Abstract
We present a probabilistic model for the description of martensitic avalanches. Our approach to the analysis of the model is based on an associated general branching random walk process. Comparisons are reported for numerical and analytical solutions and experimental observations.
Highlights
A martensitic phase-transformation is a first-order diffusionless transition involving a change of shape of the underlying crystal lattice
Discontinuous, kinematically compatible, deformation gradients evolve in space and time, causing the propagation of ultrasonic elastic waves, which generate acoustic emissions (AEs) that are a characteristic signature of martensitic transformations
Experimental eviae-mail: ball@maths.ox.ac.uk be-mail: p.cesana@latrobe.edu.au ce-mail: hambly@maths.ox.ac.uk dence [8] shows that the exponents determined experimentally for different materials can be grouped into universality classes according to the symmetry of the martensitic phase. This observation seems to suggest that there are features of the dynamics of the transformation that depend only on the symmetry reduction at the transition [8]. In this contribution we present a simple probabilistic model for the description of avalanches, in which we imagine that the martensite forms through the nucleation and propagation of thin martensitic plates parallel to the allowed habit planes
Summary
A martensitic phase-transformation is a first-order diffusionless transition involving a change of shape of the underlying crystal lattice. Discontinuous, kinematically compatible, deformation gradients evolve in space and time, causing the propagation of ultrasonic elastic waves, which generate acoustic emissions (AEs) that are a characteristic signature of martensitic transformations This process is activated by the free-energy difference between austenite and martensite, and takes place through a sequence of jerks or avalanches. It is thought that the intermittent character of this transformation is strongly influenced by the disorder of the system, that is by lattice defects and impurities, as well as by the onset of long-range interactions of an elastic nature In this contribution we present a simple probabilistic model for the description of avalanches, in which we imagine that the martensite forms through the nucleation and propagation of thin martensitic plates parallel to the allowed habit planes. For a different theoretical approach to martensitic avalanches in terms of a corresponding sandpile model see [6, 7]
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