PSI - Issue 13

Volume 13 • 201 8

ISSN 2452-3216

ELSEVIER

ECF22 - Loading and Environmental effects on Structural Integrity

Guest Editors: Aleksandar Sedmak Zoran R adakovi ć Marko R akin

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www.elsevier.com/locate/procedia XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 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. ECF22 - Loading and Environmental Effects on Structural Integrity Editorial A. Sedmak a, *, M. Rakin b , Z. Radaković a a Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade, Serbia b Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, Serbia Probably only few would remember that Serbia was already involved in European Conference of Fracture (ECF) organization. It was not destined to happen in ex-Yugoslavia, back in 1992, but it has happened in Varna, Bulgaria, instead, organized as mission impossible by Prof. Stojan Sedmak, from Belgrade. Interestingly enough it was after Italy, ECF8 in Turin, 1990, just like this one, after Catania, ECF21, in 2016. I have been involved in organization of ECF9, and it is maybe right moment to say now thank you Italy, thank you Donato Firrao for your help in early nineties, and thank you Francesco Iacoviello for everything you did to make ECF22 successful event. Anyhow, let me also emphasize one significant difference. Namely, organizing ECF9 was tedious job because of hardly any communication with outside world, and except Donato, it was only Stefan Vodenicharov and his team from Bulgaria, whom I remember as big help. On the contrary, ECF22 was a straightforward job, since we just followed great successes of Kazan in 2012, Trondheim in 2014 and Catania in 2016, relaying strongly on support of not only chairmen of three preceding conferenc s (Valery Shlyannikov, Zhiliang Zhang and Francesco Iacoviello), but lso on many other ESIS m mbers, actually too many to be listed here. C incidently or not, these Conferenc s ha pened during th presidency of L slie Banks-Sills. Well, fin tely not a coincidenc , since the first female officer in ESIS history was also the best ver president, if I may say. © 2018 The Authors.Published by Elsevier B.V. Peer-review und r responsibil ty of the ECF22 organizers. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. ECF22 - Loading and Environmental Effects on Structural Integrity Editorial A. Sedmak a, *, M. Rakin b , Z. Radaković a a Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade, Serbia b Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, Serbia Probably only few would remember that Serbia was already involved i European Conference of Fracture (ECF) organization. It was not destined to happen in ex-Yugoslavia, back in 1992, but it has happened in Varna, Bulgaria, instead, organized as mission i possible by Prof. Stojan Sedmak, from Belgrade. Interestingly enough it was after Italy, ECF8 in Turin, 1990, just like this one, after Catania, ECF21, in 2016. I have been involved in organization of ECF9, and it is maybe right mom nt to say now thank you Italy, thank you Donato Firrao for your help in early nineties, and thank you Francesco Iacoviello for everything you did to make ECF22 successful event. Anyhow, let me also emphasize one significant difference. Namely, organizing ECF9 was tedious job because of hardly any communication with outside world, and xcept Donato, it was only Stefan Vodenicharov and his te m from Bulgaria, whom I remember as big help. On the contrary, ECF22 was a straightforward job, since we just followed great successes of Kazan in 2012, Trondheim in 2014 and Catania in 2016, relaying strongly on support of not only chairmen of three preceding conferences (Valery Shlyannikov, Zhiliang Zhang and Francesco Iacoviello), but also on many other ESIS members, actually too many to be listed here. Coincidently or not, these Conferences happened during the presidency of Leslie Banks-Sills. Well, definitely not a coincidence, since the first female officer in ESIS history was also the best ever president, if I may say. © 2018 The Authors.Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. Keywords: Laser shot peening; Nimonic; Macrostructural surface tests.

Keywords: Laser shot peening; Nimonic; Macrostructural surface tests.

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. * Corresponding author E-mail address: aleksandarsedmak@gmail.com * Corresponding author E-mail address: aleksandarsedmak@gmail.com

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

2452-3216  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.001

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A. Sedmak et al. / Procedia Structural Integrity 13 (2018) 1–2 Author name / Structural Integrity Procedia 00 (2018) 000–000

