- - 1

Finite Element Method analysis and Life Estimation of aircraft structure Fatigue/Fracture Critical Location

2001-88

Park Jeong Kyu, Lee Doo Han, Lee Cheol Jae, Chung Bong Cheul, Chun Kyu Tae

(Korea Aerospace Industries, Sacheon City, South Korea, 055-851-2667, pjk6771@koreaaero.co.kr)

Abstract

Economical life estimated about aircraft structure should be known to carry out the structure

force management of aircraft. Through it schedule and method of inspection, maintenance and repair being used during operation of aircraft are determined .

When the main items of aircraft structure are failed, they may affect directly safety of aircraft and aircraft fracture and the main items of aircraft structure are called Primary Structure Element(PSE) or Fatigue/Fracture Critical Location(FCL).

The selection of FCL of aircraft structure should be carried out through detailed review such as stress analysis, fatigue analysis, fatigue test, service experience and so on. When FCL is selected, t hey should be considered with minimum margin of safety, location with tension/shear or stress concentration and so on. Therefore the strength, stiffness and the estimation of fatigue life of them should be carried out necessarily.

It was carried out finite element analysis about FCL of small aircraft using MSC.Patran and MSC.Nastran. Also, fatigue analysis and life estimation was performed using the result of stress analysis, material data and load history. For this analysis, MSC.Fatigue was used. In this report, one example of stress and fatigue analysis was shown. Therefore, we can know the static and fatigue safety of design requirements, the technical approach method of load and boundary condition from the results of analysis.

- - 2

1. Introduction Economical life estimated about aircraft structure should be known to carry out the structure force

management of aircraft. Through it schedule and method of inspection, maintenance and repair being used during operation of aircraft are determined . When the main items of aircraft structure are failed, they may affect directly safety of aircraft and aircraft fracture and the main items of aircraft structure are called Primary Structure Element(PSE) or Fatigue/Fracture Critical Location(FCL). PSE consists of single part or assembly type, and numbers in about 40-70 Structure Element. The number is variable according to the type of aircraft.

Selection of FCL should be done after reviewing stress analysis, fatigue analysis, results of full scale or component fatigue test, flight experience, structu re drawing, and so on. When FCL is selected, they should be considered with minimum margin of safety and location subjected to tension/shear, high stress concentration and corner intersected by components, subjected to severe load spectrum or high cycle load, subjected to high stress when subordinate component was failed, fracture toughness or characteristic of crack growth resistance is low, or likely to initiate fatigue crack and be path of crack growth. Therefore the selection of FCL of aircraft structure should be carried out and strength, stiffness and the estimation of fatigue life of them should be carried out

In this report, the stress analysis of main fitting lugs was performed by finite element analysis method and the critical area of FCL is selected according to the results. And then, fatigue analysis and life estimation of fitting lugs should be performed with the result of stress analysis, material and load history and so on. 2. Problem Definition

Table 1. shows the list of some Fitting Lugs(some parts of FCL) connecting PSE, that is, main wing, fuselage, horizontal stabilizer. Fitting Lugs are subjected to concentrated load converted from distributed load according to variable load condition of aircraft. After that, it delivers the concentrated load to adjacent structure. So, high load was applied to these Fitting Lugs. One example is shown in Figure 1. This is Front Pick_Up Lug connected wing and fuselage by a rod and the dimension is shown in Figure 2.

