NUMERICAL STUDY ON HONEYCOMB BEHAVIORS UNDER COMBINED SHEAR-COMPRESSION

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Folding events in successive crushing

Zhao and Abddenadher found that the folding cycles are composed of two stages. At the start, crush is obtained by bending in the middle of the flat plates (the two trapezoids around nodes B or B′ in Figure 2.12) and there exist small areas around the four corner lines (the two adjacent triangles around node A in Figure 2.12) which remain vertical and can support more external load. The second stage begins with the buckling of the corner line areas as shown on the right of Figure 2.12. The buckling of these edge zones corresponds to a decrease of the global crushing load.

Mechanism of dynamic enhancement

Zhao and Abdennadher explained the dynamic enhancement of initial peak by adopting directly the dynamic enhancement mechanism for double-plate model. It is found in Figure 2.14 that the nominal stress of tube follows the stress-strain curve of the base material as predicted by the simplified inertia effect model. Nevertheless, the dynamic enhancement mechanism in successive crushing period is more complicated. Zhao and Abdennadher found that the stress and strain distributing in the corner region is obviously higher under dynamic loading than under quasi-static loading, which agrees well with the concept of inertial effect model. In summary, Zhao and Abddennadher proposed in their work a simple model basing on inertia effect to explain the strength enhancement of square tube under dynamic loading. In order to adapt this mechanism into cellular materials, such as honeycomb, some further investigations on their work maybe helpful. First, a macrosize tube structure is employed in the study of Zhao and Abddennadher, which has obvious difference with the dimensions of thin-walled structure as in honeycomb. A dynamic enhancement mechanism which is dominated by inertia effect is supposed to have relations with model dimensions and a micro-size tube model should be involved. Second, the stress and strain elevation in square tube under dynamic compression has been validated, however, as to the reason, no direct evidence is provided in their work to show the collapse delay due to the inertia effect. Finally, the strain hardening behavior of base material is an important factor in the concept of inertia effect model, and its influence on the dynamic enhancement of cellular materials should be investigated.

Details on square tube crushing process

In this subsection, we are going to investigate the deformation details of the square tube in order to check the adaptability of inertia effect model to the dynamic enhancement. The complete deformation process is examined carefully and the relation between tube deforming configurations and the overall carrying capacity is determined.
Figure 2.18 presents the force/crush of square tube made of Material 1 under impact velocity of V2=30m/s. The whole deforming process is from zero crush to compressive displacement of δ=6mm. In Figure 2.18, segment a represents the elastic deformation period, b, d and c, e are respectively the two ascending and descending segments of in successive crush. Points A, C, B and D denote respectively the two peaks and two troughs of the curve.

Dynamic enhancement of the first peak

As illustrated in 2.2.3, the initial peak of force/crush curve of the square tube has relations with the collapse of the tube walls. This process is comparable to the collapse process of double-plate model and the validity of the inertial effect model in tube structure has been confirmed by Zhao and Abdennadher[27]. Here, we present in Figure 2.21 the stress distributions on tube walls at the moment of initial collapse for three loading cases. It is observed that the central area of one fold is under loading and the top and bottom of this part is unloading. Moreover, the stress level at the central area is found to increase with loading velocity, and the maximum value of which are respectively 305MPa for quasi-static loading, 359MPa for dynamic loading with V2=30m/s and 403MPa for V3=60m/s.
The stress distributing along the central line is also checked for the three loading cases. As shown in Figure 2.22, the increase of loading velocity elevates not only the maximum stress but also the whole stress distribution on the tube walls, which results in finally the initial peak enhancement of the tube.

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Table of contents :

