the max membrane stress stayed the same (17.2 Ksi) and the max fiber stress
Joints Eccentricity Joint Stresses
Secondary bending
Caused by step in neutral line Bending moment depends on
Step size (eccentricity)
Thickness Load transfer
Overlap length (row distance)
Loads on Joint
Tensile stresses Secondary bending
Contact surface: Tensile stress + bending stress Outer surface: Tensile stress bending stress
Joints Eccentricity 6” Antenna
Tensile & bending stresses in the skin at the doubler edge. Pressur e = 8.6 psi (8.0 psi for 0.036"t skin ) Dblr R (in.)
74
100
Skin
0.040
0.050
0.056
0.063
0.071
0.080
0.090
0.095
0.100
0.125
0.036 tensile
17,506
17,638
17,770
17,910
18,055
0.036 ten+ben
25,807
26,264
26,383
26,411
26,329
0.040 tensile
16,833
17,013
17,135
17,267
17,404
17,577
17,721
17,832
17,891
18,142
0.040 ten+ben
24,912
25,450
25,620
25,705
25,687
25,694
25,619
25,849
25,914
26,145
0.050 tensile
13,563
13,624
13,711
13,818
13,927
0.050 ten+ben
20,418
20,587
20,691
20,712
20,855
0.063 tensile
10,886
10,968
11,053
11,141
0.063 ten+ben
16,211
16,455
16,633
16,735
0.063 tensile
14,605
14,751
14,876
15,003
15,062
15,119
0.063 ten+ben
21,686
21,713
21,797
21,813
21,794
21,765
0.071 tensile
13,028
13,135
13,246
13,297
13,347
13,565
0.071 ten+ben
19,057
19,163
19,200
19,203
19,200
19,120
0.080 tensile
11,639
11,739
11,787
11,834
12,048
0.080 ten+ben
17 363
17 477
17 518
17 597
17 773
Joints Eccentricity 12” Antenna
Tensile & bending stresses in the skin at the doubler Pressure = 8.6 psi (8.0 psi for 0.036"t ski n) edge. Dblr
R (in.)
74
100
Skin
0.040
0.050
0.056
0.063
0.071
0.080
0.090
0.100
0.125
0.036 tensile
18,455
18,240
18,122
17,998
17,875
0.036 ten+ben
28,596
28,141
27,667
26,994
27,027
0.040 tensile
16,670
16,763
16,894
17,261
17,173
0.040 ten+ben
27,901
27,678
27,349
26,714
26,150
0.050 tensile
13,329
13,428
13,533
13,641
13,756
0.050 ten+ben
21,962
21,658
21,218
21,619
21,535
0.063 tensile
10,752
10,842
10,933
11,025
0.063 ten+ben
16,683
17,145
17,547
17,883
0.063 tensile
14,612
14,557
14,671
14,796
14,910
0.063 ten+ben
22,480
22,385
22,170
22,077
22,146
0.071 tensile
12,876
12,971
13,077
13,175
13,385
0.071 ten+ben
19,612
19,413
19,529
19,613
19,588
0.080 tensile
11,475
11,565
11,649
11,832
0.080 ten+ben
17 003
17 164
17 255
17 399
Joints Eccentricity 18” Antenna
Tensile & bending stresses in the skin at the doubler edge. Pressure = 8.6 psi Doubler R (in.)
0.071
0.080
0.090
0.100
0.125
0.063 tensile
14,120
14,246
14,374
14,495
14,781
0.063 t ensile+bendin g
24,712
24,328
23,719
22,999
23,509
0.071 tensile
12,580
12,657
12,772
12,876
13,085
0.071 tesile+bending
21,923
21,509
20,917
20,545
21,297
0.080 tensile
11,254
11,356
11,450
11,640
0.080 t ensile+bendin g
18,859
18,304
18,516
19,231
Skin
100
Crack Growth Analysis AFGROW
To account for the combined effects of tensile, bending and bearing stress components in crack growth analysis AFGROW software offers the necessary options.
Choose the tension and bending stress fraction according to the skin tensile and bending stresses calculated at the edge of the doubler, as provided in the previous tables. Calculate the bearing stress due to load transfer through each critical fastener row. Use AFGROW “help” to properly enter each of the 3 stress components.
Joints Eccentricity Validation Fracture Surfaces
Figures below shows comparison for the two primary cracks at the joints with eccentricity and the respective fracture surfaces.
