PSI - Issue 8

Volume 8 • 201 8

ISSN 2452-3216

ELSEVIER

AIAS2017 - 46th Conference on Stress Analysis and Mechanical Engineering Design, 6-9 September 2017, Pisa, Italy

Guest Editors: D ario Amodio N icola Bonora Ga b riele Arcidiacono L uigi Bruno Francesco Frendo Giuse pp e Mirone Francesco I acoviello

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www.elsevier.com/locate/procedia AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6-9 September 2017, Pisa, Italy Editorial Dario Amodio a , Nicola Bonora b *, Gabriele Arcidiacono c , Luigi Bruno d , Francesco AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6-9 September 2017, Pisa, I aly Editorial Dario Amodio a , Nicola Bonora b *, Gabriele Arcidiacono c , Luigi Bruno d , Francesco 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. Copyright © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis Frendo e , Giuseppe Mirone f , Fracesco Iacoviello b a Università Politecnica delle Marche, via Brecce Bianche 2, 60131 Ancona, Italy b Università di Cassino e del Lazio Meridionale, via G. Di Biasio 43, 03043 Cassino, Italy c Università “Gugliel mo Mar coni”, Via Plinio 44, 00193 Rome, Italy d Università della Calabria, Via P. Bucci, 87036, Arcavacata di Rende (CS), Italy e Università di Pisa, Largo Lucio Lazzarino, 2, 56122 Pisa, Italy f Università di Catania, ia S. Sofia, 64, 95123 Catania, Italy © 2017 The Authors. Published by Elsevier B.V. Peer-r view under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. The Italian Association for Stress Analysis (AIAS) was founded in 1971 by researchers from academia, research centers and industry. AIAS was intended as a community where to discuss, share and develop scientific knowledge related to all technical aspects of stress analysis. In the years, from an initial focus on experimental techniques, AIAS contributed considerably t the development of oder numerical meth ds and computational techniques for the mechanical engineering d sign. In 2015, AIAS turned in the Italian Scientific Society o Mechanical Engin eri g Desi n. Today, AIAS is an institutional partner that supports the instances from academia in subject area f the mechanical engineering design. Every year, AIAS organizes a technical conference offering the possibility to present research updates, share new ideas and foster collaborations. The AIAS conference has become a fundamental event for all those interested in current developments in mechanical engineering design and stress analysis, where to meet researchers, testing equipment and software developers. The 46 th AIAS Conference edition was held in Pisa, Italy. Over 150 oral pres ntat ns w e given and a selection of these has been collect d in this volume. Thes contributions cover diverse areas of m chanical engineering d sign such as fatigue, racture and damage, numerical simulation of multi-physics problems, and material characterization. This year, in addition to the traditional topical sessions, a Frendo e , Giuseppe Mirone f , Fracesco Iacoviello b a niversità Politecnica delle Marche, via Brecce Bianche 2, 60131 Ancona, It ly b Università di Cassino e el Lazio Meridionale, via G. Di Biasio 43, 03043 Cassino, Italy c Università “Gugliel mo Mar coni”, Vi Plinio 44, 00193 Rome, Italy d Università della Calabria, Via P. Bucci, 87036, Arcavacata di Rende (CS), Italy e Università di Pisa, Largo Lucio Lazzarino, 2, 56122 Pisa, Italy f Università di Catania, Via S. Sofia, 64, 95123 Catania, Italy © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Com ittee of AIAS 2017 International Conference on Stress Analysis. The Italian Association for Stress Analysis (AIAS) was founded in 1971 by researchers from academia, research centers and industry. AIAS was intended as a community where to discuss, share and develop scientific knowledge related to all technical aspects of stress analysis. In the years, fro an initial focus on experimental techniques, AIAS contribut d considerably to the velopment of m dern numerical m thods and computational te hniques for the mechanical engineering design. In 2015, AIAS turne in the Italian Scientific Soci ty of M chanical Engineering Design. Today, AIAS is an institutional partner that supports the instances from academia in subject area of the mechanical engineering design. Every year, AIAS organizes a technical conference offering the possibility to present research updates, share new ideas and foster collaborations. The AIAS conference has become a fundamental event for all those interested in current developments in mechanical engineering design and stress analysis, where to meet researchers, testing equipment and software developers. The 46 th AIAS Conference edition was held in Pisa, Italy. Over 150 oral presentation were given and a selection of these has been collected in this volume. These contributions cov r diverse areas of mechanical engineer ng design such as fatigue, fracture and damage, numerical simulation of multi-physics problems, and material characterization. This year, in addition to the traditional topical sessions, a © 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.: +30-0776-299-3693; fax: +30-0776-299-3390. E-mail address: bonora@unicas.it

