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2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal Madeira, Portugal

Probabilistic fatigue crack growth assessment of Al 7075-T6 aerospace component aerospace component Thermo-mechanical modeling of a high pressure turbine blade of an Ahmed Bahloulaa*,Amal Ben Ahmedbb,Chokri Bouraouiaa Ahmed Bahloul *,Amalgas Benturbine Ahmed ,Chokri airplane engineBouraoui Laboratoire de Mécanique de Sousse, Ecole Nationale d’Ingénieurs de Sousse, Université de Sousse,BP 264, Cité Erriadh, 4023 Sousse,

fatigue crackPCF growth assessment of Al 7075-T6 XV Probabilistic Portuguese Conference on Fracture, 2016, 10-12 February 2016, Paço de Arcos, Portugal

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a Laboratoire de Mécanique de Sousse, Ecole Nationale d’Ingénieurs de Sousse, Université de Sousse,BP 264, Cité Erriadh, 4023 Sousse, Tunisie.b a b c Tunisie.b Laboratoire de Mécanique, Matériaux et Procédés, Ecole Nationale d’Ingénieurs de Sousse, Université de Sousse,BP 264, Cité Erriadh, 4023 b Laboratoire de Mécanique, Matériaux et Procédés, Ecole Nationale d’Ingénieurs Sousse, Tunisie. de Sousse, Université de Sousse,BP 264, Cité Erriadh, 4023 a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Sousse, Tunisie. Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal Abstract c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, In this paper, an engineering approach of fatigue crack Portugal growth mechanism of Al 7075-T6 aerospace component is b

P. Brandão , V. Infante , A.M. Deus *

In this paper, engineering approach fatigue crackbygrowth mechanism of Al Finite 7075-T6 aerospace component is proposed. Theanproposed approach wasofimplemented coupling of Extended Element Method (XFEM), proposed. The proposed was implemented coupling Extended(MCS) Finitemethod. ElementParticular Method focus (XFEM), Residual Corrected Stress approach intensity Factor (RC-SIF) andby Monte Carloof simulation was Residual Correctedthe Stress intensity Factor (RC-SIF)and andthe Monte Carlo simulation (MCS) method. Particular focus was put on considering effect of material dispersions residual stress distribution near the crack tip for evaluating Abstract put considering theattachment effect of material dispersions and the residual stress distribution near the material crack tip behavior. for evaluating FCGonlife of cracked lug. Lemaitre-Chaboche’s model has been used to describe The FCG life their of cracked lug. Lemaitre-Chaboche’s model been used describe material behavior. During operation, modern aircraft engine components subjected to increasingly demanding conditions, iso-probabilistic a-N attachment curves corresponding to5%, 50% andare 95% ofhas reliability aretodetermined. Theoperating reliability ofThe the especiallyengineering the high pressure turbine (HPT) blades. Such cause parts toare undergo types of time-dependent iso-probabilistic a-N curves corresponding to5%, 50% and 95% of these reliability determined. The reliability of the proposed approach is verified through a conditions comparison with experimental FCGdifferent life data. degradation, one of which is creep. model through using the afinite element method (FEM) was developed, order to be able to predict proposed engineering approach is A verified comparison with experimental FCG life in data.

behaviourPublished of HPT by blades. Flight © the 2017creep The Authors. Elsevier B.V.data records (FDR) for a specific aircraft, provided by a commercial aviation © 2017 The Authors. Published by Elsevier B.V.and mechanical data for three different flight cycles. In order to create the 3D model company, were used to obtain thermal © 2017 The Authors. Published by Elsevier B.V. Committee of ICSI 2017. Peer-reviewunder under responsibility ofScientific the Scientific Peer-review of the Committee of ICSI 2017 and its chemical composition and material properties were needed forunder theresponsibility FEM analysis, HPT blade scrap was scanned, Peer-review responsibility ofa the Scientific Committee of ICSI 2017. obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D Keywords:MCS method; Fatigue life prediction, XFEM;RC-SIF; Aerospace component rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The Keywords:MCS method; Fatigue life prediction, XFEM;RC-SIF; Aerospace component overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

1. Introduction 1.©Introduction 2016 The Authors. Published by Elsevier B.V. Fatigue life isunder random in nature (Ghonem and Dore (1987)) models seem to be unable for predicting Peer-review responsibility of the Scientific Committee of and PCFdeterministic 2016. Fatigue randomstructures in naturein(Ghonem and Dore deterministic seem to be unable for predicting FCG lifelife of is cracked more efficient and(1987)) reliableand way. Looking formodels a model /Engineering approach which FCG life ofHigh cracked structures in more efficient and reliable Looking for a model /Engineering approach which Keywords: Pressure Turbine Blade; Creep; Finite Element Method; way. 3D Model; Simulation.

