A coarse semi-analytical lattice model for lifetime statistics of loaded hierarchical materials

Department of Chemistry, 152 Davey Laboratory, The Pennsylvania State University University Park, PA 16802, USA

Received: 4 March 2003
Accepted: 28 May 2003

Abstract

The mechanical behavior of heterogeneous materials is often modeled with the use of elastic lattices, in which the defects can be imitated by the removal of lattice structure elements. This paper shows that in the case of lifetime calculations it may be possible to replace a conventional 3D elastic lattice by a 2D ordinary site percolation lattice. The considered case of crystalline polymeric materials, constant tensile moderate load and global defect nucleation rate results in Weibull lifetime distribution. The Weibull shape parameter is shown to be proportional to the power of the inverse load, which is confirmed by well-known experimental data.