The MSD growth model using the tension and bending stresses from the previous data demonstrates good correlation with the striation data.
Fwd (Crack 1)
Aft (Crack 4) 0.12
0.2 0.18
0.1 0.16
MSD Simulation Striation Count
0.14
0.08
AFGROW Strip
h t g n e L 0.06 k c a r C
h 0.12 t g n e L 0.1 k c a r C0.08
0.04 0.06 0.04
0.02
0.02 0
0 0
10000
20000
30000 Airframe Cycles
40000
50000
60000
0
10000
20000
30000
40000
50000
Airframe Cycles
Ref: D. Steadman, R. Ramakrishnan and M. Boudreau, (2006), "Simulation of Multiple Site Damage Growth", 9th Joint FAA/ DoD /NASA Aging Aircraft Conference , Atlanta, GA., pp 12 DoD
60000
Fatigue Analysis Handling Combined Tensile & Bending in Fatigue
Method 1: A convenient and simple method to handle the combination of tensile and bending stresses for fatigue analysis of joints such as antenna installations is:
For notched details, such as open hole and joint details, the best approach is to adjust Kt to include the combined effects of tension and bending. Then use one or the other stress as the the reference stress to determine a fatigue margin.
For instance, if you were analyzing a hole detail with a tension Ktg of 3.2 and a bending Ktg of 2.2 (from Peterson's textbook or a similar source), in case Ft=10 Ksi and Fb=5 ksi (taking the stresses to be the GAG gross stresses at the hole) GAG fpeak at the hole = 3.2×10 + 2.2×5 = 43 ksi Then, the effective Ktg = 43/10 = 4.3, if the reference stress is taken as the tension component of the stress.
Fatigue Analysis Handling Combined Tensile & Bending in Fatigue
Method 1 works reasonably well when analyzing joint details, as long as the bending-to-tension (membrane) stress ratios are close to constant for the most damaging flight conditions, and the bending stresses are not the dominant stresses, since most fatigue manual’s notched and open hole values and load transfer factor curves are all based on tension data.
In our example, using this approach, S -N curves would be conservatively adjusted by the ratio of 3.0/4.3 = 0.698 (3.0 is taken as the 'reference' for Ktg in S-N curves). This seems like a large knockdown, but note that the reference stress would be the tension component only (no bending).
Fatigue Analysis Handling Combined Tensile & Bending in Fatigue
Method 2: Empirical prediction method (Fokker)
S-N data available for reference joints. Similarity principle: Similar peak stresses in different joints give similar fatigue lives. Peak stresses depend on load transfer, by-pass load, and secondary bending. S K S peak
is percent load transmitted
to the other sheet in the critical row (R1/p)
t
tension
K t K t , pin 1 K t ,hole ,tension k B K t ,hole ,bending k B
S bending S tension
Other parameters included in S-N curve Joints should be similar
Other rational approaches can be proposed.
Residual Strength Loading Residual Strength Stresses Evaluation
Residual Strength Requirements for Damage Tolerance Evaluation are Given in 25.571(b)(5)(i)&(ii) NOT 25.365 Two Conditions Must be Considered
Condition (i) - Normal Pressure Combined with Limit Flight Loads Condition (ii) - Factored Pressure Loading Only
Residual Strength Loading Residual Strength Stresses Evaluation
Up thru amendment 25-86
Condition (i) p + paero + limit symmetric maneuver at Vc or, ‘‘ + limit gust up to Vc or, ‘‘ + limit roll maneuver up to Vc or, ‘‘ + Limit yaw maneuver up to Vc ,whichever is greater Condition (ii) 1.1 p + paero 1g
where, p = normal operating differential pressure paero = aerodynamic pressure associated with limit condition being considered paero1g = aerodynamic pressure for 1g flight
Residual Strength Loading Residual Strength Stresses Evaluation
Amendment 25-96 and higher
Condition (i) - Same as before except limit symmetric maneuver at all speeds up To Vc Condition (ii) 1.15 (p + paero 1g)
Residual Strength Stresses Longitudinal and Circumferential Cracks
Longitudinal cracks, Hoop, Res = (1.1 p + 0.5)R/t (Up to Amendment 25-86) Hoop, Res = 1.15 (p + 0.5)R/t (Amendment 25-96 and higher)
Circumferential cracks
Long, Res = PR/2t + Nz 1g,MAX (aft of front spar) Long, Res = PR/2t + Nz(L/S)1g,MAX (fwd of front spar) p = normal operating pressure at maximum design altitude P = normal operating pressure at maximum design altitude plus
0.5 – 1.0 psi for aerodynamic pressure Nz = maximum design limit load factor (at least 2.5 but not greater that 3.8)
Critical Crack Size Residual Strength Calculation H T G N E R Yield T S L C A U D I RES S E R
Lesser of: 1) acrit = (1/)(KA/C )2 2) Net Section Yield
KA
acrit
CRACK SIZE, a
Crack Growth Rate Three Regions
Region I – Growth rate decreases asymptotically with decreasing K. Below a threshold value of K (i.e. KTH) there is no growth. Region II – Growth rate and K follow a Log-Log linear relationship and can be reasonably approximated using the Paris Equation where;
m = Slope of line C = Intercept of da/dN axis
Region III – Growth rate increases asymptotically with increasing K.
