A constitutive law for continuous fiber reinforced brittle matrix composites with fiber fragmentation and stress recovery
A constitutive law for continuous fiber reinforced brittle matrix composites with fiber fragmentation and stress recovery
复制标题
具有纤维破碎和应力恢复的连续纤维增强脆性基复合材料本构定律
DOI：
10.1016/0022-5096(93)90085-t
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发表时间：
1993
影响因子：
5.3
通讯作者：
J. Neumeister
中科院分区：
文献类型：
--
作者：
J. Neumeister
研究了基体后裂纹饱和条件下脆性基体复合材料的拉伸行为。考虑了遵循威布尔分布的纤维强度分散以及主要微观结构变量的影响。由于主要由摩擦控制的纤维-基体界面行为，假设纤维中的应力在失效周围线性恢复。分析了这种复合材料的本构行为。给出了简化和精炼的近似描述的结果，并与纤维断裂的精确分析理论得出的分析进行了比较。结果表明，精化模型的应力-应变关系很好地遵循了精确解，并且给出了应力和应变最大值的位置，误差在 1% 以内；对于大多数材料来说，这种一致性甚至更好。它还表明，所有关系都可以标准化为仅依赖于两个变量；应力参考和威布尔指数。对于纤维强度分散程度较低的系统，简化模型足以确定应力最大值，但不能确定后临界行为。此外，简化模型给出了最大应力和相应应变的明确解析表达式。这些模型都不包含任何体积依赖性或统计分散性，但应力-应变关系给出的最大应力构成了复合材料极限拉伸强度的上限。
The Tensile Behaviorof a brittle matrix composite is studied for post matrix crack saturation conditions. Scatter of fiber strength following the Weibull distribution as well as the influence of the major microstructural variables is considered. The stress in a fiber is assumed to recover linearly around a failure due to a fiber-matrix interface behavior mainly ruled by friction. The constitutive behavior for such a composite is analysed. Results are given for a simplified and a refined approximate description and compared with an analysis resulting from the exact analytical theory of fiber fragmentation. It is shown that the stress-strain relation for the refined model excellently follows the exact solution and gives the location of the maximum to within 1% in both stress and strain; for most materials the agreement is even better. Also it is shown that all relations can be normalized to depend on only two variables; a stress reference and the Weibull exponent. For systems with low scatter in fiber strength the simplified model is sufficient to determine the stress maximum but not the postcritical behavior. In addition, the simplified model gives explicit analytical expressions for the maximum stress and corresponding strain. None of the models contain any volume dependence or statistical scatter, but the maximum stress given by the stress-strain relation constitutes an upper bound for the ultimate tensile strength of the composite.