Fracture is an inherently statistical phenomenon as it is a function of micro-structural heterogeneities such as distributed defects and inclusions. This is evidenced by scatter in the toughness of seemingly identical specimens. Therefore, deterministic approaches do not give full picture of scatter in fracture behaviour. More suitable probabilistic methods have been devised to describe the scatter associated with fracture. While the probabilistic approaches provide a sound scientific basis for capturing the scatter in the fracture data through assuming a probability for the presence of fracture initiators, their microstructurally agnostic assumptions can limit their predictive capability. This is because there is no information on the microstructure such as grain size and morphology, texture, and other important features considered in them. An alternative class of models which take into account the distribution of toughness is cellular automata finite element models (CAFE). CAFE models are stronger in simulating the scatter in the fracture data through their ability to represent the microstructure although so far, they have been limited to fully brittle or quasi-brittle materials. In addition, the CAFE models they are computationally expensive, and their running time can be prohibitive for their application to large scale engineering components thus reducing their appeal. In this study, a CAFE model was developed to take advantage of the microstructural fidelity of CAFE but presented within the context of a probabilistic fracture approach. The CAFE based model calculates the macroscopic strain from the continuum FE model. The strain is then used to load a model which is defined in the cellular automata space. The CAFE model then simulates the initiation and propagation of fracture in the microstructure to fully capture the heterogeneity of the material at the lower length scale. The critical stress acting normal to the cleavage plane of each grain is calculated in the CAFE model and used to decide the onset of cracking in a probabilistic manner; the stress depends on the orientation of the grain in which microcrack initiates as well as depending on the orientation of the surrounding grains. To evaluate its performance, the model was calibrated using a set of experimental fracture toughness data and the results of its prediction were compared with an intendent and separate set of warm prestress experiments of the same material. Good agreement between the prediction and the experiment of the second set was observed giving confidence in the model.

断裂是一种固有的统计现象，因为它是微观结构异质性的函数，例如分布的缺陷和夹杂物。看似相同的样本的韧性分散证明了这一点。因此，确定性方法并不能给出断裂行为分散的全貌。已经设计了更合适的概率方法来描述与断裂相关的散射。虽然概率方法通过假设裂缝引发剂存在的概率为捕获裂缝数据中的分散提供了可靠的科学基础，但它们的微观结构不可知假设可能会限制它们的预测能力。这是因为没有关于微观结构的信息，例如晶粒尺寸和形态、纹理以及其中考虑的其他重要特征。考虑韧性分布的另一类模型是元胞自动机有限元模型 (CAFE)。尽管到目前为止，CAFE 模型仅限于完全脆性或准脆性材料，但它们通过其表示微观结构的能力，在模拟断裂数据中的分散性方面更强大。此外，CAFE 模型的计算成本很高，并且它们的运行时间对于将它们应用于大型工程组件而言可能会令人望而却步，从而降低了它们的吸引力。在本研究中，开发了 CAFE 模型以利用 CAFE 的微观结构保真度，但在概率断裂方法的背景下呈现。基于 CAFE 的模型根据连续体 FE 模型计算宏观应变。然后使用应变加载在元胞自动机空间中定义的模型。然后，CAFE 模型模拟微观结构中断裂的开始和扩展，以在较低的长度尺度上充分捕捉材料的异质性。在 CAFE 模型中计算垂直于每个晶粒解理面的临界应力，并用于以概率方式确定开裂的开始；应力取决于产生微裂纹的晶粒的取向以及周围晶粒的取向。为了评估其性能，该模型使用一组实验断裂韧性数据进行校准，并将其预测结果与相同材料的一组有意和单独的暖预应力实验进行比较。