* Corresponding author. Tel.: +216-28-062-275. * Corresponding author. Tel.: +216-28-062-275. E-mail address:[email protected] E-mail address:[email protected] 2452-3216 © 2017 The Authors. Published by Elsevier B.V. 2452-3216 © 2017 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby Scientific Committee of ICSI 2017. Peer-review underauthor. responsibility the Scientific Committee of ICSI 2017. * Corresponding Tel.: +351of 218419991. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017 10.1016/j.prostr.2017.07.192

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could evaluate FCG life of mechanical structures with an acceptable confidence level, still remains among a challenging point in several industrial sectors. Lug type joint is considered as the most critical engineering component in the aerospace industry. It is used generally to assemble components with other mechanical structures such as wings to fuselage and spoilers to wings. Since lug type joints are a very sensitive component in the aeronautical industry, several researches [Kim et al.(2003), Mikheevskiy et al. (2012), Baljanovic and Maksimovic (2014), Naderi and Iyyer (2015) and Bahloul et al. (2017) ] have dealt with the problem of fatigue crack growth for these structures. The present paper aims at developing an engineering approach for FCG life prediction of 7075-T6 Aluminum alloy cracked lug component taking into account the effect of residual stress distribution around the crack tip and material dispersions. The XFEM was implemented for FCG modeling. The RC-SIF parameter is proposed to consider the effect of residual stress distribution near the crack tip and the MCS is used to determine the iso-pobabilistic a-N curves corresponding to 5%, 50% and 95% of reliability. A comparison between the suggested approach and available experimental data is performed. 2. Computational Engineering Approach 2.1. Numerical procedure for FCG life prediction In fatigue fracture analysis, traditional empirical models examine the FCG rate within the framework of linear elastic fracture mechanics (LEFM). However, a crack tip plastic zone can be almost developed when a growing crack occurs in ductile materials. This plastic zone’s size varies depending on various parameters such as specimen thickness, crack length, applied load, yielding stress…etc. It is generally admitted that the local strains/stresses, located in this zone, control the FCG mechanism. It was showed [Noroozi et al.(2007)] that the relationship between the stress intensity factor and the stresses/strains field near the crack tip is often affected by residual stresses generated by reversed plastic deformations. Since stress intensity factor is defined as a driving force parameter for predicting crack growth path, FCG rate and fatigue life, it is necessary to quantify the residual stress impact in terms of SIF. Using the weight function method, the residual stresses can be converted to residual stress intensity factor K res as follows: 𝑥𝑥=𝑎𝑎

𝐾𝐾𝑟𝑟𝑟𝑟𝑟𝑟 = ∫ 𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 𝑚𝑚(𝑥𝑥, 𝑎𝑎)𝑑𝑑𝑑𝑑 𝑥𝑥=0

(1)

Where 𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎(𝑥𝑥, 𝑎𝑎) are the residual stress in the vicinity of crack tip and the weight function expression [21], respectively. 𝑥𝑥 1⁄2 𝑥𝑥 1 𝑥𝑥 3⁄2 2 ⌊1 + 𝑀𝑀1 (1 − ) + 𝑀𝑀2 (1 − ) + 𝑀𝑀3 (1 − ) ⌋ 𝑚𝑚(𝑥𝑥, 𝑎𝑎) = 𝑎𝑎 𝑎𝑎 𝑎𝑎 √2𝜋𝜋(𝑎𝑎 − 𝑥𝑥) (2) The coefficient 𝑀𝑀1 , 𝑀𝑀2 𝑎𝑎𝑎𝑎𝑎𝑎𝑀𝑀3 are dependent on the cracked component geometry. It was assumed that for a positive stress ratio, only the maximum stress intensity factor is affected by the crack tip residual stress distribution, without significant changes in the minimum stress intensity factor [Noroozi et al.(2007)]. Therefore, the residual-corrected stress intensity factor (RC-SIF) can be written as: ∆𝐾𝐾𝑟𝑟𝑟𝑟 = ∆𝐾𝐾𝑒𝑒𝑒𝑒 + 𝐾𝐾𝑟𝑟𝑟𝑟𝑟𝑟 (3) Hence, the number of load cycles for each step of crack propagation can be determined as follows: ∆𝑁𝑁𝑖𝑖 =