PSE Description Location Applied Load

Case

Wing&Fuselage Main Pick_Up Lug PORT 13 Main wing

Wing&Fuselage Rear Pick_Up Lug PORT 13

Wing&Fuselage Front Pick_Up Lug PORT 14

Wing&Fuselage Rear Pick_Up Lug PORT 13

Wing&Fuselage Rear Pick_Up Lug STBD 13 Fuselage

Fuselage&H/T Rear Pick_Up Lug PORT 13

Horizontal Stabilizer Fuselage&H/T Rear Pick_Up Lug PORT 13

Table 1. List of some Fitting lugs

- - 3

Figure 1. Front Pick_Up Lug shape connected Main Wing and Fuselage by a rod

Figure 2. Dimension of Front Pick_Up Lug

3. Finite Element Method Analysis and Life Estimation 3.1. Finite Element Method Analysis 3.1.1. Finite Element Modeling 3.1.1.1. Procedure of Finite element modeling

a. Geometry should be directly generated by MSC.Patran or imported through converting by P3_Catia_Express from CATIA or CAD system.

b. Geometry in MSC.P atran forms Solid to coincide each nodes of finite element.

Fuselage

Main Wing

Front Pick_Up Lug Rod

- - 4

c. Mesh Generator in MSC.Patran creates elements and nodes. d. Duplicated nodes should be deleted. e. Status of created elements and nodes should be inspected by Verify function in MSC.Patran

3.1.1.2. The type of finite element model is 8-node Hexahedral Solid Element like Figure 3.

Figure 3. 8-node Hexahedral Solid Element used Finite element model

3.1.1.3. Finite element modeling of Fastener and Fastener hole To perform Finite Element Analysis of fastener hole, Finite element model of fastener and

Finite element model connecting fastener and fastener hole were created. Finite Element model of fastener is 8-node hexahedral solid element. And Finite Element model contacting fastener and fastener hole was used gap element. Element around fastener hole where be subjected high stress known from result of lug hole analysis were meshed finally by using mesh generation method which was obtained from Verification of Finite Element Model contacted by fastener in Section 3.1.3. 3.1.1.4. Node and element number and one example of Finite element models

Node and element number of Table 1. list are shown in Table 2. and one example of Finite element model is shown in Figure 4.

Table 2. Node and Element number of each Finite element models

PSE Description Node number Element Number

Wing&Fuselage Main Pick_Up Lug 3946 2274 Main wing

Wing&Fuselage Rear Pick_Up Lug 3791 2228

Wing&Fuselage Front Pick_Up Lug 5746 3469

Wing&Fuselage Rear Pick_Up Lug 1600 732

Wing&Fuselage Rear Pick_Up Lug 1600 732 Fuselage

Fuselage&H/T Rear Pick_Up Lug 2858 1369

Horizontal Stabilizer Fuselage&H/T Rear Pick_Up Lug 1556 668

- - 5

Figure 4. One example of Finite element model(Wing&Fuselage Front Pick_Up Lug)

3.1.2. Finite Element Stress Analysis 3.1.2.1. Finite Element Stress Analysis of Fitting Lug Hole

Using finite element models created in section 3.1.1, linear static stress analysis was performed to calculate stress distribution and local stress around hole of fitting lug 3.1.2.1.1. Load Condition

Compatible load condition should be applied to geometry or element to perform finite element analysis. When load condition was applied, load status applied fitting lug hole through fitting connection component was simulated as followings.

a. Whole reaction force(R) is calculated considering the number of lug holes and concentrated force delivered through fitting connection component

b. Load should be considered Fitting Factor (F.F.).

RFFR ×= ..' -------------------------------(1)

c. Considering contact area between connecting component and lug hole, the concentrated load is changed to distributed load by sine or cosine function.

θsin×= AP -------------------------------(2)

∫∫ ⋅⋅⋅⋅=⋅⋅⋅⋅=ππ

θθθθ00

sinsin R' dtrAdtrP ---------------(3)

π×××

=tr

RA

'2 -------------------------------(4)

Where, P is pressure distribution, r is radius of lug hole, and t is thickness. d. If direction of load is more than two, each pressure was applied independently and whole

pressure was distributed by sum of vector. e. Applied load cases is shown in Table 3.

PSE Load Case Applied load No.

