Laser-Raman Measurement and Analytical Evaluation of Matrix Creep Induced Stress Relaxation in Broken Fibers

长脆性纤维增强单向金属基和聚合物基复合材料在恒定的外加应力作用下可能发生蠕变断裂，因为断裂纤维中的应力随时间而松弛。本文通过激光拉曼应力测量和分析评价来研究这种应力松弛，得到以下结果：为明确基体蠕变对纤维应力分布的影响，采用单纤维模型复合材料进行了纤维拉拔试验。用拉曼光谱法测量了嵌入聚合物中的碳纤维的应力。采用普通环氧树脂、柔性环氧树脂和光固化丙烯酸树脂三种聚合物基体。结果表明，基质蠕变越明显，纤维应力随时间的变化越明显。此外，利用单纤维模型复合材料和拉曼光谱测量了断裂纤维中的应力松弛。研究发现，当基体蠕变越明显时，断裂纤维中的应力松弛现象也越明显。以增量形式提出了一种基于互补能量的泛函。结果表明，该泛函具有满足剪切滞后微分方程的平稳函数。然后，利用纤维应力曲线的双线性近似，在平稳条件下得到了轴对称纤维断裂和纤维拔出模型的解析解。上述解析解适用于本实验结果。从所采用的聚合物的蠕变试验中确定了蠕变常数。由此可见，解析解很好地反映了实验中观察到的趋势。

Unidirectional metal-matrix and polymer-matrix composites reinforced forced with long brittle fibers may suffer from creep rupture under constant applied stress, since the stress in broken fibers is relaxed with time. In the present work, laser-Raman stress measurement and analytical evaluation were performed to investigate such stress relaxation, resulting in the following findings :1. Fiber pull-out tests were done using single-fiber model composites for the purpose of clarifying the effect of matrix creep on the stress profile of fiber stress. The stress of carbon fibers embedded in polymers was measured by means of Raman spectroscopy. Three kinds of polymer matrices, i.e., normal epoxy, flexible epoxy and UV-curable acrylic, were employed. It turned out that the profile of fiber stress changes with time more markedly if the matrix creeps more significantly.2. Moreover, the stress relaxation in broken fibers was measured using single-fiber model composites and Raman spectroscopy. It was found that the stress relaxation in broken fibers also occurs more markedly if the matrix creeps more significantly.3. A functional based on complementary energy was presented in an incremental form. It was shown that the functional has a stationary function satisfying a shear lag differential equation. Then, by employing the bilinear approximation of fiber stress profiles, analytical solutions for axisymmetric fiber breakage and fiber pull-out models were obtained from the stationary condition.4. The analytical solutions mentioned above were applied to the present experimental results. The creep constants were identified from creep tests of the polymers employed. It was thus shown that the analytical solutions represent well the tendencies observed in the experiments.