It was not only due to ESIS agreement with Elsevier, but even more due to big success of ECF21 Procedia Structural Integrity, that we now present ECF22 proceedings as its second edition. We hope that at least partly ECF22 Procedia Structural Integrity will follow this success. It was a big effort of many people to manage more than 500 presentations during ECF22, and to review and prepare 371 papers for proceedings. Big impact came from mini symposia, listed here, especially the one on Hydrogen Embrittlement with 50 presentation:  Milos Djukic, William Curtin, Zhiliang Zhang, "Recent Advances on Hydrogen Embrittlement Understanding and Future Research Framework"  Siegfried Schmauder, Zeljko Bozic, "Multiscale Damage Analysis of Fatigue and Fracture of Metals"  Vadim Silberschmidt "Damage and Fracture of Biological and Biomedical Materials"  Uwe Zerbst, Stefano Beretta, Andrea Carpinteri, "Defects and fatigue"  Jose Antonio Correia, Vladimir Moskvichev, "Risk Analysis and Safety of Technical Systems"  Giacomo Risitano, "Energy Methods for Fatigue Assessment". The essence of every conference are plenary lectures. Although they are not published here, since all of them presented already published results, let us remember brilliant lectures given by James Rice on Perspectives on dynamic fracture arising from study of earthquake ruptures, Jovo Jaric on Conservation laws of J integral type, Youshi Hong on The State of the Art in Very-High-Cycle Fatigue Research, Uwe Zerbst on Application of fracture mechanics to S N curve prediction, Meinhard Kuna on Micromechanical Modeling of Fracture in Metallic Materials, Robert Ritchie on Damage Tolerance in Biological and Metallic Material, Yonggang Huang on Soft Network Composite Materials with Deterministic and Bio-Inspired Designs, Takayuki Kitamura on Challenge toward Nanometer Scale Fracture Mechanics, William Curtin on Mechanisms of Hydrogen Embrittlement: Insights from Atomistic Studies, Drazan Kozak and Nenad Gubeljak on Integrity of pipeline by using pipe-ring testing. It was our utmost privilege to have James Rice with us who delivered also the special lecture on the occasion of 50 th anniversary of J integral, making the 5 th Summer School, held on the eve of ECF22, a memorable event. All papers from ESIS/Elsevier young researcher best paper award competition deserve special attention, not only the winner, Junhe Lian, and the second best, Guian Quin, but also Aziz Tokgoz, Mor Mega, Yaroslav Khaburskyi, Anke Schmiedt, Que Zaiqing, Yaroslav Dubyk. Another, newly established award for the best weldment fracture mechanics paper, in memory of Prof. Stojan Sedmak (thanks to the Turkish welding community and Galip Buyukyildirim) also attracted high quality papers, just to mention the winner, Fedor Fomin. I do hope this completion and award will become a tradition. Finally, let me once again praise the Local Organizing Committee, International Scientific Committee and National Scientific Board for their contribution to the success of ECF22 and proceedings presented here. ECF 22 Chairman, on the behalf of Editors Prof. Aleksandar Sedmak

