轉(zhuǎn)載自公眾平臺：npj計(jì)算材料學(xué)

在金屬增材制造過程中，理解和預(yù)測材料微觀結(jié)構(gòu)演化非常重要。相場（PF）由于對相關(guān)物理進(jìn)行了詳細(xì)建模，且和熱力學(xué)基礎(chǔ)一致，被認(rèn)為是一種相對準(zhǔn)確的數(shù)值模擬方法。

然而，高保真PF方法常常受到計(jì)算量的困擾，因?yàn)樗ǔＰ枰蠼庖唤M連續(xù)場變量的耦合偏微分方程系統(tǒng)，且空間離散化必須足夠好，以分辨晶界等微觀結(jié)構(gòu)特征。目前針對金屬增材制造過程中微觀結(jié)構(gòu)演化的PF模擬，仍存在計(jì)算成本高、可擴(kuò)展性差等缺點(diǎn)。因此，開發(fā)一種高計(jì)算速度、大空間尺度、精度高的金屬增材制造的相場模擬框架非常重要。

來自美國西北大學(xué)機(jī)械工程系的曹堅(jiān)教授團(tuán)隊(duì)，提出了一種物理嵌入式圖網(wǎng)絡(luò)（PEGN），利用一種簡潔圖形來表示晶粒結(jié)構(gòu)，并將經(jīng)典的PF理論嵌入到圖網(wǎng)絡(luò)中。

通過將經(jīng)典的PF問題重新定義為圖網(wǎng)絡(luò)上的無監(jiān)督機(jī)器學(xué)習(xí)任務(wù)，PEGN有效地解決了溫度場、液/固相分?jǐn)?shù)和晶粒方向變量，以最小化基于物理的損失/能量函數(shù)。

作者使用316L不銹鋼的粉末床融合體作為試驗(yàn)臺來證明所提出的PEGN的有效性，并通過通過多層和多軌道的例子證明了PEGN的可擴(kuò)展性。

此外，作者利用有限差分方法對PEGN和經(jīng)典的直接數(shù)值模擬方法在溫度場、熔體池開發(fā)和晶粒演化等關(guān)鍵方面進(jìn)行了比較。他們發(fā)現(xiàn)，該方法可以在顯著提高精度的同時提高PF方法的速度。

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

本研究對提供了一種金屬增材過程微觀結(jié)構(gòu)演化的相場模擬框架，對材料制造具有重要意義。相關(guān)論文發(fā)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及其翻譯

Physics-embedded graph network for accelerating phase-field simulation of microstructure evolution in additive manufacturing (增材制造中加速相場模擬微觀結(jié)構(gòu)演化的物理嵌入圖網(wǎng)絡(luò))

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.

摘要相場（PF）方法是一種基于物理的模擬界面形態(tài)的計(jì)算方法。它已被用于金屬增材制造（AM）中的粉末熔化、快速凝固和晶粒結(jié)構(gòu)演化的模擬。然而，傳統(tǒng)的直接數(shù)值模擬方法（DNS）由于網(wǎng)格尺寸足夠小，計(jì)算成本很高。本文提出了一種物理嵌入式圖網(wǎng)絡(luò)（PEGN），它利用一種簡潔圖形來表示晶粒結(jié)構(gòu)，并將經(jīng)典的PF理論嵌入到圖網(wǎng)絡(luò)中。通過將經(jīng)典的PF問題重新定義為圖網(wǎng)絡(luò)上的無監(jiān)督機(jī)器學(xué)習(xí)任務(wù)，PEGN有效地解決了溫度場、液/固相分?jǐn)?shù)和晶粒方向變量，以最小化基于物理的損失/能量函數(shù)。在CPU和GPU實(shí)現(xiàn)中，該方法至少比DNS快50倍，同時仍然能捕獲關(guān)鍵的物理特性。因此，PEGN可以有效地模擬大規(guī)模的多層、多軌AM構(gòu)建。