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Similar to uniaxial compression of Al foam, pressure vs. volumetric strain response of hydrostatic compression shows three distinct regimes; linear elastic, hardening plastic and densification. The strain hardening in hydrostatic compression is however higher than that in uniaxial compression as depicted in Figure 2.15, The specimen size effects on the mechanical behavior of Alporas closed cell and Duocell open cell Al foams were determined by Andrews et al. (Andrews, et al. 2001, Onck, et al. 2001) . It was reported that Young's modulus and plastic collapse strength of both foams increased with increasing the ratio of specimen size to cell size, L/d. It was also detected that the decrease in Young's modulus and strength values with decreasing the ratio of specimen size to cell size in open cell foams was more rapid than in closed cell foams, mainly due to the lack of cell faces in open cell foam. The size effect on the shear strength was found to disappear for the specimens with a thickness at last twice the cell size as shown in Figure 2.16. Figure 2. 15. .The uniaxial and hydrostatic stress-strain curves of Alulight foams. (Source: Shridhar and Fleck 2005) 20
Figure 2.16. Shear strength, normalized by the bulk value, against the ratio of specimen thickness, t, to the cell size, d, for Alporas closed-cell foam (Source: Andrews, et al. 2001). The effect of foam cell structure parameters on the compression behavior of Al foam was investigated by Dequing et. al. (Deqing, et al. 2005). With increasing foam cell size, foam density (Figure 2.17(a)) and cell wall and node size (Figure 2.17(a)) decreased. It was further postulated that the collapse plastic stress and energy absorption ability could be improved by the smaller cell size. Similar results were also found by Miyoshi et. al. (Miyoshi, et al. 1999). By reducing the cell edge length of conventional Alporas Al foams from 2.68 mm to 1.91 mm, the energy absorption per volume increased by 40% . (a) (b) Figure 2. 17. Variation of a) foam density and b) foam cell wall and node size with foam cell size of Al foam (Source: Deqing, et al. 2005). 21
Page 1 and 2: OPTIMIZATION OF THE AXIAL CRUSHING
Page 3 and 4: ACKNOWLEDGEMENTS My PhD quest has b
Page 5 and 6: ÖZET KAPALI HÜCRELİ ALUMİNYUM K
Page 7 and 8: CHAPTER 4 EXPERIMENTAL DETAILS ....
Page 9 and 10: CHAPTER 8 ALUMINUM CRASH BOX OPTIMI
Page 12 and 13: Figure 3.7. Simulations of the defo
Page 14 and 15: Figure 4.9. Dimensions of tensile t
Page 16 and 17: Figure 6.21. Sequential deformation
Page 18 and 19: Figure 7.20. Sequential deformation
Page 20 and 21: LIST OF TABLES Table Page Table 4.1
Page 22 and 23: Figure 1. 1. The body in white stru
Page 24 and 25: Figure 1. 4. Commercial crash boxes
Page 26 and 27: CHAPTER 2 AL CLOSED CELL FOAMS: PRO
Page 28 and 29: The processing methods and mechanic
Page 30 and 31: Figure 2. 5 The preferred particle
Page 32 and 33: Figure 2. 8. Typical cellular struc
Page 34 and 35: Figure 2. 10. Manufacturing cost of
Page 36: Figure 2. 12. Laser assisted foamed
Page 43 and 44: Figure 2. 19. Yield strength vs. re
Page 45 and 46: Figure 2. 21. Unit cell geometry an
Page 47 and 48: Figure 2. 24. Load-displacement cur
Page 49 and 50: Figure 2. 26. The photographs of a
Page 51 and 52: CHAPTER 3 CRUSHING BEHAVIOR OF TUBU
Page 53 and 54: Figure 3.2. Diamond deformation mod
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(a) (b) Figure 4.3.Pictures of a) f
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oxes are shown in Figure 4.6. The l
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Figure 4.7. The method of trigger m
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4.4. Compression Tests of Crash Box
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4.5.2. Uniaxial Compression Testing
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Table 4.1 (Cont.) G1 T3 F2 G1T3F2 3
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Table 4.2 (Cont.) G1 T2.5 WP F2 G1T
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CHAPTER 5 SIMULATION AND OPTIMIZATI
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considered in axial and transverse
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were constrained. Since the width o
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5.4. The Crashworthiness Optimizati
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great effect on the crushing behavi
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CHAPTER 6 EXPERIMENTAL RESULTS 6.1.
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Figure 6.3.Tensile stress-strain cu
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(a) (b) Figure 6.5. Sequential defo
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plate (Figure 6(b)). The trigger is
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(a) (b) Figure 6.9. Deformation seq
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Figure 6.12. Sequential deformation
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Figure 6.18. (cont.) (c) (a) (b) Fi
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Figure 6.20.(cont.). (b) (c) 6.5.4.
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Figure 6.21.(cont.) (b) (c) 122
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Figure 6.22.(cont.) (c) Figure 6.23
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Figure 6.24.(Cont.) (b) (c) (a) Fig
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Figure 6.26.(cont.) (b) (c) 6.6. Dy
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Figure 6.27. (cont.) (b) (c) 130
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CHAPTER 7 MODELING RESULTS OF FOAM,
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experimental tensile stress-strain
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significant effect of weld seem ope
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Figure 7.7. Deformation photo of fi
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Figure 7.11. Deformation photos of
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(a) (b) (c) Figure 7.14. Load-displ
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7.4. Simulation of Empty and Partia
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Figure 7.16. (cont.) (c) (a) Figure
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(a) (b) Figure 7.18. Sequential def
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Figure 7.19. (cont.) (b) (c) 150
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Figure 7.20. (cont.) (c) (a) Figure
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(a) (b) Figure 7.26. Experimental a
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The constructed response surface of
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Table 8.1. R 2 , Radj 2 and RMSE va
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(a) (b) Figure 8.7. Response surfac
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an empty tube wall thickness higher
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where, K is a dimensionless constan
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The dynamic simulation and analytic
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Figure 9.4. (cont.) (c) (d) Figure
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Figure 9.6. (cont.) (c) (d) (a) Fig
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Equation 9.7 can also be rewritten
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(a) (b) Figure 9.10. Energy-absorbi
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Figure 9.11. (cont.) (d) The variat
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foam filling were evaluated. The re
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13. The interaction between foam fi
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Arora, J. S.,2004,Introduction to O
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Dannemann, K. A. and Lankford, J.,
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Hall, I. W., Guden, M. and Yu, C. J
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Kim, D-K. and Lee, S., 1999, Impact
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Mamalis, A. G., Manolakos, D. E., I
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Pugsley, A. G. and Macaulay, M., 19
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T. Miyoshi, M. Itoh S. Akiyama A. K
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Zhao, H., Elnasri, I. and Girard, Y
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