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XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 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. ECF22 - Loading and Environmental e ff ects on Structural Integrity 3D Stress Fields Versus Void Distributions Ahead Of a Notch Tip For Semi-crystalline Polymers L. Laiarinandrasana a, ∗ , N. Selles a , Y. Cheng b , L. Helfen b,c , T.F. Morgeneyer a a PSL-Research University, MINES ParisTech, MAT-Centre des Mate´riaux, CNRS UMR7633, BP 87, F-91003 Evry Cedex, France b European Synchrotron Radiatio Facility (ESRF), BP 220, F-38043 Gre oble Cedex, France c Institute for Photon Science and Synchrotron Radiation (IPS), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen, Germany Abstract The creep durability of engineeri g structures relies on the theory of Fracture Mechanics for Creeping Solids (FMCS). The studied material is a semi-crystalline polymer. The lifespan of plastic pipes being generally specified in terms of years of service, its prediction requires reliable constitutive models accounting for time dependent deformation under multiaxial stress states and failure criteria based on the mechanisms of damage and failure. Here, an experimental approach was developed so as to analyze the mechanisms of deformation and cavitation at the microstructural scale by using 3D imaging (tomography / laminography). Three stress triaxiality ratios were addressed using various notched specimen geometries. The void characteristic dimensions (volume fractio , height and diameter) w e then measured by defining a volume of interest. The sp tial distributions of these chara teristics at a prescribed creep time w re o served to be dependent on the stress triaxiality r tio. A finite element constitutive model using the porosity as an internal variable, was selected. Comparison of the multiscale experimental database with those simulated at the macroscopic scale as well as at the microstructure level was satisfactory. In the light of the finite element results, the principal stress singularities ere in good agreement with the void characteristic lengths. c 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. Keywords: Type your keywords here, separated by semicolons ; © 2018 The Authors. Published by Els vier B.V. Peer-review under responsibil ty f the ECF22 organizer . ECF22 - Loading and Environmental e ff ects on Structural Integrity 3D Stress Fields Versus Void Distributions Ahead Of a Notch Tip For Semi-crystalline Polymers L. Laiarinandrasana a, ∗ , N. Selles a , Y. Cheng b , L. Helfen b,c , T.F. Morgeneyer a a PSL-Research University, MINES ParisTech, MAT-Centre des Mate´riaux, CNRS UMR7633, BP 87, F-91003 Evry Cedex, France b European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France c Institute for Photon Science and Synchrotron Radiation (IPS), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen, Germany Abstract The creep durability of engineering structures relies on the theory of Fracture Mechanics for Creeping Solids (FMCS). The studied material is a semi-crystalline polymer. The lifespan of plastic pipes being generally specified in terms of years of service, its prediction requires reliable constitutive models accounting for time dependent deformation under multiaxial stress states and failure criteria based on the mechanisms of damage and failure. Here, an experimental approach was developed so as to analyze the mechanisms of deformation and cavitation at the microstructural scale by using 3D imaging (tomography / laminography). Three stress triaxiality ratios were addressed using various notched specimen geometries. The void characteristic dimensions (volume fraction, height and diameter) were then measured by defining a volume of interest. The spatial distributions of these characteristics at a prescribed creep time were observed to be dependent on the stress triaxiality ratio. A finite element constitutive model using the porosity as an internal variable, was selected. Comparison of the multiscale experimental database with those simulated at the macroscopic scale as well as at the microstructure level was satisfactory. In the light of the finite element results, the principal stress singularities were in good agreement with the void characteristic lengths. c 2018 The Authors. Published by Elsevier B.V. r-review under responsibility of the ECF22 organizers. Keywords: Type your keywords here, separated by semicolons ;

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

1. Introduction 1. Introduction

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

Engineering structures made of semi-crystalline polymers are subjected to complex thermo-mechanical loadings. Lifetime prediction in terms of years of service for these industrial structures requires reliable constitutive models of time dependent deformation and multiaxial stress states. Here, a multiscale experimental approach was developed on notched and pre-cracked specimens. The results combined macroscopic data consisting of the creep displacements and data sets at the microstructural scale by using 3D imaging (tomography / laminography). A better understanding of the Engineering structures made of semi-crystalline polymers are subjected to complex thermo-mechanical loadings. Lifetime prediction in terms of years of service for these industrial structures requires reliable constitutive models of time dependent deformation and multiaxial stress states. Here, a multiscale experimental approach was developed on notched and pre-cracked specimens. The results combined macroscopic data consisting of the creep displacements and data sets at the microstructural scale by using 3D imaging (tomography / laminography). A better understanding of the

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. ∗ Correspon ing author. Tel.: + 33-1-60-76-30-64; fax: + 33-1-60-76-31-50. E-mail address: lucien.laiarinandrasana@mines-paristech.fr 2210-7843 c 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. ∗ Corresponding author. Tel.: + 33-1-60-76-30-64; fax: + 33-1-60-76-31-50. E-mail address: lucien.laiarinandrasana@mines-paristech.fr 2210-7843 c 2018 The Authors. Published by Elsevier B.V. Peer-revi w under responsibility of the ECF22 orga izers. * Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.367

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a)

b)

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Fig. 1. Material and specimens: a) Spherulitic microstructure; b) Notched round bar with 4 mm notch root radius; c) Notched round bar with 0.45 mm notch root radius; d) CT specimen (thickness = 2 mm).

mechanisms of deformation and cavitation was obtained: the void volume fraction was measured by using a prescribed volume of interest. Moreover, the average void heights and diameters within this volume of interest were determined. The spatial distributions of these characteristics were plotted. Instead of using the digital volume correlation technique to compare the strain fields, the approach here consisted of using Finite Element (FE) analysis to correlate the void characteristic lengths to the principal stresses.

