PSI- Issue 9

Volume 9 • 201 8

ISSN 2452-3216

ELSEVIER

IGF Workshop “ Fracture and Structural Integrity ”

Guest Editors: Francesco I acoviello L uca Susmel

D onato Firrao Giuse pp e Ferro

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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 Gruppo Italiano Frattura (IGF) ExCo. IGF Workshop “Fracture and Structural Integrity” Editorial Francesco Iacoviello a *, Luca Susmel b , Donato Firrao c , Giuseppe Ferro c a Università di Cassino e del Lazio Meridionale, via G. Di Biasio 43, 03043 Cassino (FR) Italy b University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK c Politecnico di Torino, Corso Duca degli A ruzzi 24, 10129, Torino, Italy © 2018 Th Authors. Published by Els vier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: Editorial; Short IGF history. Since its foundation in 1982, Gruppo Italiano Frattura (the Italian Group of Fracture, IGF) organized dozens of national and international events, including Workshops, Conferences and Summer Schools. During these 40ish years, seven presidents (i.e., G. Caglioti, G. Angelino, D. Firrao, S. Reale, A. Carpinteri, G. Ferro and F. Iacoviello) worked together with almost one hundred Executive Com ittee Members not only to spread and promote the results from research work focused on fracture phenomena, but also to support different activities aiming to develop standards for testing of material and structures. As we have already written in the Editorial of the 3 rd Issue of Procedia Structural Integrity (that was published last year), keywords like “Fracture” and “Structural Integrity” return ot only a wide range of materials being investigated (such as, for inst nce, concrete, stainles steel, rocks, and p lymers) but also a large number of di ferent numerical and experimental approach s being used. This results in the fact that it is difficult for us to define th pr file of the “typical” IGF member: a metallurgist or a materials scientist? a civil engineer or a mechanical engineer? a “PC addicted” person or a “lab rat” scientist? All these different profiles of researchers happily live together under the IGF umbrella, with the IGF making a big effort over the last 40ish years to offer them the best support we possibly could give. In 2015, the 23 rd edition of the IGF Conference was the first one organized as an international event. It was held in Favignana, a wonderful Sicilian island, with the Proceedings from this event being published in “Procedia Engineering”. Last ear, the IGF organized its second inst tutional conf rence as an international event in Urbino, Italy, and published for the first time the associated Proceedings in “Procedia Structural Integrity”. “Procedia Structural Integrity” is a recently © 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.: +39.07762993681; fax: +39.07762993781. E-mail address: iacoviello@unicas.it

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 Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2018.06.001 * 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 Gruppo Italiano Frattura (IGF) ExCo.

Francesco Iacoviello et al. / Procedia Structural Integrity 9 (2018) 1–2 Author name / Structural Integrity Procedia 00 (2018) 000–000

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launched collection of technical articles (covering those research areas related to Fracture, Fatigue and Structural Integrity) that are published under the auspices of the European Structural Integrity Society (ESIS) and its Technical Committees as well as under the auspices of the National Groups that are affiliated with ESIS itself. The present issue of “Procedia Structural Integrity groups” together those technical articles that were presented at the IGF Workshop entitled: “Fracture and Structural Integrity” that was held in Cassino, Italy, from the 4 th till the 6 th of June 2018, with this workshop being the third one run as an international event. In this issue, the reader will find an exhaustive overview of the research work that is being carried out in Italy on fracture and structural integrity related issues as well as many contributions coming from different countries (such as, for instance, Greece, Morocco, and Ukraine). According to the IGF tradition, the majority of the presentations given in Cassino are available on the IGF YouTube channel at: https://www.youtube.com/c/IGFTube. We hope the readers of these Proceedings will enjoy both the technical articles and the recorded talks. To conclude, a big “thank you” goes to all the members of the IGF Ex-Co for supporting not only the publication of this Proceedings, but also all the different activities done by the IGF on a daily basis: the fantastic results that the IGF has obtained in recent years have been possible also, and above all, thanks to the hard work done by everyone…

actually, probably, the best Ex-Co that the IGF has ever had, i.e.: Vittorio Di Cocco (Università di Cassino e del Lazio Meridionale) Giuseppe Ferro (Politecnico di Torino, Vice President) Angelo Finelli (Treasurer) Donato Firrao (Politecnico di Torino, Vice President) Francesco Iacoviello (Università di Cassino e del Lazio Meridionale, President)

