单向纤维增强复合材料强度的统计分析
STATISTICAL ANALYSIS OF FAILURE OF UNIDIRECTIONALLY FIBER-REINFORCED COMPOSITES WITH LOCAL LOAD-SHARING
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摘要: 在本文中,我们提出了一个用于研究单向纤维增强复合材料中纤维载荷集中的剪滞分析模型。用此模型推导出了包含r根断纤维的裂纹的尖端纤维的载荷集中因子的解析表达式,并由此计算了裂纹尖端纤维的最大载荷集中因子,其计算结果与Hedgepeth[2]的结果非常一致。其次,我们提出了平均载荷集中因子的概念,并通过载荷集中因子的大小定义了裂纹尖端纤维的影响长度。它的物理意义明确,而且,在裂纹的扩展过程中是逐渐增大的,这与实际情况相符。在前面分析的基础上,应用裂纹临界核模型[2,3],我们对单向纤维增强复合材料的强度问题进行了统计分析,其计算结果与实验值是一致的,其中使用平均载荷集中因子计算所得到的强度值与实验值更接近。数值结果说明了裂纹临界核模型的正确性以及用平均载荷集中因子和影响长度进行裂纹扩展分析的可行性。Abstract: A shear-lag model is presented for analysis of load concentration of fibers adjacent to a crack in unidirectionally fibei-reinforced composites.The analytic solutions of stress concentration factors of fibers adjacent to a crack-tip are obtained by using this model.The maximum stress concentration factors are calculated of the fiber at the tip of a crack,and the numerical results show little difference with Hedgepeth's results.In addition,the concept of the average stress concentration factor is presented,and the affected length of the crack-tip fiber is defined by means of the value of the stress concentration factor.Its physical meaning is clear,and it increases gradually with expansion of the crack,which is in accordance with the actual case.Based upon the previous analysis,statistical analysis of failure of unidirectionally fiber-reinforced composites is done by;applying the method of the ultimate crack core model[2,3].The results are close to the experimental data,and those obtained by using the average stress concentration factors approach the experim ental data more closely.The ccmparison of the results here with the experimental data chows correctness of the method of the ultimate crack core model and feasibility of the affected ogrl and the average stress concentration factor in the analysis of crack propagetion.
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