Crack Prediction on Aircraft Wing Spar

Crack Prediction on Aircraft Wing Spar

Antony Samuel Prabu G

Assistant. Professor, MVJ College of Engineering,

Vishnu Raj

Assistant. Professor, MVJ College of Engineering

Amogh Ballolli

Assistant. Professor, MVJ College of Engineering

Akhil A Chandran

Assistant. Professor, MVJ College of Engineering

Abstract – This paper presents the results of Crack propagation rate of an aircraft wing spar. For this I- section spar is considered. Computational analysis and analytical calculations are calculated from the I-section spar. Crack surface is considered on the root of the wing spar. Spar section is modelled in Catia V5 R21 software. Crack propagation rate is calculated from the crack surface of I-section spar using Ansys 14.5 workbench software. For the crack surface area analytical calculations are calculated. Stress intensity factor and crack propagation rate is calculated analytically and graph is plotted with the results. Number of cycles to failure is calculated using the analytical method. S-N curve is plotted for the fatigue lifecycles. Crack propagation rate vs. stress intensity factor graph is plotted from the analytical and computational results. Comparison of results is done by plotting the graph and hence the graph has been validated.

Keywords – (Crack propagation rate, Fatigue, S-N curve, stress intensity factor.)

INTRODUCTION

Determination of the crack-growth rate: The Fatigue crack growth rate has been dictated by estimating the separation between the progressive exhaustion split development groups from the split inception to the most remote weariness split development band. The stress intensity factor K. The fracture toughness, Kc. The applicable fatigue crack growth rate expression. The initial crack size. The final or critical crack size, .Material Fracture Toughness: Material fracture toughness might be characterized as the capacity to convey stacks or disfigure plastically within the sight of a score. Crack Size: Crack size starts from discontinuities that can change from to a great degree little splits to significantly bigger weld or weakness splits.

THE THREE MODES OF FRACTURE:

1.) Mode I – Opening mode 2).Mode II – Sliding mode3). Mode III – Tearing mode.

Fig 1: Three Modes Of Fracture

Fatigue Life Calculation: Count of fatigue life is completed by utilizing Miners Rule. For the fatigue calculation, the variable range stacking is disentangled as piece stacking. Each piece comprises of load cycles relating to 100 flights. Damage count is done for the entire administration life of the aircraft. The load factor "g" is characterized as the proportion of the lift of an aircraft to its weight and speaks to a

worldwide measure of the load to which the structure of the aircraft is subjected to Rule.

ANALYTICAL CALCULATION

1. Stress Intensity Factor: The Stress intensity factor is utilized as a part of break mechanics to foresee the pressure state close to the crack tip of a crack caused by a remote load or leftover burdens.

   A).Center Crack Stress Intensity Factor Calculation

   3.14

   1

   3

   5

   7

   9

   =

   [16.7( )2 104.7( )2 + 369.9( )2 573.8( )2 + 360.5( )2]

   P=applied load, B=thickness, a=crack length, w=width.

   P=13459 N, B=.164M, a=0.1mm, w=5M

   13459

   3.14

   .1 1

   .1 3

   .1 5

   .1 7

   .1 9

   =

   .164

   [16.7( )2 104.7( )2 + 369.9( )2 573.8( )2 + 360.5( )2]

   5 5 5 5 5 5

   (0.1) = 135650; (0.2) = 169976; (0.3) = 185272; (0.4) = 197532

   B).Edge Crack Stress Intensity Factor Calculation

   =S

   2

   3

   4

   1.99 0.41 ( ) + 18.7 ( )

   S= P

   BW

   38.48( )

   + 53.85( )

   (0.1)=16413

   .1 .1 2

   .1 3

   .1 4

   0.1 1.99 0.41 ( ) + 18.7 ( )

   5 5

   38.48( )

   5

   + 53.85( )

   5

   (0.1) = 10365; (0.2)=14524; (0.3)=17813; (0.4)=21280

2. CRACK PROPAGATION RATE:

A).Center Crack Propagation Rate Calculation

=c cm=material constants

=

–

, =crack growth rate per cycle.