Carmine Maletta (Università della Calabria) Giacomo Risitano (Università di Messina) Andrea Spagnoli (Università di Parma) Luca Susmel (University of Sheffield, Secretary)

ScienceDirect Available online at www.sciencedirect.com Av ilable o line at ww.sciencedirect.com Sci ceDirect Structural Integrity Procedia 00 (2016) 000 – 000 Procedia Structural Integrity 9 (2018) 92–10 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2018) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2018) 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. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. IGF Workshop “Fracture and Structural Integrity” A coupled ALE-Cohesive formulation for interfacial debonding propagation in sandwich structures Marco Francesco Funari a , Fabrizio Greco a , Paolo Lonetti a * a Department of Civil Engineering, University of Calabria, Via P. Bucci, Cubo39B, 87030, Rende, Cosenza, Italy. Abstract A numerical model to predict debonding phenomena in sandwich structures based on soft core and high performance external skins is proposed. In particular, the proposed model incorporates shear deformable beams to simulate the face sheet and a 2D elastic domain to model the core of the structure. Debonding processes is simulated by means a moving interface elements, introduced between the core and the face. The numerical interface strategy is consistent to a moving mesh technique based on Arbitrary Lagrangian–Eulerian (ALE), in which weak based moving connections are implemented by using the FE formulation. The moving mesh technique combined with a multilayer formulation ensures a reduction of the computational costs required to predict crack onset and subsequent evolution of the debonding phenomena. The accuracy of the proposed approach is verified by means comparisons with experimental and numerical results. Moreover, simulations in dynamic framework are developed to identify the influence of inertial effects pro uced by different typologies of core on debonding phenomena. The investigation revels the impact of mechanical properties of core on the dynamic debonding mechanisms. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: ALE; sandwich panels; FEM; debonding. IGF Workshop “Fracture and Structural Integrity” A coupled ALE-Cohesive formulation for interfacial debonding propagation in sandwich structures Marco Francesco Funari a , Fabrizio Greco a , Paolo Lonetti a * a Department of Civil Engineering, University of Calabria, Via P. Bucci, Cubo39B, 87030, Rende, Cosenza, Italy. Abstract A numerical model to predict deb nding phenomena in s ndwich structures ased on oft core and high performance external skins is proposed. In particular, the proposed model i corporates h ar deformable beams to simulate the face she t and a 2D elastic domain to model the cor of the struct re. Debo ding processes is simulated by means a moving interface lem nts, introduced between the cor d the face. T e numeric l interface strategy s consistent to a moving mesh technique b sed on Arbitrary Lagrangia –Eulerian (ALE), in which weak based movi g connections are implem nted by using the FE formulation. The moving mesh technique combined with a multilay r formulation ensures a r du tion of the computational costs required to predict cr ck onset and subsequent evolu ion of the debonding phenomena. The accuracy of the propos d approach is verified by means comparisons with experimental and numerical results. More ver, simulations in dynamic framework are devel d o identify he influ nce of inertial eff ct pr duced by different typ logies of ore on debonding phenome a. The inv stigation revels the impact of mechanical properties of core on the dynamic debonding mechanisms. © 2018 The Authors. Publ shed by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: ALE; sandwich panels; FEM; debonding.

© 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.

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 Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2018.06.016 * Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt 2452 3216 © 2018 Th Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. * Correspon ing author. Tel.: +39-0984-496917; fax: +39-0984-496917. E-mail address: lonetti@unical.it * Corresponding author. Tel.: +39-0984-496917; fax: +39-0984-496917. E-mail address: lonetti@unical.it

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Nomenclature a

initial crack length

length of the internal discontinuities

b

B

width of the specimen crack growth function mode I energy release rate mode II energy release rate

k f g I G

II G IC G IIC G

mode I critical strain energy release rate mode II critical strain energy release rate

