PSI - Issue 2_B

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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. Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ). Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.333 ∗ Corresponding author. Tel.: + 39-0521-905927; fax: + 39-0521-905924. E-mail address: spagnoli@unipr.it 2452-3 16 c 2016 The Authors. Published by Elsevi r B.V. Peer-r view under responsibility of the Scientific Committee f ECF21. A solid or struct re under oscillatory loading might develop permanent deformations which after a certain number of load cycles no longer progress, so that the structural response to load becomes purely elastic. Under such circum stances, it is said that the solid or structure elastically shakes down. The knowledge of shakedown limit is relevant if one has to assess energy dissipation conditions in a material, possibly with the aim of quantifying hysteretic damping under vibratory loading and / or damage under fatigue loading. The problem of shakedown has been deeply explored in the context of monolithic bodies whose mechanical behaviour is described by elastic-plastic material models. One of the main achievement is the development of limit analysis methods which allow the determination of shakedown conditions with simpler procedures in comparison to more laborious step-by-step incremental solutions. Shakedown limit analysis is centred on Melan’s theorem, Melan (1936), which following a static approach was originally con ceived for the special case of elastic-perfectly plastic bodies with associative flow rule. The dual kinematic approach is due to Koiter (1960). In the case of frictional contact of elastic bodies transmitting normal and tangential loads through the contact surface, microslips can occur along limited portions of the contact surface at load levels well below those needed ∗ Corresponding author. Tel.: + 39-0521-905927; fax: + 39-0521-905924. E-mail address: spagnoli@unipr.it 2452-3216 c 2016 The Auth rs. Publi hed by Elsevier B.V. Pe r-review under responsibility of the Scientific Committee of ECF21. A solid or structure under oscillatory loading might develop permanent deformations which after a certain number of load cycles no longer progress, so that the structural response to load becomes purely elastic. Under such circum stances, it is said that the solid or structure elastically shakes down. The knowledge of shakedown limit is relevant if one has to assess energy dissipation conditions in a material, possibly with the aim of quantifying hysteretic damping und r vibratory loading and / or damage under fatigue loading. The problem of shakedown has been deeply explored in the context of monolithic bodies whose mechanical behaviour is described by elastic-plastic material models. One of the main achievement is the development of limit analysis methods which allow the determination of shakedown conditions with simpler procedures in comparison to more laborious step-by-step incremental solutions. Shakedo n limit analysis is centred on Melan’s theorem, Melan (1936), which following a static approach was originally con ceived for the special case of elastic-perfectly plastic bodies with associative flow rule. The dual kinematic approach is due to Koiter (1960). In the case of frictional contact of elastic bodies transmitting normal and tangential loads through the contact surface, microslips can occur along limited portions of the contact surface at load levels well below those needed ∗ Corresponding author. Tel.: + 39-0521-905927; fax: + 39-0521-905924. E-mail address: spagnoli@unipr.it 2452-3216 c 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21. 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. 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy Shakedown in an elastic-plastic solid with a frictional crack A. Spagnoli a, ∗ , M. T rzano a , A. Klarbing b , J.R. Barber c a Department of Civil-Environmental Engineering & Architecture, University of Parma, Viale Usberti 181 / A, 43124 Parma, Italy b Department of Mechanical Engineering, Linko¨ping University, S-581 83 Linko¨ping, Sweden c Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA Abstract When subjected to periodic loading, elastic systems containing contact interfaces might exhibit frictional slip which ceases after some loading cycles. In such cases, it is said that the system shakes down. For elastic discrete systems presenting complete contacts, it has been proved that Melan’s theorem, originally proposed for elastic-plastic problems, o ff ers su ffi cient condition for the system to shake down, provided that the contact is of an uncoupled type. In the present paper, the application of Melan’s theorem is speculated for systems involving plasticity and friction. A finite element example of an elastic-plastic solid containing a frictional crack is discussed. c 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21. Keywords: shakedown; Coulomb friction; Associate plasticity; Melan’s theorem. 1. Introduction A solid or structure under oscillatory loading might velop p rmanent deformations which after a c rtain number of load cycles no longer progress, so that the structural response to load becomes purely elastic. Under such circum stances, it is said that the solid or structure elastically shakes down. The knowledge of shakedown limit is relevant if one has to assess energy dissipation conditions in a material, possibly with the aim of quantifying hysteretic damping under vibratory loading and / or damage under fatigue loading. The problem of shakedown has been deeply explored in the context of monolithic bodies whose mechanical behaviour is described by elastic-plastic material models. One of the main achievement is the development of li it analysis methods which allow the determination of shakedown conditions with simpler procedures in comparison to more laborious step-by-step incremental solutions. Shakedown limit analysis is centred on Melan’s theorem, Melan (1936), which following a static approach was originally con ceived for the special case of elastic-perfectly plastic bodies with associative flow rule. The dual kinematic approach is due to Koiter (1960). In the case of frictional contact of elastic bodies transmitting normal and tangential loads through the contact surface, microslips can occur along limited portions of the contact surface at load levels well below those needed 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy Shakedow in an elastic-plastic solid with frictional cra k A. Spagnoli a, ∗ , M. Terzano a , A. Klarbing b , J.R. Barber c a Department of Civil-Environmental Engineer g & Architecture, University of Parma, Viale Usberti 181 / A, 43124 Parma, Italy b Department of Mechanical Engineering, Linko¨ping University, S-581 83 Linko¨ping, Sweden c Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA Abstract When subjected to periodic loading, elastic systems containing con act interface might exhibit fricti al slip which ceases after some loading cycles. In suc cases, it is said that the system shakes down. For elastic discrete systems presenting complete c ntacts, it has be n proved that Melan’s theorem, originally proposed for elastic-plastic problems, o ff ers a su ffi cient condition for the system to shake down, provided that the contact is of an uncoupled type. In the present paper, the application of Melan’s theorem is speculated for systems involving plasticity and friction. A finite element example of an elastic-plastic solid containing a frictional crack is disc ssed. c 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21. Keywords: shakedown; Coulomb friction; Associate plasticity; Melan’s theorem. 1. Introduction 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy Shakedown in an elastic-plastic solid with a frictional crack A. Spagnoli a, ∗ , M. Terzano a , A. Klarbing b , J.R. Barber c a Department of Civil-Environmental Engineering & Architecture, University of Parma, Viale Usberti 181 / A, 43124 Parma, Italy b Department of Mechanical Engineering, Linko¨ping University, S-581 83 Linko¨ping, Sweden c Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA Abstract When subjected to periodic loading, elastic systems containing contact interfaces might exhibit frictional slip which ceases after some loading cycles. In such cases, it is said that the system shakes down. For elastic discrete systems presenting complete contacts, it has been proved that Melan’s theorem, originally proposed for elastic-plastic problems, o ff ers a su ffi cient condition for the system to shake down, provided that the ontact is of an uncoupled type. In the present paper, the pplication of Melan’s theorem is speculated for systems involving plasticity and friction. A finite element example of an elastic-plastic solid containing a frictional crack is discussed. c 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21. Keywords: shakedown; C ulo b friction; Associate plasti ity; Melan’s theorem. 1. Introduction Copyright © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). -review under esponsibility of the Scientific Committee of ECF21. © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of PCF 2016. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. * Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt