Micromechanics for Random System and Its Application to Small Crack Problems

1. 考虑陶瓷随机微观结构的强度特性分析：推导了应力强度因子的修正因子作为随机系统中新的力学参数，使陶瓷微观结构的影响能够反映在参数中。为了评估修正因子，将单个晶粒的刚度和尺寸变化作为微观组织的差异，对裂纹尖端应力场进行了数值分析。裂纹尖端的应力场受裂纹周围晶粒刚度的影响较大，而受晶粒尺寸的影响较小。从上述分析中得到的修正因子随着裂纹长度的增加而减小。利用修正因子的模拟分布，采用阻力曲线概念，基于准则估计了强度分布。估计的强度分布在实验结果中较好地呈现平均趋势。考虑随机微观结构的金属材料疲劳特性分析：以形变六边形为单元对金属多晶高线材料进行建模。在对两相微观结构进行建模时，采用随机数从元素中选择相，以使选择符合各相在微观结构中所占的比例。对于由这些元素组成的多晶材料，基于初始裂纹的连接模式和单个裂纹的扩展模式之间的竞争，构建了裂纹扩展模型。利用该模型，采用蒙特卡罗方法对4种不同组织的金属材料的缺口构件进行了多轴疲劳统计模拟。结果表明，模拟寿命的分布范围足以覆盖实验观察到的失效寿命。

1. Analysis of Strength Characteristic by Considering Random Microstructure in Ceramics : The modification factor for the stress intensity factor was derived as a new mechanical parameter in a random system so that the influence of microstructures in ceramic could be reflected in the parameter. To evaluate the modification factor, numerical analyses on the crack-tip stress field were conducted by taking account of variations in the stiffness and size of individual grains as the difference of microstructures. The stress filed was significantly affected by the stiffness of grains around the grain at the crack-tip, but hardly influenced by the grain-size. The modification factor obtained from the aforementioned analyses was found to become smaller for a longer crack length. Using the simulated distribution of the modification factor, the strength distribution was estimated based on the criterion using the resistance curve concept. The estimated strength distribution was able to show an average tendency in experimental results well.2. Analysis of Fatigue Characteristic by Considering Random Microstructures in Metallic Materials : Deformed hexagons were adopted as elements in modeling metallic polycrys-talline materials. In modeling a microstructure with two phases, the phases were selected from elements by using random numbers so that the selection should correspond to the proportion of each phase occupied in the microstructure. For polycrystalline materials composed of such elements, a crack growth model was constructed based on the competition between the linkage mode of initiated cracks and by the propagation mode of an individual crack. Using the model, notched components for four kinds of metallic materials with different microstructures under multiaxial fatigue were statistically simulated by using a Monte Carlo procedure. It was shown that the distribution range of the simulated life sufficiently covered the failure life observed experimentally.