work of separation for unit area

C G

L

length of the specimen thickness of the core internal discontinuity

c h

2 

0 

characteristic parameter of the work of separation

L 

process zone on the left direction of the internal discontinuity

R 

process zone on the right direction of the internal discontinuity

1. Introduction Composites materials are widely used in several structural applications ranging from aerospace, marine (Calsson and Kaddomateas (2011)) and civil engineering (Spadea et al. (2017), Ascione et al. (2017)). In particular, sandwich structures typically consist of two thin face sheets made from stiff and strong relatively dense material such as metal or fiber composite bonded to a thick core made from low density material, namely core (Calsson and Kaddomateas (2011)). These systems are able to ensure a good resistance and a very low weight, offering a great variety of lightweight structural systems. However, these structures can be subject to macroscopic and microscopic damage phenomena. From physical and mathematical points of view there are two issues: the propagation of the fracture in the core of the structure (Morada et al. (2017)) and the delamination between the face sheet and the core (Odessa et al. (2018)). These problems have been studied by means different numerical approaches. In order to predict the angle of crack propagation in the solids, mesh-based methods like the finite element method (FEM) and the boundary element method (BEM) have shown difficulties to predict crack propagation due to extensive meshing and re-meshing procedures (Nishioka (1997)). Alternatively, Extended Finite Element Method (XFEM) are proposed to eliminate some of such difficulties, but complexities in the definition enrichment functions still exist. Others methodologies based on Meshfree Methods (MMs) have been formulated in the last decades providing alternatives to study such problems (Daxini and Prajapati (2014)). Another important failure mechanism in sandwich structures is the delamination at the skin/core interfaces. In terms of modeling, the Cohesive Zone Method (CZM) introduces interface elements at skin/core debonding lines, with effective Traction Separation Law (TSL) constitutive relationships. The CZM was firstly developed, alternatively to Fracture Mechanics, by introducing the possibility to mitigate stress singularity and to simulate large scale decohesion phenomena. In this framework, several models are proposed in literature, which are mainly classified as either non-potential or potential-based models (Rabinovitch (2008)). However, CZMs present computational limits, which are essentially related to the use of a dense mesh. To avoid such problems, a formulation based on CZM and moving mesh approach has been proposed (Funari et al. (2016), Funari and Lonetti (2017)), in which the multiple delaminations in layered structures, discretized by means shear deformable beams, have been investigated in both static and dynamic frameworks. In particular, this numerical approach has been

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extended in others works to study the produced effect by z-pins during the process of delamination (Funari et al. (2016), Funari et al. (2018)). The main goal of this paper is to generalize the numerical implementation reported in Funari et al. (2016), making able to describe delamination phenomena in the sandwich structures. Despite existing methods, the proposed strategy is concerned to introduce a low number of computational points in the whole geometry, reducing the complexity and the computational cost. This is achieved by using a moving mesh strategy based on Arbitrary-Lagrange Eulerian (ALE) formulation, which is able to reproduce mesh movements according to the process zone motion, ensuring accuracy in the definition of the fracture variables. The outline of the paper is as follows. Section 2 presents the theoretical and numerical aspect of the implementation. In Section 3, numerical comparisons with existing formulations are proposed and a parametric study is carried out to identify the influence of inertial effects produced by different typologies of core during debonding process. 2. Theoretical Formulation and Numerical implementation The proposed model is formulated in the framework of the sandwich structures, which consist of an internal core, modelled by using a 2D plane stress formulation whereas the skins follow a one dimensional modelling based on Timoshenko beam kinematics. According to Funari and Lonetti (2017), in order to simulate initiation and growth of interfacial defects, at the interface between skin and core a cohesive interface is introduced. This is achieved by the use of interface elements based on a moving mesh technique, which ensures an accurate description of the fracture variables and the application of cohesive interlaminar stresses in the process zone. A synoptic representation of the model is reported in Fig. 1(a).

Fig. 1(a) Synoptic representation of the proposed model; (b) Moving and referential coordinate systems in ALE description.

According to Funari and Lonetti (2017), in order to simulate the crack growth, a preliminary task to be achieved is to identify the position in which the onset of interfacial mechanisms is produced and subsequently to simulate the evolution of the cracked length. Such two steps are explained separately in the following subsections.

