THE PISA CODE. Roberta Lazzeri Department of Aerospace Engineering Pisa University Via G. Caruso, Pisa, Italy

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1 3/2 THE PISA CODE Roberta Lazzeri Department of Aerospace Engineering Pisa University Via G. Caruso, Pisa, Italy Abstract. A numerical model to simulate the fatigue behaviour of typical aeronautical structures, such as riveted joints and stiffened panels, is presented. On this basis a computer code has been developed to perform a lot of simulations to obtain answers about crack nucleation, crack growth and probability of failure. This code has been validated during the Brite Euram SMAAC (Structural Maintenance for Ageing Aircraft) programme, whose aim was the research about ageing aircraft concerned with the Multiple Site Damage (MSD) problem. The code has been also used to perform parametrical studies about maintenance methodologies. 1. INTRODUCTION The aeronautical structures are designed in such a way (Safe Life, Damage Tolerance) to avoid catastrophic failures during their operating life. The fullfillment of this requirement is usually done by using a deterministic approach, i.e. by the identification of a mean service life (Safe-Life) or the most critical conditions (Damage-Tolerance) and by applying to them appropriate safety factors. The most critical conditions are mainly connected with crack nucleation time and inspection ability, but also material properties, such as crack growth rate and fracture toughness, have to be taken into account, [1]. The Safe Life and the Damage Tolerance approaches can be generally very conservative, and the safety factors used too penalizing, but they can also be unsafe as has been recognized in failure in Safe- Life designed aircraft. Nowadays, the increased knowledge in fatigue phenomena and the improvement in the description of stochastic behaviours could allow a probabilistic approach. So it is possible to find the probability of occurence of a particular event, such as the failure (risk analysis), by an accurate modelling of the stochastic behaviour of the phenomena. In this way it is possible also to take into account problems like MSD, which were managed with difficulty by using a deterministic approach, [1]. In fact these small undetectable cracks can nucleate at several holes and grow simultaneously up to the linkup, especially in ageing aircraft. In this context, numerical methods can be implemented to execute a high number of simulations. The Department of Aerospace Engineering has developed a computer code, named PISA (Probabilistic Investigation for Safe Aircraft), to simulate the fatigue behaviour of typical aeronautical structures, such as riveted joints and stiffened panels, [2]. 2. THE PISA CODE The PISA code can simulate the fatigue behaviour of simple specimens such as panels with one or more open holes and of typical aeronautical structures, such as riveted joints and stiffened panels (Fig. 1). The fatigue behaviour is simulated from crack nucleation in correspondence with riveted holes, their growth, possible inspection, up to final failure. The PISA code can reproduce the stochastic behaviour of fatigue phenomena through the following parameters, [2, 3]: the Time to Crack Initiation (TTCI) or the Equivalent Initial Flaw Size (EIFS), the crack growth rate, evaluated by means of the constant C of the Paris law, the fracture toughness K c. Beside these, the PISA code can also simulate the probability of detecting a crack during a maintenance action by using the analytical expression of the Probability of Detection (POD) as a function of the crack size. 17

