Multi-phase-field study of the effects of anisotropic grain-boundary properties on polycrystalline grain growth

Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth

“…If numerical modeling by considering heterogeneous values of GB mobility and GB energy remains a complex discussion, it has in fact been widely studied at the polycrystalline scale with a large variety of numerical approaches: multi phase-field [6][7][8], Monte Carlo [9,10], molecular dynamics [11], orientated tessellation updating method [12], vertex [13], front-tracking Lagrangian or Eulerian formulations in a finite element (FE) context [14][15][16], and level-set (LS) [17][18][19], to cite some examples. During annealing, two properties have been widely studied: the GB energy and mobility.…”

“…Heterogeneous models were proposed, in which each boundary has its own energy and mobility [10,18,19,[24][25][26][27][28][29][30][31]. For instance, every grain could be related with an orientation, thus the mobility and energy can be computed in terms of the disorientation [7,19], but the mis-orientation axis and inclination dependence are frequently not taken into account. Finally, general frameworks in which the five parameters, mis-orientation, and inclination are discussed have been proposed, and these models could be categorized as fully anisotropic [32][33][34].…”

A novel highly efficient Lagrangian model for massively multidomain simulation applied to microstructural evolutions

“…These both rely on the definition of each domain by the use of signed LS functions to perform their computations allowing the definition of sharp interfaces 1 of domains, while their evolution is in general formulated via a transport equation. Another model with a high affinity with the LS model is the Phase-Field (PF) method [31,32,33,34,35,36,37,38,39,40,41,42] where the main difference with the LS method is the use of diffuse interfaces 2 , their evolution is formulated based on the minimisation of the free energy of the system. Aditionally to the MC, CA, LS and PF methods, models based on the Lagrangian displacement of interfaces can be used as in vertex approaches [43,4,44,45,46,47] or Front-Tracking approaches [48,5,49,50,51,52] which have been taken as inspiration for the developement of a new front-tracking method topological REmeshing in lAgrangian framework for Large Interface MOTION (RealIMotion hereafter TRM) introduced in a previous publication [53].…”

S-PFM model for ideal grain growth

“…However, phase-field methods are computationally very demanding, especially when accurate statistical measurement is needed. As an example, we detail the conditions that have to be fulfilled to measure an accurate steady-state grain size distribution, a question that has been recently the focus of several phase-field works [25][26][27][28].…”

“…• First, the accurate measurement of a grain size distribution requires a large enough number of grains and, based on the calculations in [27], about 3 × 10 4 grains are necessary.…”