Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

Sankarasubramanian, R and Jog, CS and Abinandanan, TA (2002) Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity. In: Metallurgical and Materials Transactions A, 33 (4). pp. 1083-1090.

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Abstract

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

Item Type:	Journal Article
Publication:	Metallurgical and Materials Transactions A
Publisher:	The Minerals, Metals & Materials Society
Additional Information:	Copyright of this article belongs to The Minerals, Metals & Materials Society.
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering Division of Mechanical Sciences > Materials Engineering (formerly Metallurgy)
Date Deposited:	28 Jul 2011 04:46
Last Modified:	28 Jul 2011 04:46
URI:	http://eprints.iisc.ac.in/id/eprint/39439

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