2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. * Corresponding author. Tel.: +30-0776-299-3693; fax: +30-0776-299-3390. E mail address: bonora@un cas.it

2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis.

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt

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

2452-3216 Copyright  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis 10.1016/j.prostr.2017.12.001

Dario Amodio et al. / Procedia Structural Integrity 8 (2018) 1–2

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Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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special topical session dedicated to Design for Additive Manufacturing was organized by the AIAS Working Group on Design for Additive and Lean Manufacturing. This volume was made possible thanks to the active participation of all AIAS members, to the work of the AIAS Scientific Committee and conference Organizing Committee, and to the support of the Italian Group of Fracture (IGF) and for this, their outstanding contribution is gratefully acknowledged.

AIAS Editorial Committee, Dario Amodio, President Nicola Bonora, Scientific Coordinator Gabriele Arcidiacono Luigi Bruno Francesco Frendo Giuseppe Mirone Francesco Iacoviello, IGF President

ScienceDirect Available online at www.sciencedirect.com Av ilable o line at ww.sciencedire t.com Scie ceDirect Structural Integrity Procedia 00 (2016) 000 – 000 Procedia Structu al Integrity 8 (2018) 174–183 ScienceDirect Structural Integrity Procedia 00 (2017) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2017) 000–000

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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. Copyright © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibil ty of the Scientific Committee of AIAS 2017 Int r ational Conference on Stress Analysis AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6-9 September 2017, Pisa, Italy Accelerated cyclic plasticity models for FEM analysis of steelmaking components under thermal loads J. Srnec Novak a , L. Moro a *, D. Benasciutti b , F. De Bona a a Politechnic Department of Engineering and Architecture (DPIA), University of Udine, via delle Scienze 208, Udine 33100, Italy b Department of Engineering, University of Ferrara, via Saragat 1, 44122, Ferrara, Italy Abstract Steelmaking components are often subjected to thermo-mechanical loads applied cyclically. In this case the choice of a suitable cyclic plastic model to be used in the numerical simulation is a crucial aspect in design. Combined (kinematic and isotropic) model permits the cyclic material behavior to be captured accurately. On the other hand, such model often requires unfeasible computational time to arrive at complete material stabilization. Simplified or accelerated models have then been proposed to make simulation faster. In this work, the thermo-mechanical analysis of a round mold for continuous casting is addressed as a case study. Due to axi-symmetry, a plane model can be adopted. This permits a finite element (FE) analysis with a combined model to be performed until complete stabilization. A comparison with other models able to speed up the simulation (accelerated models with increased values of saturation speed, Prager and stabilized models) was performed. It was found that only accelerated models give equivalent strain range values that do not significantly differ from the (reference) combined model, independently fro the speed of saturation adopted. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. Keywords: cyclic plasticity models; finite element method; thermo-mechanical analysis AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6-9 September 2017, Pisa, Italy Acc lerated cyclic plasticity models for FEM analysis of steelmaking components under thermal loads J. Srnec Novak a , L. Moro a *, D. Benasciutti b , F. De Bona a a Politechnic Department of Engineering and Architecture (DPIA), University of Udine, via delle Scienze 208, Udine 33100, Italy b Department of Engineering, University of Ferrara, via Saragat 1, 44122, Ferrara, Italy Abstract Steelmaking omponents are often subjected to thermo-mech nical loads applied cyclically. In this case the choice of a suita l yclic plastic mod l to be used in the numerical simulation is a crucial aspect in d sign. Combined (kinematic a d isotropic) model permits the cyclic material behavio t b c ptured ccurately. O the other hand, s ch model often requires unfeasible compu tional ti e to arrive at complete material stabilization. Simplified or accelerated models have t en been proposed to mak simulation faster. In this work, the thermo-mech nical analysis of a round mold for continuous casting is addressed as a case study. Due to axi-symmetry, a pla e mo el can be a opted. This permits finit element (FE) anal sis with a ombin l to b performed until complete tabilizati n. A comp rison with other models abl to speed up the simulation (acc l rated odels with increased values of saturation speed, Prager and stabilized models) was performed. It was found that only accelerated models give equivalent strain range values that do not significantly differ from the (reference) combined model, independently from the speed of saturation adopted. © 2017 The Authors. Published by Elsevier B.V. P er-review under responsibility of th Scientific Committee of AIAS 2017 International Conference on Stress Analysis.

