Fatigue life investigation of damaged aluminum alloy material plate.
Fatigue life have play major role on the engineering materials. Damages, vend, dots, cracks are spoiled the fatigue life in aero industries. A high cost engineering materials are used in aircraft parts and the small damages are allowed the safe life engineering materials. Aluminum alloy is a one of the high cost material. It used in aero engineering structural application. The prediction of an aluminum fatigue loading is the important design task for the aero structures. In present investigation to predict the damaged aluminum alloy plate and also studied the FEM model of the aluminum plate.
Schijve  survived the failures of fatigue accident and resist improved the fatigue life of aircraft structures. Damaged materials also used in the engineering aircrafts. J.CNewman  studied the life of metallic materials using small crack theory for various materials and analyzed the micro structure cracks for the aluminum alloy. Magnusen  investigated the fatigue performance in aluminum alloy used for airplane structural application. Benachour  discuss the stress ratio of the prepare aluminum alloy structure. Repair technique as used to damaged structure and stop the cracks. Cheng Wang  investigated the fatigue crack growth of 2024/d4 aluminum alloy under amplitude loading, fatigue growth are predicted by the experimental data. Hai-tai experimental the vibration fatigue life of the aluminum stiffed plate the influence of section and spacing of stiffener plate on the vibration fatigue behavior of the investigated. XUE-song , developed the fatigue characteristics A7N01 welded joints, life based model was a fatigue crack incitation model was proposed. Gwochung tsai  performed the stress analysis of the four different aluminum plates including with and without crack of the composite plates and finite element to predict the fatigue life. Frangopol, D.M  the proposed approach enables the active integration of fatigue limit state in the lifecycle management framework in which inspection and maintenance. Eurocode  discussed the details of aluminum structures; various design guides provide rules for the fatigue design.
In this paper, fracture mechanics approach is adopted, an analytical approach as a preliminary step investigation of fatigue life and crack growth rate is estimated in a structure. Numerical approach as a preliminary step study and investigation of fatigue life and crack growth rate is estimated in structure with damage, the damage area is model in numerical approach, once meshing is done, applied the boundary condition and static loaded in area, once the stress states are extracted, the fatigue analysis is performed. The following figure to illustrate the analytical and numerical approach followed for the investigation.
A. Stress distribution for structure:
A panel of dimension 100 X 100 mm is considered for analysis with a hole of diameter 10mm to simulate the effect of damages like dents, cracks, gouges and scratches critical being the crack, thickness of the panel is 20mm. Damage is simulated by removing the material at the centre of the plate. The material properties considered is Aluminium alloy and its properties are Elastic Modulus, E (pa) = 7.1x[10.sup.10] and Poisson's Ratio = 0. 33.
The calculations of maximum stress are as follows:
1. Total load applied in X-direction, P = 1000 N
2. Applied stress, [sigma] = P/(w - a)t = 555555 N/[m.sup.2]
Width of plate w =100 mm, Hole diameter a = 10mm
3. Stress Concentration Factor, SCF, = a/w = 0.1
From graph SCF, [K.sub.tg] = 2.7
4. SCF= [[sigma].sub.max] / [[sigma].sub.nor] = 2.7 = [[sigma].sub.max] / 555555 = 2.7x555555 N/[m.sup.2] Maximum stress [[sigma].sub.max] = 1500000 N/[m.sup.2]
B. Crack growth analysis using fracture mechanics approach:
The maximum stress is observed in the location of centre of the panel. The panel life estimation of fatigue crack growth behavior was estimated using Paris law. The number of cycles for the crack growth from the initial value .Where the crack size of the stress intensity factor (SIF) reaches to fracture toughness of the material. Knowing the allowable number of cycles based on 'C' checks the life is estimated. Paris crack growth law for life estimation is given (for Centre Crack)
da/dn = C [([DELTA]K).sup.N] (1)
Crack Configuration= through crack
Max Stress, [[sigma].sub.max] = 1500000 N/[m.sup.2]
Min stress, [[sigma].sub.min] = 0
Half crack size a/2=5mm
Half Plate width= b = w/2= 50mm
Applied Stress, [[sigma].sub.app] = [[sigma].sub.max] - [[sigma].sub.min] = 1500000 N/[m.sup.2]
C. Fatigue crack growth estimation for center crack:
Iteration of crack [a.sub.i] = [a.sub.i]-1 + [DELTA]a
Shape function Fi= [1+ 0.128 ([a.sub.i]/w) -0.285[([a.sub.i]/w).sup.2] + 1.523 [([a.sub.i]/w).sup.3]]
Fracture toughness ([DELTA]K)= Fi * [[sigma].sub.app] * [square root of [pi]] a
da/dn = C [([DELTA]K).sup.n] (C=2.14x[10.sup.-9] M.N/[m.sup.2][square root] m, n=2.87) 
[(dn).sub.i] = [DELTA]a/da/dn (2)
No of cycle N= [summation] [dn.sub.i] (3)
Where, [a.sub.i] - Half crack size at ith iteration,
[DELTA]a - Step size for crack growth,
[F.sub.i] - Shape Function,
[DELTA] [K.sub.i] - fracture toughness.