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2.1. Crack onset position At this stage, it is only required to identify the positions in which the onset conditions are satisfied. To this end, the cohesive interfaces are introduced between each skin/core interfaces, in which the crack initiation could be potentially activated. An accurate description of the local stress distribution is not required; the model is discretized by means a relatively coarse mesh. It is worth nothing that until the crack onset condition is not satisfied, the ALE equations are inactive and the computation mesh points are expressed in the Referential Frame (RF) described by 1 2    , which at this stage coincides with the Moving Frame (MF), described in the following subsection, i.e. 1 2 X X  .The crack onset definition is described by means of a mixed crack growth, which is a function of the fracture variables, coinciding with the ratio between ERR mode components and corresponding critical values, as follows:

r

r

( ) 1 k

( ) 1 k

æ ç ç ç ç ç è

2 ö æ ÷ ç ÷ ç + ÷ ç ÷ ç ÷ ç ø è ÷

ö ÷ ÷ ÷ ÷ ÷ ÷ ø

G X

II G X

2

( ) 1 k

I

k g X

1

(1)

=

-

f

G

G

IC

IIC

where k represents the generic k-th interface in which debonding phenomena may occur, r is the constant utilized to describe fracture in different material and ( ) , IC IIC G G are the total area under the traction separation law, whereas ( ) , I II G G are the individual energy release rates, which could be discretized by means a bilinear nonlinear relationship. It should be noted how the proposed model is quite general to include other existing cohesive formulations based on a different TSL or stress based initiation criteria, just by modifying the analytical expressions defined in Eq.(1) The positions, in which the cracks onset occur, are evaluated by enforcing the following condition:   1 1 0 0 1 k k k k ,i ,i f d g X with X L,i ,N     (2) with the index i represents the number of the i- th debonding mechanism potentially activated at the k- th interface and k d N is the number of material discontinuities activated at the k- th interface. 2.2. Description of debonding process in the moving frame It should be noted that at this step, the model presents a mesh enrichment on the interface around the defined positions by those values 1 k X , which ensure accuracy in the prediction of fracture variables in proximity of the crack onset positions. Starting from the onset coordinate 1 k X , a small geometric discontinuity with length equal to 2  is introduced in the numerical model, producing two potentially independent debonding mechanisms that could evolve along left and right directions (Fig.1(b)). ALE strategy has been implemented in the interface region to accurate describe the evolution of debonding phenomena (Bruno et al. (2009), Funari et. al (2016)). In particular, each interface is modified by the ALE equations, making able to reproduce the moving traction forces acting at the skin/core interfaces. From the mathematical point of view, the relationship between RF and MF is guaranteed by the introduction of a mapping operator  (Fig.1(b)), which relies a particle in a RF to the one in MF, as follows:   X ,t with : RF MF        (3) In particular, the prescribed motion is expressed in terms of the following Laplace-based equations developed for Static (S) or Dynamic (D) frameworks:

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  ,t

  ,t

2

3

j  

j  





X 

(4)

0

0

j

j

X

( S )

( D )













1

1

,

,





2

2

t  



1 

1 

where j , with j =L, R, represents the index referred to the Left (L) or Right (R) process zones, whereas 1 to the mesh displacement and it is evaluated by means the follow equation (Lonetti (2010)):   1 1 1 j j j X X t     The prescribed mesh motion introduces a rigid displacement of the process zone, which is identified on the basis of internal lengths for the left and right crack directions, namely L  or R  (Fig. 1(b)). From the geometrical point of view, the process zone is assumed to be moved rigidly by using of the ALE strategy (Funari et al. (2016)). Such task is performed by means a simple procedure, which consists, at first, to predict the values of the fracture function at their extremities and, subsequently by enforcing that during the crack growth a null value of the fracture is achieved. Therefore, by using a linear approximation function along the debonding region, the current nominal crack tip displacement can be expressed by means the following relationships:       1 1 1 1 1 0 0 0 L ,R k f L ,R L ,R k L ,R k f f L ,R L ,R k k L ,R f f g X X g , X g g X g X           (6) Governing equations are formulated by means a numerical formulation based on the FE methods. The proposed model takes the form of a set of nonlinear differential equations, whose solution is obtained by using a customized FE subroutine in the framework of COMSOL Multiphysics software, by means of scripting capabilities of MATLAB® language (COMSOL (2014)). The proposed procedure is quite general and can be solved in both static on dynamic frameworks, taking into account the time dependent effects produced by the inertial characteristics of the structure and the boundary motion involved by debonding phenomena. Since the governing equations are essentially nonlinear, an incremental-iterative procedure has been adopted to evaluate the current solution. 3. Results In this section, the proposed model is verified by means of several comparisons with numerical and experimental data. The first step in the validation scheme is developed with the purpose to analyze the consistency of the proposed formulation with respect to classical DCB (Fig. 2(a)) and MMB (Fig.2(b)) loading schemes. In particular, according to standard test methods, the static behavior of interfacial crack propagation at the upper interface between face-sheet and core is investigated. The main aim of the comparison with the numerical (Odessa et al. (2017)) and experimental (Carlsson and Kardomateas (2011)) data is to validate the proposed model and to examine its ability to describe the debonding failure mechanism in sandwich panels. Subsequently, the dynamic behavior will be studied to identify the influence of inertial effects, produced by different level of the loading rate and by different core typologies. 3.1. DCB test At first, the analyses are developed with reference to loading schemes based on classical DBC test. The loading, the boundary conditions and the geometry are illustrated in Fig. 2(a). whereas, according to data recovered in (Odessa et al. (2017)), mechanical properties assumed for the skins, core and interfaces, are summarized in Tab.1. In Fig. 3(a) the relationship between resistance, applied displacement and nominal crack tip position, for two different core thickness configurations, i.e. h c =15-20 mm, are reported. The results obtained by the proposed model are in agreement with the experimental (Prasad and Carlosson (1994)) and numerical (Odessa et. Al (2017)) results. It is that worth noting that the results show how an increment in the core thickness does not produce significant variations in the loading curve. j X  correspond (5)