© 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. Keywords: cyclic plasticity models; finite element method; thermo-mechanical analysis

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

* Corresponding author. Tel.: +39 0432 558048 E-mail address: luciano.moro@uniud.it * Corresponding author. Tel.: +39 0432 558048 E-mail address: luciano.moro@uniud.it

2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis.

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt

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

2452-3216 Copyright  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis 10.1016/j.prostr.2017.12.019

J. Srnec Novak et al. / Procedia Structural Integrity 8 (2018) 174–183 Author name / Structural Integrity Procedia 00 (2017) 000–000

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1. Introduction

Frequently steelmaking components undergo thermo-mechanical loads applied cyclically. Typical examples are Nomenclature b speed of stabilization R ∞ saturation value b a accelerated speed of stabilization α ´ back stress deviator tensor C initial hardening modulus γ nonlinear recovery parameter C lin initial hardening modulus (Prager model) Δ ε eq equivalent strain range E Young’s modulus Δ ε pl plastic strain range E s Young’s modulus – stabilized cycle ε pl plastic strain N number of cycles ε pl,acc accumulated plastic strain N stab number of cycles to stabilization σ ´ stress deviator tensor q thermal flux σ 0 initial yield stress q max maximum thermal flux σ 0* actual yield stress R drag stress Δ e relative error discussed by Srnec Novak at al. (2015), Benasciutti (2012), Benasciutti et al. (2015), Benasciutti et al. (2016), Moro, Benasciutti et al. (2017), for applications spanning from molds for continuous casting to rolls for hot strip rolling and to anodes adopted in electric arc furnaces. All these components operate in contact to steel at high temperature (close to the melting point) and therefore they must be water cooled. It follows that very high thermal gradients occur, producing stresses that frequently exceed yielding. It was recently observed that, in the numerical model adopted to investigate on the mechanical behavior of such components, the choice of the material model could significantly affect the results. As an example, considering a mold for continuous casting, only a combined cyclic plasticity model permits the cyclic material behaviour and permanent distortion, to be simulated accurately, as suggested by Srnec Novak at al. (2015) and Moro, Srnec Novak et al. (2017). As pointed out by Manson (1966), in principle the durability assessment of a component under thermal loads can be performed only if the cyclic behavior is simulated until material stabilization occurs. As materials stabilize approximately at half the number of cycles to failure, it follows that a huge number of cycles must be considered and an unfeasible simulation time would be required by the combined model. Accelerated models have thus been proposed in literature. In particular, in presence of creep and thermal fatigue, authors such as Arya et al. (1990), Dufrenoy and Weichert (2003), Amiable et al. (2006) suggest only a limited number of cycles to be simulated; even if this procedure seems not well defined, it has to be considered that the presence of visco-elasticity generally strongly reduces the stabilization time. If creep constitutes the damage criteria, a more rigorous approach was proposed by Kiewel et al. (2000) and Kontermann et al. (2014), where an extrapolation technique is developed to speed up the simulation. An alternative approach, suggested by Chaboche and Cailletaud (1986) makes use of accelerated models, in particular increasing the value of the parameter b that controls the speed of stabilization in the combined model. Recently, such an approach was adopted by Srnec Novak at al. (2015) to deal with a squared mold for continuous casting. It has been shown that the accelerated model gave the most conservative results, as the lowest value of number of cycles to failure was obtained. On the other hand, the geometry of the squared mold required a 3D FE simulation. Even taking into account symmetries, the number of cycles needed to reach stabilization was approximately 60567 cycles for the considered value of thermal flux, which clearly not permitted simulation to be continued up to complete material stabilization. In order to validate accelerated models against results from a fully-stabilized simulation, a simpler axi-symmetric round mold is considered in this work as described by Galdiz et al. (2014). Due to axi-simmetry, a plane model can be used and numerical simulations can be performed quite fast until complete material stabilization, which can thus be taken as a reference in the comparison with accelerated models.

