Calculations on compact disc cracking

Abstract

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. A 221 , 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'.