ABSTRACT An approach to simulate the hysteresis loops of an unidirectionally SiC fiber-reinforced titanium matrix composite during tension-compression(T-C) fatigue loading has been developed in this paper. The T-C fatigue process of one cycle was divided into four stages of tension loading (TL), tension unloading (TU), compression loading (CL) and compression unloading (CU). It is assumed that fiber sliding relative to matrix occurs in the whole interfacial debonding area during TL. And there exists a closure stage of matrix crack during CL. Based on the BHE model, the stress–strain relationships during four stages have been derived. By combining the experimental normalized stiffness with the stress–strain relationship during TL, the average matrix crack spacing during various cycles are obtained. Combining the matrix cracking evolution law with another two damage evolution laws, the fatigue hysteresis loops of various cycles under T-C fatigue loading have been acquired. The theoretical results have been compared with experimental data of an unidirectionally SiC fiber-reinforced titanium matrix composite. And the effects of different damages on the hysteresis loops of TMCs have been investigated. Graphical Abstract

中文翻译：

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单向碳化硅纤维增强钛基复合材料拉压滞回线模拟

摘要 本文开发了一种模拟单向 SiC 纤维增强钛基复合材料在拉伸 - 压缩 (TC) 疲劳加载过程中滞后回线的方法。一个循环的TC疲劳过程分为拉伸加载（TL）、拉伸卸载（TU）、压缩加载（CL）和压缩卸载（CU）四个阶段。假设在 TL 期间，纤维相对于基质的滑动发生在整个界面脱粘区域。并且在CL过程中存在基体裂纹的闭合阶段。基于 BHE 模型，推导出了四个阶段的应力-应变关系。通过将实验归一化刚度与 TL 期间的应力-应变关系相结合，可以获得不同循环期间的平均基体裂纹间距。结合基体开裂演化规律和另外两种损伤演化规律，得到了TC疲劳载荷作用下各循环的疲劳滞后回线。理论结果与单向碳化硅纤维增强钛基复合材料的实验数据进行了比较。并研究了不同损伤对 TMC 磁滞回线的影响。图形概要