J. Srnec Novak et al. / Procedia Structural Integrity 8 (2018) 174–183 Author name / Structural Integrity Procedia 00 (2017) 000–000

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2. Cyclic plasticity models

Combined material model (nonlinear kinematic + nonlinear isotropic) is able to capture monotonic elasto-plastic and cyclic hardening/softening behavior of a material. The von Mises yield surface is expressed in Chaboche (2008) as:

( 2 3 0 = − − − − = σ R f σ α σ α ) ( ' ' ' : ' )

0

(1)

where σ ´ and α ´ are the deviatoric stress tensor and the back stress tensor, respectively, R is the drag stress and σ 0 is the initial yield stress. Kinematic part is controlled by α (translation of the yield surface), while isotropic part is related to R , which controls the homothetic expansion of the yield surface during cyclic loading. According to Chaboche (2008), the increment of the back stress, d α , is expressed as a function of the increment of plastic strain, d ε pl , and accumulated plastic strain, d ε pl,acc :

α α = ∑

3 , d 2 α i =

d C ε

γ i i α

(2)

d

−

ε

i

i

pl

pl,acc

i

where C is the initial hardening modulus; the recall parameter γ controls decrease rate of the initial hardening modulus as the plastic strain accumulates. Chaboche model is a superposition of several nonlinear kinematic models. The model with one pair ( C 1 , γ 1 ) is known as the Armstrong and Frederick model. Furthermore, considering γ =0 the Prager model (i.e. linear kinematic) is obtained and relation (2) can be expressed as:

(3)

3 d 2 α

ε

C =

lin d

pl

Expansion of the yield surface is controlled by the nonlinear isotropic model: ( ) pl,acc d d ε R b R R = − ∞

(4)

where b defines the speed of stabilization and R ∞ is the saturation value of the yield surface. R ∞ can be either positive or negative, giving rise to cyclic hardening or softening behavior, respectively. Integration of (4) gives a relationship between R and ε pl,acc : ( ) pl, acc 1 ε b R R e − ∞ = − (5) A stabilized condition is obtained when R reaches R ∞ . Hardening/softening kinetics is mainly governed by the speed of stabilization b and the accumulated plastic strain ε pl,acc . If the amount of the accumulated plastic strain is relatively small, a huge number of cycles in needed to obtain R = R ∞ . Since the accumulated plastic strain depends on loading conditions and cannot be changed, the only available parameter that can be modified to accelerate material stabilization is the speed of stabilization b . Models with increased b parameter, known as “accelerated models”, were firstly introduced in Chaboche and Cailletaud (1986). It was proposed to use a speed of stabilization in the range of (50÷150) b .

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3. Thermo-mechanical analysis of the round mold

3.1. Component description

In the continuous casting process, see Fig. 1, molten steel flows from a ladle, through a tundish and thus into the mold, where the liquid steel solidifies against the water-cooled copper walls, to form a solid shell sufficient in strength to contain its liquid core, as explained by Thomas (2001). Downstream of the mold, a further cooling section permits a complete solidification of the steel to be achieved. The mold is then a key element of the overall process; in fact, it substantially affects the shape and therefore the quality of semi-finished metal casting product. In the case of billets or blooms, the mold is basically a water cooled tube generally with square or round section. The latter case will be studied in this work.

Fig. 1. Schematic description of the continuous casting process of steel.