2. Experiments

The material studied was a semi-crystalline Polyamide 6 (PA6) with a spherulitic microstructure (fig. 1a) as re ported in Laiarinandrasana et al. (2012). Three notched and cracked specimens, described in fig. 1b,c,d, were chosen. They allowed the stress multiaxiality and the profile of the stress gradient in the microstructure to be controlled (La iarinandrasana et al. (2016)). These specimens were subjected to creep crack growth tests. The failure occurred during the apparent tertiary creep stage. The applied net stress and creep displacement were recorded throughout the tests. Some of the creep tests were stopped at the onset of the tertiary stage. The deformed specimens (after unloading) were inspected using tomography-laminography techniques (Laiarinandrasana et al. (2012), Laiarinandrasana et al. (2016)) to better understand the evolution of spherulitic microstructures during the creep deformation. The mech anisms viewed at the microscopic scale, within a prescribed volume of interest, were then synchronized with the macroscopic strain level. These multiscale experimental data were used to analyze the time dependent deformations involved during creep. A constitutive model accounting for these deformations and implemented in an in-house FE code (Besson and Foerch (1997)) was then used to simulate the creep tests. To this end, the two notched round bars to gether with the CT specimen were meshed. Attention was paid to make the mesh size in the vicinity of the notch / crack front coincide with the “experimental” volume of interest.

3. Results

3.1. Opening displacement rates

As mentioned above, the opening displacements ( δ c ) were recorded during each creep test. The symbols in fig. 2 show some examples of the evolution of ( δ c ) as well as that of the opening displacement rate (d δ c / dt) for the three

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Fig. 2. Notch / Crack opening displacement (rates) for: a) NT4 round bar; b) NT045 round bar; c) CT specimen.

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Fig. 3. Void morphology and distribution for: a) NT4 round bar (side and top views); b) NT045 round bar (side view: examinations / measured V f ); c) CT specimen (top view of the fracture surface: examinations / measured V f ).

geometries during the creep tests. Each test in fig. 2 was stopped and unloaded at the last point of the diagram. These data was useful to calibrate the material coe ffi cients in the FE modelling.

3.2. Voiding due to creep

Creep deformed round bars and CT sample were inspected by tomography and laminography respectively. The main results of these examinations were detailed in Selles et al. (2016). The tomography / laminography data sets in fig. 3 summarize the morphology and the distribution of voids (black pixels). For NT4 (fig. 3a), it was observed that voids became more numerous and larger from the surface to the centre. Depending on their location within the net section, voids were cylindrical with variable height (h v ) and diameter ( φ ). For NT045, Selles et al. (2017) described the data treatment allowing the distribution of V f to be displayed as a contour map shown in fig. 3b (bottom). In this geometry, it was clearly indicated that the maximum void volume fraction V f was located in between the centre and the notch root radius, in opposition to what was observed on NT4. Moreover, for this high triaxiality geometry most of voids were penny shaped. For the CT specimen inspected by laminography (fig. 3c), the crack front was not straight but slightly curved (deviation of about 100 µ m). Additionally, a significant thickness reduction was observed near the crack front. The contour map indicates that the maximum V f was located at the mid-thickness and at a small distance ahead of the crack front. Further to the V f distributions, the individual void height (h v ) and diameter ( φ ) were plotted with respect to its position in a cylindrical coordinate: (r , θ, z) where z is the load direction. As it is straightforward for the round bars, these characteristic lengths were plotted according to the normalized radius of the net section r / R. For CT specimen,

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Fig. 4. Void height (h v ) and diameter ( φ ) vs. principal stress through the 3 directions of the coordinates (z being the load direction). From top to bottom, porosity contour maps, void height vs. maximum principal stress σ zz , void diameters vs. transverse stresses: a) NT4 round bar; b) NT045 round bar; c) CT specimen.

r and θ corresponded to the crack propagation and the thickness directions respectively. h v and φ were the plotted through r and through the normalized thickness coordinate (2t / T). The main results are illustrated in the bottom rows of diagrams in figs. 4a,b,c. The symbols (open squares and circles) represent the void characteristic lengths corresponding to the first Y-axis. As mentioned earlier voids were cylindrical showing here a 3D shape with a “unique” height but with an elliptical basis, thus two diameters: φ r , φ θ . For NT4 and NT045 notched round bars (figs. 4a,b), it was observed that the circumferential diameter φ θ was the major axis, that is, greater than φ r . The diagram relative to the CT specimen (fig. 4c, bottom left) indicates the particular case where the ellipse major axis φ r followed the crack propagation direction.