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Fig. 2(a) DCB scheme; (b) MMB scheme.

Table 1. DCB test: mechanical and interface properties.

11 s E [MPa]

12 s G [MPa]

s  [Kg/mc]

s 

Face – sheet aluminum

70 10 3

26 10 3

0.33

2700

1 c E [MPa]

12 c G [MPa]

c  [Kg/mc]

s 

Core – PMI AIRES R 90.400

420

220

0.25

400

0  [mm]

c G [N mm -1 ]

- -

- -

Interface properties

0.550

0.12

3.2. MMB test In this subsection the analyses are referred to loading scheme based on classical MMB test, as shown in Fig. 2(b). The values of mechanical and interface properties assumed for the structure are reported in Tab. 2. In Fig. 3(b) the calibration procedure of the cohesive model is performed varying the value of the mixed mode ratio (changing c length). The proposed model shown a good agreement with the experimental data (Carlosson and Kardomateas (2011), Quispitupa et al. (2009)). Previous analyses, developed essentially in static, are extended in a dynamic framework. The main aims of the results are to investigate the influence of the loading rate and the inertial effects produced by different typologies of core. The loading history is assumed to be governed by an applied velocity with ramp curve with a constant speed (v 0 ) at the time t 0 , which is assumed to be proportional to the first period of vibration (T 1 ) of the structure (t 0 =0.5T 1 ). At first, in order to verify the influence of the loading rate, parametric results in terms of v 0 are proposed. In particular, the following value of v 0 are considered:  v 0 =1ms -1 ;  v 0 =5ms -1 ;  v 0 =10ms -1 .

Table 2. MMB test: mechanical and interface properties.

11 s E [MPa]

12 s G [MPa]

s  [Kg/mc]

s 

Face – sheet glass/polyester

16.4 10 3

2.7 10 3

0.17

1500

1 c E [MPa]

12 c G [MPa]

c  [Kg/mc]

s 

Core – DIVINYCELL H100

135

35

0.32

100

0  [mm]

c G [N mm -1 ]

- -

- -

Interface properties

0.800

0.10

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Fig. 3(a) DCB test: comparisons in terms of loading curve with experimental (Prasad and Carlosson (1994)) and numerical data (Odessa et al. (2017)); (b) MMB test: comparisons in terms of loading curve with experimental data (Carlosson and Kardomateas (2011)).

Table 3. Mechanical properties DIVINYCELL H.

11 s E [MPa]

12 s G [MPa]

s  [Kg/mc]