- - 6

Manuever 3

Ground 8

Flap Operation 2 Wing&Fuselage connect

fitting lug

Yawing 1

Abruptly Pitching 5

Ground 6 Fuselage&H/T connect

fitting lug Flap Operation 2

Table 3. Applied load cases

3.1.2.1.2. Boundary Condition In geometrical boundary condition, Fastener hole was constrained in 6 DOF. If finite

element surface exist in Fastener hole, the node of that element was constrained in 6 DOF. 3.1.2.1.3. Material Property(AL7050-T7451)

? Utimate Strength : 510.4 MPa

? Yield Strength : 441.4 MPa

? Elastic Modulus : 71039 MPa

? Piosson's ratio : 0.33

3.1.2.1.4. Analysis Tool

MSC.P atran V9.0 was used to create finite element model of fitting lug and analysis was performed by MSC.N astran V70.5. Hardware was used RS6000 Workstation and analysis for each finite element model was completed in about 15 min.

3.1.2.1.5. Results of stress analysis

After analysis completed, total input load were compared with accuracy of input load wanted through OLOAD in *.F06 file, and EPSILON was examined to verify conversion about all load case. Also, MSC.P atran Post-Processing of analysis result was performed to look into local stress distribution around fitting lug hole. Results of Finite Element anal ysis is shown Table 4. and one example is shown Figure 5. Local stress distribution of fitting lug hole shows that Stress Concentration Factor resulted from net tension stress of fitting lug is lower than 3 or so. And static strength has enough Margin of Safety because all local stress distribution of fitting lug hole is under the yield strength.

- - 7

PSE Description Yield stress (MPa)

Maximum stress (MPa)

Wing&Fuselage Main Pick_Up Lug 441.4 180.9 Main wing

Wing&Fuselage Rear Pick_Up Lug 441.4 162.7

Wing&Fuselage Front Pick_Up Lug 441.4 226.6

Wing&Fuselage Rear Pick_Up Lug 441.4 158.0

Wing&Fuselage Rear Pick_Up Lug 441.4 162.2 Fuselage

Fuselage&H/T Rear Pick_Up Lug 441.4 97.7

Horizontal Stabilizer Fuselage&H/T Rear Pick_Up Lug 441.4 46.7

Table 4. Results of Finite Element analysis around fitting lug hole

Figure 5. One example of Finite element analysis(Wing&Fuselage Front Pick_Up Lug)

3.1.2.1.6. Selection of critical area Under critical load case, selection of critical area was decided from maximum stress and the location is around lug hole like shown Figure 5. 3.1.2.2. Finite Element Analysis of Fastener Hole

Using finite element models created in section 3.1.1, linear static stress analysis was performed to calculate stress distribution and local stress around fastener hole. 3.1.2.2.1. Load Condition

Load condition is like those of lug hole except fitting factor was not applied because contact between fastener and fastener hole was simulated by ga p element

3.1.2.2.2. Boundary Condition

In geometrical boundary condition, nodes of fastener center were constrained with 6 DOF

Critical Area

- - 8

and nodes around fastener hole contacted by fastener head were constrained with translation of vertical direction to surface of upper nodes.

3.1.2.2.3. Material Property

a. AL7050-T7451

? Utimate Strength : 510.4 MPa

? Yield Strength : 441.4 MPa

? Elastic Modulus : 71039 MPa

? Piosson's ratio : 0.33

b. AISI4130N

? Utimate Strength : 655.2 MPa

? Yield Strength : 517.3 MPa

? Elastic Modulus : 200013 MPa

? Piosson's ratio : 0.32

3.1.2.2.4. Analysis Tool

MSC.P atran V9.0 was used to create finite element model of fitting lug and analysis was performed by MSC.N astran V70.5. Hardware was used RS6000 Workstation and analysis for each finite element model was completed in about 15 min.

3.1.2.2.5. Results of stress analysis

After analysis completed, total input load were compared with accuracy of input load wanted through OLOAD in *.F06 file, and EPSILON was examined to verify conversion about all load case. Also, MSC.P atran Post-Processing of analysis result was performed to look into local stress distribution around fastener hole contacted by fastener. Results of Finite Element Analysis is shown in Table 5. and Figure 6. And static strength has enough Margin of Safety because all local stress distribution of fastener hole is under the yield strength.

