Recursive grain remapping scheme for phase‐field models of additive manufacturing

Abstract

The phase‐field method is an attractive tool in modeling microstructural evolution due to rapid solidification under additive manufacturing conditions, but typical polycrystalline models are prone to grain coalescence. Grain tracking and remapping schemes can eliminate artificial coalescence and increase the number of grains and crystallographic orientations that may be considered in a simulation, but previous tracking and remapping schemes may not efficiently capture the complex grain morphologies that form during additive manufacturing. A new recursive scheme is derived from a binary tree of axis‐aligned bounding boxes that can efficiently represent columnar and irregularly shaped grains. We demonstrate the power of this approach by simulating microstructures with hundreds to thousands of grains and quantify the reduction in the number of order parameters required to represent the microstructure. The new scheme leads to orders of magnitude fewer computational resources as compared to the naïve paradigm of one grain per order parameter, and also offers a substantial improvement over algorithms derived from bounding spheres.

The Effects of Melt Pool Geometry and Scan Strategy on Microstructure Development During Additive Manufacturing

“…The numerical implementation of the model is identical to the previous studies and includes grain remapping to reduce the number of order parameters [7,8]. The model parameters, which are identical to those in [8], represent an analogue of 316L stainless steel and are listed in table 1.…”

“…The numerical implementation of the model is identical to the previous studies and includes grain remapping to reduce the number of order parameters [7,8]. The model parameters, which are identical to those in [8], represent an analogue of 316L stainless steel and are listed in table 1. A rectilinear geometry with dimensions 192 μm × 76.8 μm × 38.4 μm in the 𝑥, 𝑦, and 𝑧 directions, respectively, is generated that initially contains 3,169 grains with an average grain size of 6.7 ± 2.9 μm.…”

“…In the present study, we employ the PFM of the PBF process proposed by Chadwick and Voorhees [7,8]. The total Helmholtz free energy of the system, 𝐹, is constructed as a functional of diffuse phase-field order parameters, their gradients, and the latent heat of fusion:…”

“…Additionally, grains that had <100> crystallographic directions parallel to the normal direction of the solid-liquid interface later in the solidification process competed more effectively, as they were more likely to be favourably aligned with the melt pool boundary in the regime where kinetic anisotropy became significant. Subsequently, we have implemented a novel approach to reassign grains between the diffuse order parameters of the PFM that prevents grains from merging together into one feature [8]. This permits more grains and crystallographic orientations to be sampled in the resulting simulations.…”

Multi-Phase-Field Framework for Epitaxial Grain Growth in Selective Laser Melting Additive Manufacturing with Multi-Track and Multi-Layer

“…The cellular automaton 43,44 model has been widely used [45][46][47][48] , and it enables the prediction of material microstructure under melt flow [49][50][51] . The PF method is also used as a coarse-grained model [52][53][54][55][56][57] . Chadwick and Voorhees 55 studied the development of epitaxially grown grains using a multi-phase-field (MPF) coupled with the Rosenthal equation 58 .…”