Influence of secondary damage on flight cycles and inspection interval for an aircraft wing panel


The present paper discusses the methodology for analytical estimation of an aircraft wing bottom panel flight cycles (FC) and inspection interval (II) at primary damage location based on critical value of FC due to secondary damage. The repeated type of fatigue spectrum is generated using the Air Force Fracture Mechanics and Fatigue Crack Growth Analysis software, which is further used for prediction of FC, and II of a finite Aluminum alloy plate (Al alloy: 2014 T-351) using Nasgro model. The influence of combined load, compressive load, composite reinforcement and delamination on critical FC, and II at primary damage location of wing bottom panel are investigated based on critical flight cycle due to secondary damage. The present methodology for estimation of FC and II is validated w.r.t. analytical estimation and published experimental results.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


L′ and D′:

Lift and drag force

M, xcp :

Moment and aerodynamic center

W :

Width of plate, mm

B :

Hole offset distance, mm

T :

Panel thickness, mm

c, a :

Corner flaw length on surface and thickness, mm

c 2 :

Through crack length, mm

2a :

Total though crack length, mm

σ :

Nominal or applied stress, MPa

K 1 :

Mode-I stress intensity factor

c 3 :

Edge crack length, mm

n 1 :

Paris exponent

C1 :

Paris coefficient

f :

Crack closure parameter

p, q :

NASGRO equation exponents

W p :

Width of composite patch, mm

ΔKth :

Crack propagation threshold value of the stress intensity factor range, MPa(m)1/2


Inspection interval


Scatter factor

D :

Diameter of bolt, mm

K max :

Maximum stress intensity factor, MPa(m)1/2

K min :

Minimum stress intensity factor, MPa(m)1/2

ΔK :

Difference in stress intensity factor, MPa(m)1/2

K :

Stress intensity factor

K d :

Stress intensity factor of composite patch with disbond, MPa(m)1/2

D h :

Disbond height

Ep, Er :

Modulus of elasticity for plate and reinforcement

tp, tr :

Thickness of plate and reinforcement

K r :

Stress intensity factor of composite patch without disbond

N 1 :

Corner crack flight cycles

N 2 :

Through crack flight cycles

N 3 :

Edge crack flight cycles

N crit :

Critical crack flight cycle

a crit :

Critical crack length

N det :

Detectable crack cycle

a det :

Detectable crack length

σ F :

Axial stress, MPa


Equivalent stress

β :

Normalized stress intensity factor

σ b :

Bearing or pin stress, MPa

K c :

Plane stress fracture toughness, MPa(m)1/2

K IC :

Plane strain fracture toughness, MPa(m)1/2

t l :

Laminate thickness, mm


  1. 1.

    Yang JN, Donath RC (1983) Statistical fatigue crack propagation in fastener holes under spectrum loading. J Aircr 20(12):1028–1032

    Article  Google Scholar 

  2. 2.

    Skorupa M (1999) Load interaction effects during fatigue crack growth under variable amplitude loading—a literature review. Fatigue Fract Eng Mater Struct 22:905–926

    Article  Google Scholar 

  3. 3.

    Zhang XP, Wang CH, Mai YW (2002) Prediction of short fatigue crack propagation behaviour by characterization of both plasticity and roughness induced crack closures. Int J Fatigue 24:529–536

    Article  Google Scholar 

  4. 4.

    Master FJ, Smith DJ (2001) Predictions of fatigue crack growth in aluminium alloy 2024-T351 using constraint factors. Int J Fatigue 23:93–101

    Article  Google Scholar 

  5. 5.

    Merati A, Eastaugh G (2007) Determination of fatigue related discontinuity state of 7000 series of aerospace aluminum alloys. Eng Fail Anal 14(4):673–685

    Article  Google Scholar 

  6. 6.

    Kamaya M (2008) Growth evaluation of multiple interacting surface cracks. Part I: experiments and simulation of coalesced crack. Eng Fract Mech 75:1336–1349

    Article  Google Scholar 

  7. 7.

    Gasiak G, Rozumek D (2004) ΔJ-integral range estimation for fatigue crack growth rate description. Int J Fatigue 26:135–140

    Article  Google Scholar 

  8. 8.

    Jones R, Molent L, Walker K (2012) Fatigue crack growth in a diverse range of materials. Int J Fatigue 40:43–50

    Article  Google Scholar 

  9. 9.

