Abstract

A composite with periodically distributed particulate reinforcements is usually preferred in some industrial engineering areas to enhance the damage resistance of materials. The bonding of the matrix and enhancements may be fractured during manufacturing or operating by cracks that are evenly distributed. In this study, a cracked composite is simplified as an infinite plane with repeatedly distributed units containing inhomogeneities and cracks. The inhomogeneities can be in arbitrary shapes and cracks are assumed horizontally oriented. In formulating the governing equations, each inhomogeneity is homogenized according to the Equivalent Inclusion Method with equivalent eigenstrains to be determined, and each crack of mixed modes I and II is modeled as a distribution of climb and glide dislocations using the Distributed Dislocation Technique with dislocation densities to be determined. The fast Fourier transform is used to speed up the calculation while taking into account the interactions of the inhomogeneities and cracks in the plane. Effective moduli of the composites are obtained from average stresses and strains and samples are reported to demonstrate the generality of the model.

摘要

在某些工业工程领域，通常首选具有周期性分布的颗粒增强材料的复合材料，以增强材料的抗损伤性。在制造或操作过程中，基体和增强物的结合可能会因均匀分布的裂缝而断裂。在这项研究中，破裂的复合材料被简化为一个无限平面，其重复分布的单元包含不均匀性和裂缝。不均匀性可以是任意形状，裂缝被假定为水平方向。在制定控制方程时，根据等效包含方法对每个不均匀性进行均匀化，并确定等效特征应变，并且使用分布式位错技术将混合模式 I 和 II 的每个裂纹建模为爬升和滑行位错的分布，其中位错密度有待确定。快速傅里叶变换用于加速计算，同时考虑到平面中不均匀性和裂缝的相互作用。复合材料的有效模量是从平均应力和应变中获得的，并且报告了样品以证明模型的一般性。