On The Mechanical And Fracture Properties Of The Hierarchical Cellular Structure

The introduction of hierarchy into structures has been credited with changing mechanical properties.Substructures of the usual hierarchical honeycombs are mainly regular honeycomb lattice,and relatively little attention has been paid for the stochastic Voronoi honeycombs.Therefore,in this study,periodically hierarchical honeycomb with irregular Voronoi honeycomb sub-structure cells has been designed by replacing the solid cell wall of the original regular hexagonal honeycombs with the equal mass,and the possibility of designing a new class of hierarchical honeycomb with the tailorable properties was discussed.The Voronoi sub-structure cell were built based on the Voronoi tessellation algorithm.Numerical investigation has been performed to determine the influence of structural hierarchy and irregularity on the in-plane elastic properties.The results showed that the effective Young's modulus of the hierarchical honeycomb could be 300 percent larger than these of first-order regular hexagonal honeycomb at the same mass.In contrast,there was no obvious indication that the effective Young's modulus and the Poisson ratio were affected significantly by the irregularities.Both the Young's modulus and the Poisson's ratio decreased gradually with increasing the relative density.In addition,the cell-wall thickness-to-length ratio of the super-structure had noticeable effect on the Young's modulus and the Poisson ratio.Although the effective Young's modulus increased as the hierarchical length ratio increased,the Poisson ratio was relatively insensitive to the hierarchical length ratio.Based on the work,it is suggested to further optimize the hierarchical structure in terms of both the cell wall misalignment and the sub-structuresBesides,a finite element based method has been used to calculate the fracture toughness of the hierarchical honeycomb for mode ?,mode ? and mixed-mode loading.Influences of the key geometrical parameters on fracture toughness of the hierarchical honeycomb are explored.Our study reveals that the fracture toughness is sensitive to the overall model size and converges as the model size is increased.There is no indication that mode ? and mode ? fracture toughness are affected significantly by cell irregularities.The hierarchical honeycombs always have a greater resistance to fracture in mode ? compared to mode ? regardless of the cell regularity.The predicted fracture toughness scales as (?),and the exponent d hovers around 2.0.It has also been shown that both the thickness-to-length ratio of super-structure and the hierarchical length ratio have significant influence on the predicted fracture toughness.With careful design,the introduction of hierarchy can elevate fracture toughness of honeycombs.However,for elastic-brittle cell wall material,excessive hierarchy has a deleterious effect upon the fracture toughness.The fracture locus are obtained in(K?,K?)space which comprises the inner convex envelope of a series of straight lines,corresponding to a particular failure site.Additionally,the fracture toughness decreases with the increase of the negative T-stresses similar to the fully dense elastic-plastic solids.