自增韧氮化硅陶瓷的显微结构模拟与力学性能预测
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摘要
随着计算机技术、人工智能技术的不断进步，材料设计逐渐成为与材料实验和材料理论并行发展的三个方向之一。本文以自增韧氮化硅陶瓷为设计对象，运用主成分分析法(Principle Component Analysis：PCA)对自增韧Si_3N_4陶瓷的显微结构和力学性能进行数据空间降维，获得自增韧Si_3N_4陶瓷显微结构控制的主要因素，进而简化了表征参量变量和准则；运用模糊神经网络(Fuzzy Neural Networks：FNN)建立了自增韧Si_3N_4陶瓷设计专家系统，能实现工艺—微结构—性能的正向预测及反向设计；运用Monte-Carlo方法(MC)进行自增韧Si_3N_4陶瓷的晶体生长模拟，然后进行裂纹扩展模拟，探索建立工艺—微结构—力学性能预测模型的思路。最后对材料设计的统一模式进行了探讨。主要研究结果如下：
1．自增韧Si_3N_4陶瓷的显微结构可以用第一个主成分——综合结构指标来表征，它反映了显微结构的综合特征，并反映了显微结构综合表征值与显微结构偏差之间的对比。通过第一主成分的计算证实了显微结构相近的材料具有相近的性能。为了获得结构优良的自增韧Si_3N_4陶瓷，需要保证致密(d_1小、ρ′)的基体、长径比AR_2大、直径均匀(Y_2×100小)的增韧相。
2．自增韧Si_3N_4陶瓷的性能可以用第一、二主成分来表征，分别称其为性能稳定性指标和平均性能指标。它们分别代表材料受显微结构波动影响的性能和材料的平均性能。
3．由新的表征变量建立了更简单明确的显微结构和力学性能分类准则：当F_1≥3.8，则为粗大晶粒组织；当0≤F_1＜3.8，则为中等晶粒组织；当F_1＜0，则为细晶粒组织。当F′_1＞0.7且-0.5＜F′_2＜1.5，则为力学性能较高且稳定的白增韧氮化硅陶瓷。
4．FNN是一种高效的非线性建模方法，当材料制备、服役的微结构控制因素不清楚时，将材料研究中的模糊语言描述与精确的实验数据相结合，用FNN可以迅速建立工艺—微结构—性能的预测与设计模型并可投入实际应用。
基于MC三维晶体生长模拟，得到直径呈单峰分布的p一Si3N;晶体结构。
跨出了细观力学结合有限元方法模拟裂纹扩展的现有模式，从微观尺度上模
拟晶体的生长形态，结合细观力学、损伤力学建立裂纹扩展判据，实现了快
速的裂纹扩展模拟。基于晶体生长物理机制获得的晶体网格比数学意义上的
网格更能反映真实材料的微结构情况，材料破坏的模拟更科学合理。
以“微结构组装”和“场作用”为核心思想，提出了材料优化设计理论与方
法框架的思路:即从微观、细观到宏观的跨尺度材料设计构想及实现方法，
运用数理运算(逻辑、能量等)在计算机上进行跨尺度的材料微结构组装，
采用能量最小化判据确定材料的稳态结构:并且将材料制备和服役过程中的
环境提升到“场”的高度来认识，在实际“场”中模拟微结构控制单元的力
学行为，从“场模拟”的角度开展可实现的材料设计，这就将材料设计贯穿
于整个材料制备和服役过程，统一于“场作用”理论之中。通过实际材料制
备与服役条件下材料行为的观察，论证了该框架的合理性和可行性。
With the development of computer and artificial intelligence techniques, materials design is becoming one of three main parts of materials science and technology with experiments and theories. Taking in-situ toughened silicon nitride as a design object, principle component analysis (PCA) is applied to study the microstructure and mechanical properties, to find out the main microstructure controlling factors, and to simplify the characterization variables and criterions; fuzzy neural networks (FNNs) is also applied to develop a design expert system for this material, which can realize the forward prediction from processing, microstructure to mechanical properties, and backward design from mechanical properties or microstructure to processing; Monte-Carlo method is applied to simulate the grain growth of this material, and then crack propagation is simulated, which is another way based on physics and chemistry to developing prediction models from processing until to mechanical properties. Uniform pattern of materials design is discussed finally. The main results are listed below:
1. Microstructure of in-situ toughened Si3N4^ can be characterized with the first principle component of the original eight characterization variables, namely, a complex microstructure index. This index reflects the comprehensive microstructure characteristics and the contrasts between the micro structure's comprehensive status and its variance. Compact matrix (large value of ρ') with fine grains (small value of d1) and uniform large grains (small value of Y2 × 100 ) with great aspect ratio (large value of AR2) must be ensured in order to get in-situ toughened Si3N4 with excellent microstructure.
