A nondimensional framework for size dependent quasi-brittle fracture criteria

Abstract

It is well known that the quasi-brittle fracture behaviors of plain specimens and cracked specimens with sufficiently long cracks can be predicted satisfactorily by the material strength theory and the linear elastic fracture mechanics, respectively. However, the transition between these two classical limits is relatively complicated and vague, so that intensive attentions have been paid to explain this size dependent phenomenon during the past three decades. Although the fracture process zone (FPZ) is a well-accepted mechanism for this size effect, the stress distribution in the FPZ is still not well understood, which usually results in introducing additional parameters supplementary to conventional material parameters to fit the testing data. In order to establish reasonable fracture criteria without additional parameters, this paper proposes a general construction framework based on the dimensional analysis, in which different stress distributions in the FPZ generate different trial functions. The criteria construction process is firstly demonstrated by using three uniform stress FPZ models. It is found that the well-known line method of the theory of critical distances is consistent with the modified Irwin’s model. Furthermore, a new criterion is established by constructing the stress gradient continuous model (SGCM), in which the stress distribution in the FPZ is not only continuous but also smooth. Finally, experimental results of different quasi-brittle materials are used to examine the validities of these criteria, some of which can achieve reasonable agreements with testing data without additional parameters, and the criterion based on the SGCM shows a better performance for certain cases. Therefore, one can envisage that optimized quasi-brittle fracture criteria could also be established based on the proposed general framework by adopting more realistic FPZ models for specific materials.