The study analyzed the influence of random defects on plateau stresses of honeycomb materials with varied relative densities and established a computational model of honeycomb materials considering random defects. The results show that the plateau stress decreases evidently as the random defects increase, which is closely related to the relative density of honeycomb materials. It also set up a functional relationship between relative plateau stresses and random defects as well as that between relative plateau stresses and relative densities. Taken topological structure, random defects and strain rate effect into consideration, and it proposed a dynamic constitutive model of honeycomb materials under low-middle impact loading. And the proposed constitutive model possesses a better applicability to match the stress-strain relationship of honeycomb materials in existing impact experiments. The proposed constitutive model could make a theoretical foundation in material design and practical application of honeycombs containing random defects.
Honeycomb and foam materials, as a type of functional materials, have existed widely in nature [
In terms of mechanical performances of honeycombs, Yang [
The existing researches have made it clear that the random defects can make a great influence on the service performances of honeycomb materials. Liu and Zhang [
Based on the existing researches, the fact can be known that their service performances of honeycomb materials are affected by multiple factors, including properties of basic materials, topological structure, cell configuration, and loading condition. Summarizing the existing studies about honeycomb materials, a recent status can be found that there have been so many studies focusing on phenomenological mechanical properties and few investigations on its constitutive model of this material. In basis of existing results, the explicit finite element method (FEM) software, ANSYS LS-DYNA, was applied for simulation of dynamic responses of honeycomb materials subjected to impact loading. This paper aims to analyze the influence of material random defects on plateau stress and establishes a constitutive model of honeycomb materials taking random defects, strain rate as well as topological structure into consideration. In the proposed constitutive model, a coefficient representing defects is introduced to reflect the influence of random defects in honeycomb on dynamic mechanical properties. It offers a reference for the further investigations about honeycomb materials and the design of cellular materials in practical engineering.
Here, the configuration of honeycomb cells is regular hexagon, and honeycombs are assembled with diverse cells with different cell wall sizes, respectively. The cell wall lengths include 2 mm, 3 mm, and 4 mm, and the wall thickness of all honeycombs is set to 0.6 mm. The sizes of the overall model specimen are 100 × 100 × 2 mm. The random defects in honeycomb are generated by removing cell walls randomly, and the rate of defects in honeycombs can be represented by
Here, for the random defects, random removing of cell walls was conducted via an algorithm. In terms of this algorithm, there are three major parameters to rule this removing process. They are summation of removing cells, number of removing cell, and the summation of reserving cells, respectively. When all of the major parameters are given, the software, ANSYS/LS-DYNA, will produce a random number
For the honeycomb structure, its topological entirety would be destroyed if its rate of defects overmatches 35%. And coherent voids would be generated when the rate of defects is over 25% [
Finite element model of honeycombs with random defects.
Meanwhile, the relative density of honeycombs without defects is represented as
Here, the basic material is aluminum [
Material parameters of aluminum metal.
Elastic modulus |
Yield strength |
Poisson’s ratio |
Density |
---|---|---|---|
69 | 76 | 0.3 | 2700 |
To validate the finite element models in this study, a simulation of impact experiment [
Stress-strain curves of honeycomb materials.
Comparison of deformation modes.
Random defects are generated inevitably during its producing process. The influence of defects on its relative density can be ignored in reality. Hence, the threshold rate of random defects in honeycombs was set among 0∼25%. This section aims to investigate the effect of random defects on mechanical properties of honeycombs.
Varied stress-strain curves of honeycombs with different defect rates are shown in Figure
Strain-stress curves of honeycomb material under impact loading.
Meanwhile, in this paper, the plateau stress of honeycombs can be calculated as equation (
From Figure
Effect of random defect ratio on the plateau stress.
Figure
The relative plateau stress with random defects and its relationship.
The coefficients of relative plateau stress on equation (
Relative density |
Coefficient |
|
Reference | |
---|---|---|---|---|
|
|
|||
0.3535 | 1.023 | 0.0119 | 0.926 | |
0.2407 | 0.985 | 0.0062 | 0.842 | |
0.1865 | 0.965 | 0.0051 | 0.851 | |
0.3302 | 1.014 | 0.007 | 0.887 | [ |
0.1406 | 0.979 | 0.0027 | 0.844 | [ |
What showed in Figure
The relationship of coefficients and relative density of honeycomb.
The mechanical performances are affected by mechanical parameters of its base materials as well as cell structure configurations. And under impact loading, the effect of strain rate of honeycombs should not be ignored. Therefore, the constitutive model of honeycombs subjected to impact loading should contain factors of base material property, topological structure, and loading condition. Many existing researches [
Schematic of simplified constitutive model.
In the foundation of the concept diagram in Figure
And a calculation formula about the constitutive model of honeycombs is proposed as
Constitutive model shape coefficients and its function curves.
In this constitutive model, it is combined with four functions about random defects, relative density of mass, characterization of three-stage curve for porous materials, and effect of strain rate, respectively. In equation (
It can be seen from Figure
Experimental curves and its theoretical curves of honeycomb material.
The relative density of honeycomb materials and its constitutive model coefficients.
Reference | Relative density | Constitutive coefficients | |
---|---|---|---|
|
|
||
This article | 0.186 | 0.25 | 2.5 |
0.241 | 0.22 | 1.8 | |
0.334 | 0.24 | 1.8 | |
[ |
0.085 | 0.3 | 10 |
0.089 | 0.23 | 6.2 | |
[ |
0.0723 | 0.235 | 19 |
0.0563 | 0.45 | 21.2 | |
[ |
0.0822 | 0.43 | 6.5 |
[ |
0.048 | 0.2 | 6 |
Constitutive model coefficients and its relative density.
Significantly, it is noteworthy that the stress-strain curve of foam metal [
From Table
According to the data in Table
In order to verify the proposed constitutive model in this study, stress-strain curves of honeycombs under static and impact loading condition are compared with their calculated curves, respectively, which are shown in Figure
Stress-strain curves and its constitutive model: (a) the stress-stain curves of honeycomb without defects; (b) the stress-stain curves of honeycomb with, random defects under 20 m/s impact loading; and (c) experimental and theoretical curves of open-cell metal foam under various strain rates.
From Figure
The comparison results indict that the established constitutive model of honeycombs could be used to investigate the dynamic performances of honeycombs subjected to punching whether with random defects or not. Meanwhile, the proposed model has a wide application range of cellular materials, such as foam metal and cellular honeycombs. Otherwise, when the first section of equation (
Applying finite element analytical software, dynamic responses of honeycombs with varied defect rates are simulated. Based on simulation results and existing experimental data, a constitutive model of honeycombs taking topological structure, basic material parameters, and effect of strain rate into consideration was proposed. In this proposed constitutive model, three major influential aspects were contained, including material factor as well as loading condition. For the proposed constitutive model, coefficients of
Based on the proposed model, the future work about honeycomb materials containing random defects will focus on the dynamic performances, like energy absorption and impact resistance. On the other hand, the model proposed in this paper contains several empirical parameters. Explaining their engineering meanings of parameters and exploring the explicit formula among parameters and material performances may be an interesting work in future.
The data used to support the findings of this study are available from the corresponding author upon request.
All the authors declare that there are no conflicts of interest regarding the publication of this article.
Hu Jun and Ren Jianwe contributed equally to this work.
The present work about this paper was financially supported by the National Science Foundation of China (Grant no. 51778003) and the Key Research Program Funds of College Natural Science for Anhui Province Education Department (Grant no. KJ2017A486).