CAREER: Effects of Microstructural Randomness in Composite Processing

9875067Baxter职业奖支持材料加工和性能数学建模方面的研究和教育。研究工作将考察随机微观组织对金属基复合材料在固结处理后冷却过程中热机械应力和应力集中发展的影响。为了研究微观结构的随机性对加工过程中应力发展的影响，本工作将采用移动窗口-GMC技术。它使用细观力学模型，称为广义胞格方法(GMC)，在移动窗口过程中为给定的材料微结构生成材料属性场。然后使用统计方法来开发与场相关的概率密度函数、自相关函数和互相关函数。这些函数将与蒙特卡罗技术一起使用，以生成具有与原始数据相同的统计数据的其他材料属性字段。用来模拟固结降温的标准有限元方法将使用原始和模拟的特性作为输入。对这些模型输出结果的分析，例如残余应力状态，将用于改进对复合材料有效使用前性能的预测。与该项目相关的教育计划有几个重点领域。计划开发两个新课程。第一个是数值方法方面的高级本科班。这门课的重点是解决问题的技术；通过识别经典工程问题来定义问题，选择解决技术，并通过适当的技术平台实施方法。第二个班是数学建模的本科班。它将提高本科工程师提出问题和确定问题的能力。还计划以研讨会或跨学科课程的形式，为本科生开设专题短期课程，以及与该奖项下的研究工作相结合的竞争性本科生研究项目的开发。

9875067BaxterA CAREER award supports research and education in mathematical modeling of materials processing and properties. The research work will examine the influence of random microstructure on the development of thermo-mechanical stresses and stress concentrations in metal matrix composites during cooling after consolidation processing. In order to investigate the effect of randomness in microstructure on the development of stresses during processing this work will employ the Moving Window-GMC technique. It uses the micromechanics model, known as the generalized method of cells (GMC), in a moving window procedure to generate material property fields for a given material microstructure. Statistical methods are then used to develop probability density, auto- and cross correlation functions associated with the fields. These functions will be used with Monte Carlo techniques to generate additional material property fields with the same statistics as the original. Standard finite element methods, used to model consolidation cool down, will use the original and simulated properties as input. The analysis of the output from these models, e.g. residual stress states, will be used to improve predictions of the effective pre-use properties of the composite material.The educational plan associated with this project has several focus areas. The development of two new courses is planned. The first is an advanced undergraduate class in Numerical Methods. The emphasis of this class would be on problem solving techniques; problem definition through identification with classic engineering problems, choice of solution technique and implementation of the method via appropriate technological platforms. The second class is an undergraduate class in mathematical modeling. It will improve the ability of undergraduate engineers to set up and define problems. Also planned are short courses for undergraduates on special topics, in the format of seminars or interdisciplinary classes, as well as development of competitive undergraduate research projects integrated with the research work under this award.***