2. Mechanical properties of in-situ toughened Si3N4 can be characterized with the first and the second principle components, namely, mechanical properties stability index and average mechanical properties index. The former index reflects fracture toughness and Weibull modulus which are affected by the fluctuation of microstructure; the later one reflects the average mechanical property, namely rupture strength.
3. Simpler microstructure and mechanical properties classification criterions have been established. If F1≥ 3.8, the grains must be large grains; if 0 ≤F1<3.8, the
grains must be medium grains; if F1 < 0 , the grains must be fine grains. In-situ toughened Si3N4 with highest and stable mechanical properties can be obtained if
F1'>0.7 and -0.5 4. FNN is a high efficient nonlinear method for modeling. Combining fuzzy linguistic descriptions with accurate experimental data, models for predicting and designing between processing, microstructure and mechanical reciprocally can be developed and put into practice easily with FNN method, which is very necessary especially when the microstructure' s controlling factors of preparations, performances are not clear enough.
5. The distribution of β- Si3N4 grain is one-peak according to three dimensions MC grain growth simulation.
6. Crack propagation is simulated based on physical grid instead of mathematical grid in this paper. Physical grid, attained with Monte-Carlo simulation for grain growth, is more accurate and reasonable than the grid attained with finite element methods (FEM). Based on micromechanics and damage mechanics, proper crack propagation criterions are developed and crack propagation simulation can be finished in few seconds with common computers.
7. Based on two core concepts, "microstructure assembling" and "fields action", some theories and methods of materials design are brought forward. Materials design that spans microscopic and macroscopic can be realized with the uniform theories and methods. Microstructure units can be assembled with mathematical operations and stable microstructure can be attained with minimum energy criterion. The environment of materials preparation and performance are considered as "fields", and behaviors of macrostructure controlling units
1．自增韧Si_3N_4陶瓷的显微结构可以用第一个主成分——综合结构指标来表征，它反映了显微结构的综合特征，并反映了显微结构综合表征值与显微结构偏差之间的对比。通过第一主成分的计算证实了显微结构相近的材料具有相近的性能。为了获得结构优良的自增韧Si_3N_4陶瓷，需要保证致密(d_1小、ρ′)的基体、长径比AR_2大、直径均匀(Y_2×100小)的增韧相。
2．自增韧Si_3N_4陶瓷的性能可以用第一、二主成分来表征，分别称其为性能稳定性指标和平均性能指标。它们分别代表材料受显微结构波动影响的性能和材料的平均性能。
3．由新的表征变量建立了更简单明确的显微结构和力学性能分类准则：当F_1≥3.8，则为粗大晶粒组织；当0≤F_1＜3.8，则为中等晶粒组织；当F_1＜0，则为细晶粒组织。当F′_1＞0.7且-0.5＜F′_2＜1.5，则为力学性能较高且稳定的白增韧氮化硅陶瓷。
4．FNN是一种高效的非线性建模方法，当材料制备、服役的微结构控制因素不清楚时，将材料研究中的模糊语言描述与精确的实验数据相结合，用FNN可以迅速建立工艺—微结构—性能的预测与设计模型并可投入实际应用。
基于MC三维晶体生长模拟，得到直径呈单峰分布的p一Si3N;晶体结构。
跨出了细观力学结合有限元方法模拟裂纹扩展的现有模式，从微观尺度上模
拟晶体的生长形态，结合细观力学、损伤力学建立裂纹扩展判据，实现了快
速的裂纹扩展模拟。基于晶体生长物理机制获得的晶体网格比数学意义上的
网格更能反映真实材料的微结构情况，材料破坏的模拟更科学合理。
以“微结构组装”和“场作用”为核心思想，提出了材料优化设计理论与方
法框架的思路:即从微观、细观到宏观的跨尺度材料设计构想及实现方法，
运用数理运算(逻辑、能量等)在计算机上进行跨尺度的材料微结构组装，
采用能量最小化判据确定材料的稳态结构:并且将材料制备和服役过程中的
环境提升到“场”的高度来认识，在实际“场”中模拟微结构控制单元的力
学行为，从“场模拟”的角度开展可实现的材料设计，这就将材料设计贯穿
于整个材料制备和服役过程，统一于“场作用”理论之中。通过实际材料制
备与服役条件下材料行为的观察，论证了该框架的合理性和可行性。
With the development of computer and artificial intelligence techniques, materials design is becoming one of three main parts of materials science and technology with experiments and theories. Taking in-situ toughened silicon nitride as a design object, principle component analysis (PCA) is applied to study the microstructure and mechanical properties, to find out the main microstructure controlling factors, and to simplify the characterization variables and criterions; fuzzy neural networks (FNNs) is also applied to develop a design expert system for this material, which can realize the forward prediction from processing, microstructure to mechanical properties, and backward design from mechanical properties or microstructure to processing; Monte-Carlo method is applied to simulate the grain growth of this material, and then crack propagation is simulated, which is another way based on physics and chemistry to developing prediction models from processing until to mechanical properties. Uniform pattern of materials design is discussed finally. The main results are listed below:
