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Title: Shear-transformation-zone theory of yielding in athermal amorphous materials

Abstract

Yielding transitions in athermal amorphous materials undergoing steady-state shear flow resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, conclude that the yielding transition is not truly critical. Specifically, for realistic many-body models with short-range interactions, there is a correlation length that grows rapidly but ultimately saturates near the yield point.

Authors:
 [1]
  1. Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1223678
Alternate Identifier(s):
OSTI ID: 1198731
Grant/Contract Number:  
AC05-00OR22725; AC05-00OR-22725
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 92; Journal Issue: 1; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Langer, J. S. Shear-transformation-zone theory of yielding in athermal amorphous materials. United States: N. p., 2015. Web. doi:10.1103/PhysRevE.92.012318.
Langer, J. S. Shear-transformation-zone theory of yielding in athermal amorphous materials. United States. doi:10.1103/PhysRevE.92.012318.
Langer, J. S. Wed . "Shear-transformation-zone theory of yielding in athermal amorphous materials". United States. doi:10.1103/PhysRevE.92.012318. https://www.osti.gov/servlets/purl/1223678.
@article{osti_1223678,
title = {Shear-transformation-zone theory of yielding in athermal amorphous materials},
author = {Langer, J. S.},
abstractNote = {Yielding transitions in athermal amorphous materials undergoing steady-state shear flow resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, conclude that the yielding transition is not truly critical. Specifically, for realistic many-body models with short-range interactions, there is a correlation length that grows rapidly but ultimately saturates near the yield point.},
doi = {10.1103/PhysRevE.92.012318},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 1,
volume = 92,
place = {United States},
year = {2015},
month = {7}
}

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Cited by: 10 works
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