3.3. Finite Element analysis

A porous-visco-plastic constitutive model already implemented in the FE code Zset was used under finite strain formulation (Selles et al. (2017)). The material parameters were optimized thanks to the macroscopic data ( δ c ) in fig. 2 as well as the local distribution of V f . The obtained set of parameters allowed a good agreement between the simulations (lines) and the experimental data (symbols) in fig. 2. Moreover, the porosity contour maps in fig. 4 (top row) were in accordance with those of the measured V f in fig. 3 (bottom row). Following then Laiarinandrasana et al. (2016), the principal stresses ( σ rr , σ θθ , σ zz ) were computed and compared with the void characteristic lengths, according to their specific directions. As shown in fig. 4 diagrams, a fair agreement was obtained between the void characteristic lengths and the corresponding FE stress components. It is to be noted that these stress space distributions were obtained at the onset of the tertiary stage, that is at the end of the secondary creep stage. The discussion on the time singularities of the stress is out of the scope of this work.

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4. Conclusion

This work considers a semi-crystalline polymer (Polyamide 6) subjected to creep loading with various multiaxial stress states. The e ff ects of the stress triaxiality ratio were investigated using notched round bars NT4 and NT045 (notch root radii of 4 mm and 0.45mm respectively) and a small CT specimen. Additionally to the macroscopic creep opening displacement, the spatial distributions of the void volume fraction, the average void height and diameter (measured by 3D imaging) at the onset of the tertiary creep stage were plotted. It was observed that voids were cylindrical with an elliptical basis. The space evolutions of the void height, major and minor diameters were obtained. The interpretation of these data in 3D at the microscopic scale was performed in the light of FE analysis in terms of principal stresses. A good agreement was obtained between the void characteristic lengths and the corresponding principal stresses. Laiarinandrasana, L., Morgeneyer, T.F., Proudhon, H., N’Guyen, F., Maire, E., 2012. E ff ect of Multiaxial Stress State on Morphology and Spatial Distribution of Voids in Deformed Semicrystalline Polymer Assessed by X-ray Tomography. Macromolecules 45, 4658–4668. Selles, N., N’Guyen, F., Morgeneyer, T.F., Proudhon, H., Ludwig, W., Laiarinandrasana, L., 2016. Comparison of voiding mechanisms in semi crystalline polyamide 6 during tensile and creep tests. Polymer Testing 49, 137–146. Selles, N., King, A., Proudhon, H., Saintier, N., Laiarinandrasana, L., 2017. Time dependent voiding mechanisms in polyamide 6 submitted to high stress triaxiality: experimental characterisation and finite element modelling. Mechanics of Time Dependent Materials, 1–21. Besson, J., Foerch, R., 1997. Large Scale Object-Oriented Finite Element Code Design. Computer Methods in Applied Mechanics and Engineering. 142, 165–187. Laiarinandrasana, L., Klinkova, 0., N’Guyen, F., Proudhon, H., Morgeneyer, T.F., Wolfgang, L., 2016. Three dimensional quantification of anisotropic void evolution in deformed semi-crystalline polyamide 6. International Journal of Plasticity 83, 19–36. References