∆𝑎𝑎 𝑚𝑚 𝐶𝐶∆𝐾𝐾𝑟𝑟𝑟𝑟

(4)


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Finally, the total FCG life at the end of each iteration is evaluated as follows: 𝑁𝑁𝑖𝑖 = 𝑁𝑁𝑖𝑖−1 + ∆𝑁𝑁𝑖𝑖

(5)

2.2. FE modeling 2D FE analysis using ABAQUS commercial software was implemented. The attachment lug was considered to estimate the residual fatigue life under different load ratios (R=0.1 and R=0.5). The geometry of the lug is shown in Fig.1, having L=200 mm, D=38.1 mm, t=12.7 mm and w=3D. A crack was positioned near the hole edge with an initial size equals to 0.635 mm. In order to compute the high stress distribution in the vicinity of the crack, a very fine structured mesh has been modeled around the crack region with 0.05 mm element size. The finite element mesh of the cracked lug is illustrated in Fig.1. The non-linear isotropic/kinematic hardening model is considered to describe the material behavior. This plasticity model is capable to characterize the material behavior during cyclic loading considering the Baushinger effect, mean stress relaxation, ratcheting and cyclic hardening. During FE analysis, a growing crack is considered. When the applied load reaches its maximum value, a constant crack growth increment length is released during a loading cycle. The residual stress distributions near crack tip are evaluated at each crack growth increment at the end of the unloading step, from which the residual stress intensity factor can be evaluated using the weight function. 2.3. Computation of FCG Reliability In this section, a probabilistic approach for predicting FCG life of cracked attachment lug, under cyclic loading is implemented. The main procedure for developing the probabilistic model using FE-analysis, RC-SIF and Monte Carlo simulation method is summarized as follows: (i) In the first stage, a FE model is developed upon ABAQUS commercial code. An elastic-plastic analysis using the non-linear isotropic/kinematic hardening model is used to extract the residual stress distribution surrounding the crack tip. Crack growth path is simulated using XFEM .In this context, a numerical fatigue crack growth code was developed by an iterative procedure within the framework of Python script. (ii) The residual corrected stress intensity factor RC-SIF parameter is used to predict the FCG life of the cracked attachment lug. (iii) Due to the significant fatigue data scatter of the attachment lug, the proposed approach was carried out by taking into account the effect of residual stress distribution near crack tip and material dispersions which are assumed to be normally distributed. The reliability is computed using the Monte Carlo simulation method. (iv) The iso-probabilistic a-N curves of the cracked attachment lug are determined at 5% ,50% and 95% of reliability. 3. Results and discussion (i)

FCG simulations are determined using the XFEM. In this context, a numerical code was developed within the framework of Python script. In the first step, model geometry, mesh generation, loading conditions and material parameters are implemented in Abaqus. Then, the Python code was called to extract SIF for each increment in which the first five contour integrals are chosen for evaluating the average of SIFs. Fig.2 shows the crack growth path of different structure configurations, under cyclic loading.

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Fig. 1. Finite element mesh of the cracked lug

Fig. 2. FCG path simulation

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(ii)

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Fig.3 shows the crack growth path simulation of the cracked attachment lug. A good agreement is found between experimental and numerical result In order to highlight the effect of residual stress distribution ∆𝐾𝐾 near the crack tip on the stress intensity factor (SIF) range. Tab.1 shows the evolution of 𝑟𝑟𝑟𝑟⁄∆𝐾𝐾 versus crack length for the attachment lug. Two different stress ratios are considered (R=0.1 and R=0.5). It is ∆𝐾𝐾𝑟𝑟𝑟𝑟⁄ observed that the ratio ∆𝐾𝐾 decreases as the crack length increases. The difference between ∆𝐾𝐾𝑟𝑟𝑟𝑟 𝑎𝑎𝑎𝑎𝑎𝑎 ∆𝐾𝐾 can reach 20% for the attachment lug as illustrated in Tab.1. This result can be explained by the fact that the plastic zone surrounding the crack tip increases as the crack size increases. Accordingly, a compressive residual stress occurs and reduces the effect of the tensile stress during crack propagation.

