Fracture toughness from the standpoint of softening hyperelasticity
Fracture toughness from the standpoint of softening hyperelasticity
复制标题
从软化超弹性的角度来看断裂韧性
DOI：
10.1016/j.jmps.2008.02.009
复制
发表时间：
2008
影响因子：
5.3
通讯作者：
P. Trapper
中科院分区：
文献类型：
--
作者：
K. Volokh;P. Trapper
脆性材料的断裂韧性是在实验中校准的，其中具有预先存在的裂纹/缺口的样品被加载到静态失稳开始的临界点。例如，陶瓷的实验表明，韧性与裂纹/缺口的尖锐程度有明显的相关性：裂纹越尖锐，韧性就越低。这些实验结果与原始的Griffith脆性断裂理论并不完全兼容，在该理论中，裂纹的尖锐度是次要的。1为了定性地解释实验观察，我们模拟了具有有限且可变尖锐度的小裂纹的薄板的拉伸。在模拟中，我们引入平均键能作为Hookean固体储存能量的限制器。能量限制器会导致软化，表明材料失效。因此，带软化的弹性可以捕捉裂纹板静态失稳开始的临界点，该临界点对应于裂纹尖端的失效扩展开始。在数值模拟中，我们发现，与实验一致的是，断裂韧性的大小不能唯一确定，因为它取决于裂纹的尖锐度：裂纹越尖锐，韧性就越低。根据所得到的结果，我们认为只有当裂纹尖端的特征尺寸与材料微观结构的特征长度(如晶粒度、原子距离等)相当时，脆性材料的韧性才能达到稳定的量级。换句话说，只有在连续介质假设不成立的情况下，才能校准韧性。
Fracture toughness of brittle materials is calibrated in experiments where a sample with a preexisting crack/notch is loaded up to a critical point of the onset of static instability. Experiments with ceramics, for example, exhibit a pronounced dependence of the toughness on the sharpness of the crack/notch: the sharper is the crack the lower is the toughness. These experimental results are not entirely compatible with the original Griffith theory of brittle fracture where the crack sharpness is of minor importance.1To explain the experimental observations qualitatively we simulate tension of a thin plate with a small crack of a finite and varying sharpness. In simulations, we introduce the average bond energy as a limiter for the stored energy of the Hookean solid. The energy limiter induces softening, indicating material failure. Thus, elasticity with softening allows capturing the critical point of the onset of static instability of the cracked plate, which corresponds to the onset of the failure propagation at the tip of the crack. In numerical simulations we find, in agreement with experiments, that the magnitude of the fracture toughness cannot be determined uniquely because it depends on the sharpness of the crack: the sharper is the crack, the lower is the toughness. Based on the obtained results, we argue that a stable magnitude of the toughness of brittle materials can only be reached when a characteristic size of the crack tip is comparable with a characteristic length of the material microstructure, e.g. grain size, atomic distance, etc. In other words, the toughness can be calibrated only under conditions where the hypothesis of continuum fails.