DIVINYCELL H35 DIVINYCELL H100 DIVINYCELL H250

40

12 35 97

38

135 400

100 250

In Fig. 4(a), results in terms of resistance curve are reported. At low value of v 0 , static and dynamic solutions are overlapped. Contrarily, when the value of v 0 increases, the resistance curve denotes an increment of the peak load with an oscillating behavior. In Fig. 4(b), results are investigated also in terms of measured nominal crack tip speed. From these analyses, it transpires that the crack speeds are much larger in the initiation phase. Subsequently, during the process of delamination, the crack speed tends to decrease. Finally, the influence of the mechanical properties of the core is investigated. The data concerning the core typology are reported in Tab. 3. The loading rate is described by the same ramp curve used to the results presented above, in which a value of v 0 equal to 10 [ms -1 ] is adopted. In Fig. 5(a), the resistance curves are not influenced in terms of peak load, whereas more marked differences in terms of initial stiffness are observed. In particular, the specimen characterized by the use of a heavier core present smaller increment in terms stiffness and peak load. Instead, the use of a lighter core can guarantee important capacity in terms of deformability during the crack propagation. Finally, in Fig. 5(b), an investigation in terms of crack speed is presented. The results show that an increment in the core weight does not produce relevant amplifications of the nominal crack speed. 4. Conclusions The proposed model is developed with the purpose to study the behavior of sandwich structures affected by debonding phenomena. The numerical model is inspired by the previous works of the authors, performed in the framework of the layered structures and here generalized to sandwich structures.

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Fig. 4(a) MMB test: influence of the loading rate in terms of loading-displacement curve; (b) MMB scheme: influence of the loading rate in terms of nominal crack tip speed.

Fig. 5(a) MMB test: influence of the core typology in terms of loading-displacement curve; (b) MMB test: influence of the core typology in terms of nominal crack tip speed.

In this work, the numerical model is based on a 2D plane stress formulation to simulate the internal core, whereas the face-sheets follow a one dimensional model based on Timoshenko beam kinematics. In order to describe the delamination process, the proposed approach combines ALE formulation with a CZM. Compared to existing formulations available i literature, this model presents lower computational complexities in the governing equations. In particular, the combination between CZM and ALE formulations, gives the possibility to introduce nonlinear interface elements in a small region containing the crack tip front, whereas in the remaining one, linear constrain equations are introduced to simulate perfect adhesion. Comparisons with experimental and numerical results are proposed to verify the consistency of the proposed modeling.

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References

Ascione, F., Lamberti, M., Razaqpur, A.G., Spadea, S., 2017.Strength and stiffness of adhesively bonded GFRP beam-column moment resisting connections. Composite Structures 160, 1248-1287. Bruno, D., Greco, F., Lonetti, P. 2009. Dynamic mode I and mode II crack propagation in fiber reinforced composites. Mechanics of Advanced Materials and Structures, 16 (6), 442-445 Carlsson, L.A., Kardomateas, G.A., 2011. Stuctural and Failure Mechanics of Sandwich Composites. Solid Mechanics and its Applications, Springer. COMSOL Multiphysics reference guide, 2014. Daxini, S.D, Prajapati, J.M., 2014. A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications. The Scientific World Journal, (http://dx.doi.org/10.1155/2014/247172). Funari, M.F., Greco, F., Lonetti, P., 2016. A moving interface finite element formulation for layered structures. Composites Part B: Engineering 96, 325-327. Funari, M.F., Greco, F., Lonetti, P., 2017. A cohesive finite element model based ALE formulation for z-pins reinforced multilayered composite beams. Procedia Structural Integrity 2, 452-459. Funari, M.F., Greco, F., Lonetti, P., 2018. An interface approach based on moving mesh and cohesive modeling in Z-pinned composite laminates. Composites Part B: Engineering 135, 207-217. Funari, M.F., Greco, F., Lonetti, P., 2017. Dynamic debonding in layered structures: A coupled ALE-cohesive approach. Fracture and Structural Integrity 41, 524-535. Funari, M.F., Greco, F., Lonetti, P., 2017. A coupled ALE-Cohesive formulation for layered structural systems. Procedia Structural Integrity 3, 362-369. Funari, M.F., Lonetti, P., 2017. Initiation and evolution of debonding phenomena in layered structures. Theoretical and Applied Fracture Mechanics 92, 133-145. Höwer, D., Lerch, B.A., Bednarcyk, B.A., Pineda, E.J., Reese, S., Simon, J.-W, 2018. Cohesive zone modeling for mode I facesheet to core delamination of sandwich panels accounting for fiber bridging. Composite Structures 183, 568-581. Lonetti, P., 2010. Dynamic propagation phenomena of multiple delaminations in composite structures, Computational Materials Science 48 ,563 575. Morada, G., Vadean, A., Boukhili, R., 2017. Failure mechanisms of a sandwich beam with an ATH/epoxy core under static and dynamic three point bending. Composite Structure 176, 281-293. Muthu, N., Maiti, S.K., Falzon, B.G., Wenyi Yan, 2016 . Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T stress and kinking angle using a variant of EFG Method. Engineering Analysis with Boundary Elements 72,11-26. Nishioka, T., 1997. Computational dynamic fracture mechanics. International Journal of Fracture 86, 127-159. Odessa, I., Frostig, Y., Rabinovitch, O., 2017. Modeling of interfacial debonding propagation in sandwich panels. International Journal of Solids and Structures. (in press). Prasad, S., Carlsson L.A., 1994. Debonding and Crack Kinking in FoamCore Sandwich Beams -II. Experimental Investigation. Engineering racture Mechanics 47, 825-841. Quispitupa, A., Berggreen, C., Carlsson, L.A., 2009. On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization. Engineering Fracture Mechanics 76, 594-613. Rabinovitch, O., 2008. Cohesive interface modeling of debonding failure in FRP strengthened beams. Journal of Engineering Mechanics-Asce 134, 578-588. Spadea, S., Orr, J., Ivanova, K., 2017. Bend-strength of novel filament wound shear reinforcement. Composite Structures 176, 244-253.

