A body consists of two materials bonded at an interface. On the interface there is a crack. The body is subject to a load, causing the two faces of the crack to open and slide relative to each other. When the load reaches a critical level, the crack either extends along the interface, or kinks out of the interface.

Due in class, Tuesday, 4 May 2010

A crack pre-exists in a body. When the body is loaded, the two faces of the crack may simultaneously open and slide relative to each other. The crack is said to be under a mixed-mode condition. When the load reaches a critical level, the crack starts to grow, and usually kinks into a new direction. Subsequently the crack often grows along a curved path.

This lecture discusses the critical condition to initiate the growth, the direction of the kink, and the method to predict the curved path.

Due in class, Thursday, 22 April 2010

Lecture 1 introduced the crack bridging model. The model is also known as the cohesive-zone model, the Barenblatt model, or the Dugdale model. The model consists of two main ingredients:

Due in class, Thursday, 15 April 2010

Following Griffith (1921), we distinguish two processes: deformation in the body and separation of the body. Up to this point, the process of deformation has been described by field theories of various kinds, such as

Lecture 1 described the Begley-Landes experiment, and the blunting of a crack due to large deformation. Lecture 2 is motivated by the following considerations.

When a rubber containing a crack is loaded, before the crack extends, strain everywhere in the rubber can be large. By contrast, when a metal containing a crack is loaded, before the crack extends, strain in the metal is typically small, except near the tip of the blunted crack. Consequently, to analyze deformation in the metal, at a distance a few times the crack opening displacement away from the crack tip, we can use the field theory of infinitesimal deformation.

Due in class, Thursday, 8 April 2010

Decouple elastic deformation of the body and inelastic process of separation. Up to this point we have been dealing with the following situation. When a load causes a crack to extend in a body, a large part of the body is elastic, and the inelastic process of separation occurs in a zone around the front of the crack. Inelastic process of separation includes, for example, breaking of atomic bonds, growth of voids, and hysteresis in deformation.

For a crack in an elastic body subject to a load, the elastic energy stored in the body is a function of two independent variables: the displacement of the load, and the area of the crack. The energy release rate is defined by the partial derivative of the elastic energy of the body with respect to the area of the crack.

This definition of the energy release rate assumes that the body is elastic, but invokes no field theory. Indeed, the energy release rate can be determined experimentally by measuring the load-displacement curves of identically loaded bodies with different areas of the cracks. No field need be measured.

Due in class, Thursday, 1 April 2010

Fracture mechanics without invoking any field theory. In Lecture 1 on Fracture of Rubber, we considered the extension of a crack in an elastic body subject to a load. Following Rivlin and Thomas (1953), we regarded the elastic energy stored in the body as a function of two independent variables: the displacement of the load, and the area of the crack. The partial derivative of the elastic energy with respect to the area of the crack defined the energy release rate.

Actually, I don't know much about Fracture Mechanics. This is the book that my previous teach in Beijing Inst of Tech recommended it to me. I think it is good.

A rubber band can be stretched several times its original length. This large deformation may hide its brittleness: the strain to rupture can be markedly reduced by the presence of a crack. This lecture describes fracture mechanic of highly deformable materials, such as rubbers and gels.

Demonstrate in class the effect of a crack on a rubber band. Use a wide rubber band. Show the class that the rubber band can be stretched several times its original length. Then use scissors to cut a crack into the rubber band. Pull the rubber band to rupture. Note that the strain to rupture is markedly reduced by the crack. Pass the scissors and some rubber bands around. Invite every student to try.

Fracture Mechanics, Fundamentals and Applications, T.L. Anderson, CRC Press, 3rd Ed., 2004.

This book is in line with what Zhigang is teaching in class. Because Kejie and Widusha have already recommended this book, I would like to introduce you some other books as well as a different approach to cracks and Fracture Mechanics.

The book I recommend for reading is Fracture mechanics: fundamentals and applications, by T.L.Anderson, 3rd edition, 2005. I first saw this book on the top list of reading materials of Brown U. When I have it I found so pleasent to read through it. Here is the short-list of its content

Chapter 1: Introduction: History and overview

Chapter 2:Fundamental concepts: linear elastic fracture mechanics

Chapter 3: Elastic-plastic mechanics

Chapter 4: Dynamic and time-dependent fracture

Chapter 5: Material behavior: Fracture mechanics in metals

Chapter 6: Fracture mechanics in nonmetals (engineering plastics, polymers, fiber-reinforced plastics, ceramics)

Chapter 7: Fracture toughness testing of metals

Dynamic fracture mechanics is written by a very well known professro-L B Freund. Honestly, I have only read a small part of the book. However, I recommend this book because after reading this book, you can learn many things which haven't be touched in the class, as stated by Zhigang in the beginning of the class.

Generally speaking, dynamic fracture just include the inertia effect during the fracture process. The inertia effect can either from fast loading or the stress wave radiated from the crack tip. The concept of dynamic fracture in earthquake and other geophysics phenonmenon become extremmely import. The prediction of crack path and the instability of crack propagation also make the study of dynamic fracture important.

A glass may withstand a static load for a long time (days, weeks, or years) and then, without warning, breaks suddenly. Here are salient empirical observations:

• The delay time depends on the magnitude of the load: The smaller the load, the longer the delay time.
• The phenomenon is environment-sensitive. Glass suffers delayed fracture in moisture, but not in vacuum. The lower the humidity, the longer the delay time.
• The phenomenon is thermally-activated. The lower the temperature, the longer the delay time.

The phenomenon occurs to all materials to some degree in some environments. The phenomenon is known variously as

This book is an introduction to molecular and atomistic modeling techniques applied to solid deformation and fracture.  Focusing on various brittle, ductile and geometrically confined materials, this book includes computational methods at the atomistic scale, and describes how these techniques can be used to model the dynamics of crack, dislocations and other deformation mechanisms.

I like this book a lot because it covers a variety of research fields which include material science, computer science and bioengineering, as well as providing a comprehensive and up-to-date review on the development of the molecular dyanamics simulation, with a focus on the application of fracture mechanics.

I think this book is a good complement to the course Fracture Mechanics ES 247. There are several reasons:

1. This book is written from an engineering point of view, which is different from our class. In the first chapter Introduction, the book gives some engineering cases of fracture and fatigue. In chapter 3, the stress field is given for the different cracks with engineering importance. This book has two parts. one is Principle, and the other is Application, with a lot of engineering practical problems. Although I haven't read the second part, I think it will well complement our course.

Book reviews are available at

http://www.amazon.com/Fatigue-Materials-Cambridge-Science-Second/product-reviews/0521578477/ref=dp_top_cm_cr_acr_txt?ie=UTF8&showViewpoints=1

Due in class, Thursday, 11 March 2010

Required reading. P.C. Paris, M.P. Gomez and W.E. Anderson, A rational analytic theory of fatigue. The Trend in Engineering 13, 9-14 (1961). I went online and found that the Trend in Engineering is the alumni newsletter of the College of engineering, of the University of Washington.  I could not find this paper online. John Hutchinson offered to write to Paul Paris for a copy of the paper, which Paris sent by airmail. A scanned copy of the paper is attached with this lecture.