PSE Description Yield stress (MPa)

Maximum stress (MPa)

Wing&Fuselage Main Pick_Up Lug 441.4 392.8 Main wing

Wing&Fuselage Rear Pick_Up Lug 441.4 365.3

Wing&Fuselage Front Pick_U p Lug 441.4 312.0

Wing&Fuselage Rear Pick_Up Lug 441.4 117.9

Wing&Fuselage Rear Pick_Up Lug 441.4 145.6 Fuselage

Fuselage&H/T Rear Pick_Up Lug 441.4 182.5

Horizontal Stabilizer Fuselage&H/T Rear Pick_Up Lug 441.4 70.4

Table 5. Results of Finite Element analysis around fastener hole

- - 9

Figure 6. First example of Finite element analysis(Wing&Fuselage Front Pick_Up Lug)

3.1.2.2.6. Selection of critical area Under critical load case, selection of critical area was decided from maximum stress and the location is around fastener hole like shown Figure 6.

3.1.3. Verification of Finite Element Model contacted by fastener Situation that fitting lug was constrained by each Fastener should be simulated to know local

stress distribution of Fastener Hole supporting fitting lug. Therefore, appropriate finite element type and boundary condition should be selected to consider contact between fastener and fastener hole. In this report, Benchmark model was used to select best result. Variation of stress magnitude and distribution was examined according to Finite Element model and boundary condition. And the result was used as finite element model type and boundary condition to analyze real fitting lug hole and fastener hole.

3.1.3.1. Benchmark Test Model( Material : AL7050-T7451 )

To perform Benchmark Test, Benchmark model was created as shown in Figure 7.

Figure 7. Dimension of Benchmark Test Coupon

The purpose of benchmark test is to observe stress magnitude and distribution around plate hole according to Finite Element model shape and type and boundary condition. The result of benchmark test was used to verify selected Finite Element model shape and type and boundary condition. Procedure is as follows.

Critical Area

L = 800 mm T = 10 mm

W=66.67 mm P = 98.1 N

R=5mm

- - 10

a. Confirm that stress distribution around plate hole is symmetric in case of Clamp boundary condition at the opposite face of load applied and that stress concentration factor is about 2.58(Reference List Guide, BOOK (2)) to verify the accuracy of Finite Element model

b. Confirm that stress concentration factor around fastener hole is about 7.43 - 8.25(Reference List Guide, BOOK (2)) to verify variation of stress magnitude/distribution and stress concentration factor according to Finite Element model and boundary condition in many case of Finite Element model and boundary condition to consider contact between fastener and fastener hole.

c. Determine Finite Element model type, material property and geometrical boundary condition to be applied real Finite Element model.

3.1.3.2. Benchmark Test Result

a. Stress concentration factor is about 2.55 in case of Clamp boundary condition at the opposite face of load applied and stress distribution around plate hole is symmetric. The result is similar to 2.58 of Reference List Guide, BOOK (2) an d are shown in Table 6. and Figure 8.

Net Tension Stress (MPa)

Maximum Stress (MPa)

Concentration factor (Kt)

0.173 0.4419 2.55

Table 6. Stress concentration factor of Benchmark Test Result in clamp constraint

Figure 8. Stress distribution of Benchmark Test Result in clamp constraint

b. After many test to consider contact between fastener and fastener hole, Finite Element

model type with the best result was Gap Element. And effect of friction could be considered in Gap Elem ent with appropriate material property. Also, In the boundary condition the node around fastener hole compressed by fastener head was constrained z-direction DOF and the center of fastener was constrained 6 DOF. In this result, stress distribution was symmetric in transverse direction and asymmetric in longitudinal direction. Stress concentration factor is about 8.09, it is similar to 7.43 - 8.25 of Reference List Guide, BOOK (2) Reference List Guide, BOOK (2). The result is shown in Table 7. and Figure 9.

