On the Size Effect in Fracture of Ceramic-Ceramic Composite Materials

Abstract

It is well known that self-similar notched structural elements become more brittle as their size increases. This size effect is predicted by fracture mechanics, as opposed to the classical theory of plastic collapse, which is insensitive to the specimen dimensions. For a single-edge notch tension specimen, such as the one depicted in Figure la, the strength criterion predicts a nominal failure stress,σN, given by, $${{\sigma }_{N}} = {{\sigma }_{t}}(1 - {{a}_{0}}/d)$$ (1) where a o is the initial notch length,d is the specimen width, and σt stands for the tensile strength.On the other hand,linear elastic fracture mechanics (LEFM) leads to a nominal failure stress expressed by $${{\sigma }_{N}} = \frac{{{{K}_{{Ic}}}}}{{Y({{a}_{0}}/d)\sqrt {{{{a}_{0}}/d}} }} \cdot \frac{1}{{\sqrt {d} }}$$ (2) whereK Ic,is the material fracture toughness,and Y(ao/d) is the stress intensity factor shape function for this particular geometry and a/d ratio. Both failure loci have been plotted vs. the width d in bilogarithmic coordinates in Figure lb for self-similar specimens having the same a o /d ratio. Equations (1) and (2) are upper bounds for the failure load, and experimental results lie on the thin line in Figure lb. Very large specimens (over a critical size d LEFM ) behave in accordance with LEFM predictions, whereas the maximum carrying capacity of smaller samples has to be determined by using non-linear fracture mechanics (NLFM). On the other hand, very small specimens follow the behaviour predicted by the maximum strength criterion. The failure of LEFM to analyse the behaviour of specimens below d LEFM is due to the breakdown of the LEFM hypotheses, mainly that the length of the fracture process zone has to be small as compared with d,a o, and d — a o,regardless of the physical nature of fracture mechanism (either plasticdeformation, microcracking, or crack wake surfaces interaction). d LEFM is a function of both specimen geometry (through Y(ao/d)) and material fracture toughness. As tough materials usually havelarge process zones, the minimum specimen size to apply LEFM (d LEFM ) increases with K 1 c .