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: Mondays and Wednesdays 9:45-11:00 am ET (8:45 – 10:00 am 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 9/23/2024).
  • HW2: link (Due 10/14/2024).
  • HW3: link (Due 11/06/2024).
  • Term project 1: Presentation day 12/05/24, 2:15-5:30 pm:
    Please e-mail me or upload on canvas (through the assignment created) the presentations by 2 pm.

    • The presentation is 10 minutes + 2 minutes Q/A. Given the time allocated and number of students, I’ll give time updates a few times during the presentation and end the presentation at 10 minutes.
    • Please focus more on key concepts rather going to too much details in your presentation as there is not much enough time for discussing complex equations. The goal is to broadly introduce an interesting topic to others.
    • Have some hidden slides (or upload / send a separate presentation) containing more material from your literature survey, computational work, etc., so I can better assessment of your work.
  • Computational Term project, Due 11/27/2024
    • 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.
      • Short demo of J-integral: link.
    • 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
    • Abaqus: Please refer to this link for the calculation of J integral using the EDI method:
    • COMSOL: Please refer to this link for similar calculations with COMSOL.
  • HW3: link (Due 11/29/2024).
  • Final exam: link (Due 12/13/2024).

Class timeline

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

  1. 08/19/2024 Lecture: notes video          2. History; 3.1 Fracture classification; 3.2 & 3.3 Ductile and brittle fracture. 
  2. 08/21/2024 Lecture: notes video          3.2 & 3.3 Ductile and brittle fracture.
  3. 08/26/2024 Lecture: notes video          3.2 & 3.3 Ductile and brittle fracture.
  4. 08/28/2024 Lecture: notesvideo 4. Linear Elastic Fracture Mechanics (LEFM), 4.1.1. Atomic view of fracture, 4.1.2. Effect of flaws.
  5. 09/04/2024 Lecture: notes,video 4.1.2. Effect of flaws, Griffith experiment; 4.1.3. Energy equation, Fracture Resistance (R).; 4.1.4. Energy Release Rate (G).
  6. 09/09/2024 Lecture: notes,video        4.1.4. Energy Release Rate (G) calculation.
  7. 09/11/2024 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
  8. 09/16/2024 Lecture: notes,video       4.2.1. Airy stress functions; 4.2.2. Complex variables and cylindrical coordinate. Mode I, II, and III fracture propblems.
  9. 09/18/2024 Lecture: notes,video       4.2.4. Crack tip stress and displacement fields, SIF.
  10. 09/23/2024 Lecture: notes,video       4.2.4. Crack tip stress and displacement fields, SIF; Notch problem. Crack displacement field.
  11. 09/25/2024 Lecture: notes,video      4.2.4. Crack tip displacement fields, SIF; Mixed mode fracture, evaluation of KI and KII.
  12. 09/30/2024 Lecture: notes,video      4.2.4. Mixed mode fracture, evaluation of KI and KII; 4.2.5. Relation between K & G.
  13. 10/02/2024 Lecture: notes,video (not recorded)    5.2. Plastic zone models: 5.2.1. 1D models: Irwin model.
  14. 10/09/2024 Lecture: notes,video (not recorded)    Plastic zone models 1D and 2D models, 5.2.1 and 5.2.2 (part 2).
  15. 10/14/2024 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
  16. 10/16/2024 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
  17. 10/21/2024 Lecture: notes,video            5.3.2.Relation between J and G.
    Link: Derivation of the relation J = G; 5.Plastic crack tip fields; Hutchinson, Rice and Rosengren (HRR).
  18. 10/23/2024 Lecture: notes,video           5.Plastic crack tip fields; Hutchinson, Rice and Rosengren (HRR) – part 2; 5.3.4. Energy Release rate, crack growth, and R curves.
  19. 10/28/2024 Lecture: notes,video          5.3.7.Fracture mechanics versus material (plastic) strength; 5.3.6. large scale yielding (LSY) and 5.4. Crack tip opening displacement (CTOD) – part 1.
  20. 10/30/2024 Lecture: notes,video         5.4. Crack tip opening displacement (CTOD) – part 2; 5.3.6. large scale yielding (LSY).
  21. 11/04/2024 Lecture: notes,video        5.3.6. large scale yielding (LSY) – part 2; 6. Computational fracture mechanics.
  22. 11/06/2024 Lecture: notes,video        6. Computational fracture mechanics, 6.1.3. Extraction of K (SIF) & G.
  23. 11/11/2024 Lecture: notes,video       6.1.4. J integral. Comparison of different computational mehods for evaluating K.
  24. 11/13/2024 Lecture: notes,video       6.1.4. J integral; Demo of computation of K in Ansys (from displacement method and J integral).
  25. 11/18/2024 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).
  26. 11/20/2024 Lecture: notes,video       6.2. TSRs (part 2)
  27. 11/10/2024 Lecture: notes video    6.2. TSRs (part 3); 4.3. Mixed mode fracture (part 1).
  28. 11/15/2024 Lecture: notes video    4.3. Mixed mode fracture (part 1), 4.3.2. Nucleation criteria.
  29. 11/22/2024a Lecture: notes video    8. Fatigue; 8.1. Fatigue regimes; 8.2. S-N curves.
  30. 11/22/2024b Lecture: notes video   8.3. Paris law, part 1.
  31. 11/29/2024 Lecture: notes video   8.3. Paris law, part 2, variable loading, statistical approach, Dynamic Fracture (part 1): LEFM solutions for dynamic fracture
  32. 112/06/2024 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).