Net Tension Stress (MPa)

Maximum Stress (MPa)

Concentration factor (Kt)

0.173 1.4 8.09

Table 7. Stress concentration factor of Benchmark Test

- - 11

Figure 9. Stress distribution of Benchmark Test Result in gap and z-direction constraint

c. Some additional Finite Element model type and boundary condition applied to real model was

discovered from benchmark test about contact between fastener and fastener hole. And variation of stress concentration factor according to Finite Element model and boundary condition is similar to those of Peterson’s book. Therefore, the boundary condition and fastener modeling method obtained from benchmark test is used to calculate local stress around fitting lug hole and fastener.

3.2. S/N Analysis and Life Estimation

3.2.1. S/N Analysis Procedure

3.2.1.1. Critical Area Selection

Critical area found around fastener hole and fitting lug hole from Finite Element analysis should be selected to analyze fatigue analysis.

- - 12

3.2.1.2. Generation of S/N curve data of AL7050-T7451 material S/N curve data of AL7050-T7451 material should be calculated and it was obtained from

“Best-Fit S/N curves for unnotched AL7075 -T7451 plate" in MIL-HDBK-5F. Its S/N curve data is shown in Figure 10.

Figure 10. S/N data of AL7050-T7451

The constants of equation were determined from this data.

)(1

)1(

2

11

N

N

C

NSRLS

b

bc ××= ---------------------------(5)

The constants of equation (5) were shown in Figure 11. and Table 8.

Figure 11. S/N data constants to make S/N curve in pfmat

Log(S)

Log(N)

Log(SRL1)

Log(Nc1)

Log(FL)

b1

b2

- - 13

Table 8. S/N data constants of AL7050 -T7451 Material property should be obtained by pfmat (Material property generation program) in

MSC.Fatigue, using Table 8.

3.2.1.3. Generation of Stress Spectrum Stress Table should be made from the result of Finite element analysis carried out with each

load case. And using stress Table, each stresses should be arranged according to load generation order by Mission Mix in each load case. And then, one stress spectrum is created. The stress spectrum should be converted by ptime(Spectrum Generation Program) in MSC.Fatigue and one example of stress spectrum is shown in Figure 12.

Figure 12. One example of Stress spectrum

3.2.1.4. S/N(Stress life) Analysis

MSC.Fatigue calculate a point of time when damage equals to 1. This calculation was performed by result of Finite Element analysis(*.op2 file), stress spectrum file and material property file. Where, Goodman’s equation is mean stress correction method and linear Miner’s rule was used to calculate damage.

3.2.2. Analysis Tool MSC.Fatigue and RS6000 Workstation(Hardware) were used for fatigue analysis. 3.2.3. S/N Analysis Result

Fatigue analysis was performed about 2 critical areas selected from finite element of each fitting lug. S/N(Stress Life Analysis) method was used. This method is proper because maximum stress of all fitting lug does not exceed yield stress, so plastic deformation will not occur. S/N analysis parameter is shown in Table 10.

SRL1(MPa) Nc1(Cycle) b1 b2 S.E.

2692 1195000 -0.2109 -0.137 0.507

- - 14

Mean Stress Correction Goodman

Stress Combination Max.Abs.Principle Solution

Parameter

Certainity of Survival(%) 50%

Material AL7050-T7451(Kt=1.0 Ftu=510.4Mpa)

Lug Hole Good Machined Surface Finish Fastener Hole AVG. Machined

Surface Treatment Nitrided

Material Information

K f 1.0

Table 10. S/N analysis parameter

Design life of each fitting lug is 10,000 Flight hours and Table 11. shows summary of fatigue

analysis result for each fitting lug. Where, HIGH indicates that life is more than 1.0×107 Fhrs. And one

example of fatigue analysis result is shown as Log of Life Plot in Figure 13.

