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Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

Dayal, Kaushik and Bhattacharya, Kaushik (2006) Kinetics of phase transformations in the peridynamic formulation of continuum mechanics. Journal of the Mechanics and Physics of Solids, 54 (9). pp. 1811-1842. ISSN 0022-5096. https://resolver.caltech.edu/CaltechAUTHORS:DAYjmps06

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Abstract

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces. We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves. We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jmps.2006.04.001DOIArticle
ORCID:
AuthorORCID
Dayal, Kaushik0000-0002-0516-3066
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:Author preprint. Formal article, Copyright © 2006 Elsevier Ltd. Received 25 November 2005; revised 26 March 2006; accepted 1 April 2006. Available online 5 June 2006. We thank Stewart Silling, Mathias Jungen, James Knowles, Markus Zimmermann, and Rohan Abeyaratne for useful discussions. We are grateful for the financial support of the Sandia National Labs and the National Science Foundation.
Funders:
Funding AgencyGrant Number
Sandia National LaboratoriesUNSPECIFIED
NSFUNSPECIFIED
Subject Keywords:Microstructures; Phase transformation; Shape-memory effect; Peridynamics; Stability and bifurcation
Issue or Number:9
Record Number:CaltechAUTHORS:DAYjmps06
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:DAYjmps06
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3594
Collection:CaltechAUTHORS
Deposited By: Kaushik Dayal
Deposited On:22 Jun 2006
Last Modified:12 Dec 2019 17:06

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