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XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Thermo-mechanical modeling of a high pressure turbine blade of an airplane gas turbine engine P. Brandão a , V. Infante b , A.M. Deus c * a Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Abstract During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 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. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. ECF22 - Loading and Environmental effects on Structural Integrity Adaptation of hydrogen transport models at the polycrystal scale and application to the U-bend test Y. Charles a *, M. Gaspérini a , K. Ardon a , S. Ayadi a , S. Benannoune a , J. Mougenot a a Université Paris 13, Sorbonne Paris Cité, Laboratoire des Sciences des Procédés et des Matériaux, LSPM, CNRS, UPR 3407, 99 avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France Abstract Hydrogen transport and trapping equations are implemented in a FE software, using User Subroutines, and the obtained tool is applied to get the diffusion fields in a metallic sheet submitted to a U-Bend test. Based on a submodelling process, mechanical and diffusion fields have been computed at the polycrystal scale, from which statistical evaluation of the risk of failure of the sample has been estimated. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. Keywords: Hydrogen diffusion, Kinetic Trapping, Finite elements calculations, Abaqus, User Subr uti e ; crystal plastici 1. Introduction The selection of material for applications in hydrogen environment (gaseous, cathodic, or even plasma) needs to account for th interactions between materials and hyd ogen atoms, nd especially th decreases of the fail re resistance (hydrogen embritt ement). Several tests, such as the disk pressure test [1,2] or the U-Bend one [3], in which metallic sheet undergo important plastic straining, are thus used to qualify materials in such context. Their specifications, however, remains mainly based on phenomenological experimental data. To get a better understanding of the link between the in-service reliability of structure and such tests, it is required to conduct numerical computations, accounting for interactions between hydrogen transport, trapping (induced by plastic deformation), and eventually, failure initiation. The pioneering work of Sofronis [4], later completed by ECF22 - Loading and Environmental effects on Structural Integrity Adaptation of hydrogen transport models at the polycrystal scale and application to the U-bend test Y. Charles a *, M. Gaspérini a , K. Ardon a , S. Ayadi a , S. Benannoune a , J. Mougenot a a Université Paris 13, Sorbonne Paris Cité, Laboratoire des Sciences des Procédés et des Matériaux, LSPM, CNRS, UPR 3407, 99 avenue Je n-B ptist Clément, F-93430 Villetan us , Fr nce Abstract Hydrogen transport and trapping equations are implemented in a FE software, using User Subroutines, and the obtained tool is applied to get the diffusion fields in a metallic sheet submitted to a U-Bend test. Based on a submodelling process, m chanical nd diffusion fields have been computed at the polycrystal scale, from which tatistical evaluation of the risk of failure of the sample has been estimated. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. Keywords: Hydrogen diffusion, Kin tic Trapping, Finite lements calculations, A aqus, User Subroutine ; crystal plasticity 1. Introduction The selection of material for applications in hydrogen environment (gaseous, cathodic, or even plasma) needs to account for the interact ons be we n ma erials and hydrogen atoms, and especially the dec eases of the f ilure resistanc (hydrog n embrittl ment). Several tests, such as the disk pressure test [1,2] or the U-B nd one [3], in which metallic sheet undergo i portant plastic straining, are thus used to qualify materials in such context. Their specifications, however, remains mainly based on phenomenological experimental data. To get a better understanding of the link between the in-service reliability of structure and such tests, it is required to conduct numerical computations, accounting for interactions between hydrogen transport, trapping (induced by plastic deformation), and eventually, failure initiation. The pioneering work of Sofronis [4], later completed by © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +33-1-49-40-34-61 ; fax: +33-1-49-40-39-38 . E-mail address: yann.charles@univ-paris13.fr * Corresponding author. Tel.: +33-1-49-40-34-61 ; fax: +33-1-49-40-39-38 . E-mail ad ress: yann.charles@univ-paris13.fr

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. Peer review under r sponsibility of the ECF22 o ganizers.

2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016.

2452-3216  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.169

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Krom [5], in which a generalized hydrogen transport equation has been exhibited, accounting for the trapping by dislocation, led to FE simulations in the framework of small scale plasticity. In these works, trapped and diffusive hydrogen concentrations are assumed to be at equilibrium, following Oriani [6], while kinetic trapping might also be considered [7,8]. Recently, these kind of computations have been adapted to the polycrystal scale [9], from which statistical analysis of failure initiation risk can be extracted. This paper focused on the U-Bend test modeling, at both macroscopic and polycrystalline scale. First, modeling assumptions are presented. The U-bend test setup is then introduced, and few results shown.

Nomenclature C L

Diffusive hydrogen concentration Trapped hydrogen concentration

C T N T N L  T  L

Trap density

Interstitial site density 

Trap sites occupancy, C T =N T  T Interstitial sites occupancy, C L =N L  L

2. Modeling of the material hydrogen interactions In this work,  -iron is considered, for which all of the relevant parameters can be found in the literature. Transport and trapping equations are first presented, and then, the mechanical behaviour, at both macroscopic and crystal scale. In this case, only the 12 slip systems {110}  111  for bcc structures are considered. All of the models are implemented in Abaqus FE software, as explained in previous works [8-10]. 2.1. Transport and trapping model The hydrogen concentration C is partitioned in two populations, namely the diffusive one ( C L ) and the trapped one ( C T ) [5]. Considering that hydrogen diffusion is assisted by mechanical stress field though the hydrostatic pressure [4,11,12], the temporal evolution of C might be written as [4,5]

L T     C C  



D V

C

  

  

L H

(1)

 



C P 

D C

L L

L H

  

t

t

t

RT

with





T  



C

N

T

T

(2)





N

T

T







t

t

t

N T is assumed to depend only on the equivalent plastic strain (for pure iron material, see [4,13]). Two trapping modelling are used: one based on the McNabb and Foster kinetic equation (so called “transient trapping”) [7,8] and the other based on the Oriani’s equilibrium assumption (so called “equilibrium trapping”) [6-8]. Diffusion and kinetic trapping parameters for  -iron are extracted from literature [4,5,14-16]. 2.2. Mechanical behavior Both isotropic mechanical behavior and anisotropic crystal plasticity are considered to describe mechanical behavior. At the macroscopic scale, isotropic elasticity is described with Young modulus E and the Poisson ratio  , while isotropic hardening is described by a Voce-type law   0 1 C p Y sat R e        (3) where 0 , R sat and C are material parameters identified from tensile test.