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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. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. IGF Workshop “Fracture and Structural Integrity” Analysis of Elastic Wave Parameters in the Elements of the "Striker – Gasket – Reinforced Concrete Beam" System K. Sobianin a , I. Shardakov a *, A. Shestakov a , I. Glot a a Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm, N614013, Russian Federation Abstract Application of automated monitoring systems ensures the deformation safety of structures. Such deformation control systems are supplemented with the tools, which allow evaluation of the criticality of the structure state on the basis of vibration measurements. These are acoustic emission registration systems and shock wave diagnostics systems. The results obtained in this study are directly related to the shock-wave vibrodiagnostics of reinforced concrete structures. Particular attention is given to vibrodiagnostics in a "spare mode", which causes no inelastic deformation to appear in the elements of the examined structure. The objective of this work is to find local impact parameters for excitation of mechanical oscillations of a desired spectrum in the structure and to excite an elastic wave with required wavefront characteristics. One of the main impact parameters determining these characteristics is the pulse duration. Based on the results of the numerical experiment performed on the basis of a mathematical model of dynamic elastic interaction of the elements of the "striker – gasket – reinforced concrete beam" system, the duration of the impulse action on the beam was determined depending on various factors. Thus, within a specified range of these factors the greatest interval of impulse duration is obtained under variation of the striker velocity within the interval from 0.1 ms to 3 ms. Assuming that the impulse duration defines one of the main wave frequencies of vibrations one may conclude that frequencies will vary in the range from 300Hz to 10000Hz. © 2018 The Authors. Published by Elsevi r B.V. Peer-review und r responsibil ty of the Gruppo Italia o Frattura (IGF) ExCo. IGF Workshop “Fracture nd Structural I tegrity” Analysis of Elastic Wave Parameters in the Elements of the "Striker – Gasket – Reinforced Concrete Beam" System K. Sobianin a , I. Shardakov a *, A. Shestakov a , I. Glot a a Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm, N614013, Russian Federation Abstract Application of automated monitoring syst ms ensur s the d formation safety of structures. Such deformati control systems are supplem ted with the tools, which allow evalu tion of the criti lity of th structure state on the basis of vibration measurements. These ar acoustic emission registration systems and shock wave diagnostics systems. results obtained in this study are directly related to the shock-wave vibrodiagnostics f reinf rced concret structures. Particula attention is giv n to vibrodi gnostics in a "spare mo e", which causes no inelastic deformation to appear in the ele ent of the examined structure. The objective of this work is to find local impact param ters for excitation of mechanical oscillations of a desired spectru in the structure and to excite a elastic wave with r quired wav front char cteri tics. One of the main impact pa ameters determining these characteristics is the pulse duration. Based on the results of the numerical experiment performed on the basis of a mathe atical model of dynamic elastic interaction of the elements of the "striker – gask t – reinforced c ncrete beam" system, th duration of the impuls action on the beam was determined depending on various factors. Thus, within a specified range of these factors the greatest interval of impulse duration is obtained under variation of the striker velocity within the interval from 0.1 ms to 3 ms. Assuming that the impulse duration defines one of the main wave frequencies of vibrations one may conclude that frequencies will vary in the range from 300Hz to 10000Hz.

