Homogenization Analysis and Experimental Verification for Creep of Unidirectional Fiber Reinforced Composites

1.针对具有周期性内部结构的时变非线性复合材料，建立了均匀化理论，将扰动位移速率分解为与时间无关的弹性部分和与时间相关的粘塑性部分。推导了宏观本构关系和细观应力演化方程.将上述理论应用于连续纤维增强单向复合材料的横向蠕变和弹粘塑性变形分析。假设纤维取向为平面应变条件，并采用正方形和六边形纤维阵列，结果表明，正方形和六边形纤维阵列分别表现出显著的和可忽略的宏观各向异性.假设胞内分布关于胞心点对称，讨论了扰动位移率场。结果表明，扰动位移速率场关于胞腔面心和胞腔中心是点对称的，扰动位移速率在这些中心处为零。这一发现导致了引入半单胞，在其边界上，扰动位移率的点对称性作为其边界条件.应用该理论分析了六边形纤维排列复合材料的偏轴弹粘塑性变形。结果表明，小的偏轴角会使粘塑性流动应力显著降低，但当偏轴角大于45 °时，粘塑性流动应力变化不大.将上述分析结果与混杂复合材料GLARE 2的实验结果进行了比较，结果表明，本文分析揭示的弹粘塑性行为对偏轴角的依赖性是实验观察到的。

1. A homogenization theory was formulated for time-dependent nonlinear composites with periodic internal structures, so that perturbed displacement rate is decomposed into time-independent elastic and time-dependent viscoplastic parts. Then a macroscopic constitutive relation and a microscopic evolution equation of stress were derived.2. The theory mentioned above was applied to analyzing transverse creep and elastic-viscoplastic deformation of unidirectional composites reinforced with continuous fibers. Assuming the plane strain condition in the fiber orientation, and employing the square and hexagonal arrays of fibers, it was shown that the square and hexagonal arrays exhibit significant and negligible anisotropy in macroscopic behavior, respectively.3. The field of perturbed displacement rate was discussed by assuming the point symmetry of internal distributions with respect to a cell center. It was thus shown that the field of perturbed displacement rate is point-symmetric with respect to cell facet centers as well as the cell center, and that perturbed displacement rate vanishes at these centers. This finding led to introducing a semiunit cell, on the boundary of which the point symmetry is imposed on perturbed displacement rate as its boundary condition.4. The present theory was employed to analyze off-axial elastic-viscoplastic deformation of a hexagonally fiber-arrayed composite. It was then found that a small off-axis angle gives rise to significant decrease of viscoplastic flow stress, but that viscoplastic flow stress changes little for off-axis angles larger than 45 degree.5. Comparison of the analytical result mentioned above with experimental results on a hybrid composite GLARE 2 showed that the dependence of elastic-viscoplastic behavior on off-axis angle revealed in the present analysis is observed experimentally.