增材制造中的相场模拟：图网络

转载自公众平台：npj计算材料学

在金属增材制造过程中，理解和预测材料微观结构演化非常重要。相场（PF）由于对相关物理进行了详细建模，且和热力学基础一致，被认为是一种相对准确的数值模拟方法。

然而，高保真PF方法常常受到计算量的困扰，因为它通常需要求解一组连续场变量的耦合偏微分方程系统，且空间离散化必须足够好，以分辨晶界等微观结构特征。目前针对金属增材制造过程中微观结构演化的PF模拟，仍存在计算成本高、可扩展性差等缺点。因此，开发一种高计算速度、大空间尺度、精度高的金属增材制造的相场模拟框架非常重要。

来自美国西北大学机械工程系的曹坚教授团队，提出了一种物理嵌入式图网络（PEGN），利用一种简洁图形来表示晶粒结构，并将经典的PF理论嵌入到图网络中。

通过将经典的PF问题重新定义为图网络上的无监督机器学习任务，PEGN有效地解决了温度场、液/固相分数和晶粒方向变量，以最小化基于物理的损失/能量函数。

作者使用316L不锈钢的粉末床融合体作为试验台来证明所提出的PEGN的有效性，并通过通过多层和多轨道的例子证明了PEGN的可扩展性。

此外，作者利用有限差分方法对PEGN和经典的直接数值模拟方法在温度场、熔体池开发和晶粒演化等关键方面进行了比较。他们发现，该方法可以在显著提高精度的同时提高PF方法的速度。

Fig. 6 Quantitative comparison of grain size and morphology between DNS and PEGN.

本研究对提供了一种金属增材过程微观结构演化的相场模拟框架，对材料制造具有重要意义。相关论文发表于npj Computational Materials 8: 201 (2022).

Editorial Summary

During metal additive manufacturing (AM) processes, it is of critical importance to understand and predict microstructure evolution. The phase-field (PF) method is regarded as a relatively accurate method due to its detailed modeling of relevant physics and thermodynamically consistent foundations. However, the high-fidelity PF method is plagued by being extremely expensive in computation because it usually requires solving a system of coupled partial differential equations for a set of continuous field variables and the spatial discretization must be fine enough to resolve microstructure features like grain boundaries. Existing PF simulations for microstructure evolution during metal AM processes still have disadvantages of high computing cost and poor scalability. Therefore, it is of great importance to develop a PF simulation framework for metal AM processes, which possesses advantages of high computing speed, large simulation scale and high accuracy. 

A team led by Prof. Jian Cao from the Department of Mechanical Engineering, Northwestern Universit, proposed a physics-embedded graph network (PEGN) to leverage an elegant graph representation of the grain structure and embed the classic PF theory into the graph network. By reformulating the classic PF problem as an unsupervised machine learning task on a graph network, PEGN efficiently solves temperature field, liquid/solid phase fraction, and grain orientation variables to minimize a physics-based loss/energy function. The authors used powder bed fusion of 316L stainless steel as a testing bed for demonstrating the effectiveness of the proposed PEGN, and demonstrated the scalability with multi-layer and multi-track examples. Furthermore, by comparing PEGN with the classic DNS approach with the finite difference method in several key aspects such as temperature field, melt pool development and grain evolution, the authors showed that the proposed approach can speed up the PF method by orders of magnitude while preserving significantly high accuracy. This study provides a phase field simulation framework for the microstructure evolution of metal AM processes, which is of great significance in the field of material manufacturing. This article was published in npj Computational Materials 8: 201 (2022).

原文Abstract及其翻译

Physics-embedded graph network for accelerating phase-field simulation of microstructure evolution in additive manufacturing (增材制造中加速相场模拟微观结构演化的物理嵌入图网络)

Tianju Xue, Zhengtao Gan, Shuheng Liao & Jian Cao

Abstract The phase-field (PF) method is a physics-based computational approach for simulating interfacial morphology. It has been used to model powder melting, rapid solidification, and grain structure evolution in metal additive manufacturing (AM). However, traditional direct numerical simulation (DNS) of the PF method is computationally expensive due to sufficiently small mesh size. Here, a physics-embedded graph network (PEGN) is proposed to leverage an elegant graph representation of the grain structure and embed the classic PF theory into the graph network. By reformulating the classic PF problem as an unsupervised machine learning task on a graph network, PEGN efficiently solves temperature field, liquid/solid phase fraction, and grain orientation variables to minimize a physics-based loss/energy function. The approach is at least 50 times faster than DNS in both CPU and GPU implementation while still capturing key physical features. Hence, PEGN allows to simulate large-scale multi-layer and multi-track AM build effectively.

摘要相场（PF）方法是一种基于物理的模拟界面形态的计算方法。它已被用于金属增材制造（AM）中的粉末熔化、快速凝固和晶粒结构演化的模拟。然而，传统的直接数值模拟方法（DNS）由于网格尺寸足够小，计算成本很高。本文提出了一种物理嵌入式图网络（PEGN），它利用一种简洁图形来表示晶粒结构，并将经典的PF理论嵌入到图网络中。通过将经典的PF问题重新定义为图网络上的无监督机器学习任务，PEGN有效地解决了温度场、液/固相分数和晶粒方向变量，以最小化基于物理的损失/能量函数。在CPU和GPU实现中，该方法至少比DNS快50倍，同时仍然能捕获关键的物理特性。因此，PEGN可以有效地模拟大规模的多层、多轨AM构建。