Decrease of apparent tensile and bending strength with specimen size: Two different explanations based on fracture mechanics

Abstract

The influence of the shape and size distribution of defects on material strength is investigated. Constant reference is made to Weibull Theory and Fracture Mechanics, and a family of regular polygonal voids is considered with the two limit-cases of Griffith cracks and circular pores. A defect size distribution of proportionality is defined, for which the maximum defect size turns out to be proportional to the linear size of the body. In this way, a very general analytical expression for the tensile strength decrease with size is obtained and then confirmed by experimental evidence.Specimen size is also shown to have a fundamental influence on global structural behaviour, which can range from ductile to brittle when strain softening and strain localization are taken into account. The brittle behaviour coincides with a snap-back instability in the load-deflection path, which shows a positive slope in the softening branch. Such a virtual branch may be revealed only if the loading process is controlled by a monotonically increasing function of time (e.g. the crack opening displacement). Otherwise, the loading capacity will present a discontinuity with a negative jump.A general explanation of the well-known decrease in bending strength by increasing the specimen sizes is given in terms of dimensional analysis. Due to the different physical dimensions of strength [FL−2] and toughness [FL−1 ], the true value of such material property may be found exactly only with comparatively large specimens.