Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-01T00:01:20.202Z Has data issue: false hasContentIssue false

7 - Elements of linear fracture mechanics

Published online by Cambridge University Press:  05 April 2015

François Henri Cornet
Affiliation:
Université de Strasbourg
Get access

Summary

As pointed out in chapter 2, an elastic material may be modeled by a spring, and it is quite intuitive that a spring cannot be extended indefinitely: some maximum force, and correlatively some maximum spring extension, must exist that defines an elastic limit. When the force, or the spring extension, becomes larger than this maximum value the spring either breaks or extends further but with a nonreversible component, so that some residual deformation exists when the loading is relaxed. In a crude way, this defines two possible post-elastic behaviors: either the spring breaks, in which case the material used to make the spring is said to be brittle, or the spring deforms in a nonelastic manner, so that a permanent deformation is observed when the load is relaxed, in which case the material is said to be ductile.

While a spring may help illustrate elastic phenomena in one dimension, we saw in chapters 3–5 that for three-dimensional problems of elasticity we must introduce three dimensional stresses and strains. These quantities are second-order tensors, and elasticity implies a linear relationship between the stress and small-strain components. By comparison with the spring's behavior, we may anticipate that when the principal stress (or principal strain) magnitudes, or some function of them, become larger than some critical values, either the material breaks into pieces or it deforms according to a nonreversible process. As for the case of a spring, we call the post-elastic behavior brittle when the material fails because of the extension of fractures. We call the post-elastic behavior ductile when the material deforms continuously with occurrence of a nonreversible component. The object of the present chapter is to discuss brittle failure; ductility is discussed in chapters 8 and 9.

Different types of laboratory experiments may be conducted on rock samples to determine their strength, or more precisely to investigate the phenomena that take place after the elastic limit has been reached (e.g. Jaeger and Cook, 1979, chapter 6).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×