3.2. Finite element model

A thermo-mechanical analysis of a round mold used in the continuous casting process was performed by means of the finite element method. The analyzed mold is 1000 mm long, with 200 mm inner diameter and 16 mm in thickness, similarly to the case presented by Galdiz (2014). Generally, molds are made of copper alloy in order to achieve high thermal conductivity and good mechanical strength. In this study, a CuAg0.1 alloy was assumed, whose characteristic were experimentally obtained by Srnec Novak (2016). Due to axi-symmetry, a 2D finite element model was adopted, thus strongly decreasing the computational speed. The finite element model has 760 elements and 2487 nodes. The mesh was refined in the meniscus area close to the liquid free surface, see Fig. 3a, where the maximum thermal gradients occur. For the thermal analysis, plane elements with 8 nodes were adopted. A thermal flux was imposed at the inner surface, while convection was considered on the outer surface to simulate water cooling. The thermal flux proposed in Galdiz (2014) was increased of around 50%, to reach a maximum temperature close to 300 °C, for which material parameters are available in Srnec Novak (2016). As a consequence, an increase in the amount of plastic strain was obtained. The temperature of the cooling water is 40 °C and the convection coefficient is 48000 W/m 2 K. In thermal analysis, the variation of the thermal flux in Fig. 2 was simulated by a sequence of steady state analyses. A nonlinear solution was carried out to simulate the temperature dependence of thermal properties. 3.3. Thermal analysis and results

J. Srnec Novak et al. / Procedia Structural Integrity 8 (2018) 174–183 Author name / Structural Integrity Procedia 00 (2017) 000–000

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Fig. 2. Schematic description of mold working conditions.

As can be seen in Fig. 3b, the maximum temperatures and thermal gradients occur in the region close to the meniscus. The location of the maximum temperature (298 °C) is labeled with the letter “A”.

Fig. 3. FEM model a), temperature distribution b), equivalent plastic strain c).

3.4. Mechanical analysis and results

The mechanical analysis was done by imposing as the input data the temperature distribution previously calculated in the thermal analysis. Plane elements with 8 nodes were used. Since the component is free to expand, no mechanical constraints were imposed in the numerical model. Temperature dependence of material parameters was taken into consideration. A combined plasticity model, with parameters taken from Srnec Novak (2016), was used. The goal of this work is to cyclically load the component until stabilization by using different material models, which are then compared in terms of equivalent strain range, Δ ε eq . A criterion has to be chosen to establish when material stabilization actually occurs. In this work, it was assumed that material stabilizes when the increment of

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6

maximum von Mises stress was lower than a certain threshold (0.001 MPa in this case). Results obtained with the combined model were compared with those achieved adopting accelerated models with 6 different values of the parameter b a : 10 b , 20 b , 30 b, 100 b , 200 b , 300 b , covering a wider range with respect to that proposed in Chaboche and Cailletaud (1986). Prager and stabilized models were also implemented for comparison. Firstly, the combined material model was considered. As proposed by Chaboche (2008), the relation 2 bN stab Δε pl ≈ 5 was used to estimate the number of cycles N stab needed to reach stabilization, Δε pl being the plastic strain range computed in the first cycles. Considering all three components of plastic strain range ( Δ ε pl,a =0.0004945 axial direction, Δ ε pl, ϴ =0.0006474 hoop direction and Δ ε pl,r =0.001145 radial direction) calculated by FE after 10 cycles and assuming b ≈ 5, it would be necessary to simulate N stab,a =1011, N stab, ϴ =772 and N stab,r =438 cycles, respectively. The previous approximate estimations were also confirmed by simulation. As shown in Fig. 4 and Fig. 7, the material stabilizes within 600 cycles. Fig. 4a shows axial, hoop, radial and von Mises maximum stresses at each cycle, versus the number of cycles computed at the critical point A. In this location, a biaxial state of stress occurs, as the radial stress obviously vanishes (free surface). Three components of strain range and the equivalent strain range, evaluated as proposed by Manson (1966) , versus the number of cycles are presented in Fig. 4b. It can be observed that the hoop strain range is almost constant, whereas the other two components increase until stabilization. This behaviour can be clearly observed also in Fig. 5, where hoop and axial stress-strain evolution is presented. For the sake of clarity, only the first five cycles, the 200 th , the 400 th and the final stabilized cycles are presented. The softening phenomenon is more pronounced at the beginning of the cyclic loading, i.e. first five cycles.

160

0.4

140

0.35

120

Δ ε θ Δ ε a Δ ε r Δ ε eq

100

0.3

σ θ ,max σ a,max σ r,max σ vM,max

80

Δ ε (%)

60 σ (MPa)

0.25

40

0.2

20

0

0.15

b)

a)

0

100

200

300

400

500

600

0

100

200

300

400

500

600

N

N

Fig. 4. Maximum stress versus number of cycles a), strain range versus number of cycles b).