Finite element analysis of crack growth approach:
The half crack panel of 100* 50 mm cross section having a aluminium alloy property is considered for the FEA, once meshing is done, constraints are given to the panel, static force 1000N is applied for the analysis for the applied boundary condition, the stress state of the uniformly centerd crack is extracted which has maximun stress, once the sress state are extracted. This maximum stress occurs on the crack area.
A. Static analysis:
For applied the boundary conditions, the stress state of the uniformly centered crack is extracted which has maximum stress as 1.536x[10.sup.8] N/[m.sup.2] This maximum stress occurs on the crack area.
B. Fatigue analysis:
Uniformly centre crack anlysed in fatigue loading. That crack size in incresed. It shown in above Fig 5. its fatigue life is 1e8 For fatigue analysis uniformed crack centre reach 1e8 cycle for various type loading history
RESULTS AND DISCUSSIONS
Finally the fatigue crack analysis and maximum life is estimated, this work was done by both analytical and finite element analysis technique. Both result are finely matched, small variation between analytical and FEA method. This result is show in below Table3,
B. Fatigue crack growth for an analytical result:
For this work, using the analytical procedure, the crack growth are obtained and estimated no of cycle. From this above graph (6) initial crack size is 5mm finally it reached crack is 17.5mm. It needs for 22.356x[10.sup.8] cycles to reach the final stage. If the cycles are repeated, that crack propagating rate and damage were increased.
For this work, using the FEA procedure, the crack growth are obtained and estimated no of cycle. From this above graph (7) initial crack size is 5mm finally it reached crack is 17.5mm. It needs for 25x[10.sup.8] cycles to reach the final stage. If the cycles are repeated, that crack propagating rate and damage diameter were increased. That analytical graph small variation is here. In FEA graph fine linear graph is plotted, small error variation between the analytical and FEA approach
In the present study fatigue crack growth of aluminium plate have been evaluated numerical and analytically. The following conclusion can be drawn.
1. A fatigue growth behaviour of centrally cracked aluminium plate was investigated. FEM approach of the aluminium plate fatigue life has been evaluated and justified base on analytical results.
2. The crack dimensions is increased the fatigue life of aluminium plate was decrease.
3. It is recommended to their verified method to extend the fatigue life of the composites plates. Discuss the importance of fatigue and the maximum life of the aluminium plate are analysed.
With great pleasure and deep gratitude, the authors wish and express their sincere thanks to Professor.S.Senthil Kumar, Department of Aeronautical Engineering, Karpagam Institute of Technology, and Coimbatore whose assistance played a big role in this work and have been immeasurable value
[1.] Frangopol, D.M., A.C. Estes, 1997. Slightly extended by fatigue crack growth,(Structural Engineering Inter), pp: 193-198.
[2.] Schijve fatigue of aircraft structure, international journal of fatigue volume/1994.
[3.] Newman, J.C., 199. if the splits, M.H swanned Fatigue life methodology using small crack theory, international journal of fatigue, pp: 109-119.
[4.] Megnusenpucci P., 1998. Hinkle analysis and fatigue of micro structural effect on long term fatigue performance on aluminum aerospace alloy, international journal of fatigue, pp: S275-283.