    Ergun E, Tasgetiren S, Topcu M (2010) Fatigue and fracture analysis of aluminum plate with composite patches under the hygrothermal effect. Compos Struct 92:2622–2631

    Article  Google Scholar 

  10. 10.

    Benachour M, Benguediab M, Hadjoui A, Benachour N (2010) Prediction of fatigue crack growth of aeronautical aluminum alloy. World Acad Sci Eng Technol 4:1052–1055

    Google Scholar 

  11. 11.

    Chen C-D, Liu C-I, Chen J-M, Armstrong Yu, Hsu H-T (2008) The effects of material variations on aircraft inspection schedules based on stochastic crack growth model. Int J Fatigue 30:861–869

    Article  Google Scholar 

  12. 12.

    Bombardier Y, Liao M (2010) A new stress intensity factor solution for cracks at an offset loaded fastener hole. In: 51st AIAA/ASME/ASCE/AHS/ASC structural dynamics, and materials conference, pp 1–18

  13. 13.

    Bombardier Y, Liao M (2011) stress intensity factors solution for cracks at an offset loaded fastener hole. J Aircr 48(3):910–918

    Article  Google Scholar 

  14. 14.

    Nikolic VR, Jumper EJ, Nelson RC (1996) Modified, discrete-vortex method for studying wing-loading effects on wake dynamics. J Aircr 33(1):1–4

    Article  Google Scholar 

  15. 15.

    Brune GW, Hallstaff TH (1985) Wing span loads of complex high-lift systems from wake measurements. J Aircr 22(9):831–832

    Article  Google Scholar 

  16. 16.

    Harter JA (2014) AFGROW users guide and technical manual. Version, Air Force Research Lab. Wright–Patterson AFB, OH

  17. 17.

    Srivastava AK, Lal A (2013) Determination of fracture parameters for multiple edge cracks of a finite plate. J Aircr 50(3):901–910

    Article  Google Scholar 

  18. 18.

    Srivastava AK, Lal A (2014) Dynamic simulation of multiple offset-edge crack of a finite plate. J Aircr 51(3):849–860

    Article  Google Scholar 

  19. 19.

    Ayatollahi MR, Karo S (2012) Mode I fracture initiation in limestone by strain energy density criterion. Theoret Appl Fract Mech 57(1):14–18

    Article  Google Scholar 

  20. 20.

    Ast A, Ghidelli M, Durst K, Goken M, Sebastiani M, Korsunsky AM (2019) A review of experimental approaches to fracture toughness evaluation at the micro-scale. Mater Des 173:107762

    Article  Google Scholar 

  21. 21.

    Paris PC, Sig GC (1965) Stress analysis of cracks. Am Soc Test Mater 391:30–81

    Google Scholar 

  22. 22.

    Newman JC (1997) The merging of fatigue and fracture mechanics concepts: a historical perspective. National Aeronautical and Space Administration, Virginia

    Google Scholar 

  23. 23.

    Jiang S, Wei Z, He J, Wang Z (2016) Comparative study between crack closure model and Willenborg model for fatigue prediction under overload effects. Chin J Aeronaut 29(6):1618–1625

    Article  Google Scholar 

  24. 24.

    Skorupa M, Machniewicz T, Schijve J, Skorupa A (2007) Application of the strip-yield model from the NASGRO software to predict fatigue crack growth in aluminium alloys under constant and variable amplitude loading. Eng Fract Mech 74:291–313

    Article  Google Scholar 

  25. 25.

    Rose LRF (1982) A cracked plate repaired with bonded reinforcements. Int J Fract 18(2):35–144

    Article  Google Scholar 

  26. 26.

    Baker AA (1999) Bonded composite repair for fatigue-cracked primary aircraft structure. Compos Struct 74:431–443

    Article  Google Scholar 

  27. 27.

    Perez R, Tritsch DE, Grandt AF (1986) interpolative estimates of stress intensity factors for fatigue crack growth predictions. Eng Fract Mech 24(4):629–633

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Amit Kumar Srivastava.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Technical Editor: João Marciano Laredo dos Reis.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Srivastava, A.K., Arora, P.K. & Srivastava, S.C. Influence of secondary damage on flight cycles and inspection interval for an aircraft wing panel. J Braz. Soc. Mech. Sci. Eng. 42, 337 (2020).

Download citation


  • Flight cycles
  • Corner flaws
  • Through crack
  • Inspection interval