________________________________________________________________________________________________
Effect of Composite Patch on Aircraft Flight Cycle and Inspection Interval
1Amit Kumar Srivastava, 2Achchhelal Lal
1Research Scholar, Department of Mechanical Engineering, S.V. National Institute of Technology, Surat, India
2Assistant Professor, Department of Mechanical Engineering, SVNIT, Surat, Post doctorate research fellow, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University; Blacksburg, VA;
Email: 1[email protected]/[email protected] Abstract— In the present paper, effect of composite patch
on aircraft control surface flight cycle (FC) is predicted considering corner flaws, and through crack under Transport Wing Standard Load (TWIST) using Nasgro model available in Afgrow software. The effect of complex load and panel thickness on FC is also examined. The typical numerical prediction of critical FC is validated with analytical estimation, and published experimental results.
Keywords Flight cycle; Crack length; Corner flaw;
Through crack; Inspection interval
I. INTRODUCTION
The prediction of fatigue crack growth rate at repaeted loading, or random variable loading are utmost interest for many aerospace applications, aerospace, automotive, structures, machines, pipes…etc. The capability to accurately and efficiently predict fatigue life of aircraft structural components is therefore essential to perform quantitative risk assessment study. Different experimental tests are carried out in order to quantify crack growth rates, thresholds and to calibrate the analytical model available in literature [1] such as strip- yield model [2] able to keep into account the “plasticity- induced crack closure” phenomenon [3-4]. These models are included in widespread life prediction software’s, such as AFGROW and Nasgro. These softwares are most flexible and powerful crack propagation tools since they allow to compute crack opening levels under arbitrary load histories [5-6]. A problem in fracture mechanics based life prediction is to determine the initial crack size for crack growth analysis. One practice is to use an empirically assumed crack length, such as 0.25–1 mm for metals [7].
Safety is the major concern for all fighter and civil aircraft, since design stage to entire duration of the service life. Aircraft maintenance and modification is essential as per certification requirements. The presence of cracks reduces strength and stability of components considerably. The typical scenario of primary damage on aircraft control surface is shown in Figs. 1(a-b). The primary damage site is assumed to contain a rogue flaw, resulted from poor workmanship or an error. The authors were unable to detect the influence of composite
patch on critical FC, and II considering the plasticity ahead of the crack tip for multiple-crack configurations in the available literature. The present study also focuses the parameters which influencing corner flaws and through crack FC.
(a) Top view of panel
(b) Sectional details along section A-A
Fig.1 Typical crack initiation scenario of aircraft control surfaces (a) Top view of panel, and (b) Sectional details
along section A-A
II. SIMULATION OF FATIGUE CRACK GROWTH
2.1. Material and specimen
In present investigation, two types of crack models are used. Fig. 2(a) shows detail of corner crack at offset hole model used for corner flaws analysis, whereas Figs. 2(b- c) show detail of through crack model used for examination of FC and II. Specimen wise fatigue loading and dimensional details are discussed in subsequent section 4. Table 1(a-b) show different material properties used in present study.
2.2. Plane stress and Plane strain conditions
As soon as crack tip stress intensity factor (SIF) reaches to value of fracture toughness failure is assumed to occur. The nature of plastic deformation near crack tip is strongly influenced by assumption of two-dimensional idealization. Once crack is in plane strain, tri-axial stress field requires for plastic deformation. Hence, in plane strain condition, tendency of failure is brittle in nature with flat surface normal to principal tensile stress. For thinner material under plane stress condition, tendency of failure is ductile in nature with a slant fracture surface, as plastic deformation is not constrained [8-9].
Under plane stress, stress along the thickness direction is zero (z 0)
The difference between maximum and minimum principal stress can be written as
yz
y0
yt (1)It can be seen under plane stress condition from Eq. [1] , once stress is equal to or more than yield stress in tension, plastic deformation occurs.
Under plane strain, strain along the thickness direction is zero (
z 0
)
0
z x y
z E E
(2)
Re-arranging Eq. [2] and υ = 0.33, typical for aluminium alloy. Stress state at crack tip in thickness direction can be estimated as
x y
z
0 . 33
(3) If
x
y, Eq. [3] can be written as
y y
yz
0.33 0.66 (4)The difference between maximum and minimum principal stress can be written as
y 0.66
y
yt (5)
Eq. [5] can be written as
yt
y
3
(6)It can be seen from Eq. [6], under plane strain, stress must be three times yield stress in tension for plastic
deformation. Under these circumstances cohesive strength of material exceeds before plastic deformation occurs, resulting brittle fracture.
The equation normally used to determine plane stress or plane strain conditions are as follows
t
t K
yt IC
2
2
1 (7)
2
5 .
