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Mechanical Study of an Aircraft's Structural Condition Mechanical Mechanical Study of an Aircraft’s Structural Condition Tiago Alexandre Rosado Martins Thesis to obtain the Master of Science Degree in Mechanical Engineering Supervisors: Prof. Virgínia Isabel Monteiro Nabais Infante Prof. Luís Alberto Gonçalves de Sousa Examination Committee Chairperson: Prof. Luis Filipe Galrão dos Reis Supervisor: Prof. Virgínia Isabel Monteiro Nabais Infante Member of the Committee: Prof. Ricardo Miguel Gomes Simões Baptista June 2019 ii Acknowledgments I would like to express my gratitude to professors Lu´ıs Sousa and Virg´ınia Infante for the invitation to write this thesis and for their continuous support and attention whenever necessary. I also wish to thank the kind people of the Portuguese Air Force’s Department of Programs and Engineering, Capts. Serrano, Prieto, Cardoso and Bastos and Lts. Diniz, ... for their support and guidance. My thanks to the staff of Esquadra 101 at Base Aerea´ no 1 for having received me and allowing me to spend many hours around their stunning aircraft. I would also like to thank the staff at Critical Materials, especially Doc. Paulo Antunes for the numerous advices regarding finite element analysis and software. Also, many thanks to Prof. Ricardo Baptista for the advice regarding crack propagation and his willingness to give them. To my classmates which provided me with hours of much welcome company in the writting of this thesis, Bogdan Sandu, Lu´ıs Abreu, Ricardo Ferreira and Beatriz Lopes. Lastly, I would like to thank my family and friends, near and far, whose love and support has kept me going through all of this life’s trials. Without you the journey so far would been much less joyful. iii Resumo O objectivo do presente trabalho e´ a estimac¸ao˜ do tempo de vida a` fadiga da frota Epsilon TB-30 da Forc¸a Aerea´ Portuguesa, e a instalac¸ao˜ de um sistema de aquisic¸ao˜ de dados de acelerac¸ao˜ e extensometria nos componentes cr´ıticos em voo, que servira´ no futuro como input para a interface de Structural Health Monitoring PRODDIA c . Informac¸ao˜ de estudos experimentais anteriores e dos carregamentos na aeronave foi usada num processo de engenharia inversa na construc¸ao˜ de um modelo de elementos finitos do componente cr´ıtico do aviao.˜ Deste modelo, estimaram-se os campos de tensoes˜ para hotspots estruturais previamente identificados. O dano acumulado na estrutura foi calculado com base em carregamentos de referencia,ˆ usando a regra de Miner e criterios´ de fadiga apropriados. Os factores de intensidade de tensao˜ para as fendas previstas por analises´ anteriores foram estimados utilizando os metodos´ dos elementos finitos, e o mais recente XFEM integrados no software ABAQUS c . A propagac¸ao˜ de fenda foi depois modelada fazendo uso das leis de Paris, Walker, NASGRO e Forman. Os parametrosˆ utilizados nas varias´ equac¸oes˜ foram obtidos atraves´ de dados experimentais de ensaios anteriores para a liga AA 2024-T3. Por ultimo,´ o autor sugere uma revisao˜ ao programa de manutenc¸ao˜ das aeronaves atraves´ do ajuste dos per´ıodos de inspec¸ao˜ definidos pelo fabricante. Palavras-chave: Fadiga, Propagac¸ao˜ de Fenda, Structural Health Monitoring, XFEM iv Abstract The purpose of this work is the estimation of the Fatigue Lifetime of the Portuguese Air Force’s Epsilon TB-30 fleet, and the installation of a data acquisition system to measure vertical acceleration and strain on critical components of the aircraft which will later serve as input to the Structural Health Monitoring interface PRODDIA c . Experimental studies and prior knowledge of aircraft loads was used to reverse engineer a suitable Finite Element Model of the structure, from which the stress fields in previously identified structural hotspots were retrieved. Cumulative damage on the structure is calculated for reference loading spectra using the Palgrem-Miner rule and adequate fatigue criteria. The Stress Intensity Factors at the critical component’s notched geometry were estimated using the Finite Element and Extended Finite Element Methods from ABAQUS c . Crack propagation was then modelled using various laws (Paris, Walker, NASGRO, Forman). A comparison between the two numerical methods and the results of the several propagation laws is presented. Parameters for the various equations for AA 2024-T3 are obtained through the fitting of experimental data. Lastly, the author suggests a revision of the aircraft’s maintenance program through the adjustment of the inspection periods defined by the manufacturer. Keywords: Fatigue, Crack propagation modelling, Structural Health Monitoring, XFEM v Contents Acknowledgments ........................................... iii Resumo................................................. iv Abstract................................................. v List of Tables.............................................. ix List of Figures ............................................. x List of Abbreviations.......................................... xiii List of Symbols............................................. xv 1 Introduction 1 1.1 Background............................................ 