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Journal of Computational and Nonlinear Dynamics | Volume 2 | Issue 2 | Research Paper
RESEARCH PAPERS

Study of Viscoplasticity Models for the Impact Behavior of High-Strength Steels

[+] Author and Article Information
N. Peixinho

Department of Mechanical Engineering, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugalpeixinho@dem.uminho.pt

A. Pinho

Department of Mechanical Engineering, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal

J. Comput. Nonlinear Dynam 2(2), 114-123 (Nov 17, 2006) (10 pages) doi:10.1115/1.2447129 History: Received April 03, 2006; Revised November 17, 2006
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This study reports on modeling the mechanical behavior of high-strength steels subjected to impact loading. The materials studied were steel grades of interest for crashworthiness applications: dual-phase and transformation induced plasticity (TRIP) steels. The challenges associated with the numerical simulation of impact events involving these materials include the modeling of extensive plastic deformation, particularly the change of material properties with strain rate. Tensile testing was performed at different strain rates on the materials studied. The test results were used to compare and validate constitutive equations that provide a mathematical description of strain-rate dependence of the material properties. The Cowper–Symonds equation and modified variants were examined. The crashworthiness performance of thin-walled sections made of dual-phase and TRIP steels was also investigated. Axial crushing tests were performed at different speeds on top-hat and hexagonal tubes. The experimental results were compared with numerical simulations obtained using an explicit finite element program (LS-DYNA) and the original and modified Cowper–Symonds equations.
Copyright © 2007 by American Society of Mechanical Engineers
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+Variation of strength properties with strain rate: (a) DP600; and (b) TRIP600
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Variation of strength properties with strain rate: (a) DP600; and (b) TRIP600
Figure 1

Variation of strength properties with strain rate: (a) DP600; and (b) TRIP600

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+Results of Cowper–Symonds equation for DP600 steel: (0) Rp0.2 proof stress; (◇): intermediate stress; UTS: (a) reference: UTS; range: 0.0001–141∕s; D=64,601.9∕s; p=3.22; and (b) reference: Rp0.2; range: 0.0001–141∕s; D=1587.6∕s; p=2.33
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Results of Cowper–Symonds equation for DP600 steel: (0) Rp0.2 proof stress; (◇): intermediate stress; UTS: (a) reference: UTS; range: 0.0001–141∕s; D=64,601.9∕s; p=3.22; and (b) reference: Rp0.2; range: 0.0001–141∕s; D=1587.6∕s; p=2.33
Figure 2

Results of Cowper–Symonds equation for DP600 steel: (0) Rp0.2 proof stress; (◇): intermediate stress; UTS: (a) reference: UTS; range: 0.0001–141∕s; D=64,601.9∕s; p=3.22; and (b) reference: Rp0.2; range: 0.0001–141∕s; D=1587.6∕s; p=2.33

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+Results of Cowper–Symonds equation for TRIP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS: (a) UTS; 0.0001–209.8∕s; D=160,171.4∕s: p=3.54; and (b)Rp0.2; 0.0001–209.8∕s; D=11,410.6∕s; p=3.28
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Results of Cowper–Symonds equation for TRIP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS: (a) UTS; 0.0001–209.8∕s; D=160,171.4∕s: p=3.54; and (b)Rp0.2; 0.0001–209.8∕s; D=11,410.6∕s; p=3.28
Figure 3

Results of Cowper–Symonds equation for TRIP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS: (a) UTS; 0.0001–209.8∕s; D=160,171.4∕s: p=3.54; and (b)Rp0.2; 0.0001–209.8∕s; D=11,410.6∕s; p=3.28

Grahic Jump Location
+Results of Eq. 7 for DP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS reference interval: 0.0001–141∕s; Du=64,601.9∕s; Dy=1587.6∕s; pu=3.22; py=2.33
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Results of Eq. 7 for DP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS reference interval: 0.0001–141∕s; Du=64,601.9∕s; Dy=1587.6∕s; pu=3.22; py=2.33
Figure 4

