A two-dimensional analysis of the evolution of coherent precipitates in elastic media

Journal Article · Sat Feb 01 04:00:00 EST 1992 · Acta Metallurgica; (United States)

DOI:https://doi.org/10.1016/0956-7151(92)90306-Y· OSTI ID:7306745

McCormack, M; Morris, J W ^[1]; Khachaturyan, A G ^[2]

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1. Lawrence Berkeley Lab., CA (United States). Center for Advanced Materials
2. Rutgers--the State Univ., New Brunswick, NJ (United States). Dept. of Mechanics and Materials Science

In this paper the morphological evolution of coherent inclusions in elastic media is studied in two-dimensions. The inclusions are simple dilations with isotropic surface energy in a system with homogeneous elastic constants of negative anisotropy. The equilibrium sizes at which a circular inclusion transforms to a rectangle or square, and at which a square splits into a doublet or quartet of separated inclusions are computed analytically. A finite-element model is then constructed to simulate the evolution of an arbitrary distribution of inclusions along the minimum-energy path. In the model, the circle evolves into a square, which splits into a doublet by hollowing from its center, or, if this if forbidden, by drawing in a perturbation on its surface. The sizes at which shapes spontaneously transform are compared to the equilibrium values. Finally, the simulation is used to study the evolution of a random distribution of inclusions. The first metastable state assumed by the distribution depends on the elastic interaction, surface energy and areal fraction of the inclusion phase through a single dimensionless parameter that groups these three effects. The results are compared to prior theoretical and experimental work on coarsening patterns in three dimensions.

• Sponsoring Organization: NSF; National Science Foundation, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 7306745
• Journal Information: Acta Metallurgica; (United States), Journal Name: Acta Metallurgica; (United States) Vol. 40:2; ISSN 0001-6160; ISSN AMETA
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360102* -- Metals & Alloys-- Structure & Phase Studies
360103 -- Metals & Alloys-- Mechanical Properties
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANISOTROPY
CHEMICAL REACTION KINETICS
ELASTICITY
ENERGY LEVELS
EXCITED STATES
FINITE ELEMENT METHOD
FRACTURE MECHANICS
INCLUSIONS
KINETICS
MATERIALS
MECHANICAL PROPERTIES
MECHANICS
METASTABLE STATES
MORPHOLOGY
NUMERICAL SOLUTION
PHASE TRANSFORMATIONS
REACTION KINETICS
TENSILE PROPERTIES
TWO-DIMENSIONAL CALCULATIONS