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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Homogenization of the elastic properties of pyrolytic carbon based on an image processing technique
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Homogenization of the elastic properties of pyrolytic carbon based on an image processing technique

机译：基于图像处理技术的热解碳弹性特性的均质化

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In this work, the linear elastic material properties of differently textured variants of pyrolytic carbon are homogenized from the submicro- to the micro-scale. In high resolution transmission electron microscope (HRTEM) lattice fringe images, the microstructure of pyrolytic carbon manifests itself in terms of projections of graphene layers. According to their orientation distribution, different textures of pyrolytic carbon have been classified. Assuming a von Mises-Fisher distribution for the spatial orientation of single graphene layers, the orientation distribution function of the projected layers in the image plane is analytically found to be a modified Struve function. For each pyrolytic carbon texture, Maximum-likelihood estimates for the mean orientation and the concentration parameter of the von Mises-Fisher distribution are obtained numerically. Hereby, Fourier transformation and appropriate filters are used to determine the probabilities for discrete orientations of the graphene layers directly from HRTEM images. First- and second-order bounds of the linear elastic properties of pyrolytic carbon of the different textures are computed. Elastic constants of graphite and pyrolytic graphite have been used for modeling the elastic behavior of the graphene layers within a continuum mechanical setting. Due to the high anisotropy of all analyzed textures of pyrolytic carbon, the differences even between the second-order bounds are quite large. In this work, the linear elastic material properties of differently textured variants of pyrolytic carbon are homogenized from the submicro- to the micro-scale. Assuming a von Mises-Fisher distribution for the spatial orientation of single graphene layers, the orientation distribution function of the projected layers in the image plane is analytically found to be a modified Struve function. For each pyrolytic carbon texture, Maximum-likelihood estimates for the mean orientation and the concentration parameter of the von Mises-Fisher distribution are obtained numerically. Hereby, Fourier transformation and appropriate filters are used to determine the probabilities for discrete orientations of the graphene layers directly from HRTEM images. First- and second-order bounds of the linear elastic properties of pyrolytic carbon of the different textures are computed.
机译：在这项工作中，不同质地的热解碳变体的线性弹性材料特性从亚微米级到微米级均质化。在高分辨率透射电子显微镜（HRTEM）晶格条纹图像中，热解碳的微观结构以石墨烯层的投影形式表现出来。根据它们的取向分布，已经对不同质地的热解碳进行了分类。假设单个石墨烯层的空间取向具有冯·米塞斯-费舍尔分布，则分析得出图像平面中投影层的取向分布函数是修正的Struve函数。对于每个热解碳织构，通过数值获得平均取向的最大似然估计和冯·米塞斯-费舍尔分布的浓度参数。因此，傅立叶变换和适当的滤波器用于直接根据HRTEM图像确定石墨烯层离散取向的概率。计算不同质地的热解碳的线性弹性特性的一阶和二阶边界。石墨和热解石墨的弹性常数已用于在连续机械设置内对石墨烯层的弹性行为进行建模。由于热解碳所有已分析织构的高各向异性，即使二阶边界之间的差异也很大。在这项工作中，不同质地的热解碳变体的线性弹性材料特性从亚微米级到微米级均质化。假设单个石墨烯层的空间取向具有冯·米塞斯-费舍尔分布，则分析得出图像平面中投影层的取向分布函数是修正的Struve函数。对于每个热解碳织构，通过数值获得平均取向的最大似然估计和冯·米塞斯-费舍尔分布的浓度参数。因此，傅立叶变换和适当的滤波器用于直接根据HRTEM图像确定石墨烯层离散取向的概率。计算不同质地的热解碳的线性弹性特性的一阶和二阶边界。

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