Results of Eq. 7 for DP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS reference interval: 0.0001–141∕s; Du=64,601.9∕s; Dy=1587.6∕s; pu=3.22; py=2.33

Grahic Jump Location
+Results of Eq. 7 for TRIP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS reference interval: 0.0001–209.8∕s; Du=160,171.4∕s; Dy=11,410.6∕s; pu=3.54; py=3.28
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Results of Eq. 7 for TRIP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS reference interval: 0.0001–209.8∕s; Du=160,171.4∕s; Dy=11,410.6∕s; pu=3.54; py=3.28
Figure 5

Results of Eq. 7 for TRIP600 ; (0) Rp0.2 proof stress; (◇) intermediate stress; UTS reference interval: 0.0001–209.8∕s; Du=160,171.4∕s; Dy=11,410.6∕s; pu=3.54; py=3.28

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+Detail of trigger and laser weld
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Detail of trigger and laser weld
Figure 6

Detail of trigger and laser weld

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+Nominal dimensions of sections: (a) top-hat; and (b) hexagonal
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Nominal dimensions of sections: (a) top-hat; and (b) hexagonal
Figure 7

Nominal dimensions of sections: (a) top-hat; and (b) hexagonal

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+Finite-element model of top-hat tube
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Finite-element model of top-hat tube
Figure 8

Finite-element model of top-hat tube

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+Experimental and numerical load-time histories, DP600, test dt4
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Experimental and numerical load-time histories, DP600, test dt4
Figure 9

Experimental and numerical load-time histories, DP600, test dt4

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+Experimental and numerical load-time histories, DP600, test dt2
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Experimental and numerical load-time histories, DP600, test dt2
Figure 10

Experimental and numerical load-time histories, DP600, test dt2

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+Experimental and numerical load-time histories, TRIP600, test dt5
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Experimental and numerical load-time histories, TRIP600, test dt5
Figure 11

Experimental and numerical load-time histories, TRIP600, test dt5

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+Experimental and numerical load-time histories, TRIP600, test dt7
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Experimental and numerical load-time histories, TRIP600, test dt7
Figure 12

Experimental and numerical load-time histories, TRIP600, test dt7

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+Final deformed shapes obtained experimentally and numerically for DP600: (a) dt4, dp1; and (b) dt2, dp6
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Final deformed shapes obtained experimentally and numerically for DP600: (a) dt4, dp1; and (b) dt2, dp6
Figure 13

Final deformed shapes obtained experimentally and numerically for DP600: (a) dt4, dp1; and (b) dt2, dp6

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+Final deformed shapes obtained experimentally and numerically for TRIP600: (a) dt5, trip2; and (b) dt7, trip6
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Final deformed shapes obtained experimentally and numerically for TRIP600: (a) dt5, trip2; and (b) dt7, trip6
Figure 14

Final deformed shapes obtained experimentally and numerically for TRIP600: (a) dt5, trip2; and (b) dt7, trip6

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+Experimentally obtained variation of velocity of mass after striking specimen (velocities are determined from high speed film): (•–•): experimental data; (– – –) best curve fit (19)
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Experimentally obtained variation of velocity of mass after striking specimen (velocities are determined from high speed film): (•–•): experimental data; (– – –) best curve fit (19)
Figure 15

Experimentally obtained variation of velocity of mass after striking specimen (velocities are determined from high speed film): (•–•): experimental data; (– – –) best curve fit (19)

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+Comparison of velocity–time histories of the different numerical simulations of Otubushin’s benchmark using Cowper–Symonds equation and modified version
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Comparison of velocity–time histories of the different numerical simulations of Otubushin’s benchmark using Cowper–Symonds equation and modified version
Figure 16

Comparison of velocity–time histories of the different numerical simulations of Otubushin’s benchmark using Cowper–Symonds equation and modified version

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