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Engineering Sciences 242r: Fracture Mechanics of Thin Films and Composite Materials

Time. Thursday and Tuesday. 1:30-3:00 pm (Harvard University), 12:30-2:2:00 pm (University of Nebraska). First meeting: 1 February 2007

Place. Harvard University: Fairchild 102 (map). University of Nebraska: 111 Walter Scott Engineering Center

Course website (this page): node/754


Teaching fellows

Students and why they take this course.


Homework Sets

Auxilary notes

Online resources

Offline resources

Brief Outline of Topics

  • Fracture Mechanics. Energy release rate. Stress intensity factor. Mixed mode fracture. Representative solutions. Fracture specimens. Fracture toughness, crack growth resistance. Plastic zones. Plane stress vs. plane strain. Small scale yielding. J integrals. Cohesive zone modeling. (HRR field. A blunting crack tip. Fatigue. Environment-assisted cracking)
  • Thin films and layered materials. Origin of residual stresses. Curvature of layered materials due to residual stresses. Channel cracks. Debonding. Delamination. Buckle-delamination.
  • Composites. Toughening. Test specimens for delamination. Matrix cracking. Size effects. Bridging.


  • Prerequisite: a graduate course on solid mechanics.
  • No textbook is required. Notes will be posted periodically.
  • The posts concerning this course will have at least three tags: ES 242r, fracture mechanics, Spring 2007. Thus, the URL for all posts of this course is taxonomy/term/551,32,528
  • To be alerted of any new content added to this course, please subscribe to the RSS feed of the course. The URL of the feed is: taxonomy/term/551,32,528/0/feed
  • You can ask questions or add comments to the comment section of each post. You can also subscribe to the RSS feed for the comments to all the posts of this course: crss/term/551

IT officers


Teng Li's picture

John and Zhigang:

Interesting idea to offer a course on two campuses at the same time, with the aid of iMechanica.  I'm wondering how this works, John teaches at Nebraska and Zhigang teaches at Harvard?

Distance (Remote) education has a rather long history. Radio, TV, and recently Internet have all been used to deliver the content in distance education.  In the age of Web2.0, people have started to talk about eLearning 2.0.

I'm imagining, with an online platform like iMechanica, plus podcasts of  lectures (audio, and even video later on), a mechanics course  can be offered for iMechanicians of interest.  This concept can be readily adapted to many other disciplines.  Detail logistics aside, such a teaching/learning process may have significant impact on our trational education system in the future.  Can we get rid of the barrier between universities, and provide education without boundary?


     You raise some good questions.  There has been talk of using the internet to enhance teaching for many years, and, while some advances have been made, it is surprizing that the internet has not be more exploited for this purpose.  Zhigang and I wanted to see how this collaboration with the University of Nebraska would work--we view this as a noble experiment!   Stay tuned.

Henry Tan's picture

Good company and motivation can hardly be achieved through internet teaching. These are values for on-campus classroom teaching.

MichelleLOyen's picture

I could not disagree more with the idea that online teaching is mutually exclusive of "good company and motivation" especially when the students in question have been raised in the time of email, instant messaging, and now web-based social networking forums such as My Space. This is a generation of students who are accustomed to forming relationships online and thus there are no real disadvantages of internet-based teaching. A potential key advantage includes the potential for less frightening participation in online chats or other forms of nontraditional discussion for students who might be too shy to speak up in a traditional classroom setting.

That is very interesting idea sir,if  imechanica can provide a distance education from all field of engineering mechanics.The whole world is watching all the comments and suggestion in this site. Maybe, We here from asia can be benefited in your great proposal " Education without boundary" reagardless of distance,races,ethnics and culture..

Henry Tan's picture

Instant discussion is the kernel of iMechanica.
In the old times without internet, we had books. Students could read the same book; in this sense the education had no boundary even at those old times.
However, book readers can not exchange ideas, ask questions. In iMechanics, things are different; we can put our concerns, even stupid ones, on the table.

zhuling's picture

Dr. Hutchinson and Suo,I am taking the fracture mechanics class from Lincoln Nebraska now.  During my literature reading, I come across two terms :the Crack Opening Displacement (COD) and the Crack Tip Opening Displacement(CTOD). What is the difference between these two terms? Can COD be used as a criterion to predict a crack's propagation?  For example, for a given material, can we say the crack will propagate if the opening displacement exceeds a certain value?  Appreciate your help.

My friends keep talking of COD's and CTOD's and though they learn at the Ohio Dominican University they couldn't tell me the difference between the two notions. Thanks for asking and thanks to all of you who answered.

Dear Ling, COD as a criterion is used for crack growth in elastoplastic materials, for which the K-criterion does not hold due to the finite plastic zone near crack tip. However, within the framework of SSY, COD-criterion is equivalent to K-criterion (Kanninen and Popelar, 1985). COD-criterion is considered as a supplementary fracture criterion for elastoplastic materials before the evaluation of J-integral (A.A. Wells, 1979) to be discussed in this class. The typical definition of CTOD for cracking in ductile materials can be found in the following link:  

Based on my understanding, COD and CTOD indicate the same term though they may have a little difference in literature here and there. For example, the COD-criterion was discussed in detail in the classic textbook: Advanced Fracture Mechanics (Kanninen and Popelar, 1985), in which the term COD is actually also the CTOD. While in the textbook Cracks and Fracture (Broberg, 1999, pp. 575), it says that COD and COA (crack opening angle) are often written as CTOD (crack tip opening displacement) and CTOA (crack tip opening angle). Also, in some literature, it says that COD is the total displacement at crack tip (usually mixed-mode crack), while CTOD indicates the crack tip opening displacement due to pure mode I loading [e.g. Sha et al., Int. J. Fracture 104 (2000) 409-423]. There may be many others. Therefore, when we use COD or CTOD, we need to take care of the definition used in context. Hope this would make it clear.

Gopinath Venkatesan's picture

To my knowledge, COD is first introduced by Boyle [1962] for measuring cracklength directly (I mean without measuring from microscope readings). This is essentially a strain gage reading for compliance (inverse of stiffness, COD/Load). I thought CTOD is the displacement of the crack tip and is different from COD. All these days, I convinced myself that CTOD is developed for elastoplastic while COD can take care of LEFM area but now confused. I will go through the references cited by Wu. Thanks.  


Distance education open up many possibilities, more and more courses are being available, which I believe benefits both the university and the people, knowledge that before was limited to a few can now be accessed to many.

Li Han's picture

Dear Zhigang,

        I remember the course has been recorded. I am just wondering who to contact to revisit these valuable materials. Thank you. 

Li Han 


Zhigang Suo's picture

Li Han:  I don't recall that the full course was recorded, but some lectures might be.  I don't know who has these CDs.

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