PSI - Issue 2_B

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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. 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy Modelling mixed-mode fracture in poly(methylmethacrylate) using peridynamics Francesco Caimmi a, 0 F0 F *, Elyas Haddadi b,c , Naghdali Choupani b,c , Claudia Marano a , Luca Andena a a Chemistry, Materials and Chemical Engineering Department "Giulio Natta", Politecnico di Milano, P.za Leonardo da Vinci 32, I-20133 Milano, Italy b Faculty of Mechanical Engineering, Sahand University of Technology,Sahand NewTown,51335-1996, Tabriz, Iran c Institute of Polymeric Materials, Sahand University of Technology, Sahand NewTown,51335-1996,Tabriz, Iran Abstract Peridynamics (Silling (2000)) is a non-local continuum theory that is particularly suited to handle discontinuities in the displacement field, such as those arising during fracture. Peridynamics prescribes that each material point interacts with all its neighbors contained in a sphere of given radius; this assumption introduces a h racteristic length scale in the ontinuum description. In a nutshell, the in eractions between materi l p in s d pend o their relative distance; in the peridyna ics fram work this distance is called the “bond length”. The equ tions of motion, holding at each material point, link the material point cceleration to the integral over the point neighborhood of a force density field, whose trength depend on bond-stretches, i.e. the ratio of the actual bond-l ngth over the initial one. In these equations the displacement gr dient does not ppear, thus naturally allowing for discontinuities in the displacement field to occur. As to failure, the simplest possible damage description is provided by an interaction law prescribing the force to vanish when a critical bond-stretch threshold is crossed; this parameter can be related to the Mode I critical strain energy release rate. A single parameter is needed to describe failure, in principle under every possible loading condition. In this work the predictive abilities of peridynamics were checked against experimental results in the case of mixed-mode failure of brittle polymers. Pre-cracked poly(methylmethacrylate) (PMMA) samples were tested using different specimens, in order to obtain Mode I, Mixed-Mode and Mode II loading conditions. The material was assumed to behave according to a peridynamics brittle elastic material model; the parameters needed to calibrate the elastic behavior were determined from Mode I tests, as was the critical stretch.The peridynamics simulations of mixed-mode tests were able to catch the correct fracture initiation load and to provide a fair description of the crack path under different conditions. The peridynamics model was also able to qualitatively capture the typical “nail” shape assumed by the crack front during propagation. 21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy Modelling mixed-mode fracture in poly(methylmethacrylate) using peridynamics Francesco Caimmi a, 0 F0 F *, Elyas Haddadi b,c , Naghdali Choupani b,c , Claudia Marano a , Luca Andena a a Chemistry, Materials and Chemical Engineering Department "Giulio Natta", Politecnico di Milano, P.za Leonardo da Vinci 32, I-20133 Milano, Italy b Faculty of Mechanical Engineering, Sahand University of Technology,Sahand NewTown,51335-1996, Tabriz, Iran c Institute of Polymeric Materials, Sahand University of Technology, Sahand NewTown,51335-1996,Tabriz, Iran Abstract Peridynamics (Silling (2000)) is a non-local continuum theory that is particularly suited to handle discontinuities in the displacement field, such as those arising during fracture. Peridynamics prescribes that each material point interacts with all its neighbors contained in a sphere of given radius; this assumption introduces a characteristic length scale in the continuum description. In a nutshell, the interactions between aterial points depend on their relative dist ce; in the peridynamics framework this distance is called the “bond length”. The equations of motion, holding at each material point, link the material point acceleration to the integral over the point neighborhood of a force density field, hose strength depend on bond-stretches, i.e. the ratio of the actual bond-length over the initial one. In these equations the displacement gradient does not appear, thus naturally allowing for discontinuities in the displacement field to occur. As to failure, the simplest possible damage description is provided by an interaction law prescribing the force to vanish when a critical bond-stretch threshold is crossed; this parameter can be related to the Mode I critical strain energy release rate. A single parameter is needed to describe failure, in principle under every possible loading condition. In this work the predictive abilities of peridynamics were checked against experimental results in the case of mixed-mode failure of brittle polymers. Pre-cracked poly(methylmethacrylate) (PMMA) samples were tested using different specimens, in order to obtain Mode I, Mixed-Mode and Mode II loading conditions. The material was assumed to behave according to a peridynamics brittle elastic material model; the parameters needed to calibrate the elastic behavior were determined from Mode I tests, as was the critical stretch.The peridynamics simulations of mixed-mode tests were able to catch the correct fracture initiation load and to provide a fair description of the crack path under different conditions. The peridynamics model was also able to qualitatively capture the typical “nail” shape assumed by the crack front during propagation. Copy ght © 2016 The Authors. Published by Elsevier B.V. This is an open access artic under t e CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility 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.: +39.02.2399.4711; fax: +39.02.7063.8173. E-mail address: francesco.caimmi@polimi.it,

* Corresponding author. Tel.: +351 218419991. E-mail address: amd@tecnico.ulisboa.pt * Corresponding author. Tel.: +39.02.2399.4711; fax: +39.02.7063.8173. E-mail address: francesco.caimmi@polimi.it, 2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.

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.2016.06.022 2452-3216 © 2016 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ECF21.