Impact Resistance And Fracture Toughness Of Hierarchical Cellular Materials

Hierarchical cellular materials differ from traditional ones in that their cell wallsare also cellular. Recent studies showed that they have a higher specific strength andthere is potential to further improve their mechanical properties by proper design oftheir microstructure. In this thesis, the impact resistance and fracture toughness ofhierarchical cellular materials are studied by a combination of theoretical and numericalanalyses.By modifying an earlier theoretical model for the core compaction stage ofsandwich beams, a one-dimensional shock wave theory is developed for the impactresistance of clamped sandwich beams with a cellular core. Finite element method(FEM) is used to simulate the responses of sandwich beams with a traditional cellularcore (regular hexagonal honeycomb) to impact loading. Obtained numerical resultsshow that, compared to the earlier model, the developed theory provides improvedpredictions of the maximum lateral deflection of the front face and the boundary of thetwo regions where the cellular core is totally and partly compacted.The developed theoretical model is then employed to investigate the impactperformance of a sandwich beam with a self-similar hierarchical hexagonal honeycombcore. First, the property of the core is explored. It is shown that, if failed by plasticyielding of cell walls, the yield strength of the considered self-similar hierarchical coresmay decrease or stay unchanged with the hierarchical order increasing. As aconsequence, the impact resistance of the corresponding sandwich beam decreases asthe hierarchical order increases. Moreover, even if the strength of the hierarchicalcellular core is higher than that of a traditional cellular core, the increase in the impactresistance of the sandwich beam is found to be limited.The in-plane compressive responses of regular hexagonal honeycomb (1st order)and a2nd order hierarchical hexagonal honeycomb with corrugated core sandwich walls(abbreviated as corrugated hexagonal honeycomb) are studied by FEM. An optimaldesign of the corrugated hexagonal honeycomb is identified. Its mechanical properties,including Young’s modulus, elastic limit, peak strength, fracture toughness and crackopening displacement of mode I crack under plane strain condition, are compared to those of the1st order hexagonal honeycomb. It’s found that, when the relative density issmall, the optimized corrugated hexagonal honeycomb is superior to its1st ordercounterpart. However, the effect of hierarchy is reversed when the relative density ishigh. Moreover, the Young’s modulus, elastic limit and peak strength under plasticfailure mode, and the fracture toughness of the optimized corrugated hexagonalhoneycomb are shown to depend linearly upon the relative density.The yield loci and the mode I and mode II crack tip plastic zones of1st orderregular hexagonal honeycomb and2nd order hierarchical hexagonal honeycomb withsandwich ribs (2nd order hexagonal honeycomb) in plane strain condition are examinedtheoretically. Obtained results show that the in-plane yield loci of both1st order and2ndorder honeycombs can be approximated to be isotropic. Correspondingly, the plasticzones are only slightly affected by the crack direction. In addition, the yield loci of the1st order and2nd order hexagonal honeycomb are very similar in shape becausehexagonal honeycombs are bending dominated, but are different in size. Similarconclusion is obtained for the crack tip plastic zones.