2
yt
KIC
x
t (8)
(a)
(b)
(c)
Fig. 2 Specimen details (a) Corner crack at offset hole, (b) Through crack, (c) Sectional detail of through crack
Table 1(a) Mechanical properties of Al alloys
Specimen material E (GPa) υ σy
(MPa) Kc MPa(m)1/2
KIC MPa(m)1/2
c n p q
2024-T351 ( Plt & sht; L-T ) 73 0.33 372 74 37 1.71e-10 3.353 0.5 1 7075-T7351,( Plt & sht; L-T ) 71.7 0.33 427 63.7 31.8 6.96e-10 2.529 0.5 1
Table 1(b) Mechanical properties composite material Material Adhesive
thickness, mm
Thickness of ply, mm
Longitudinal stiffness, MPa
Transverse stiffness, MPa
Poission’s ratio
Modulus of rigidity, MPa
Boron epoxy 1.3 206843 19305 0.2 5171
FM-73 0.15 413
III. METHODOLOGY
2.3. Fatigue crack growth model
The concept of stress intensity factor to fatigue crack growth is first proposed by Paris, Gomez, and Anderson [10]. They proposed that crack growth rate is proportional to stress intensity factor range ΔK.
Kn
dN C
da (9)
The most complex equation developed so far is NASGRO equation, valid for entire range of da/dN versus ΔK curve. Nasgro model used in NASA crack growth life prediction program is as follows [11]:
q
crit P n th
K K
K K R K
C f dN da
1 max 1 1
1 (10)
In this paper, the fatigue crack growth rate for corner flaws and through crack of a finite Al alloy sheet (panel) is investigated numerically using Afgrow educational license version 5.2.2.18. The critical FC is predicted using Nasgro law by adding the FC during corner flaws analysis, and through crack analysis. First, the primary damage (rogue flaws) under fatigue loading propagates to the surface through thickness. Once, the corner flaws became through crack, in next step through crack starts propagating till failure of specimen. The critical FC is predicted using Nasgro law by adding the FC during corner flaws analysis, and through crack analysis.
Retardation effect during crack growth is considered using Willenborg plasticity model as Ref. [12]. Fracture toughness of material is used as failure criterion, once the SIF value during the crack growth became more than Kc, failure of the specimen is considered. Detectable crack life is estimated based on detectable crack length Where, f present the contribution of crack closure and the parameters, C is the Paris coefficient, n is the Paris exponent, p, q are Nasgro equation
Based on critical and detectable FC, II is estimated considering scatter factor three using Eq. [11].
SF N
IINcrit det (11)
IV. VALIDITY OF FLIGHT CYCLE AND DISCUSSION
The Afgrow predicted FC and II for different crack configurations, and validation of analysis results discussed in subsequent section 4.1-4.5.
4.1. Examination of single edge crack
Table 2(a) shows normalised SIF for different crack length using analytical approach [13] and finite element approach using Abaqus software. The β increases with increase of crack length, as SIF is directly proportion to square root of crack size [13]. These β are further used in Afgrow software for FC prediction as shown in Table 2(b). The Afgrow predicted FC shows good agreement with respect to analytical and finite element based predicted FC.
4.2. Validity with published experimental results Table 3 shows comparison of Afgrow predicted critical FC using Nasgro model versus published experimental results [14]. Experiments are performed for the specimen width and thickness 38.1 mm, and 2.54 mm and edge crack length 9.6mm. An excellent agreement is seen between the Afgrow predicted FC using Nasgro law with respect to experimental results.
4.3. Effect of thickness on flight cycle
Table (4) shows panel detail with fatigue load used for examination of thickness effect on FC. As specimen thickness increases fracture, toughness decreases as shown in Fig. 3(a). It is because of panel thickness approaching from plane stress to plane strain condition.
In plane strain condition, crack propagation is faster as very little amount of plastic deformation in front of crack tip occurring.
Fig. 3(b) shows flight cycle versus thickness curve from plane stress to plane strain condition. Initially, FC is constant with increase of thickness for same through crack length. It is because fracture toughness for plane stress condition remains same. Once thickness reaches to intermediate stage, fracture toughness start decreasing corresponding FC decreases until reaches to plane strain condition.