N=1-5 N=200 N=400 N stab =600

N=1-5 N=200 N=400 N stab =600

150

150

100

100

50

50

0

0

σ θ (MPa)

σ a (MPa)

-50

-50

-100

-100

-150

-150

a)

b)

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

ε θ (%)

ε a (%)

Fig. 5. Combined model - stress-strain loops: hoop direction a), axial direction b).

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7

The results obtained with the accelerated models are now described. Stabilization can be reached faster by increasing the original value of parameter b . The increased speed of stabilization is called b a (accelerated). In this study, 6 cases with different b a were studied. In the first case, a value of b a that is 10 times higher than the original one was considered, then b a values respectively 20, 30, 100, 200 and 300 times higher were also used. Only hoop stress strain evolution for the first five cycles and for the stabilized one are presented, see Fig. 6. For low values of b a (10÷30), see Fig. 6a-c, stress-strain evolution is similar to the combined model. On the other hand, when b a is high (100÷300), material is forced to stabilize within few cycles; see Fig. 6d-f.

N=1-5 N stab =212

N=1-5 N stab =81

150

150

100

100

50

50

0

0

σ θ (MPa)

σ θ (MPa)

-50

-50

-100

-100

b a =10 b

b a =20 b

-150

-150

a)

b)

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.25

-0.2

-0.15

-0.1

-0.05

0

ε θ (%)

ε θ (%)

N=1-5 N stab =95

N=1-5 N stab =39

150

150

100

100

50

50

0

0

σ θ (MPa)

σ θ (MPa)

-50

-50

-100

-100

b a =30 b

b a =100 b

-150

-150

c)

d)

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.25

-0.2

-0.15

-0.1

-0.05

0

ε θ (%)

ε θ (%)

N=1-5 N stab =43

N=1-5 N stab =36

150

150

100

100

50

50

0

0

σ θ (MPa)

σ θ (MPa)

-50

-50

-100

-100

b a =200 b

b a =300 b

-150

-150

e)

f)

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.25

-0.2

-0.15

-0.1

-0.05

0

ε θ (%)

ε θ (%)

Fig. 6. Hoop stress-strain evolution for different types of accelerated models.

Fig. 7 shows the maximum von Mises stress evolution up to stabilization for the combined and accelerated models. In order to emphasize the differences among the models occurring in first cycles, the N values of each curve are normalized with respect to the corresponding number of cycles to stabilization, N stab . Despite the different values of N stab , the zoom view shows that, at stabilization, all models reach almost the same value of von Mises stress.

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Fig. 7. Maximum von Mises stress evolution up to stabilization.

The equivalent strain range is calculated for 6 different accelerated models and compared with results obtained considering the combined model. In Fig. 8, the evolution of the equivalent strain range from 1 st to stabilized cycle is presented. Results obtained with the combined model show a well know “ s-shaped ” curve which corresponds to the adopted nonlinear isotropic model. Quite similar “ s-shaped ” curves are also obtained with the accelerated models with an increased speed of stabilization b a =10 b ÷30 b , while this shape is lost for higher values of b a ( b a =100 b ÷300 b ), for which, as already shown, the model reaches stabilization almost immediately. Finally, the Prager and the stabilized models are considered, as they constitute the “limiting” cases corresponding to initial loading and stabilized condition, respectively. Indeed, both approaches are based on kinematic models (linear and nonlinear) and therefore they are able to capture only the monotonic hardening behavior. The Prager model is often proposed in literature because parameter C lin can be estimated by simply using monotonic uniaxial test. The stabilized model, proposed in Chaboche and Cailletaud (1986), supposes that the material is already stabilized at the onset of cyclic loading. Therefore, model parameters E and σ 0 are replaced by E s and σ 0* estimated from stabilized cycles, while kinematic variables ( C, γ ) remains unaffected.

0.45

0.4

0.35

Δ ε eq (%)

Combined Acc 10b Acc 20b Acc 30b Acc 100b Acc 200b Acc 300b

0.3

0.25

10 0

10 1

10 2

N

Fig. 8. Equivalent stain range versus number of cycles up to stabilization.

