晶體塑性模型與基於深度學習之多尺度模擬於鋁合金之應用

Abstract

多尺度模擬被廣泛應用於探討微結構至非彈性機械性質，然而傳統上使用直接數值模擬(direct numerical simulation, DNS)同步的進行宏觀尺度的力學分析以及微觀尺度的材料模擬會耗費大量的計算資源，導致模擬的尺度受到了極大的限制。因此，本研究的目的為利用深度學習技術建立多尺度模擬平台，將DNS方法中微觀尺度的材料模型替換為基於機器學習的代理材料模型，利用代理材料模型極高的線上運算效率，深化多尺度模擬於工業等級尺度的應用價值。 本研究針對Al-Mg-Si高強度車用鋁合金以晶體塑性(crystal plasticity)建立DNS材料模型，透過TEM影像、EBSD分別獲取析出物物理參數以及晶體方向，此外，有鑑於鋁合金成型製程中常以中溫、高溫增加其延展性，導致鋁合金中析出物物理參數在成型過程中受到溫度效應影響而改變，因此本研究將析出物動力模型整合至晶體塑性模型，並與不同溫度下的拉伸實驗進行參數校正及驗證。 透過DNS材料模型產生資料，本研究訓練了基於循環神經網路(recurrent neural network, RNN)的代理材料模型，訓練結果顯示該模型能夠捕捉任意複雜變形下的歷史相關應力應變行為，並且能夠泛用到訓練資料集外的變形行為。此外，本研究亦將代理材料模型結合Abaqus材料副程式建立數據驅動多尺度模擬平台，並探討利用自動微分技術進行的隱式迭代求解的運算效率。

Multiscale simulation is widely used in modeling microstructure-induced inelastic mechanical behavior. However, conventional direct numerical simulation (DNS) performs mechanics analysis at the macroscale, and concurrently, performs material simulation at the microscale, leading to an expensive computational cost that makes the process infeasible. In this work, we aim to develop a data-driven multiscale simulation (DDMS) platform, in which a machine learning-based surrogate material model replaces the DNS model. We utilized the surrogate material model's extreme online prediction efficiency to increase the multiscale simulation's feasibility for large-scale applications. We proposed a crystal plasticity DNS material model for Al-Mg-Si high-strength aluminum alloys with physical parameters such as precipitate size distribution and crystallographic orientation obtained from TEM image and EBSD. In addition, the aluminum forming process at elevated temperatures is commonly used to increase ductility, leading to the dynamic growth of precipitates during the forming process. Therefore, we incorporate precipitation kinetics into the crystal plasticity model and calibrate the model with tensile tests at various temperatures. With the training data generated by the DNS material model, we trained a surrogate material model based on recurrent neural networks (RNN). The training results showed that the model is capable of capturing the historical stress-strain behavior under arbitrary complex deformations, and can be generalized to deformation behaviors beyond the training dataset. Furthermore, we implemented the surrogate material model in Abaqus material subroutine to establish an DDMS platform, and investigated the computational efficiency of implicit solver utilizing automatic differentiation techniques.