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Elastic-Plastic Fracture Mechanics. Lecture 2

These notes belong to a course on fracture mechanics

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.

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Elastic-Plastic Fracture Mechanics. Lecture 1

These notes belong to a course on fracture mechanics

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.

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The J integral

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.

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Fracture of Rubber. Lecture 2

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.

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Fracture of Rubber

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.

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Stress Corrosion

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:

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Fatigue

These notes were prepared when I taught fracture mechanics in 2010, and were updated when I taught the course again in 2014.

Notes on other parts of the course are also online.

 

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Resistance Curve

These notes were initially written when I taught fracture mechanics in spring 2010, and were updated when I taught the course again in 2014.

You can access all notes for the course on fracture mechanics

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Linear elastic fracture mechanics

These notes were initially written when I taught fracture mechanics in spring 2010.  The title of the notes was then "toughness".  In revising the notes for the class in 2014, I have changed the title of the notes to "Linear elastic fracture mechanics".

You can access all notes for the course on fracture mechanics

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Crack-tip field

These notes were initially written when I taught fracture mechanics in spring 2010.  The title of the notes was then "stress intensity factor".  In revising the notes for the class in 2014, I have changed the title of the notes to "crack-tip field".

You can access all notes for the course on fracture mechanics

 

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Applications of Fracture Mechanics

These notes were prepared when I taught fracture mechanics in 2010, and were updated when I taught the course again in 2014.

Notes on other parts of the course are also online.

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Energy release rate. Fracture energy

These notes were prepared when I taught fracture mechanics in 2010, and were updated when I taught the course again in 2014. I hope to start a conversation at a new post entitled Division of Labor.

Notes on other parts of the course are also online.

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The Griffith Paper

I wrote these notes on the Griffith (1921) paper for a graduate course on fracture mechanics taught in 2010.  The notes were updated when I taught the course in 2014, and were discussed in a new thread titled Inglis (1913) vs. Griffith (1921).

 

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Trouble with linear elastic theory of strength

A body is subject to a load. What is the magnitude of the load that will cause the body to fracture? Let us begin with a body made of a glass, which deforms elastically by small strains. A procedure you have been taught before probably goes as follows. You first determine the maximum stress in the body. You then determine the strength of the material. The body is supposed to fracture when the maximum stress in the body reaches the strength of the material.

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Engineering Sciences 247: Fracture Mechanics

Fall 2020, Tuesday and Thursday 12:00 pm–1:15 pm.

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PhD Winterschool on Dielectric Elastomer Transducers

I’ve just come back from a Winter School on Dielectric Elastomer Transducers, held at Monte Verità, Ascona, Switzerland, 10-16 January 2010.  Lectures were given by various people, covering the theory of electromechanical interaction, design of devices, development of materials, and technologies of manufacturing.  I was asked to give three lectures on the theory.  I attach the slides of my lectures.

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Dielectric elastomers of interpenetrating networks

Recent experiments have shown that a voltage can induce a large deformation in an elastomer of interpenetrating networks. We describe a model of interpenetrating networks of long and short chains. As the voltage ramps up, the elastomer may undergo a snap-through instability. The network with long chains fills the space and keeps elastomer compliant at small to modest deformation. The network with short chains acts as a safety net that restrains the elastomer from thinning down excessively, averting electrical breakdown.  It appears possible to find a dielectric elastomer capable of giant deformation of actuation.  You can read the paper, or take a look at the slides posted here.

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A new Technical Committee on Soft Materials

A growing number of mechanicians are entering the field of soft materials, such as polymers, gels, and tissues. While they interact with researchers in technical societies traditionally identified with the field, they also maintain connection with researchers in applied mechanics.

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