It is well known that the grain size has significant influence on the fracture of quasi-brittle materials. In order to give a quantitative description of this influence, many researchers have tried to find empirical relationships between the critical distance and the grain size, connecting a macroscopic parameter with the material microstructures. In this paper, a more rational model of this relationship is proposed based on the energy balance in the fracture process zone. This model naturally considers the size effect and can be implemented in both a nearly plain specimen and a specimen containing a long crack. It is not only helpful to explain the existing empirical estimations, but also reveals more underlying mechanisms of the quasi-brittle fracture.

众所周知，晶粒尺寸对准脆性材料的断裂有重大影响。为了定量描述这种影响，许多研究人员试图通过将宏观参数与材料微观结构联系起来，来确定临界距离与晶粒尺寸之间的经验关系。本文基于断裂过程带的能量平衡，提出了一种更为合理的这种关系模型。该模型自然会考虑尺寸效应，并且可以在几乎平整的试样和包含长裂纹的试样中实施。这不仅有助于解释现有的经验估计，而且揭示了准脆性断裂的更多潜在机理。