The nominal tensile strength of disordered materials: A statistical fracture mechanics approach

The aim of the present paper is to study the variation of tensile strength of disordered materials in relation to the structural size. Griffith[1] gave an explanation to this phenomenon assuming the size of the most dangerous microdefect as proportional to the specimen size. Therefore, decreasing the specimen size, the size of this microdefect decreases and the tensile strength of the specimen increases. A defect size distribution of self-similarity will be 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 can be obtained. Statistical Monte-Carlo simulations are performed to confirm this trend and to obtain the relation between the degree of disorder and the slope of the size effect law. The parameters of the defect size distribution-density and average size of the imperfections-can be obtained by experimental tensile tests. In order to consider the whole scale range, a truncated statistical model will be presented. This new model assumes a truncated defect size distribution and predicts a scale effect in complete accordance with that of the Multifractal Scaling Law proposed by Carpinteri[2] and Carpinteri et al.[3-5]. The global failure probability is obtained by the composition of the n independent local failure conditions. The paper ends with the presentation of the results obtained by this truncated model and the comparison with some experimental data. (C) 1997 Elsevier Science Ltd.