Role of specimen size upon the measured toughness of cellular solids

It is well known that the mechanical properties of cellular solids depend critically upon the specimen size and that a 'sufficiently' large test specimen is needed to obtain representative bulk values. Notwithstanding, the fracture toughness of cellular solids is still measured experimentally based on standards, such as the ASTM E399 and E813, developed for solid materials that do not possess an intermediate, 'cell-level' length scale. Experimental data in the literature appears to show that the toughness of stochastic 3D foams is, also, size-dependent. This paper presents the results of a detailed finite element (FE) study that will quantify, and identify the physical origin of, the size-dependent effect. Three-point bending of a single-edge notched (or SEN(B)) specimen, with a 2D Voronoi micro-architecture, is modelled numerically to obtain estimates of fracture toughness which are compared to those obtained with a 'boundary-layer' analysis.