Multiphase microstructure evolution model including dislocation plasticity
- PDF / 221,686 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 61 Downloads / 241 Views
We present the recent extensions of our stochastic microstructure evolution model including multiphase domain evolution and dislocation plasticity. The model was 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 (GBs) meet. GBs can be modeled as straight, curved, or discretized segments; the misorientation dependence of both grain-boundary energies and mobilities can be included to represent different textures.
I. 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 Gill2 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 minimizing velocity field are obtained and from these the microstructure evolution. Such an approach stands out as very powerful and flexible,2,3 since any term contributing to energy dissipation in the microstructure [e.g., grain sliding and rotation, matter diffusion along grain boundaries (GBs), 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. On the other hand, the approach is also computationally inefficient since it is defined in terms of a global minimization procedure, which amounts to inverting a large matrix at each time step. Moreover, global minimization implies a virtually instantaneous propagation of thermodynamic information, which is not necessarily the most general case.
a)
Also with Istituto Nazionale per la Fisica Della Materia, Roma, Italy.
1932
http://journals.cambridge.org
J. Mater. Res., Vol. 17, No. 8, Aug 2002
Downloaded: 01 Apr 2015
In a recent paper,4 we proposed a stochastic model of microstructural evolution based on a different interpretation of the Needleman-Rice variational functional, ∏ [v], which we rewrite as: 兿关兴 =
冱 冉兰
i∈ Ngb
Li
␥iin共s兲ds +
冊
兰
Li
␥i
⭸s共s兲 ds ⭸s
2n共s兲 + ds , (1) Li 2i with vn and vs the normal and parallel component of grain-boundary velocity, and Li , ␥i , µ , and i the length, energy, mobility, and curvature of the i-th grain boundary, respectively, for a system composed of Ng grains separated by Ngb GBs. It is worth stressing that only the boundaries are being tracked in our microstructural evolution model, while the grain interior is supposed to remain homogenous. Such a condition will have to be relaxed when degrees of freedom relative to the grain interior (such as lattice
Data Loading...