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At the polycrystal scale, the anisotropic elasticity is defined through C ij elastic constants, while the crystal plasticity is described by the following classical viscous formulation [17,18] 1 0 , with n c c c a h                         with 2 0 , 0 and sech s c h h qh h h             (4) q is a latent hardening coefficient and  is the cumulated shear strain. h 0 ,  0 ,  s are material- parameters, identified so that the overall response of a representative elementary volume matches with the macroscopic mechanical behavior. Last, no interactions between hydrogen and the mechanical behaviors are here accounted for. The used mechanical parameters are taken from [9]. The hydrogen related parameters at the crystal scale are the same than at the macroscopic scale, except for N T . To insure an equivalence of the hydrogen transport process at both scales (see Fig. 8 and 12b in [9]), 0.57 N T is used instead of N T .

36 mm

30 mm

R=2.5 mm R=5 mm

U=-11.33 mm

Fig. 1. U-Bend test principle: (a) three point bending test; (b) tools removal and bold tightening; (c) hydrogen charging.

P H (MPa)

(a) (c) Fig. 2. (a) Equivalent plastic strain and (b) hydrostatic pressure repartition. ¼ of the sample is removed for visualization purpose only. (c) Evolution with time of the average diffusion and trapped concentration in the sample, considering both transient and instantaneous trapping process. The arrow indicates the polycrystal location for the submodelling computations (see below, section 3.2) 3. Application on the U-bend test The U-bend test, which is not a standardized approach [3], is commonly used to characterize metallic sheets sensitivity to corrosion or hydrogen (see e.g. [19,20] for application on automotive steel characterisation). The test setup used for simulation is illustrated on Fig. 1. The considered metal sheet (1  10  80 mm 3 ) is modelled in 3D, using 62318 quadratic tetrahedron elements, with full integration. Tools are assumed to be rigid cylinders. Boundary conditions definition at step (b-c) are described in [10]. 3.1. Macroscopic results In Fig. 2 are plotted the relevant mechanical field for the transport and trapping equation (equations 1 and 2), as well as the evolution with time of the amount of hydrogen in the sample, for both transient and instantaneous trapping. All results presented correspond to the step (c) in Fig. 1, t =0s corresponding to its beginning. Accounting for a kinetic trapping leads to a faster apparent hydrogen diffusion process, due to a more progressive filling of traps, as illustrated by the fields of trap sites occupancy on Fig. 3. It can especially be observed the influence of the plastic strain on the (b)

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diffusion process: the more the plastic strain, the bigger the trap density, and the slower the transport process. 5 s 15 s 20 s 30 s 40 s

T 

(a)

(b)

Fig. 3. Trap sites occupancy, considering (a) a transient or (b) an instantaneous trapping process, for different times. ¼ of the sample is removed for visualization purpose only. 3.2. Submodelling process To perform similar computations at the polycrystal scale, a submodelling scheme is used. A synthetic 0.2 3 mm 3 cubic polycrystal based on a Voronoi tessellation is defined, made of 100 grains, defined by the Neper software [21] and reconstructed in Abaqus CAE based on python scripts. This polycrystal is meshed using 16934 quadratic tetrahedron elements, with full integration. The polycrystal location is indicated by the arrow on Fig. 2. Boundary conditions are imposed on the polycrystal faces, and set using the Abaqus ‘submodelling’ conditions: displacement or diffusive hydrogen boundary conditions applied on each external nodes of this polycrystal are extracted from the macroscopic computations results, to transpose the whole bending process at that scale. Two computations have been performed, namely for kinetic and instantaneous trapping, with the same random crystallographic texture. The resulting the hydrogen fields heterogeneities are presented on Fig. 4.