The hoop stress-strain evolution (at the critical point A) calculated with the Prager and the stabilized models are presented in Fig. 9a and 9b. As expected, both models stabilize in few cycles.

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9

N=1-5

N=1-5

150

150

100

100

50

50

0

0

σ θ (MPa)

σ θ (MPa)

-50

-50

-100

-100

-150

-150

a)

b)

-0.25

-0.2

-0.15

-0.1

-0.05

0

-0.25

-0.2

-0.15

-0.1

-0.05

0

ε θ (%)

ε θ (%)

Fig. 9. Hoop stress-strain evolution: Prager model a), Stabilized model b).

The number of cycles to stabilization and the corresponding equivalent strain range are evaluated and listed in Table 1 for all models. As can be noticed, the dependence of Δ ε eq on the applied speed of stabilization occurs only in some cases and no marked trend can be identified. Finally, a relative error Δ e =( Δ ε eq,a - Δ ε eq,c )/ Δ ε eq,c is calculated where Δ ε eq,a and Δ ε eq,c are the equivalent strain ranges for the considered accelerated and combined model, respectively. The error remains always in the range 1.16-2.63%. Due to the strong simplification adopted, Prager and stabilized models provide instead a higher relative error (-11.59% and -6.55%). This result is in good agreement with the conclusions in Chaboche and Cailletaud (1986), where it was observed that the direct use of the stabilized model leads to heavy mistakes. As the computation time is almost proportional to the number of cycles to stabilization, it is possible to conclude that the accelerated model permits a strong reduction of the computational effort, keeping the same accuracy as the combined model.

Table 1. Number of cycles to stabilization and equivalent strain range estimated at critical point A. Combined model Accelerated models

Prager model

Stabilized model

10 b 212

20 b

30 b

100 b

200 b

300 b

N stab

600

81

95

39

43

36

5

5

Δ ε eq (%) Δ e (%)

0.3948

0.3994

0.4026

0.3994

0.4041

0.4051

0.4019

0.3490 -11.59

0.3689

1.17

1.97

1.16

2.37

2.63

1.8

-6.55

4. Conclusions

The choice of the adopted material model in numerical simulations is an important task, particularly when dealing with steelmaking components under cyclic thermo-mechanical loading. Generally, one of the main goals is to capture realistic material behavior; however, very often, this requires complex and sophisticated models. Moreover, sometimes stabilized condition cannot be achieved even with the most suitable model because unfeasible computational time is required. Some alternative models have been thus proposed in literature. In this work, several models (combined, accelerated, Prager and stabilized models) have been considered and compared in terms of equivalent strain range. Based on the obtained results, it is possible to conclude that the use of too simplified models (Prager and stabilized) neglecting initial or stabilized conditions may be dangerous, as they could provide inaccurate cyclic material behavior. On the other hand, accelerated models give results that are always close to the fully-stabilized combined model, assumed as reference. It seems possible to conclude that when dealing with components with a more complex geometry than the round mold studied in this work, the choice of b a parameter must be carefully set up to get a feasible computational time.

