Abstract It is important to understand the characteristics of high speed crack in brittle materials under ultra high loading rate forming through impact loading condition, which is important for understanding the impact damage evolution of ceramics and solid explosives. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of crack path and crack velocity in brittle materials under ultra high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up. Simulations show that the path of high speed crack behave the evolution process of a single crack and then micro-branching crack and bifurcation crack finally under the influence of ultra high loading rate. The crack propagation distance between the beginning and the bifurcation decreases with the increase of the loading rate; the crack bifurcation is not immediately after the crack initiation, but as the crack propagation speed reaches the critical value, the expansion path produces more secondary cracks, and then the crack is bifurcated. With the increase of loading rate, the average velocity of cracks gradually increases in three stages, but it shows a different variation after reaching the stable value. In the single crack stage, the steady average velocity is 0.584 times the Rayleigh wave velocity (CR), and there exists only a very small velocity oscillation; the steady value of the average crack velocity corresponding to the differential fork phase is 0.5 times the Rayleigh wave velocity, accompanied by a certain oscillation; The average speed of the stable crack corresponding to the bifurcation stage is much higher than the value of the first two stages, and it can reach 0.638 times the Rayleigh wave speed. It is also accompanied by obvious speed oscillation. The study of the propagation of cracks under different loading rates can predict the internal crack growth rate, propagation direction, and extension distance of brittle materials such as ceramics and rocks.

中文翻译：

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超高加载速率下的高速裂纹扩展特性

摘要 了解冲击加载条件下脆性材料在超高加载速率下高速裂纹的特征具有重要意义，对于理解陶瓷和固体炸药的冲击损伤演化具有重要意义。本文利用能够准确显示脆性材料力学性能的点阵弹簧模型，研究了超高加载速率下脆性材料裂纹路径和裂纹速度的演化规律和机理。该模型采用Gusev提出的定量参数映射方法精确求解模型的弹簧刚度系数，并基于Griffith能量平衡原理建立模型的断裂准则。仿真表明，在超高加载速率的影响下，高速裂纹的路径表现为单裂纹、微分支裂纹和分叉裂纹的演化过程。随着加载速率的增加，开端和分叉处的裂纹扩展距离减小；裂纹分叉不是在裂纹萌生后立即发生，而是随着裂纹扩展速度达到临界值，扩展路径产生更多的二次裂纹，然后裂纹发生分叉。随着加载速率的增加，裂纹的平均速度分三个阶段逐渐增加，但在达到稳定值后呈现不同的变化。在单裂纹阶段，稳态平均速度为瑞利波速度（CR）的 0.584 倍，并且只存在很小的速度振荡；微分叉相对应的平均裂纹速度的稳定值为瑞利波速度的0.5倍，并伴有一定的振荡；分岔阶段对应的稳定裂纹的平均速度远高于前两个阶段的值，可以达到瑞利波速度的0.638倍。还伴随着明显的速度振荡。研究不同加载速率下的裂纹扩展，可以预测陶瓷、岩石等脆性材料的内部裂纹扩展速率、扩展方向和扩展距离。伴随着一定的振荡；分岔阶段对应的稳定裂纹的平均速度远高于前两个阶段的值，可以达到瑞利波速度的0.638倍。还伴随着明显的速度振荡。研究不同加载速率下的裂纹扩展，可以预测陶瓷、岩石等脆性材料的内部裂纹扩展速率、扩展方向和扩展距离。伴随着一定的振荡；分岔阶段对应的稳定裂纹的平均速度远高于前两个阶段的值，可以达到瑞利波速度的0.638倍。还伴随着明显的速度振荡。研究不同加载速率下的裂纹扩展，可以预测陶瓷、岩石等脆性材料的内部裂纹扩展速率、扩展方向和扩展距离。