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Plane Stress Analysis of Phase Transformations in Brittle Materials
Author(s) -
ALVAREZ I. S.,
COOPER A. R.
Publication year - 1977
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1977.tb14107.x
Subject(s) - fracture (geology) , materials science , stress (linguistics) , phase transition , mechanics , thermodynamics , phase (matter) , brittleness , phase boundary , plane (geometry) , slab , composite material , mathematics , geometry , chemistry , physics , philosophy , linguistics , organic chemistry , geophysics
A numerical analysis of the Crank‐Nicolson type is used to determine the temperature distribution and phase‐boundary position for a slab‐shaped sample that is cooled or heated through a phase transition under the assumption that heat transfer controls the kinetics of the transition, thus the phase boundary remains planar. First‐order and second‐order transitions (Ehrenfest) are considered, as is a mixed transformation with partially first‐order and partially second‐order behavior. Stress and temperature distributions are calculated for each type. Particular interest is attached to the surface stress. Results are presented using the thermal and elastic properties of quartz. The results are interpreted in reference to brittle fracture during cooling. When slow crack growth is possible, it is shown that, for a purely first‐order transformation, the likelihood of fracture decreases as the cooling rate increases; for a second‐order transition, fracture becomes less probable as the cooling rate decreases. For a mixed transition, an optimum cooling rate can minimize the probability of fracture.