Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics

Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for... Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is consistent with the Griffith model for fracture. Recent efforts to include inertia in this formulation have replaced elastostatics by elastodynamics. In this brief note, we examine the elastodynamic augmentation, and find that it effectively causes the Griffith surface energy to depend on the velocity of the crack. That is, considering two identical specimens that are each fractured by a single crack that grows at different velocities in the two specimens, it is expected that the final equilibrium configurations are nominally identical; however, the phase-field fracture models augmented with elastodynamics achieve final configurations—in particular, the Griffiths surface energy contributions—that depend on the crack velocity. The physical reason is that the finite relaxation time for the stresses in the elastodynamic setting enables the cracked region to widen, beyond the value observed in the quasistatic setting. Once the crack widens, the “no-healing” condition prevents it from relaxing even after the specimen reaches equilibrium. In phase-field models, crack width in the reference configuration is unrelated to the physical opening of the crack but is instead a measure of Griffiths surface energy. This observation suggests that elastodynamic phase-field fracture models should not be used in settings where the crack velocity is large. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Fracture Springer Journals

Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics

Loading next page...
 
/lp/springer_journal/dependence-of-equilibrium-griffith-surface-energy-on-crack-speed-in-dKOvZhneSD
Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Materials Science; Characterization and Evaluation of Materials; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering
ISSN
0376-9429
eISSN
1573-2673
D.O.I.
10.1007/s10704-017-0234-y
Publisher site
See Article on Publisher Site

Abstract

Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is consistent with the Griffith model for fracture. Recent efforts to include inertia in this formulation have replaced elastostatics by elastodynamics. In this brief note, we examine the elastodynamic augmentation, and find that it effectively causes the Griffith surface energy to depend on the velocity of the crack. That is, considering two identical specimens that are each fractured by a single crack that grows at different velocities in the two specimens, it is expected that the final equilibrium configurations are nominally identical; however, the phase-field fracture models augmented with elastodynamics achieve final configurations—in particular, the Griffiths surface energy contributions—that depend on the crack velocity. The physical reason is that the finite relaxation time for the stresses in the elastodynamic setting enables the cracked region to widen, beyond the value observed in the quasistatic setting. Once the crack widens, the “no-healing” condition prevents it from relaxing even after the specimen reaches equilibrium. In phase-field models, crack width in the reference configuration is unrelated to the physical opening of the crack but is instead a measure of Griffiths surface energy. This observation suggests that elastodynamic phase-field fracture models should not be used in settings where the crack velocity is large.

Journal

International Journal of FractureSpringer Journals

Published: Jul 20, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off