The Griffith equation for brittle cracking has three problems. First, it applies to an infinite sheet whereas a laboratory test sample is typically near 100 × 100 mm. Second, it describes a central crack instead of the more dangerous and easily observable edge crack. Third, the theory assumes a uniform stress field, instead of tensile force application used in the laboratory. The purpose of this paper is to avoid these difficulties by employing Gregory's solution in calculating the crack behaviour of PMMA (Poly Methyl Meth Acrylate) discs, pin loaded in tension. Our calculations showed that axial disc loading gave nominal strengths comparable with Griffith theory, but the force went to zero as the crack fully crossed the disc, fitting experimental results. Off-axis loading was more interesting because the predicted strength was lower than in axial testing, but also gave unexpected behaviour at short crack lengths, where nominal strength did not rise indefinitely but dropped as crack length went below D/10, quite different from Griffith, where strength rose continuously as cracks were shortened. Such off-axis loading leads to a size effect in which larger discs are weaker, reminiscent of the fine fibre strengthening phenomenon reported in Griffith's early paper (Griffith 1921 Phil. Trans. R. Soc. Lond. A221, 163–198. (doi:10.1098/rsta.1921.0006)).

This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction'.

脆性开裂的格里菲斯方程有三个问题。首先，它适用于无限大的片材，而实验室测试样品通常接近 100 × 100 毫米。其次，它描述了中心裂纹而不是更危险且更容易观察到的边缘裂纹。第三，该理论假设一个均匀的应力场，而不是实验室中使用的拉力应用。本文的目的是通过采用 Gregory 的解决方案来计算 PMMA（聚甲基丙烯酸甲酯）圆盘的裂纹行为，并通过销钉加载来避免这些困难。我们的计算表明，轴向圆盘载荷提供了与格里菲斯理论相当的名义强度，但随着裂纹完全穿过圆盘，力变为零，符合实验结果。离轴加载更有趣，因为预测的强度低于轴向测试，但在短裂纹长度下也会出现意想不到的行为，其中名义强度不会无限上升，而是随着裂纹长度低于 D/10 而下降，与 Griffith 完全不同，随着裂缝的缩短，强度不断上升。这种离轴载荷会导致尺寸效应，其中较大的圆盘较弱，让人想起格里菲斯早期论文中报道的细纤维强化现象（格里菲斯 1921菲尔。翻译 R. Soc。伦敦。A 221 , 163–198。(doi:10.1098/rsta.1921.0006))。

这篇文章是讨论会问题“发明新的坚韧材料的破解方法：断裂比摩擦更奇怪”的一部分。