Course Notes. Hållfasthetslära Vk MHA100. Fatigue and Fracture Analysis MHA140. General. Teachers. Goals. School of Civil Engineering Period II 1998
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1 Department of Solid Mechanics Course Notes Hållfasthetslära Vk MHA100 Fatigue and Fracture Analysis MHA140 School of Civil Engineering Period II 1998 General Additional and updated information about the course will be posted on the homepage of the course: Teachers Peter Möller Anders Ekberg phone home The division of Solid Mechanics is situated at the new M-building on Hörsalsvägen and can be reached by phone fax URL Goals Within the field of fatigue and fracture mechanics, the goal of the course is to Give an understanding of phenomena and theories. Provide an orientation on classical and modern methods and design criteria. 1
2 Teach basic numerical methods of design. Serve as an introduction for possible further studies. Give a brief introduction to current research trends in the area. After completed course, the participants should have a good foundation for industrial fracture and fatigue design, as well as a basis for continued studies. Literature Peter W. Möller: Introductory Lecture Notes on Fracture Mechanics, CTH Solid Mechanics (15 SEK) Compendium in Fracture Mechanics (50 SEK); (compiled by Tore Dahlberg) Dahlberg, Ekberg, Möller: Exercises in Fracture and Fatigue Analysis, CTH Solid Mechanics U74 (20 SEK) Tore Dahlberg: Material Fatigue, CTH Solid Mechanics U61 (40 SEK) Anders Ekberg: Fatigue a Survey, 2nd Edition, CTH Solid Mechanics U67 (25 SEK) Program The course is divided into two main parts, viz. FATIGUE ANALYSIS and FRACTURE MECHANICS. Although each of these topics may be studied independent from each other, there are some natural connections. Lectures and exercises are separated in the course program, some numerical examples may be provided in the lectures. Examination A written examination, embracing of five problems, is given December 16. The problems may consist of numerical as well as theoretical parts. The means of assistance that are allowed at the exam are All the literature listed above except for the problems collection. Handbooks and mathematical tables. This also includes textbooks on solid and structural mechanics, but no textbooks on fatigue and fracture (except for the textbooks listed above). Dictionaries. A calculator in one single unit and without external communication. Distributed copies of slides etc. This does not include distributed solved examples! Minor notes, but no solved problems, in the listed material are allowed as well. If there are any questions regarding allowed means of assistance, please contact a teacher prior to the exam. 2 COURSE NOTES
3 Program The course embrace 14 lectures and 14 exercises; 7 lectures and 6 exercises are devoted to fracture mechanics and another 7 lectures and 6 exercises treat fatigue. By the end of the course, about 1 week before the examination, 2 exercises are dedicated to repetition. Lectures take place in lecture hall VH, while exercises are conducted in VÖ12 and VÖ13 - any changes will be announced during the course. Fracture Mechanics LECTURE 1 Introduction to the course with emphasis on fracture mechanics Mechanisms of failure Equations of elasticity Principal stress; Mohr s circle Effective stress Energy and work Tensor notation LECTURE 2 Stress concentrations at voids and cracks Mohr s criteria for brittle fracture Stress concentration factors Stress intensity factors modes of loading LECTURE 3 Stress intensity factors Ð part I Detailed study of mode III loading Mode I and II solutions The stress intensity factor as a failure criterion EXCERCISE 1 Equilibrium Mohr s criterion for brittle failure Strain energy LECTURE 4 Stress intensity factors Ð part II Limitations of LFEM (Linear Elastic Fracture Mechanics) Superposition Mixed loading mode Methods to determine stress intensity factors EXCERCISE 2 Stress concentration Stress at crack tip COURSE NOTES 3
4 LECTURE 5 Energy and energy balance Surface energy Potential and strain energy Strain energy release rate G The Griffith energy balance Stable and unstable crack growth Relation between G and stress intensity factors Superposition revisited Methods to determine G EXCERCISE 3 Stress intensity factors LECTURE 6 Correction for small scale yielding (ssy) Irwin s approach The Dugdale model Plastic zone size and shape Limitation of LFEM revisited Size effects EXCERCISE 4 Surface energy Energy balance Strain energy release rate LECTURE 7 Introduction to non-linear (elastic-plastic) fracture mechanics Crack tip opening displacement The CTOD criterion The J integral and its relation to strain energy release rate Fatigue LECTURE 8 Introduction to fatigue analysis Fatigue?!? History of fatigue Fatigue design philosophy An overview of fatigue design methods Complicating factors Dynamic loading EXCERCISE 5 (FRACTURE MECHANICS) Irwin correction Plastic zone and the Dugdale model LECTURE 9 High Cycle Fatigue (HCF) Design Ð part I Underlying philosophy and physics 4 COURSE NOTES
5 The Haigh diagram Finite / infinite fatigue life The Wöhler curve EXCERCISE 6 (FRACTURE MECHANICS) Crack tip opening displacement The J integral LECTURE 10 High Cycle Fatigue (HCF) Design Ðpart II Multiaxial loading complications Equivalent stress approaches Limited fatigue life in multiaxial loading EXCERCISE 7 HCF design LECTURE 11 Low Cycle Fatigue (LCF) Design Underlying philosophy and physics Morrow design rule Coffin Manson design rule Multiaxial LCF EXCERCISE 8 HCF design LECTURE 12 Fatigue Crack Propagation Ð part I Underlying philosophy and physics Crack growth at cyclic loading Design against failure due to crack growth Basic analysis of crack growth rate EXCERCISE 9 LCF design LECTURE 13 Fatigue Crack Propagation Ð part II Influence of load magnitude Crack closure and arrestment Variable amplitude loading Short and long cracks Crack Growth Threshold Multiaxial Loading COURSE NOTES 5
6 EXCERCISE 10 LCF design EXCERCISE 11 Fatigue crack propagation LECTURE 14 Concluding remarks of fatigue analysis Fatigue of non-metallic materials Design codes (esp. BSK and BBK) Practical design Fatigue a crash course EXCERCISE 12 Fatigue crack propagation EXCERCISE 13 Repetition of the course contents problems from old exams EXCERCISE 14 Workshop test exam and/or problems from old exams 6 COURSE NOTES
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