A microstructure evolution model including dislocation plasticity
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A microstructure evolution model including dislocation plasticity Fabrizio Cleri1 and Gregorio D’Agostino Ente Nuove Tecnologie, Energia e Ambiente, Divisione Materiali Centro Ricerche Casaccia, CP 2400, I-00100 Roma, Italy 1also with Istituto Nazionale per la Fisica della Materia, Roma, Italy ABSTRACT We present a stochastic microstructure evolution model applicable to grain growth and its recent extensions, in particular relative to dislocation plasticity. The model is implemented by means of numerical simulations based on the velocity Monte Carlo algorithm. It describes the evolution of a two-dimensional microstructure by tracking the motion of triple junctions, i.e. the vertices where three grain boundaries meet. Grain boundaries can be modeled as straight or curved segments; the misorientation dependence of both grain-boundary energies and mobilities can be included, as well as grain rotation. We show simple examples of normal, abnormal and oriented grain growth. The model is already capable of dealing with a two-phase (liquid-solid) system, to simulate both grain growth and grain dissolution in the liquid. Finally, we report preliminary results of a recent extension of the model to include mechanical deformation from dislocation plasticity.
INTRODUCTION An innovative theoretical approach to microstructural evolution was presented some time ago by Needleman and Rice [1], based on a variational principle for dissipative systems. In the particular case of grain growth Cocks and Gill [2] derived a similar variational functional describing the rate of energy dissipation in a microstructure due to the competition between the reduction of the excess energy and a driving force proportional to the boundary velocity. The variational parameter in all such functionals is the continuous grain-boundary velocity field: by applying D’Alembert’s differential form of the variational principle explicit equations for the minimising velocity field are obtained, and from these the microstructure evolution. Such an approach stands out as very powerful and flexible [2-5], since any term contributing to energy dissipation in the microstructure (e.g., grain sliding and rotation, matter diffusion along grain boundaries, diffusion and plastic work in the grain bulk) can be included in the functional, provided a variational principle for each new term can be established. However, the approach is also computationally inefficient since it is defined in terms of a global minimisation procedure, which amounts to inverting a large matrix at each time step. In a recent paper [6] we proposed a stochastic model of microstructural evolution based on a different interpretation of the Needleman-Rice variational functional, Π[v], which we rewrite as:
∂vs (s) v2n (s) Π[v ] = ∑ ( ∫ γ iκ i vn (s)ds + ∫ γ i ds + ∫ ds ) L L L 2µ N ∂s i gb
i
i
Y7.3.1
i
(1)
with vn and vs the normal and parallel component of grain-boundary velocity, and Li, γi , µi and κi the length, energy, mobility and curvature of the i-th grain boundary, respectively. Our stoch
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