Class Information

Course Description

Mechanisms of fracture and crack growth; stress analysis; crack tip plastic zone; energy principles in fracture mechanics; fatigue-crack initiation and propagation; fracture mechanic design and fatigue life prediction. Analytical, numerical, and experimental methods for determination of stress intensity factors. Current topics in fracture mechanics.

Syllabus

Class information

  • Hours: Tuesdays and Thursdays 2:30-3:45 pm ET (1:30 – 2:55 pm CT)
  • Location: Online (If not, I’ll be teaching at UTK:  Dougherty 406 and students at UTSI: Main Academic Building E110 will be remotely connected).

Office Hours

By appointment, zoom: https://tennessee.zoom.us/j/4441721751

 Course requirements

  • Homework 34% + 5% (extra credit)
  • Exams: Midterm + final: 34%
  • Term project 16%: Use commercial software to evaluate stress intensity factor; Simple computations with cohesive and damage models.
  • Report and presentation on a topic on fracture 16%: 4-page report and 10-12 minute presentation at the end of the semester. Individual topics and references will be chosen by the instructor and the student.

Detail of course topics

Presentations

Announcements

  • HW1: link (Due 9/20/2022).
  • HW2: link (Due 10/13/2022).
  • Term project 1: Includes (About equal weights are allocated to each part)
    • 1) An up to 4 pages paper/proposal(including references if any) on a topic related to fracture mechanics. The format of the document is either that of a a) research article mostly focusing on introducing a topic of interest and presenting related results; b) research proposal that basically introduces a problem, discusses current state of the art and research gaps, and finally proposes a new approach to address the mentioned research gaps. The choice between research article or proposal is up to the student. The topic can be related to your own research work (as long as it is related to fracture mechanics) or any other topic related to the course that is of interest to you. I can help you in choosing a topic if needed. Please confirm your research topic by the end of 10/27/2020.
    • 2) Presentation of the article on the “Presentation day”. Each student will have about 15 minutes to present the material in the article (and related to it) to the entire class.
    • Presentation day (12/13/2022): Presentations will be in D406.
    • Term paper is due on 12/13/2022.
  • Midterm exam: link (Due 10/27/2022).
  • Computational Term project, Due 11/24/2022
    • Installing Ansys:
      • Option 1 (free academic version, link). While this is a limited version, it is sufficient for your project and is recommended due to the ease of installation.
    • Ansys_FractureMechanics: Instructions for Ansys for computing stress intensity factor (K) and J integral.
    • Instructional movies on using Ansys for fracture analysis by Dr. Omid Omidi:
      • Part 1: Model preparation, calculation of K from displacement field. In class lecture on 11/13/2014    Flash, mp4
        • Related material: Notes for performing a similar calculation for mid-domain cracks: Dr. A.-V. Phan, University of South Alabama: link. KCAL command options: link.
      • Part 2: Assigning one area per crack tip and having distinct material properties.                                   Flash, mp4
      • Part 3: Calculation of J integral and other fracture mechanics parameters                                              Flash, mp4
    • COMSOL: Please refer to this link for similar calculations with COMSOL.
  • HW3: link (Due 11/29/2022).
  • Final exam: link (Due 12/13/2022).

Class timeline

RA: reading assignment; Reference made to section numbers in “details of course topics”

