Effects of Pore/Grain-Size Interaction and Porosity on the Fracture of Electroceramics

Abstract

The strength of brittle materials decreases as the size of specimens increases, and this so-called size effect can be described by the Weibull statistical fracture theory. Recent experiments on the fracture strength of electroceramics, however, have shown that it is not always so. Electroceramics, such as zinc oxide (ZnO) applied for varistors, are mainly designed with respect to electrical rather than mechanical properties, and thus they usually contain a high degree of porosity which may act as the origin of fracture. It is suspected that the complex nature of defect-microstructure interaction and the high density of porosity are possible reasons for this insensitivity to strength scaling. In order to verify this hypothesis, more generally, to deliberate the scaling behavior of the fracture strength of electroceramics containing high densities of flaws, the effects of pore/grain-size interaction and porosity on the fracture strength in ZnO ceramics are investigated based on the finite element analysis. The numerical results show that the fracture strength is more influenced by the pore/grain-size interaction than only by the size of a pore or its shape although the stress singularity of sharp grooves around a pore is closely related to their angles. As a consequence the pore/grain-size interaction will increase the fracture probability of small pores, and lead to a homogenization of critical flaw sizes. Furthermore, the finite element analysis exhibits that the high degree of porosity, especially the heterogeneous distribution and the clustering of pores, could be conducive to further homogenization of critical crack sizes. This implies that the fracture strength of ZnO ceramics is insensitive to the size of specimens, which has been corroborated by recent experiments using specimens with various effective volumes.