12 3

=c , =1× 10 (135650)

(0.1)=2.4,

(0.2) =4.9;

(0.3) =6.3,

(0.4) =7.0

B).Edge Crack Propagation Rate Calculation

12 3

=c , =1× 10 (10365)

(0.1)=1.11,

(0.2) =3.06;

(0.3) =5.65,

(0.4) =9.36

Fig 2: Analytical Center Crack Tip & Edge Crack Graph

COMPUTATIONAL ANALYSIS

1.) Centre Crack Analysis

Fig 3: Mesh Model of Centre Crack Surface

Fig 4: Crack Propagation Rate Length

Fig 5: Crack Propagation Rate length graph

Table 1. Computational Analysis of Edge Crack Propagation Rate

2.) EDGE CRACK ANALYSIS

Fig 5: Mesh Model of Edge Crack Surface

Fig 6: Stress Intensity Factor K vs. Crack Propagation Rate Data for Edge Crack

Table 2. Stress Intensity Factor K vs. Crack Propagation Rate Data

COMPARISION OF COMPUTATIONAL Vs ANALYTICAL CRACK PROPAGATION RATE GRAPH

Fig 7: Computational Center Crack Propagation Rate Graph vs. Analytical Center Crack Propagation Rate Graph

/

Fig 8: Computational Edge Crack Propagation Rate Graph vs. Analytical Edge Crack Propagation Rate Graph

FATIGUE S-N CURVE

Table 4. S-N CURVE DATA

140000

120000

20000

fatigue limit 40000 pa

0

0.00E+00 2.00E+07 4.00E+07 6.00E+07 8.00E+07 1.00E+08 1.20E+08

Fatigue life cycles

CONCLUSION:

40000

s-n

60000

80000

100000

Stress amplitute (pa)

Fig 9: S-N Curve

Crack propagation rate vs. stress intensity factor graph is plotted from the computational and analytical results. Crack propagation rate vs. stress intensity factor graph is compared between the computational and analytical graph. S-N is plotted and found fatigue or endurance limit of 40000 pa.

REFERENCE

1. H. Tada, P. C. Paris, and G. R. Irin, The Stress Analysis of Cracks Handbook, 2nd edition, Paris Productions Inc., St. Louis, Mo, 1985.

2. G. C. Sih, Handbook of Stress Intensity Factors, Institute of Fracture and Solid Mechanics, Lehigh University, Bethleham, PA, 1973.

3. D.P. Rooke and D. J. Cartwright, Compendium of Stress Intensity Factors, Her Majesty's Stationery Office, London, 1976.

4. Aleksandar Grbovic, Bosko Rasuo,FEM based fatigue crack growth predictions for spar of light aircraft under variable amplitude loading,ELSEVIER, Engineering Failure Analysis 26 (2012) 5064.

5. Stochastic modeling of fatigue crack propagation, Asok Ray, Sekhar Tangirala, Shashi Phoha. Publisher: Elsevier, Date: 18 December 1997.

6. Marcin Ciesielski a, Jerzy Kaniowski b,*, Wodzimierz Karlin´ ski,Determination of the fatigue crack-growth rate from the fractographic analysis of a specimen representing the aircraft wing skin, ELSEVIER, International Journal of Fatigue 31 (2009) 1102 1109.

7. Sophia Hassiotis a'*, Stephen C. Gould, Fracture analysis of the F-5, 15%-spar bolt, ELSEVIER,

Engineering Failure Analysis 11 (2004) 355 360.

fatigue crack growth. Engineering Fracture Mechanics 25 (2), 177±195.

1. Ishikawa, H., Tsurui, A., Tanaka, A.H., Ishikawa, H., 1993. Reliability assessment based upon probabilistic fracture mechanics. Probabilistic Engineering Mechanics 8, 43±56.

2. Virkler, D.A., Hillberry, B.M., Goel, P.K., 1979. The statistical nature of fatigue crack propagation. ASME Journal of Engineering Materials and Technology 101 (2), 148±153.

3. Spencer, B.F., Tang, J., Artley, M.E., 1989. A stochastic approach to modeling fatigue crack growth. AIAA Journal 27 (11), 1628±1635.

4. Schueller, G.I. (Ed.), 1996. Reliability of structural and mechanical components under fatigue (special issue). Engineering Fracture Mechanics 53 (5).

5. Ray, A., Tangirala, S., 1997. A nonlinear stochastic model of fatigue crack dynamics. Probabilistic Engineering Mechanics 12 (1), 33±40.

6. Ray, A., Tangirala, S., 1996. Stochastic modeling of fatigue crack dynamics for on-line failure prognostics. IEEE Trans. Control Systems Technology 4 (2), 443±451.

7. Hertzberg RW. Deformation and fracture mechanics of engineering materials. New York: John Willey & Sons; 1989. p. 459.

8. Metals handbook. 8th ed., vol. 9, Fraktography and Atlas Fractograms. ASM; 1974. p. 85.

9. Metals handbook. 8th ed., vol. 9, Fraktography and Atlas Fractograms. ASM; 1974. p. 74.

10. Book: Fracture Mechanics, Fundamental and Applications.