Stochastic Materials Design of Fiber Reinforced Composite Laminates

应用面向设计的复合材料失效准则，建立了基于扩展结构可靠性理论的概率安全性评估模型。从复合材料可靠性设计的角度出发，对最大应力、最大应变和二次多项式等典型失效准则进行了比较。文中还提出了一种新的设计图，该图显示了与安全指标或失效概率相对应的面内应变空间上的可行域。这些随机失效包络图叠加在面内应变空间上，可以用来评价任意铺层方向的复合材料层合板在多轴应力或应变条件下的随机行为。通过断口分析、声发射等实验手段，对复合材料的复杂失效机理进行了研究。采用弹性模量退化和安全指标模拟了复合材料层合板在偏轴载荷作用下各层的连续失效路径。从模拟分析，一个典型的故障路径进行评估对应的面内应变矢量。模拟了层合板在连续铺层破坏的各个阶段的模量下降和面内应变增加等力学行为。由于多层复合材料层合板的失效路径太多而难以评估，因此有必要选择发生概率较大的重要失效路径。所提出的方法选择有效的故障路径依赖于一个分支和界限的规则，使一个有效的故障路径的发生概率更大的基础上的启发式程序。为了计算由有效失效路径引起的多层层板的失效概率，进行了扩展研究。

Design-oriented failure criteria of composite materials are applied to construct an evaluation model of probabilistic safety based on the extended structural reliability theory. Typical failure criteria such as maximum stress, maximum strain and quadratic polynomial are compared from the viewpoint of reliability-oriented material design of composite materials. A new design diagram which shows the feasible region on in-plane strain space corresponding to the safety index or failure probability is also proposed. These stochastic failure envelope diagrams which are overlayed onto in-plane strain space enables one to evaluate the stochastic behavior of the composite laminate with any lamination orientation under multi-axial stress or strain condition. Experimental studies such as fractgraphy and acoustic emission are also performed to evaluate the complicated failure mechanism of composite materials. The sequential failure path of each layer of composite laminates is simulated by means of modulus degradation and safety indices under the offaxis load conditions. From the simulation analysis, a typical failure path is evaluated corresponding to an in-plane strain vector. The mechanical behavior, such as decreasing modulus and increasing inplane strain are also simulated in correspondence with each stage of sequential ply failure. It is necessary to select the important failure path whose occurrence probabilities are greater than others, since therc are too many failure paths of multi-layer composite laminates to evaluate. The proposed method of selecting effective failure paths depends upon the heuristic procedure based on one branch and bound rule which enables one to estimate the effective failure path whose occurrence probabilities are greater. An extended study is preformed in order to calculate the failure probabilty of multiple layer laminates resulting from the effective failure path.