5 s

15 s

20 s

30 s

40 s

C L C 0

(a)

(b)

T 

(c)

(d)

Fig. 4. Evolution of (a-b) diffusive hydrogen concentration and (c-d) trapped hydrogen coverage fields in the polycrystal. Comparison of transient ((a) and (c)) or instantaneous trapping ((b) and (d)). To exhibit the effect of crystalline plasticity, a simulation with the macroscopic isotropic behaviour has also been made on the same Voronoi tessellation to compare at each Gauss point both maximal principal stresses and hydrogen concentration. FFig. 5 shows the distributions, for the maximum principal stress and for the hydrogen concentrations,

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of the ratio between the values calculated with the crystalline plasticity and those calculated with the isotropic behavior.

(a) (c) Fig. 5. Distribution of the ratios between the values from crystal plasticity computations and the ones from isotropic behavior for (a) the maximal principal stress, (b) the diffusive and (c) trapped hydrogen concentration after various exposure time. Curves with circles correspond to instantaneous trapping. The spreading of these distributions illustrates the influence of crystal anisotropy, impacting directly both the stress values and the trapped hydrogen. The principal stress in the polycrystal might be twice greater than the one computed in the homogeneous sample, and the trapped hydrogen might be 3 times greater, leading to potential hydrogen-related failure earlier than expected without considering microstructural heterogeneities. It can be observed from Fig. 5b that C L ratio in the polycrystal are much more important when considering instantaneous trapping, whatever the exposition time, due to the higher importance of the plastic strain heterogeneities on diffusion. Fig. 5c shows that the C T ratios appear to be almost time independent for instantaneous trapping, consistently with the faster trap filling leading to quasi saturation after t =5s (see Fig. 4d and Fig. 3b). 4. Conclusion The U-bend test has been modelled by finite element at both macroscopic and polycristal scale, thanks to the implementation of coupled hydrogen transport and trapping equation at both scales, and considering either a transient or an instantaneous trapping. The importance of the stress heterogeneities in polycrystals is pointed out by comparing the results obtained at the two scales, on the diffusion process and on the stress repartition. Considering the crystalline nature of metals and transient trapping for various initial boundary values problems are expected to contribute to more realistic approach of hydrogen embrittlement. Such a multiscale analysis might help to define relationships between failure stress and hydrogen concentration, provided experimental data for comparison with simulations. References [1] ISO 11114-4, Transportable gas cylinders – compatibility of cylinder and valve materials with gas contents – part 4: test methods for selecting metallic materials resistant to hydrogen embrittlement., 2005. [2] Y. Charles, M. Gaspérini, J. Disashi, P. Jouinot, Numerical modeling of the Disk Pressure Test up to failure under gaseous hydrogen, J Mater Process Technol. 212 (2012) 1761–1770. doi:http://dx.doi.org/10.1016/j.jmatprotec.2012.03.022. [3] ASTM, Standard Practice for Making and Using U-Bend Stress-Corrosion Test Specimens, 2003. [4] P. Sofronis, R.M. McMeeking, Numerical analysis of hydrogen transport near a blunting crack tip, J Mech Phys Solids. 37 (1989) 317–350. doi:http://dx.doi.org/10.1016/0022-5096(89)90002-1. [5] A.H.M. Krom, R.W.J. Koers, A.D. Bakker, Hydrogen transport near a blunting crack tip, J Mech Phys Solids. 47 (1999) 971–992. doi:http://dx.doi.org/10.1016/S0022-5096(98)00064-7. [6] R.A. Oriani, The diffusion and trapping of hydrogen in steel, Acta Metall. 18 (1970) 147–157. doi:10.1016/0001-6160(70)90078-7. [7] A. McNabb, P.K. Foster, A new analysis of the diffusion of hydrogen in iron and ferritic steels, Trans Metall Soc AIME. 227 (1963) 618– 627. [8] S. Benannoune, Y. Charles, J. Mougenot, M. Gaspérini, Numerical simulation of the transient hydrogen trapping process using an analytical approximation of the McNabb and Foster equation, Int J Hydrog Energy. 43 (2018) 9083–9093. doi:10.1016/j.ijhydene.2018.03.179. [9] Y. Charles, T.H. Nguyen, M. Gaspérini, Comparison of hydrogen transport through pre-deformed synthetic polycrystals and homogeneous samples by finite element analysis, Int J Hydrog Energy. 42 (2017) 20336–20350. doi:10.1016/j.ijhydene.2017.06.016. [10] Y. Charles, T.H. Nguyen, M. Gaspérini, FE simulation of the influence of plastic strain on hydrogen distribution during an U-bend test, Int J (b)