A strength reliability model of unidirectional fiber-reinforced ceramic matrix composites by Markov process
A strength reliability model of unidirectional fiber-reinforced ceramic matrix composites by Markov process
复制标题
马尔可夫过程单向纤维增强陶瓷基复合材料强度可靠性模型
DOI：
10.1163/156855106778392089
复制
发表时间：
2006
影响因子：
2.9
通讯作者：
N. Takeda
中科院分区：
文献类型：
--
作者：
K. Goda;T. Okabe;N. Takeda
提出了一种预测单向纤维增强陶瓷基复合材料强度和可靠性的随机过程分析方法。该分析是基于马尔可夫过程，其中它是假设，在复合材料中的损伤状态的发展与每个纤维断裂。当威布尔分布被用来描述纤维的强度分布时，处于每个状态的概率可以以封闭形式解析地求解。从材料可靠性工程的观点出发，利用概率解定量地讨论了复合材料的损伤容限问题。为了比较所提出的随机过程分析与先前提出的强度模型的基础上的经典束理论，我们得到的期望值和方差的复合应力的解决方案的概率在状态。期望值和方差均由两项组成，相当于纤维束结构和应力恢复的影响。这些结果与Phoenix和Raj [9]分析的解惊人地一致。断裂纤维中的应力恢复效应产生正的期望值和负的方差，因此是增加复合材料的强度和可靠性的重要机制。此外，我们预测的期望值的复合强度和方差的解决方案。归一化纤维应力的相应值，以获得强度和方差的预期值，与Hui等人[13]的预测值相对一致。我们进一步验证了复合材料强度服从正态分布，其具有上述预测的期望值和标准差。最后，对不同尺寸的复合材料的强度概率进行了预测，并得出结论：当纤维数量与实际使用情况相对应时，陶瓷基复合材料的强度是相当可靠的。
We propose a stochastic process analysis for predicting the strength and reliability of a unidirectional fiber-reinforced ceramic matrix composite. The analysis is based on a Markov process, in which it is assumed that a state of damage in the composite is developed with each fiber breakage. When the Weibull distribution is used to describe the strength distribution of the fiber, the probability of being in each state can be solved analytically in a closed form. Using the solutions of the probabilities, a discussion about damage tolerance of the composites is quantitatively developed, from the viewpoint of materials reliability engineering. To compare the proposed stochastic process analysis with previously proposed strength models in the basis of classical bundle theory, we obtained the expected value and variance in the composite stress from solutions of the probabilities of being in the states. The expected value and variance both consist of two terms, equivalent to the effects of both bundle structure and stress recovery in broken fibers. These are surprisingly in agreement with the solutions analyzed by Phoenix and Raj [9]. The effect of stress recovery in broken fibers produces a positive in the expected value and a negative in the variance and is thus a significant mechanism for increasing the strength and reliability of the composite. In addition we predicted the expected values of composite strengths and variances from the solutions. The corresponding value of normalized fiber stress to obtain the expected value in strength and the variance agreed relatively well with the value predicted by Hui et al. [13]. We further verified that the composite strength obeys a normal distribution, which has the expected value and standard deviation predicted above. Finally, we predicted the probabilities in strength of the composites with various sizes and concluded that the ceramic matrix composite is quite reliable in strength when the number of fibers corresponds to that in practical use.