Size effects in out-of-plane bending in elastic honeycombs fabricated using additive manufacturing : modeling and experimental results

Size effects in out-of-plane bending stiffness of honeycomb cellular materials were studied using analytical mechanics of solids modeling, fabrication of samples and mechanical testing. Analysis predicts a positive size-effect relative to continuum model predictions in the flexure stiffness of a honeycombed beam loaded in out-of-plane bending. A method of determining the magnitude of that effect for several different methods of constructing or assembling square-celled and hexagonal-celled materials, using both single-walled and doubled-walled construction methods is presented. Hexagonal and square-celled honeycombs, with varying volume fractions were fabricated in Nylon 12 using Selective Laser Sintering. The samples were mechanically tested in three-point and four point-bending to measure flexure stiffness. The results from standard three-point flexure tests, did not agree with predictions based on a mechanics of solids model for either square or hexagonal-celled samples. Results for four-point bending agreed with the mechanics of solids model for the square-celled geometries but not for the hexagonal-celled geometries. A closed form solution of an elasticity model for the response of the four-point bending configuration was developed, which allows interpretation of recorded displacement data at two points and allows separation the elastic bending from the localized, elastic/plastic deformation that occurs between the loading rollers and the specimen’s surface. This localized deformation was significant in the materials tested. With this analysis, the four-point bending data agreed well with the mechanics of solids predictions.