PSE Description Lug hole area

(Fhrs ) Fastener hole area

(Fhrs)

Wing&Fuselage Main Pick_Up Lug HIGH 24,000 Main wing

Wing&Fuselage Rear Pick_Up Lug HIGH 546,000

Wing&Fuselage Front Pick_Up Lug HIGH 539,470

Wing&Fuselage Rear Pick_Up Lug HIGH 1,443,000

Wing&Fuselage Rear Pick_Up Lug HIGH 1,088,000 Fuselage

Fuselage&H/T Rear Pick_Up Lug HIGH HIGH

Horizontal Stabilizer Fuselage&H/T Rear Pick_Up Lug HIGH HIGH

Table 11. Fatigue analysis results of each fitting lug

- - 15

Figure 13. One example of Fatigue analysis with Log of Life Plot

(Wing&Fuselage Front Pick_Up Lug)

3. Discussion Stress analysis was performed by Finite Element analysis method about fitting lugs which is fatigue/fracture critical location(FCL). If FCL was failed, aircraft shall be catastrophic situation. From result of stress analysis, critical area of FCL was selected. Also, fatigue analysis was performed by using result of stress analysis and information about FCL. As a result this analysis, life estimation was completed. In this report, we can know as followings.

a. Method of applying load condition and geometrical boundar y condition considering contact between fastener and fastener hole was acquired.

b. Maximum stress of fitting lug in limit load is below yield strength, therefore, static strength of fitting lug is enough.

c. C ritical area of fitting lug was selected by calculating local stress of fitting lug. Fatigue analysis of fitting lug was performed at critical area of maximum stress region of fitting lug hole and fastener hole.

d. As a result of fatigue analysis about critical area of fitting lug, Life was estimated more than 20,000 Flight hours against design life of 10,000 Flight hours. Therefore fatigue crack will not initiate.

4. Conclusions

a. With MSC.Nastran, MSC.Patran and MSC.Fatigue software is carried out stress analysis and fatigue analysis. and they have been demonstrated as a powerful tool for undertaking stress and fatigue analysis for Fatigue/Fracture Critical Location(FCL) b. This report is just stress analysis and S/N fatigue analysis. Crack Growth Analysis, Advanced fatigue analysis and test c omparison will be produced in some later publication.

c. In future, fatigue analysis should be performed with real stress spectrum after load/environment spectra survey again. 5. Reference List Guide

MSC PRODUCTS

(1) MSC.Patran Version 9, User’s Guide, Volume 1,2,3

- - 16

(2) John P Caffrey, John M. Lee "MSC .Nastran V68 Linear Static Analysis User's Guide" The Macneal -Schwendler Corporation, March. 1994

(3) MSC.Fatigue Version 9, User’s Guide, Volume 1,2 (4) MSC.Nastran version 70.5, Quick Reference Guide, The MacNeal -Schwendler Corporation (5) MSC.Nastran version 68, The MacNeal -Schwendler Corporation, Los Angeles, CA Autust

1995.

BOOKS (1) R. E. Peterson " Stress Concentration Factors" John Wiley & Sons New York 1974. (2) M. M. Frocht and H. N. Hill, “Stress Concentration Factors around a Central Circular Hole in a

Plate Loaded through an Pin in Hole ”, J. Appl. Mechanics,vol.7, no.1, March 1940, P.A-5 (3) Julie A. Bannantine, Jess J. Comer, James L. Handrock "Fundamentals of Metal Fatigue

Anaylsis", Prentice Hall, 1990. (4) MIL -HDBK-5F, "Metallic materials and elements for aerospace vehicle structures". (5) David Broek, "The Practical Use of Fracture Mechanics", Kluwer Academic Publishers, 1989. (6) D ARYL L. LOGAN “A First Course in the Finite Element Method” (7) JOHN WILEY & SONS “METAL FATIGUE IN ENGINEERING”