This paper investigates the unstable fracture toughness of specimens of different heights using the double-K model for three-point bending tests on notched concrete beams. It is shown that unstable fracture toughness exhibits a significant size effect. The modified maximum tangential stress (MMTS) criterion is used to explain the size effect of unstable fracture toughness. The MMTS criterion considers the higher order terms of the Williams series expansion of the stress field. The results show that the MMTS criterion can reasonably estimate unstable fracture toughness. It is recommended that the minimum height of the specimen be 200 mm when three-point bending tests on notched beams are used to determine unstable fracture toughness.

中文翻译：

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修正最大切向应力准则研究不稳定断裂韧度的尺寸效应

本文使用双K模型对带缺口混凝土梁的三点弯曲试验研究了不同高度的试样的不稳定断裂韧性。结果表明，不稳定的断裂韧性表现出明显的尺寸效应。修改后的最大切向应力（MMTS）准则用于解释不稳定断裂韧性的尺寸效应。MMTS准则考虑了应力场的Williams级数展开的高阶项。结果表明，MMTS准则可以合理地估计不稳定的断裂韧性。当使用带缺口梁的三点弯曲试验来确定不稳定的断裂韧性时，建议试样的最小高度为200 mm。