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2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. ∗ Corresponding author E-mail address: g.arcidiacono@unimarconi.it 2210-7843 c 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. ∗ Corresponding author E-mail address: g.arcidiacono@unimarconi.it 2210-7843 c 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. * Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452-3216 Copyright  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis 10.1016/j.prostr.2017.12.017 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. Copyright © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility f the Sc enti c Committee of AIAS 2017 International C nference o Stress Analysis A Kriging modeling approach applied to the railways case G. Arcidiacono a, ∗ , R. Berni b , L. Cantone c , N.D. Nikiforova b , P. Placidoli a a Department of Innovation and Information Engineering (DIIE), Guglielmo Marconi University, Via Plinio 44, 00193 Rome, Italy b Department of Statistics, Computer Science, Applications G. Parenti, University of Florence, Viale Morgagni 59, 50134 Florence, Italy c Department of Engineering for Enterprise ”Mario Lucertini”, University of Rome ”Tor Vergata”, Via del Politecnico 1, 00133, Rome, Italy Abstract This paper deals with Kriging modeling applied for optimizing the braking performances for freight trains. In particular, it focuses on mass distribution optimization to reduce the e ff ects of in-train forces among vehicles, e.g. compression and tensile forces, in train emergency braking. Kriging models are applied with covariance structure based on the Mate´rn function, and by introducing specific input parameters to better outline the payload distribution on the train, by also evaluating the shape of the payload distribu tion. Satisfactory results have been obtained considering compression forces, tensile forces and their sum, and by also evaluating residuals and diagnostic measures. c 2017 The Authors. Published by Elsevier B.V. P - eview under responsibility of the Scientific Committee of AIAS 2017 Internatio al Conference on Stress Analysis. Keywords: experimental design; computer experiments; Kriging; braking system 1. Introduction Among the di ff erent statistical models applied to engineering and technological issues, Kriging modeling is one of the most important since it allows for using simulations through computer experiments and, further, to deal with a specific and suitable covariance structure for data. Moreover, through the Kriging modeling, the experimental region is investigated by considering the reliability of prediction, e.g. the Kriging variance, which is smaller when the predicted point is located nearby the training set of start r data ( X ) and larger as moving away from X . In literature, starting from the seminal contribution of Sacks et al. (1989), the studies on Kriging have been particularly developed since 2000. Regarding to the definition of the covariance structure for the stochastic part of the model, novel issues are suggested by Del Castillo et al. (2015), while Pistone and Vicario (2013) focus a peculiar attention on the strong correlation for spatial data. Zhou et al. (2011) deal with Kriging modeling by also considering qualitative variables. Arcidiacono et al. (2012) have also developed research activities with the support of Lean Six Sigma. However, Kriging modeling approach was more appropriate for this particular application: when considering computer experiments and Kriging AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6–9 September 2017, Pisa, Italy A Kriging odeling approach applied to the railways case G. Arcidiacono a, ∗ , R. Berni b , L. Cantone c , N.D. Nikiforova b , P. Placidoli a a Department of Innovation and Information Engineering (DIIE), Guglielmo Marconi University, Via Plinio 44, 00193 Rome, Italy b Department of Statistics, Computer Science, Applications G. Parenti, University of Florence, Viale Morgagni 59, 50134 Florence, Italy c Department of Engineering for Enterprise ”Mario Lucertini”, University of Rome ”Tor Vergata”, Via del Politecnico 1, 00133, Rome, Italy Abstract This paper deals with Kriging modeling applied for optimizing the braking performances for freight trains. In particular, it focuses on mass distribution optimization to reduce the e ff ects of in-train forces among vehicles, e.g. compression and tensile forces, in train emergency braking. Kriging models are applied with covariance structure based on the Mate´rn function, and by introducing specific input parameters to better outline the payload distribution on the train, by also evaluating the shape of the payload distribu tion. Satisfactory results have been obtained considering compression forces, tensile forces and their sum, and by also evaluating residuals and diagnostic measures. c 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of AIAS 2017 International Conference on Stress Analysis. Keywords: experimental design; computer experiments; Kriging; braking syste 1. Introduction Among the di ff erent statistical models applied to engineering and technological issues, Kriging modeling is one of the most important since it allows for using simulations through computer experiments and, further, to deal with a specific and suitable covariance structure for data. Moreover, through the Kriging modeling, the experimental region is investigated by considering the reliability of prediction, e.g. the Kriging variance, which is smaller when the predicted point is located nearby the training set of starter data ( X ) and larger as moving away from X . In literature, starting from the seminal contribution of Sacks et al. (1989), the studies on Kriging have been particularly developed since 2000. Regarding to the definition of the covariance structure for the stochastic part of the model, novel issues are suggested by Del Castillo et al. (2015), while Pistone and Vicario (2013) focus a peculiar attention on the strong correlation for spatial data. Zhou et al. (2011) deal with Kriging modeling by also considering qualitative variables. Arcidiacono et al. (2012) have also developed research activities with the support of Lean Six Sigma. However, Kriging modeling approach was more appropriate for this particular application: when considering computer experiments and Kriging © 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. AIAS 2017 International Conference on Stress Analysis, AIAS 2017, 6–9 September 2017, Pisa, Italy