CHAPTER 1 INTRODUCTION
1.1 RESEARCH BACKGROUND
1.2 RESEARCH PROGRESSES
1.2.1 Dynamic enhancement of cellular materials
1.2.2 Progresses on multi-axial loading techniques
1.2.3 Multi-axial behavior of honeycombs
1.3 OUTLINE OF DISSERTATION
PART I DYNAMIC ENHANCEMENT OF HONEYCOMBS
CHAPTER 2 DYNAMIC ENHANCEMENT MECHANISM OF THIN-WALLED
STRUCTURES
2.1 LATERAL INERTIA EFFECT AND THE SIMPLIFIED MODEL
2.1.1 Lateral inertia effect
2.1.2 Simplified inertia effect model
2.2 MICRO-SIZE DOUBLE-PLATE MODEL FOR VALIDATION
2.2.1 Model installation
2.2.2 Implicit and explicit
2.2.3 Lateral inertial effect
2.3 LATERAL INERTIA EFFECT IN THE CRUSHING PROCESS OF TUBE
2.3.1 Works of Zhao and Abdennadhe
2.3.2 Micro-size tube model
2.3.3 Details on square tube crushing process
2.3.4 Dynamic enhancement of the first peak
2.3.5 Dynamic enhancement of the successive peak
2.3.6 Influence of base material on the dynamic enhancement of square tube
2.4 LATERAL INERTIA EFFECT IN THE OUT-OF-PLANE CRUSHING OF HONEYCOMBS
2.4.1 Simplified cell-model of honeycomb
2.4.2 Deformation details of cell-model and the dynamic strength enhancement
2.4.3 Definitions
2.4.4 Calculating results with different cell-size
2.4.5 Calculating results with different cell-wall thickness
2.4.6 Calculating results with different base material
2.5 SUMMARY
CHAPTER 3 EXPERIMENTAL STUDIES ON DYNAMIC ENHANCEMENT OF ALUMINIUM HONEYCOMBS
3.1 LARGER DIAMETER SOFT HOPKINSON BAR TECHNIQUE
3.1.1 Introduction of classical Hopkinson bar
3.1.2 Specific problems in cellular materials testing
3.1.3 Large diameter, viscoelastic Hopkinson bar technique
3.1.4 Wave dispersion correction of larger diameter viscoelastic Hopkinson bars
3.1.5 Data processing of SHPB for cellular materials
3.2 QUASI-STATIC EXPERIMENTS FOR CELLULAR MATERIALS
3.3 MATERIALS AND SPECIMENS
3.4 QUASI-STAIC AND DYNAMIC EXPERIMENTAL RESULTS
3.4.1 Reproducibility
3.4.2 Dynamic enhancement of honeycombs
3.4.3 Influence of cell-size
3.4.4 Influence of cell-wall thickness
3.4.5 Influence of base material
3.5 SUMMARY
PARTⅡ MULTI-AXIAL BEHAVIOR OF HONEYCOMBS UNDER COMBINED SHEAR-COMPRESSION
CHAPTER 4 COMBINED DYNAMIC SHEAR-COMPRESSION LOADING TECHNIQUE BY SHPB
4.1 COMBINED SHEAR-COMPRESSION LOADING TECHNIQUE
4.1.1 Combined shear-compression set-up
4.1.2 Effects of beveled bars on data process method
4.2 VALIDATION OF THE COMBINED SHEAR-COMPRESSION METHOD BY FEM
4.2.1 FEM model installation
4.2.2 Comparison between three basic waves
4.2.3 Estimation of friction between beveled bars and Teflon sleeve
4.2.4 Estimation of beveled bar deformation
4.3 QUAIS-STATIC COMBINED SHEAR-COMPRESSIVE EXPERIMENTS
4.4 SUMMARY
CHAPTER 5 EXPERIMENTAL RESULTS OF HONEYCOMBS UNDER COMBINED SHEAR-COMPRESSION
5.1 MATERIAL AND SPECIMEN
5.2 EXPERIMENTAL RESULTS OF HONEYCOMBS
5.2.1 Reproducibility
5.2.2 Dynamic experimental results under combined shear-compression
5.2.3 Quasi-static experimental results under combined shear-compression
5.2.4 Comparison between dynamic and quasi-static results
5.3 DEFORMATION PATTERN OBSERVATIONS OF HONEYCOMBS
5.3.1 TW loading plane
5.3.2 TL loading plane
5.4 LIMITATION OF THE COMBINED SHEAR-COMPRESSION DEVICE
5.5 SUMMARY
CHAPTER 6 NUMERICAL STUDY ON HONEYCOMB BEHAVIORS UNDER COMBINED SHEAR-COMPRESSION
6.1 INSTALLATION OF FE MODELS
6.1.1 Complete model
6.1.2 Simplified models
6.2 COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS
6.2.1 Comparison on pressure/crush curves
6.2.2 Comparison on deformation patterns
6.3 BIAXIAL BEHAVIOR OF HONEYCOMBS UNDER COMBINED SHEAR-COMPRESSION
6.3.1 Normal and shear behaviors
6.3.2 Dynamic enhancement of normal and shear behaviors of honeycombs
6.3.3 Macroscopic yield envelop estimation
6.4 SUMMARY
REFERENCES

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