Walker Equation Paris Equation Modified
Walker modified the Paris equation so that stress ratio effects could be approximated R Increasing
q
p
da/dN = C [(1.0-R) Kmax]
N d / a d g o L
Log K
da/dN vs. K
2024-T3 Sheet
Walker Constants DELTA K ( KSI-IN1/2)
R = .05 TABULAR DATA
DELTA K ( KSI-IN1/2)
R = .40 TABULAR DATA
DELTA K ( KSI-IN1/2)
R = .80 TABULAR DATA
DELTA K ( KSI-IN1/2)
R = .05 WALKER EQN
DELTA K ( KSI-IN1/2)
R = .40 WALKER EQN
DELTA K ( KSI-IN1/2)
R = .80 WALKER EQN
1000.000
(Walker Constants C=6.76E-10, p=3.72, q=.6445) 100.000
) 2 / 1 * * ) n i ( i s k ( 10.000
K
1.000 1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
da/dN (in/cycle)
1.00E-03
1.00E-02
1.00E-01
1.00E+00
Walker Equation Coefficients & Exponents Walker Constants TABLE 1. Walker Equation* Coefficients and Exponents for Room Temperature, Laboratory Air Ambient Conditions
ALLOY
FORM
DIRECTION
C
q
p
2014-T6
Sheet
L-T
9.66482 x 10-10
0.57937
3.78906
2024-T3 & -T42
Sheet
L-T
6.76125 x 10-10
0.64647
3.71980
2024-T3 & T42
Sheet
T-L
9.01566 x 10-10
0.62910
3.68842
2024-T351/T3511
Plate/Extrusion
L-T
8.86005 x 10-10
0.67178
3.71010
7050-T7452
Forging
L-T & T-L
1.08344 x 10
-9
0.68746
3.72313
7050-T74511 & T76511
Extrusion
L-T
1.98718 x 10-9
0.76890
3.60885
7050-T7651 & T7451
Plate
L-T & T-L
1.32927 x 10-9
0.57452
3.55242
7075-T6
Sheet
L-T
1.11737 x 10-9
0.60750
3.79719
7475-T7351 & T7651
Plate
L-T
1.05576 x 10
-9
0.60418
3.54815
7475-T761
Sheet
L-T
1.11412 x 10-9
0.66473
3.74701
* da/dN = C[(1.0 – R)q K max] p where, da/dN = crack growth rate, in./cycle K max = maximum (i.e. peak) stress intensity, ksi(in) 1/2 R = stress ratio, K min/K max
DTA of Repair Inspection Intervals
The period to grow a detectable crack to its critical size is know as the detectable crack growth life
Based on the confidence in the crack growth life prediction (loads, stresses, , material properties, etc.) a suitable factor between 2 and 4 should be used to determine the inspection intervals. For example:
Use a factor of 4 when there is no airplane full -scale fatigue test data and there is no airplane loads substantiation through a flight & ground loads survey. Use a factor of 3 when there has been an airplane fatigue test but no loads survey or when there has been an airplane loads survey but no fatigue test. In the event that both airplane fatigue testing and a loads survey has been accomplished, use a factor of 2 .