Table 2(a) Validation of SIFs
Specimen details, mm Stress MPa Crack length, mm Afgrow β Analytical β Abaqus β Edge crack
W=200, H=200,
T=3, c3 =40 1.62
40 1.366661 1.374218 1.39
50 1.509361 1.505027 1.54
60 1.639091 1.664739 1.71
70 1.898561 1.862182 1.92
80 2.08579 2.11074 2.18
Table 2(b) Comparison of Afgrow predicted flight cycle Material Specimen
details, mm
Numerical approach
N3 Fatigue
spectrum
SMF 2024-T351 Edge crack
W=200, H=200, T=3, c3 =40
Afgrow 82202
Repeated
load 30
Analytical 83787
Abaqus 78679
Table 3 Comparison of Afgrow predicted flight cycle with published experimental result Material Specimen details,
mm
Max/min load, kN
Published experimental result [14], N3
Afgrow predicted FC, N3
2024-T851
Edge crack c3 =9.6, w=38.1 T= 2.54
1400/420 47230 46863
7475-T7351 6.23/1.87 59270 57890
Table 4 Effect of thickness
Material Specimen details, mm Stress ratio, R Field stress, MPa
7075-T7351 Through crack
B = 120, W = 240 , D = 6, T =7, c2 = D + 1.33D 0 100
(a)
(b)
Fig. 3 Effect of thickness on (a) Fracture toughness, (b) Flight cycle
4.4. Effect of complex load
Table (5) shows the specimen detail along with fatigue load used for investigation of complex load effect on primary damage FC. As fastener bearing stress increases for same value of axial stress, surface crack FC decreases as crack grows faster for the same value of corner flaws, shown in Fig. 4(a). Similar trend is observed for thickness crack as shown in Fig. 4(b).
Once, corner flaw reaches to panel thickness, crack growth becomes constant with respect to number of cycle whereas surface crack growth is still increasing with respect FC.
4.5. Effect of composite patch on critical flight life and inspection interval
Table 6(a) shows the panel details, fatigue loading with SMF used for composite patch analysis. Multiple corner flaws each of size D/4 at fastener location of panel with spar is considered as shown in Fig. 5(a). The corner flaws under fatigue loading grow, and formed through crack, corresponding N1 is recorded. Once, corner crack became through crack, it starts propagating under fatigue loading until reaches to critical value, corresponding N2 is recorded. The critical value of FC is estimated using Kc of material. The effect of composite patch over the corner and through crack critical life is examined as shown in Fig. 5(b). In the present paper, twelve numbers of symmetrical boron fibre and epoxy plies [45/-45/0/90/0/0]S is used as a composite patch.
Adhesive (FM-73) is used for bonding Al panel with composite patch. First, SIFs for corner and through cracks for Al alloy panel are estimated, and then SIF correction factor is incorporated due to composite patch.
Equivalent SIF for Al panel along with composite patch is evaluated using principle superposition method, and further used for prediction of critical FC and II.
Table 5 Effect of complex load on primary corner flaw Material Specimen
details, mm
Stress ratio, R
Field stress, MPa 7075-
T7351
W=240, B = 120, T = 8, c = a= 1.4
D = 6
0 100
(a)
(b)
Fig. 4 Effect of bearing stress on flight cycle (a) Surface crack, and (b) Thickness crack
(a) Multiple corner flaws at fastener location of panel
(b) Through crack with composite patch Fig. 5 Effect of composite patch for (a) Multiple corner
flaws at fastener location of panel, and (b) Through crack with composite patch
Table 6(a) Panel details for corner flaw and through crack for estimation of composite patch FC
Figs. 6(a-b) show the panel FC without and with composite patch considering the disbond factor 0.8 for axial load. Adhesive disbond usually occurs around crack tip under cyclic loading and formed elliptical shape. Disbond is defined as ratio of minor to major axis for elliptical shape de-bonding around crack. Disbond value zero indicate that perfect bonding between panel and composite patch, Ref. [15]. Once, de-bonding starts around crack, critical FC start decreasing as shown in Table 6(b). The detectable crack FC under fatigue load is estimated considering 10 mm crack based on nut diameter of fastener whereas, II are predicted using Eq.
[11], and SF of three. Table 6(b) shows summary of analysis results with and without composite patch considering different value of disbond factor.
(a) Corner and through crack
(b) Composite patch with dis-bond factor = 0.8
Fig. 6 Inspection interval for pure axial stress (a) corner and through crack, and (b) composite patch with dis- bond factor = 0.8
Material Specimen details, mm Fatigue loading SMF
2024-T351 Corner flaws
W=150, B = 75, c =a=1, D=4, T = 3
Through crack
W=150, B = 75, T = 3, D=4, c1= T, c2=T, 2a= c1 + D + c2
Corner crack, and through crack
Twist spectrum 100 Corner crack, through crack,
and composite patch
Corner crack, through crack, and composite patch with de- bond factor=0.9
Corner crack, through crack, and composite patch with de- bond factor=0.8
Table 6(b) Summary of FC and II for panel with composite patch
V. CONCLUSION
Based on the analysis results, following conclusion are drawn:
Finite element predicted normalised stress intensity factor can be used for investigation of flight cycle where analytical solution of stress intensity factor is not available.
As panel thickness increases for same value of crack length flight cycle decreases.
As the bearing load increases crack growth is faster for same value of corner flaws.
Effect of bearing load is significantly observed on corner flaw crack flight cycle estimation. As bearing stress increases corner flaw flight cycle is decreasing.
