A level set approach to simulate grain growth with an evolving population of second phase particles

Abstract

In numerous polycrystalline materials, grain size is controlled by second phase particles (SPPs) that hinder the grain boundaries (GBs) by pinning mechanisms. The Smith–Zener pinning (SZP) model describes the physical interaction between SPPs and GBs. Both of them can evolve when applying a heat treatment to the material. As industrial forging processes involve hot deformation steps near the solvus temperature, it is thus of prime importance to characterize the evolution of the SPPs due to their impact on the final microstructure, notably on the grain size. The level set (LS) method is classically used to describe the influence of SPPs on grain growth (GG) by considering the simulated particles as inert and represented by static holes in the used finite element (FE) mesh. A new formalism to model GG mechanism under the influence of the SZP phenomenon, able to take into account evolving particles is proposed. It involves the representation of SPPs by a LS function and a particular numerical treatment around the grain interfaces encountering SPP, making possible the modelling of SPPs evolution without altering the undergoing pinning pressure. Validation and comparison of the new method regarding previous FE-LS formulation in 2D and 3D simulations and an application on GG under the influence of dissolving particles are described.

Dissolution of the Primary γ′ Precipitates and Grain Growth during Solution Treatment of Three Nickel Base Superalloys

“…The multiple junctions treatment based on [57] has been applied both for 2D and 3D simulations of GG in single phase materials or with static SPP using the LS approach [32,55,56,72]. A Modified Multiple Junctions Treatment (MMJT) has recently been proposed in [13] to consider the precipitates as an LS function in FE-LS GG modeling. This new description of the particles opens the possibility of making SPP evolve.…”

“…Without SPP, the MMJT is equivalent to the classical numerical treatment (Equation ( 12)). When SPP are present, it enables by successive iterations to impose the Young-Herring equilibrium for incoherent SPP (see [13] for further details).…”

“…The dissolution of primary γ precipitates in nickel base superalloys has mainly been studied experimentally [1,[8][9][10][11][12] but not so much in full-field numerical works [13][14][15] at the polycrystalline scale.…”

“…For instance, probabilistic methods such as the Monte Carlo (MC) or Pott's model [16][17][18][19] and the Cellular Automata (CA) models [20,21] were used to account for SZP. More complex models have been developed in the last decades, such as the Front-Tracking methods [22], and the Front-Capturing approaches, including the multi phase-field (MPF) [23][24][25][26][27][28][29][30] and level-set (LS) [13,[31][32][33] frameworks.…”

“…The SZP-GG coupling exhibits complex behaviors [9,31,35] that include precipitate evolution. To our knowledge, few numerical works consider the precipitate evolution, some of them using the PF method [30,36] and other using the LS approach [13]. This work adopts the LS approach presented in [13], where a special treatment at the precipitate/GB interface is made to model incoherent precipitates (i.e., assuming the precipitate/GB contact angle to be 90 • ).…”