Fig. 3.Crack growth path of the attachment lug Table 1. Effect of residual stress distribution on the SIF.

a (mm) 3 5 7.5 10 12.5 15 17.5

(iii)

R=0.5 0.957 0.939 0.933 0.918 0.914 0.897 0.903

∆𝑲𝑲𝑹𝑹𝑹𝑹⁄ ∆𝑲𝑲

R=0.1 0.923 0.891 0.879 0.853 0.845 0.816 0.826

In order to validate the proposed approach’s performance for predicting fatigue life, cracked attachment lug subjected to different load ratios are considered. The effect of residual stress distribution surrounding the crack tip is evaluated using the RC-SIF as previously mentioned. The material dispersions are assumed to be normally distributed with coefficient of variance equals to 1.75%, having for R=0.1: C=2.1E-08 and m=3.86 and for R=0.5: C=11.3E-08 and m=3.7. due to the random aspect in fatigue life data for cracked lugs, the suggested method consist in determining the iso-probabilistic a-N curves corresponding respectively to 5%, 50% and 95% fatigue reliability. Fig.4 shows a comparison between the proposed model and the relevant experimental data for various loading conditions (R=0.1 and

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R=0.5). The suggested approach exhibits good ability in predicting fatigue crack growth life of the cracked attachment lugs comparing with experimental results [Kathiresan and Hsu (1984)].The obtained iso probabilistic a-N curves are very useful in engineering application for evaluating FCG life with an acceptable confidence level. These curves can be used as a practical tool to ensure an optimal maintenance planning for cracked components. The proposed engineering approach consist in improving the deterministic models by considering the effect of residual stress distribution near crack tip and material dispersions, leading to predict the residual FCG life in more efficient and reliable way.

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Fig. 4.The iso-probabilistic curves for: (a) R=0.1; (b) R=0.5. 4. Conclusions This attempt addresses the prediction of fatigue crack growth life of cracked aircraft component. An engineering probabilistic approach was specially developed using XFEM, RC-SIF and MCS. Particular focus was put on considering the effect of residual stress distribution near the crack tip and material dispersions for predicting the residual fatigue life. According to the findings, it can be concluded that:

(i) (ii) (iii)

The XFEM presents an efficient and powerful toll for fatigue crack growth modelling. The RC-SIF parameter exibits good ability in considering the effect of residual stress distribution near crack tip. Fatigue life data is random in nature and deterministic models seem to be unable for evaluating the remaining fatigue life of cracked structures due to the material dispersions, which confirms the need for an engineering approach that takes into account this random aspect. The iso-Probabilistic a-N curves corresponding to 5%, 50% and 95% fatigue reliability loadings have been performed. This method allows engineers to be engaged in practical problems for predicting the remaining fatigue life of cracked structures in a more efficient and reliable way. .

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References Ghonem S., Dore S., 1987. Experimental study of the constant probability crack growth curves under constant amplitude loading. Eng.Fract.Mech 27:1-25. Kim JH., Lee SB., Hong SG., 2003. Fatigue crack growth behavior of Al7050-T7451 attachment lugs under flight spectrum variation. Int.J.Fatigue 40:135-144. Mikheevskiy S., Glinka G., Algera D., 2012. Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the Unigrow fatigue crack growth model. Int J Fatigue 42:88-94 Boljanovic S., Maksimovic S., 2014. Fatigue crack growth modeling of attachment lugs. Int J Fatigue 58:66-74. Naderi M., Iyyer N., 2015. Fatigue life prediction of cracked attachment lugs using XFEM . Int J Fatigue 77:186-193. Bahloul A., Bouraoui CH ., Boukharouba T. 2017. Prediction of fatigue life by crack growth analysis. The International Journal of Advanced Manufacturing Technology doi:10.1007/s00170-017-0069-8. Noroozi AH., Glinka G., Lambert S., 2007. A study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force. Int J Fatigue 29:1616-1633. Khthiresan K., Hsu TM., 1984. Advanced life analysis methods-crack-growth, analysis methods for attachment lugs. AFWAL-TR-84-3080,Vol.II.