In this paper, we use a 2D bond-based peridynamic model to investigate the strength of disk-shaped particles including pre-cracks. We use a diametral (or Brazilian) test to break the particles. For the flawless particles, we find that the stress distribution compares well with an analytical model accounting for the size of the contact zone, and the particle stiffness tends linearly to a well-defined value for increasingly resolved meshing. We then introduce cracks, which are numerically defined by reducing the Young modulus of the bonds crossing linear segments. We consider in detail the effect of a single vertical crack on the yield stress as a function of its position. We also consider a randomly distributed population of cracks with sizes generated from a Gaussian size distribution. For a parametric study with a hundred particles, we found a probability of failure that is well fit by a Weibull law. Finally, using an image analysis algorithm, we investigate the statistics of cracks and the resulting fragments.

在本文中，我们使用基于2D键的绕动力学模型来研究包括预裂纹在内的盘状颗粒的强度。我们使用直径（或巴西）测试来破碎颗粒。对于无缺陷的粒子，我们发现应力分布与考虑接触区域大小的分析模型相比具有很好的对比，并且粒子刚度线性趋于良好定义的值，以解决网格划分问题。然后，我们引入裂纹，该裂纹通过减小穿过线性链段的键的杨氏模量在数值上定义。我们详细考虑了单个垂直裂纹对屈服应力的影响，该屈服应力是其位置的函数。我们还考虑了由高斯尺寸分布生成的尺寸随机分布的裂纹。对于包含一百个粒子的参数研究，我们发现了韦伯定律非常适合的失败概率。最后，使用图像分析算法，我们调查了裂纹和产生的碎片的统计数据。