2 The stochastic behaviour can be introduced by using the Monte Carlo method; in such a way it is possible to handle different statistical distributions to simulate the complexity of fatigue phenomena. 2.1 CRACK NUCLEATION A numerical nucleation model has been determined by using experimental data (S-N curve) obtained from simple specimens, but relevant to the component. So, it has been possible to simulate the TTCI distribution, i.e. the time at which it is possible to find a crack, of a ref length, in the specimen, [4]. In the present work, a ref =2 mm, i.e. a dimension that can be seen with the chosen inspecting method and beyond the short crack behaviour, [3]. These experimental data have been used to obtain a lognormal distribution which can be directly used or backward extrapolated with a long crack growth law to obtain the EIFS distribution, i.e. a hypothetical crack distribution which would reach the actual crack size in real time (Fig. 2). 2.2 CRACK GROWTH The PISA code can evaluate crack growth by using two different crack propagation laws, according to Linear Elastic Fracture Mechanics: Paris law Forman law da dn da dn = C K = C m f K mf ( 1 R) K K The Stress Intensity Factor (SIF), K, is calculated by using the composition and superposition of known simple solutions as a function of the boundary conditions, [5, 6, 7, 8, 9, 1]. Secondary bending can also be considered as a further corrective factor, [9]. In such a way it is possible to obtain an analytical formulation of the SIF, because it is necessary to perform a lot of runs in a reasonable computing time. In fact the Monte Carlo method needs and allows us to perform a f m f high number of simulations, but it is necessary to do them consuming little computer time RIVETED LAP JOINTS In a riveted lap joint it is possible to separate the contribution to the SIF due to uniform stress S and that due to the pin loads P i (Fig. 3). As reported in [5] and [9]: 1 ( S + S ) π a + CP p π a 1 K = CR tot bypass tot 2 2 S bypass is the stress transferred by the rivets, 2a the crack length and p a uniform pressure on the hole, due to the rivet. The CR i and CP i corrective factors are functions of different boundary conditions such as: holes, other cracks, finite panel, and so on. They are compounded together to obtain CR tot and CP tot, [5]. Several verifications have been made to ensure the correctness of the analytical formulation of these factors. As an example, in Fig. 3 the effect of a circular hole on the SIF is shown, in comparison with Rooke&Cartwright s results, [6]. In Fig. 4 a comparison between the PISA crack growth in a riveted lap joint and experimental crack growth data is shown STIFFENED PANELS The PISA code can also deal with stiffened panels. By using a known solution of simple geometry (such as the presence of only a stiffener), [7, 8, 9], it has been possible to separate the SIF into various parts: K = K n [ ( K j ) ] + K j= 1 K is the SIF without the stingers and (K j - K ) is the part due to the j-th stringer, [7]. As an example, in Fig. 5 the effect of a stringer on a symmetric crack is shown, in comparison with Nishimura s results, [1, 11]. 2.3 LINK-UP AND FINAL FAILURE 18

3 Two collinear cracks can be considered linked according to the Swift criterion, i.e. when their plastic radii are tangential. Failure can be caused by the arising of yielding stress or fracture toughness. As an example, in Fig. 6 the probability of failure for different initial flaw qualities in lap joints are presented. In this case, lap joints with and without an initial flaw (rogue flaw) have been considered. A comparison between the experimental fatigue behaviour of butt-joint specimens with MSD scenarios (named MSD data) and the PISA code simulation of 1 6 specimen similar to the experimental ones, is shown in Fig. 7, [11]. 2.4 INSPECTIONS The POD of cracks can be expressed by a Weibull distribution, as a function of their sizes: POD [( a a ) ( λ )] β min a min = 1 e a min, λ, β depend on the inspecting method; for the methods used in the present work (eddy current and liquid penetrant), these values have been found by the interpolation of their POD curves, [12] (Fig. 8): - eddy current a min =.65 mm λ = 1.62 mm β = liquid penetrant a min = 1.4 mm λ = 3.5 mm β = 1.2 Further inspecting methods can be easily introduced later. 3. CONCLUSIONS The Department of Aerospace Engineering of the University of Pisa has developed a computer code to simulate the fatigue behaviour of typical aeronautical structures, such as riveted joints and stiffened panels. The first step has been the simulation of the nucleation of cracks on the structure by the TTCI approach, i.e. by using a model built on experimental nucleation data relevant to simple specimens. The second step has been the simulation of crack growth through an analytical law, such as the Paris or Forman law, according to Linear Elastic Fracture Mechanics. Particular attention has been paid to the evaluation of the SIF. It can be estimated by the compounding of known simple solutions to take into account different boundary conditions and by the superposition of different known stress distributions, taking also into account secondary bending. Through appropriate inspecting analytical models, it is possible to simulate the detection of the crack and the repair, allowing a safe operative life. Failure can be achieved, caused by section yielding or fracture toughness. The PISA code was first tested and validated during an European programme, SMAAC, with good agreement between experimental and numerical data and is being used to simulate fatigue behaviour. REFERENCES 1. Lazzeri R., A comparison between Safe Life, Damage Tolerance and probabilistic approaches to aircraft structure fatigue design, to be published on Aerotecnica. 2. Lazzeri R., Sviluppo di un codice di calcolo per la valutazione del livello di rischio in componenti strutturali aeronautici, Degree Thesis, Faculty of Aerospace Engineering, University of Pisa. 3. Cavallini G., Lazzeri R., Simulazione numerica e prove sperimentali di fenomeni di fatica in giunti metallici chiodati in presenza di widespread fatigue damage Parte I/Attività teorica, DDIA 98-6, Giugno Yang J.N., Manning S.D., Demonstration of Probabilistic-Based Durability Analysis Method for Metallic Airframes, Journal of Aircraft, Vol. 27, No. 2, 199, pp Kuo A., Yasgur D., Levy M., Assessment of Damage Tolerance Requirements and Analysis, Task I; Report Air Force WAL-TR-86-3, Vol. II, March 1986, ICAF Doc. n Rooke D.P., Cartwright D.J., Compendium of Stress Intensity Factors, Her Majesty s Stationery Office, London, Rooke D.P., Cartwright D.J., The Compounding Method Applied to Cracks in Stiffened Sheets, Eng. Fracture Mech., Vol. 8, 1976, pp