1. Microstructure of in-situ toughened Si3N4^ can be characterized with the first principle component of the original eight characterization variables, namely, a complex microstructure index. This index reflects the comprehensive microstructure characteristics and the contrasts between the micro structure's comprehensive status and its variance. Compact matrix (large value of ρ') with fine grains (small value of d1) and uniform large grains (small value of Y2 × 100 ) with great aspect ratio (large value of AR2) must be ensured in order to get in-situ toughened Si3N4 with excellent microstructure.
2. Mechanical properties of in-situ toughened Si3N4 can be characterized with the first and the second principle components, namely, mechanical properties stability index and average mechanical properties index. The former index reflects fracture toughness and Weibull modulus which are affected by the fluctuation of microstructure; the later one reflects the average mechanical property, namely rupture strength.
3. Simpler microstructure and mechanical properties classification criterions have been established. If F1≥ 3.8, the grains must be large grains; if 0 ≤F1<3.8, the
grains must be medium grains; if F1 < 0 , the grains must be fine grains. In-situ toughened Si3N4 with highest and stable mechanical properties can be obtained if
F1'>0.7 and -0.5
5. The distribution of β- Si3N4 grain is one-peak according to three dimensions MC grain growth simulation.
6. Crack propagation is simulated based on physical grid instead of mathematical grid in this paper. Physical grid, attained with Monte-Carlo simulation for grain growth, is more accurate and reasonable than the grid attained with finite element methods (FEM). Based on micromechanics and damage mechanics, proper crack propagation criterions are developed and crack propagation simulation can be finished in few seconds with common computers.
7. Based on two core concepts, "microstructure assembling" and "fields action", some theories and methods of materials design are brought forward. Materials design that spans microscopic and macroscopic can be realized with the uniform theories and methods. Microstructure units can be assembled with mathematical operations and stable microstructure can be attained with minimum energy criterion. The environment of materials preparation and performance are considered as "fields", and behaviors of macrostructure controlling units
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2. Lange M. J. Am. Ceram. Soc., 1979; 62: 428～430.
3. Drew P, Lewis M H. J. Mater. Sci., 1974; 9: 261～269.
4. Pyzik A J. Annu. Rer. Mater. Sci., 1974; 24: 189～214.
5．潘振甦，郭景坤，高技术新材料要览，北京：中国科学技术出版社，1994：236～238。
6. Hirao K, Nagaoka T, Brito M. E, Kanzaki S. in Proceedings of the 5th International Symposium on Ceramic Materials and Components for Engines, Edited by D. S. Yan, X. R. Fu and S.X.Shi, World Scientific Publishing Co.Pte. Ltd. Singapore, 1995: 185～188.
7．陈福玲，航空周刊，1996；5：9～10。
8. Pyzik A J, Schwarz D B, Dwbensky W J and Beaman D R. US Pat., No 4883776, Nov. 28, 1989.
9．邬凤英，庄汉锐，马利泰，李文兰，符锡仁，高温结构陶瓷93年论文集，上海硅酸盐所，1994：288～293。
10．黄校先，郭景坤，归林华，王荣华，李包顺，高温结构陶瓷93年论文集，上海硅酸盐所，1994：294～300。
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