Advanced Search
MyIDEAS: Login

Unified physics of stretched exponential relaxation and Weibull fracture statistics

Contents:

Author Info

  • Mauro, John C.
  • Smedskjaer, Morten M.
Registered author(s):

    Abstract

    The complicated nature of materials often necessitates a statistical approach to understanding and predicting their underlying physics. One such example is the empirical Weibull distribution used to describe the fracture statistics of brittle materials such as glass and ceramics. The Weibull distribution adopts the same mathematical form as proposed by Kohlrausch for stretched exponential relaxation. Although it was also originally proposed as a strictly empirical expression, stretched exponential decay has more recently been derived from the Phillips diffusion-trap model, which links the dimensionless stretching exponent to the topology of excitations in a glassy network. In this paper we propose an analogous explanation as a physical basis for the Weibull distribution, with an ensemble of flaws in the brittle material serving as a substitute for the traps in the Phillips model. One key difference between stretched exponential relaxation and Weibull fracture statistics is the effective dimensionality of the system. We argue that the stochastic description of the flaw space in the Weibull distribution results in a negative dimensionality, which explains the difference in magnitude of the dimensionless Weibull modulus compared to the stretching relaxation exponent.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112006759
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 391 (2012)
    Issue (Month): 23 ()
    Pages: 6121-6127

    as in new window
    Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:6121-6127

    Contact details of provider:
    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Glass; Relaxation; Fracture statistics; Theory;

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Sarabia, José María & Prieto, Faustino & Trueba, Carmen & Jordá, Vanesa, 2013. "About the modified Gaussian family of income distributions with applications to individual incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1398-1408.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:6121-6127. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.