  1. 08/25/2022 Lecture: notes video          2. History; 3.1 Fracture classification; 3.2 & 3.3 Ductile and brittle fracture. 
  2. 08/30/2022 Lecture: notes video          3.2 & 3.3 Ductile and brittle fracture.
  3. 09/01/2022 Lecture: notes video          4. Linear Elastic Fracture Mechanics (LEFM), 4.1.1. Atomic view of fracture, 4.1.2. Effect of flaws, Griffith experiment; 4.1.3. Energy equation (part 1).
  4. 09/06/2022 Lecture: notes video          4.1.3. Energy equation, Fracture Resistance (R); 4.1.4. Energy Release Rate (G).
  5. 09/06/2022 Lecture: notes video          4.1.4. Energy Release Rate (G); 4.1.5. Crack Stability, R and ∏ curve.
  6. 09/13/2022 Lecture: notes video          4.1.5. Crack Stability, R and ∏ curve (part 2), 4.2. Stress solutions, Stress Intensity Factor K (SIF): 4.2.1. Airy stress functions, 4.2.2. Complex variables and cylindrical coordinate.
  7. 09/15/2022 Lecture: notes video          4.2.3. Stress solutions, stress concentration; 4.2.4. Crack tip stress fields, SIF.
  8. 09/20/2022 Lecture: notes video         4.2.4. Crack tip stress and displacement fields, SIF; Notch problem.
  9. 09/22/2022 Lecture: notes video         4.2.4. Crack tip displacement fields, SIF; Mixed mode fracture, evaluation of KI and KII.
  10. 09/27/2022 Lecture: notes video                4.2.5. Relation between K & R (SIF & Resistance); 5.2. Plastic zone models: 5.2.1. 1D models: Irwin model
  11. 09/29/2022 Lecture: notes video                Plastic zone models 1D and 2D models, 5.2.1 and 5.2.2 (part 2)
  12. 10/04/2022 Lecture: notes video                Plastic zone models 1D and 2D models, 5.2.1 and 5.2.2 (part 3): 2D, plane strain vs plane stress
  13. 10/11/2022 Lecture: notes video                5.3. J Integral: 5.3.1. Path independence; 5.3.2.Relation between J and G.
    Link: Derivation of the relation J = G
  14. 10/13/2022 Lecture: notes video           5.3.5.Plastic crack tip fields; Hutchinson, Rice and Rosengren (HRR); 5.3.4.Energy Release Rate, crack growth and R curves.
  15. 10/18/2022 Lecture: notes video         5.3.6. large scale yielding (LSY) and 5.4. Crack tip opening displacement (CTOD).
  16. 10/20/2022 Lecture: notes video        5.3.7.Fracture mechanics versus material (plastic) strength; 6.1. Fracture mechanics in Finite Element Methods (FEM).
  17. 10/25/2022 Lecture: notes video        6. Computational fracture mechanics, 6.1.3. Extraction of K (SIF).
  18. 10/27/2022 Lecture: notes video        6. Computational fracture mechanics, 6.1.3. Extraction of G. 6.1.4. J integral.
  19. 11/01/2022 Lecture: notes video       6.1.4. J integral; Demo of computation of K in Ansys (from displacement method and J integral).
  20. 11/03/2022 Lecture: notes video     6.1.4. Ansys demo (J integral), 6.1.6, 7 Computational crack growth, Extended Finite Element Method (XFEM); 6.2. TSRs (part1), J integral calculation: video
  21. 11/08/2022 Lecture: notes video    6.2. TSRs (part 2)
  22. 11/10/2022 Lecture: notes video    6.2. TSRs (part 3); 4.3. Mixed mode fracture (part 1).
  23. 11/15/2022 Lecture: notes video    4.3. Mixed mode fracture (part 1), 4.3.2. Nucleation criteria.
  24. 11/22/2022a Lecture: notes video    8. Fatigue; 8.1. Fatigue regimes; 8.2. S-N curves.
  25. 11/22/2022b Lecture: notes video   8.3. Paris law, part 1.
  26. 11/29/2022 Lecture: notes video   8.3. Paris law, part 2, variable loading, statistical approach, Dynamic Fracture (part 1): LEFM solutions for dynamic fracture
  27. 112/06/2022 Lecture: notes video  Dynamic Fracture (part 2): Rayleigh wave speed limit for mode I fracture; intersonic propagation, crack bifurcation.

Selected Bibliography

  1. T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, 3rd Edition, CRC Press, USA, 2004 (main textbook).
  2. D. Broek, Elementary Engineering Fracture Mechanics, 4th Revised Edition, Springer, 1982 (or reprint 2013).
  3. B. Broek, The Practical Use of Fracture Mechanics, Springer, 1998.
  4. S. Murakami, Continuum Damage Mechanics: A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer Netherlands, Dordrecht, 2012.
  5. S. Suresh, Fatigue of Materials. 2nd ed. Cambridge University Press, 1998.
  6. L.B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, 1998.
  7. B. Lawn, Fracture of Brittle Solids, Cambridge University Press, 1993.
  8. M.F. Kanninen and C.H. Popelar, Advanced Fracture Mechanics, Oxford Press, 1985.
  9. R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials. 5th ed. John Wiley & Sons, Inc., 2012 (material focus).
  10. S Al Laham, Stress Intensity Factor and Limit Load Handbook, British Energy Generation Limited, 1998.
  11. H Tada, P.C. Paris, G.R. Irwin, Stress Analysis of Cracks Handbook,  3rd ed., ASME Press. 2000

Useful online courseware and links

  1. Presentation on Fracture Mechanics by Dr. N. V. Phu from University of Adelaide. With special thanks to Dr. Phu, the majority of course presentations are based on Dr. Phu’s presentations.
  2. S. Suresh, Fracture and Fatigue, MITOpen courseware.
  3. V.E. Saouma, Fracture Mechanics lecture notes, University of Colorado, Boulder.
  4. P.J.G. Schreurs, Fracture Mechanics lecture notes, Eindhoven University of Technology (2012).
  5. A.T. Zender, Fracture Mechanics lecture notes, Cornell University.
  6. K. Ramesh, Engineering fracture mechanics lecture videos, IIT, Madras, India.
  7. L. Zhigilei, MSE 2090: Introduction to the Science and Engineering of Materials, University of Virginia: Excellent lecture notes on material preliminaries such as atomic structure (ch2), crystalline solids (ch3), imperfections (ch4), mechanical properties (ch6), dislocation (ch7), and failure (ch8).