1 1.2 Motivation and Objectives.................................... 3 1.3 Thesis Outline .......................................... 4 2 Literature Review 5 2.1 An overview on the study of Fatigue .............................. 5 2.2 Physical Mechanisms of Fatigue ................................ 7 2.3 Stress-Life Approach to Fatigue in Metals........................... 8 2.3.1 Stress-Life (S-N) curves................................. 8 2.3.2 Mean Stress Influence and Criteria........................... 9 2.3.3 Cumulative Damage................................... 11 2.3.4 Other Factors Affecting Fatigue Life .......................... 12 2.4 Linear Elastic Fracture Mechanics (LEFM)........................... 12 2.4.1 The Griffith Criterion................................... 16 2.4.2 The J-Integral Concept ................................. 17 2.5 Crack Propagation........................................ 18 2.6 Finite Element Method applied to Fracture Mechanics .................... 21 2.6.1 Displacement Extrapolation Method .......................... 22 2.6.2 Crack tip elements.................................... 22 2.6.3 The Energy Method ................................... 23 2.6.4 The J-Integral Method.................................. 24 2.7 Extended Finite Element Method (XFEM) ........................... 25 2.8 Structural Health Monitoring................................... 26 2.8.1 The Forward Problem .................................. 27 vi 2.8.2 The Inverse Problem................................... 27 2.9 Manufacturer’s Results for Aircraft Useful Life......................... 27 3 Experimental Activities 28 3.1 Strain Gauges .......................................... 29 3.1.1 Sensor Principle and Description............................ 29 3.1.2 Testing and Calibration ................................. 29 3.1.3 Aircraft installation.................................... 31 3.2 Accelerometers.......................................... 31 3.2.1 Sensor Principle and Description............................ 31 3.2.2 Testing and Calibration ................................. 32 3.2.3 Aircraft Installation.................................... 32 4 Finite Element Modelling of Aircraft Structures 33 4.1 Objective of Finite Element Modelling ............................. 33 4.2 Real Structure .......................................... 33 4.3 CAD Modelling.......................................... 35 4.4 Finite Element Mesh....................................... 36 4.5 Boundary Conditions....................................... 38 4.5.1 Loading Conditions ................................... 38 4.5.2 Constraints........................................ 44 4.5.3 Structural Hotspots.................................... 47 4.6 Dynamic Analysis ........................................ 48 5 Fatigue Analysis 51 5.1 Load Spectra for Fatigue Analysis ............................... 51 5.2 Stress-Life Approach....................................... 52 5.3 PRODDIA c stress-life calculation ............................... 53 5.4 Crack Propagation........................................ 54 5.4.1 Crack Location and Geometry ............................. 55 5.4.2 Geometric Factor Estimation: XFEM.......................... 55 5.4.3 Geometric Factor Estimation: FEM........................... 58 5.4.4 Parameter Fitting for Propagation Laws ........................ 60 5.4.5 Fatigue Lifetime Estimation using Crack Propagation Models ............ 65 6 Final Remarks 69 6.1 Proposal of Maintenance Scheduling.............................. 69 6.1.1 First Inspection...................................... 70 6.1.2 Following Inspections .................................. 71 6.2 Future Work............................................ 71 6.2.1 Relating Sensor Data to Frame damage........................ 71 vii 6.2.2 Fatigue Analysis of Wing Spar ............................. 72 6.2.3 Application of Crack Arresting Solutions........................ 72 References 75 Appendix A Technical Datasheets 79 viii List of Tables Table 1.1 Aircraft Parameters .................................... 2 Table 3.1 Young’s modulus computed from linear regression of sensor data, and respective percent error to the theoretical value............................... 31 Table 4.1 Material properties used on all calculations involving AA 2024-T3 .......... 36 Table 4.2 Reactions on wing spar pinned joints for a rectangular lift distribution, calculated through finite
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