DTA of An Antenna Installation Instruction for Continuous Airworthiness (ICAW)
For each installation develop an Instruction for Continued Airworthiness, which contains:
Airplane data Complete definition of the repair location and inspection directions Inspection threshold Inspection technique, including the call out of the NDI procedure or the description for the DVI Intervals of the repeated inspections Replacement time, if any Additional information, instructions or limitations
Damage Tolerance Assessment of Repair ICAW
Some useful repair notes:
1. Confirm that the surrounding structure is corrosion and
damage free per applicable SRM inspection instructions. 2. Maintain a minimum outside trim radius of 0.38 inch and a minimum inside trim radius of 0.50 inch unless otherwise approved by engineering. 3. Stop drilling of cracks must be accomplished per SRM. This typically includes an eddy current inspection to accurately locate the end of the crack and a minimum stop drill diameter of 0.25 inch at the end of the crack, followed by an open hole eddy current inspection, followed by a minimum 1/16 inch oversize of the stop drill hole. NOTE: Stop drilling a crack with no further repair action does not constitute a repair and will not be granted FAA approval except under extremely limited circumstances.
Damage Tolerance Assessment of Repair ICAW
Some useful repair notes (continued):
4. Perform a surface eddy current inspection of all trimmed
edges and an open hole eddy current inspection of fastener holes to confirm a crack free condition. Use the appropriate non-destructive testing (NDT) instruction manual and procedure. 5. Install repair parts with BMS 5-95 sealant. Apply BMS 595 fillet seal around the edges of the repair. 6. Freeze plugging of holes must be accomplished as described in the applicable SRM. NOTE: The SRM only describes the method for installing freeze plugs. Engineering approval is required for freeze plug installation at any location. 7. Chamfer or break sharp edges. 8. Maintain a 63 RHR or better surface finish to all reworked
and new surfaces.
Damage Tolerance Assessment of Repair ICAW
Some useful repair notes (continued): 9. Treat all repair parts and all bare aluminum surfaces or
existing structure and apply one coat of primer per applicable SRM and/or Standard Overhaul Procedures Manual (SOPM) instructions. Use the appropriate primer depending upon whether the surface is exposed to the airstream. In corrosion-prone areas, two coats of primer should be used. Allow to dry between coats. 10. Do not install new repair fasteners through the skin chemmilled steps.
Damage Tolerance Assessment of Repair ICAW
Some useful repair notes (continued):
11. Observe minimum bend radius listed in the applicable SRM
or other industry reference when forming repair parts from sheet stock. It is usually advisable to form in either the annealed or quenched condition and then heat treat. If the minimum bend radius is exceeded, perform an NDT inspection (Level 3 dye penetrant inspection or better, or a surface eddy current inspection) to ensure a crack free condition. 12. Brush or bath cadmium plate corrosion resistant steel (CRES) parts and prime with two coats of primer per applicable SRM and/or SOPM instructions. Allow primer to dry between coats.
Damage Tolerance Assessment of Repair ICAW
Some useful repair notes (continued):
13. Add fillers or tapered shims as required to limit pull -up to
0.010 inch for flat stock repairs, such as skin doublers, and 0.005 inch at all other locations. Fabricate from 2024-T3 or 7075-T6 clad material. 14. Maintain 2D edge margin and 4-6D center-to-center spacing for all new fasteners.
NOTE: Larger edge margins may be required at certain locations such as door cutout corners. Consult with engineering for appro val val
15. Fill all voids and install all repair parts with corrosion
resistant faying surface sealant per the applicable SRM. 16. Install all fasteners and mating hardware per the applicable SRM. Replace initial fasteners with same type repair fastener. Oversize initial fasteners up to 1/32 inch if required to meet hole size and condition requirements.
Damage Tolerance Assessment of Repair ICAW
Some useful repair notes (continued):
17. Fastener substitutions are allowed only as specified in the 18.
19. 20.
applicable SRM, or as otherwise defined with engineering approval. If the fastener location includes steel or titanium parts, install hex drive bolts in close ream holes. If the fastener location includes only aluminum parts, install in transition fit holes unless otherwise instructed. Install per the applicable SRM. Install all bolts, including hex drive bolts, wet with corrosion resistant faying surface sealant. For increased corrosion protection, or in corrosion-prone areas, organic corrosion preventive compound may be applied per the applicable SRM.
Antenna Installations Summary
Antenna installations require DTA
Overview of the specific tasks: 1. Identify most critical detail(s) of installation 2. Perform crack growth and residual strength analyses 3. Determine inspection threshold and intervals 4. Develop an ICAW
In absence of OEM stress use conservative estimates
Consider Longitudinal and Circumferential stresses
Fastener load transfer and skin bending due to eccentricity
To establish inspection threshold use the least of
½ of rogue flaw life and ¼ of unfactored fatigue life
