Dynamic crushing of 2D cellular structures: A finite element study
Introduction
Metallic honeycombs and foams are widely used as advanced structural components in many engineering applications due to their excellent mechanical properties and energy absorption capacity. Much work has shown that the mechanical properties of cellular materials are affected by the micro-structural parameters such as relative density, cell size and cell morphology. Experimental and theoretical studies on their mechanical behavior have focused on the elastic moduli and plastic collapse strength. In recent years, finite element analyses (FEA) have been carried out to investigate the influence of the micro-structural parameters of metallic honeycombs and foams on their crushing behavior.
Gibson and Ashby have systematically presented the in-plane and out-of-plane properties of honeycombs under static crushing in their literature review [1]. Since a cellular structure is an assembly of periodically or nearly periodically basic cells, Shi and Tong [2] derived the equivalent transverse shear modulus and in-plane modulus of honeycombs based on a two-scale method for the homogenization of periodic media. Wang et al. [3] generalized the rotation stiffness method to incorporate the elastic–plastic analysis of honeycomb cell walls. They employed a representative unit cell (RUC) with imperfections to numerically simulate the mechanical behaviors of elastic–plastic deformation, instability and collapse of single-type aluminum honeycombs under uniaxial compression. Papka and Kyriakides [4], [5], [6], [7], [8] carried out experiments and full-scale numerical simulations to study the in-plane uniaxial and biaxial crushing behavior of honeycombs. The biaxial crushing is helpful to understanding the associated deformation mechanisms, but it is quite complex to perform these experiments; they have been achieved by Papka and Kyriakides [7] who designed and built a custom biaxial crushing machine (BICRUMA). Recently, full-scale numerical simulations have attracted considerable research interest due to the localization of deformation. Considering geometric and material imperfections of aluminum honeycomb specimens used in engineering applications, Triantafyllidis and Schraad [9] studied the effects of imperfections on the quasi-static deformation and failure of double-type honeycombs under biaxial loading and found that their behavior was sensitive to the imperfections. Fortes and Ashby [10] analyzed the effect of non-uniformity on the in-plane Young's modulus of 2D foams with a distribution of the cell wall lengths and thicknesses. Chen et al. [11] studied systematically the influence of six types of morphological imperfection (waviness, non-uniform thickness of cell edges, cell-size variations, fractured cell walls, cell-wall misalignments, and missing cells) on the yielding of 2D cellular solids under biaxial loading. Using the finite element method, intact and damaged honeycombs [12], Voronoi honeycombs [13], [14] and their extension exhibiting bimodal or multimodal cell size distributions [15] were employed to analyze the influence of the imperfection on the static crushing behavior.
The dynamic crushing behavior of honeycombs also attracted considerable research interest. Zhao and Gray [16] presented an experimental study on the in-plane and out-of-plane dynamic crushing behavior of honeycombs using a Split Hopkinson Pressure Bar (SHPB) apparatus. Hönig and Stronge [17], [18] presented a finite element simulation to study the in-plane crushing of honeycombs. Ruan et al. [19] investigated the influences of the cell wall thickness and the impact velocity on the mode of localized deformation and the plateau crush pressure by means of finite element simulation using ABAQUS. They found that there are three types of deformation modes in the x1 direction and two types of deformation modes in the x2 direction, which were summarized in a mode classification map.
Recently, Yu et al. [20] studied the quasi-static and dynamic crushing behavior of closed-cell aluminum foams, respectively, on an MTS810 testing system and an SHPB apparatus. Both the strain-rate effect and the cell-size effect on the crushing stress were found. The results reveal that the structural heterogeneity and irregularity have influences on the strain-rate sensitivity of cellular metals. So it is of great significance to study the influence of the micro-structural parameters on the impact crushing behavior of realistic honeycombs and foams.
In this paper two irregularity-generating methods are employed to create irregular honeycomb models. The in-plane dynamic behavior of these structures is then studied by finite element simulation using ABAQUS/Explicit code [21]. The influences of cell irregularity and impact velocity on the deformation mode and the plateau crush pressure are investigated.
Section snippets
Irregularity-generating methods
Two irregularity-generating methods are employed. One is the disorder of nodal locations of a regular hexagonal honeycomb, and the other is based on the 2D random Voronoi technique.
Deformation modes of regular honeycombs
For regular honeycombs, Ruan et al. [19] have shown that the inertia effect plays an important role in dynamic crushing. When crushing in the x1 direction, three types of deformation modes are observed. At a low impact velocity, localized deformation causes oblique “X”-shaped bands (“X” mode); at a high impact velocity, it produces transverse localized bands (“I” mode) oriented perpendicular to the loading direction and located adjacent to the loading surface; while at a moderate impact
Conclusions
Two types of irregular honeycombs are constructed to study the in-plane crushing behaviors. The influences of cell irregularity and impact velocity on the deformation mode and the plateau crush pressure are investigated by finite element method.
Three types of deformation modes are observed both in the regular honeycombs and in the irregular honeycombs. At a low impact velocity, the inertia effect is negligible and a Quasi-static mode, i.e., collapse of weak shear bands, takes place. At a high
Acknowledgements
This work is supported by the National Natural Science Foundation of China (project No. 10072059, No. 90205003 and No. 10302027) and the CAS K.C. Wong Post-doctoral Research Award Fund.
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