4 8. Sanders J.L., Bloom J.L., The Effect of a Riveted Stringer on the Stress in a Cracked Sheet, Journal of Appl. Mech., Sept. 1966, pp Broek D., Sampath S., Estimation of Requirements of Inspection Intervals for Panels Susceptible to Multiple Site Damage, ALTURI, Structural integrity of aging airplanes, pp , Nishimura T., Stress Intensity Factor of Multiple Cracked Sheet with Riveted Stiffeners, Journal of Eng. Materials and Technology, Vol. 113, July 1991, pp Cavallini G., Galatolo G., Cattaneo G., An experimental and numerical analysis of Multi-Site Damaged butt-joints, Proceedings of the 19-th Symposium of the International Committee on Aeronautical Fatigue (ICAF), Edinburgh, Scotland, Ratwani M. M. Visual and non-destructive inspection technologies, in Ageing Combat Aircraft Fleet - Long Term Applications, AGARD- LS-26, October

5 STATISTICAL INPUT SIMPLE SPECIMENS S max -TTCI CRACK GROWTH RATE FRACTURE TOUGHNESS POD Smax Log(da/dN) PDF POD Log [TTCI] TTCI, σ[ttci] Log( K) C, σ[logc], m K C, σ[logk C ] Kc a a min, λ, β D E T E R M I N I S T I C G E O M E T R Y a cr a MONTECARLO METHOD SIMULATION MAINTENANCE COST: - INSPECTION - REPAIR - SUBSTITUTION TOTAL COST LIFE I N P U T S max, R, S FS, S bypass, S bend S y, E, ν Life PROBABILITY OF FAILURE THRESHOLD INSPECTION INTERVALS P MAINTENANCE STRATEGIES Log N Figure 1 The PISA code 21

6 Figure 2 TTCI and EIFS model, [4] 3. Corrective factor due to a hole a PISA results Rooke&Cartwright's results Crack length Figure 3 Comparison between the PISA and Rooke&Cartwright s results 22

7 16 Crack dimension a a Experimental data PISA results 2 29, 295, 3, 35, 31, 315, 32, Cycles Figure 4 Comparison between experimental and numerical crack growth (S max =1 MPa R=.1, S bend =32 MPa, S bypass =4 MPa) K/K 2a 2a 2a.75.7 PISA results Nishimura's results a/h Figure 5 Comparison between PISA and Nishimura s results, [11] 23

8 24 1.E-9 1.E-8 1.E-7 1.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+ 5, 1, 15, 2, Cycles P First Detectable Crack (adet=6.35 mm) Failure without rogue flaw Failure with arogue = 1.27 mm Failure with arogue =.635 mm Failure with arogue =.127 mm Figure 6 Cumulative probability for different events obtained by the PISA code (S max =1 MPa, R=.1) Figure 7 Butt-joint life: comparison between the PISA code simulations and the experimental results, [11] 2, 4, 6, 8, 1, 12, 14, 16, 5, 1, 15, 2, 25, 3, Total Life (cycles) Propagation Life (cycles), Numerical simulation Experimental results

9 1.9.8 Probability of Detection eddy current penetrant liquid Crack length [mm] Figure 8 Probability of Detection of a crack as a function of its dimension 25

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