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 Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2018.06.033 * 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 Gruppo Italiano Frattura (IGF) ExCo. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. * Corresponding author. E-mail address: sobyanin.k@icmm.ru (K.V. Sobyanin), shardakov@icmm.ru (I.N. Shardakov) * Corresponding author. E-mail address: sobyanin.k@icmm.ru (K.V. Sobyanin), shardakov@icmm.ru (I.N. Shardakov) © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: concrete; vibration diagnostics; shock-wave method; elastisity Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. Keywords: concrete; vibration diagnostics; shock-wave method; elastisity

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1. Introduction Reinforced concrete is one of the most widely used building materials. The safety of reinforced concrete structures is mainly determined by their deformation state. Today automatic deformation monitoring systems is commonly used to ensure structural safety of these buildings and natural objects (Tsvetkov et al., 2013; Shardakov et al., 2014). As a rule, these systems incorporate experimental facilities to provide required information, the analysis of which makes it possible to estimate the deformation state of the structure regarding the development of subcritical and critical processes in its elements. In addition, the results of such analysis are used to make structural safety prognosis. In particular, among these devices, are the systems of sensors that record such deformation parameters as the components of the strain tensor at local points, the displacements and angles of rotation of the structural elements at characteristic locations, the distribution of the vertical settlements of the foundations, and so on. These measurements are generally taken in a quasistatic regime. The results of mathematical processing of these data and mathematical modeling of deformation processes allow researchers to analyze the criticality of the deformation state of the entire structure. At present, the deformation control systems are often supplemented with devices, which allow evaluation of the structure state based on the vibration measurements. Such devices include systems for recording acoustic emission (Merson et al., 2012; Carpinteri et al. 2002), as well as methods of shock-wave (vibration) diagnostics (Bykov et al. 2015). From the viewpoint of the assessment of incipient irreversible damage at local points of the structure, the informative value of these tools is rather high. They enjoy a wide-spread use due to the refinement of hardware (instrumentation pool), which makes it possible to register the parameters of the vibration processes occurring in the structure under monitoring. A very important component that ensures the effectiveness of these tools is a mathematical apparatus that provides an adequate interpretation of the measured vibration parameters (Carpinteri et al. 2002). The results presented in this article refer to the shock-wave vibrodiagnostics of reinforced concrete structures. Here the emphasis is placed on the vibration diagnostics in a "sparing mode", which implies that the force action on the structure during the diagnostics does not cause inelastic deformation in the elements of the inspected structure. This variant of vibrodiagnostics as a part of the deformation monitoring system, is implemented in the following way. The reinforced concrete structure is subjected at certain points to a local impulse force generated by a striker. The mechanical response of the structure to this impact is recorded by a set of sensors (accelerometers, velocimeters, etc.) located at different points of the structure. The response recorded at the time of installation of the monitoring system (and, even better, at the beginning of the lifecycle of the structure) is then compared with the results of measurements made at the current time. This comparison makes it possible to assess the degree of accumulation of irreversible defects and the corresponding changes in the material properties. The manner, in which this comparison is performed, and what criteria are used for this purpose, is a serious issue, which is beyond the scope of this article. The objective of this study is the identification of parameters of the local impulse force, which excites mechanical vibrations of the desired spectrum in the structure, and generates an elastic wave, which have necessary characteristics of the front. One of the main parameters of the impulse action that determine these characteristics is the duration of the impulse action. Therefore, an analysis of the dependence of the impulse duration on various factors and the evaluation of the possibility of controlling such force impulses is the focus of this study. Here, within the framework of the theory of elasticity, the results of the solution of the initial-boundary problem on the dynamic interaction of the

elements of the "striker-gasket-reinforced concrete beam" system are analyzed. 2. Mathematical formulation of the problem and its numerical implementation

The mechanical aspects of the problem studying the interactions between a striker, a gasket and a reinforced concrete beam are schematically represented in Fig.1. In the experiment, the fixed reinforced concrete beam interacted through the elastic gasket with the flying metal ball, which at the initial moment of its contact with the gasket had the velocity equal to V 0 and directed along the normal to the gasket surface. The contact interaction between the ball and the gasket gave rise to the force impulse, which initiated the shock-wave process in the reinforced concrete beam. The characteristic force impulse - time curve is given in Fig.1b.