[5.] Benachour, M., 2014. benguediad, seriari prediction of cracks repair aluminum alloy structure with double said, Physics procidia, pp: 83-89.
[6.] Cheng Wang, Xiaogui Wang, Zhenyu ding, Yangijian, 2015. Experimental investigated and numerical prediction of fatigue crack growth of 2024/d4 aluminum alloy, international journal of fatigue, pp: 11-21.
[7.] Hai-tai, yu-long li, yang-gang, 2014. Fatigue behavior of aluminum stiffened plate subjected to random vibration loading, Trans.nonferrous net.soc.china, pp: 133-1336.
[8.] LIU Xue-song, 2012. Zhang liang Wang lin-sen fatigue behavior and life prediction of A7N01 aluminum alloy welded joint, Trans, non-ferrous met, soc.china, pp: 2930-2936.
[9.] Gwo-chung, 2004. Tsai, fatigue analysis of cracked thick aluminum plate bonded with composites patches, composites structures, pp: 79-90.
[10.] Frangopoulos, D.M., A.C. Estes, 1997. Slightly extended by fatigue crack growth, (Structural Engineering Inter), pp: 193-198.
[11.] Eurocode 9, 2003. Predicted the fatigue lives of the pitted specimen's usingcrackpredict remaining life of corrosion damaged airframe structures, international Journal of Fatigue, pp: 371-377.
[12.] Design Data Book, P.S.G., pp: 7-10.
[13.] Madhan Muthu Ganesh, K., 2010. "Damage Tolerant Design for Aero Structural Materials, Natianal conference Procedings, SNS college of Engineering.
(1) K. Baluchamy, (2) M. Mugunthan, (3) D. Pravalika, (4) S. Sabareeswari, (5) K. Madhan Muthu Ganesh
(1, 2, 3, 4, 5) Department of Aeronautical Engineering Karpagam Institute of Technology, Coimbatore.641105
Received 28 January 2017; Accepted 22 March 2017; Available online 28 April 2017
Address For Correspondence:
K. Baluchamy, Department of Aeronautical Engineering Karpagam Institute of Technology, Coimbatore.641105
Caption: Fig. 1: Initial flaw, slightly extended by fatigue crack growth .
Caption: Fig. 2: Flow chart of methodology for analytical and finite element analysis.
Caption: Fig. 3: Finite element model of specimen.
Caption: Fig. 4: Static analysis of uniformly centred crack.
Caption: Fig. 5: Fatigue life
Caption: Fig 6: Fatigue crack growth for an analytical graph.
Caption: Fig. 7: Fatigue crack growth for FEA graph.
Table 1: Fatigue Crack Growth Estimation For Centre Crack-Fracture Mechanics Approach. No of iteration [a.sub.i] (mm) [a.sub.f] (da/dn) N/[m.sup.2] (mm) [square root of m] 1 2 5 5.5 2.36 x [10.sup.-11] 3 5.5 6 2.69 x [10.sup.-11] 4 6 6.5 1.24 X [10.sup.-10] No of iteration N (cycles) 1 2 2.118 x [10.sup.8] 3 1.915 x [10.sup.8] 4 0.414 x [10.sup.8] For the considered panel using the analytical procedure, the crack growths are obtained. Initial crack size of the panel is 5mm finally it reached 17.5mm, Which requires 22.356e8 cycles to reach the final stage. Table 2: Fatigue crack growth estimation for centre crack-numerical approach. No of iteration [a.sub.i](mm) [a.sub.f] N (cycles) (mm) 1 2 5 5.5 1 x [10.sup.8] 3 5.5 6 1 x [10.sup.8] 4 6 6.5 1 x [10.sup.8] For the considered panel using the FEA procedure, Initial crack size of the panel is 5mm finally it reached crack of 17.5mm, which requires 25x[10.sup.8] cycles to reach the final stage. Table 3: Comparison Table. SL.no Type of analysis Max stress (pa) Fatigue life 01 ANALYTICAL 1.5 x [10.sup.6] 22.35 x [10.sup.8] 02 FEA 1.5368 x [10.sup.6] 25 x [10.sup.8]