The paper analyzes the applicability of available nonlocal and gradient fracture criteria to brittle, quasi-brittle, and ductile fracture in notched materials. All chosen criteria use an internal size parameter as a material structure characteristic, which makes it possible to describe the scale effect under stress concentration and to extend the range of their application compared to conventional ones. However, this range is limited to brittle or quasi-brittle fracture with a small prefracture zone. For extending the criteria to quasi-brittle fracture with a developed prefracture zone, we should dismiss the hypothesis on the prefracture zone size as a constant related solely to the structure of materials. In this paper, a new physically substantiated approach is proposed which modifies the criteria of average stress, point stress, fictitious crack, and stress gradient such that their modified versions contain a complex parameter allowing for the size of a prefracture zone, structure of a material, its plastic properties, geometry, and loading conditions. Their experimental verification as applied to tensile cracking in compressed geomaterials with a round hole shows that all modified criteria provide a good description of quasi-brittle fracture and allow one to explain the experimentally observed transition from brittle to ductile fracture with increasing hole sizes.

中文翻译：

---

压缩下准脆性材料的非局部和梯度断裂准则

本文分析了可用的非局部和梯度断裂标准对缺口材料中脆性、准脆性和韧性断裂的适用性。所有选择的标准都使用内部尺寸参数作为材料结构特征，这使得描述应力集中下的尺度效应成为可能，并与传统标准相比扩大了它们的应用范围。然而，该范围仅限于具有小的预断裂带的脆性或准脆性断裂。为了将标准扩展到具有发达预断裂带的准脆性断裂，我们应该将预断裂带尺寸的假设视为仅与材料结构相关的常数。在本文中，提出了一种新的物理证实方法，该方法修改了平均应力、点应力、虚拟裂纹和应力梯度，因此它们的修改版本包含一个复杂的参数，允许预裂区的大小、材料的结构、其塑性特性、几何形状和加载条件。他们对带有圆孔的压缩地质材料中的拉伸开裂进行的实验验证表明，所有修改后的标准都提供了对准脆性断裂的良好描述，并允许人们解释实验观察到的随着孔尺寸的增加从脆性断裂到韧性断裂的转变。