Corner flaws and through crack flight cycle are significatly depend on composite patch and disbond factor.
As disbond factor increases, flight cycle, and inspection interval is decreasing.
REFERENCES
[1] Newman, J.C. Jr., “The merging of fatigue and fracture mechanics concepts: a historical perspective”, Prog. in Aer. Sciences, 34, 347- 390, 1998.
[2] Newman, J.C. Jr., “A crack closure model for predicting fatigue crack growth under aircraft spectrum loading”, ASTM STP, 748, 53-84,1981.
[3] Elber, W., “Fatigue crack closure under cyclic tension”, Eng. Fract. Mech., 2(1), 37-45, 1970.
[4] Elber, W., “The significance of fatigue crack closure”, ASTM STP, 486, 230-242,1971.
[5] Harter, J. A., “AFGROW users guide and technical manual”, U.S. Air Force Research Laboratory Technical Report AFRLVA-WP-TR-
2002-XXX, Website: http://afgrow.wpafb.af.mil, 2002
[6] Skorupa, M., “Load interaction effects during fatigue crack growth under variable amplitude loading – a literature review”, Fat. Fract. Engng Mater. Struct., 22, 905-926,1999.
[7] Merati A, Eastaugh G., “Determination of fatigue related discontinuity state of 7000 series of aerospace aluminum alloys”, Eng Fail Anal;14(4), 673–85, 2007.
[8] Isherwood D.P. and Williams J. G., “The effect of stress-strain properties on notched tensile fracture in plane stress”, Engng Fract. Mech. 2, pp 19-35,1970.
[9] Sig G. C. and Hartranft R. J.,“Variation of strain energy release rate with plate thickness”, Int. J.
Fracture, 9 pp. 75-82, 1973.
[10] Paris P C, Gomez M P, and Anderson W P. , “A rational analytic theory of fatigue”, The Trend Eng, 13; pp. 9-14, 1961.
[11] Skorupa M , Machniewicz T, Schijve and J , Skorupa A., “Application of the strip-yield model from the NASGRO software to predict fatigue crack growth in aluminium alloys under constant and variable amplitude loading”, Engineering Fracture Mechanics; 74, pp. 291-313, 2007.
[12] Yang J N, Donath R C.,“Statistical fatigue crack propagation in fastener holes under spectrum loading”, J Aircraft; 20(12), pp 1028–1032,1983.
[13] Paris P C, and Sig G C., “Stress Analysis of Cracks.”, American Society for Testing and Materials STP 1965, (391) 30–81.
[14] Chung-De Chen, Chuan-I Liu, Ju-Ming Chen, Armstrong Yu, Hsi-Tsung Hsu., “The effects of material variations on aircraft inspection schedules based on stochastic crack growth model”, International Journal of Fatigue; 30, pp.
861–869, 2008.
Panel details with multiple cracks Ncrit Ndet II Fatigue
loading
SMF Corner flaws
W=150, B = 75, c
=a=1, D=4, T = 3 Through crack
W=150, B = 75, T = 3, D=4, c1= T, c2=T, 2a=
c1 + D + c2
Corner crack, and through crack
38468 19303 6388
Twist
spectrum 100 Corner crack, through
crack, and composite patch
78464 23194 18423 Corner crack, through
crack, and composite patch with disbond factor = 0.9
50514 21185 9776
Corner crack, through crack, and composite patch with disbond factor = 0.8
51795 21327 10156
[15] Perez R., Tritsch D. E., and Grandt A. F.,
“Interpolative Estimates of Stress Intensity Factors for Fatigue Crack Growth Predictions”, Engineering Fracture Mechanics, 24(4), pp. 629- 633. 1986.
Nomenclatures
Width of plate W
Height of specimen H
Hole offset distance B
Skin thickness T
Corner flaw length on surface and thickness c, a
Through crack length c2
Total though crack length 2a
Edge crack length c3
Panel thickness T
Diameter of bolt D
Plane stress fracture toughness Kc Plane strain fracture toughness KIC
Modulus of elasticity E
Poission’s ratio υ
Normalised stress intensity factor β Maximum stress intensity factor Kmax Minimum stress intensity factor Kmin
Difference in stress intensity factor ΔK (Kmax- Kmin)
Plane stress thickness tσ
Plane strain thickness tε
Stress multiplication factor SMF Corner crack flight cycle N1 Through crack flight cycle N2
Edge crack flight cycle N3 Critical crack flight cycle Ncrit Critical crack length acrit Detectable crack cycle Ndet Detectable crack length adet
Axial stress σF
Bearing or pin stress σb
Stress component in x, y, and z direction σx ,σy and σz Strain component in x, y, and z direction εx ,εy and εz Yield stress in tension σyt
