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Research Papers

Effect of Rate Sensitivity on Necking Behavior of a Laminated Tube Under Dynamic Loading

[+] Author and Article Information
Y. Shi

Department of Mechanical Engineering,
McMaster University,
1280 Main Street West,
Hamilton, ON L8S 4L7, Canada
e-mail: shiyh@mcmaster.ca

P. D. Wu

Department of Mechanical Engineering,
McMaster University,
1280 Main Street West,
Hamilton, ON L8S 4L7, Canada

D. J. Lloyd

Novelis Global Technology Centre,
945 Princess Street,
Kingston, ON K7L 5L9, Canada

D. Y. Li

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical and Power
Energy Engineering,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China

1Corresponding author.

Manuscript received August 29, 2013; final manuscript received October 25, 2013; accepted manuscript posted October 28, 2013; published online December 13, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051010 (Dec 13, 2013) (10 pages) Paper No: JAM-13-1372; doi: 10.1115/1.4025839 History: Received August 29, 2013; Accepted October 25, 2013; Revised October 25, 2013

An elastic-viscoplastic based finite element model has been developed to study the necking behavior of tube expansion for rate independent materials, rate dependent monolithic materials, and laminated materials during dynamic loading. A numerical study shows that for rate independent materials, the dynamic loading will not delay diffused necking but localized necking; for rate dependent materials, high strain rate sensitivity can significantly delay the onset of localized necking for both monolithic and laminated sheets and affect the multiple-neck formation in high-speed dynamic loading. The model also shows that a higher volume fraction of a clad layer with positive rate sensitivity material in a laminated sheet improves the sheet ductility.

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Figures

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Fig. 1

The drawing of the quarter tube expansion under dynamic loading

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Fig. 2

Schematic representations of outer surface topographies of a tube in deformed state

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Fig. 3

Definition of localized necking strain

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Fig. 4

Predicted flow stress by the elastic-viscoplastic model. (a) Effect of rate sensitivity m on flow stress. (b) Effect of strain rate on flow stress.

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Fig. 5

Effective plastic strain contour plot, rate independent materials m = 0.0005 without imperfection δ = 0.0

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Fig. 6

Effective plastic strain contour plot, rate independent materials m = 0.0005 with imperfection δ = 0.002

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Fig. 7

Effect of imperfection, ɛinside versus ɛoutside, rate independent materials m = 0.0005 and ɛ·0 = 1385 s−1

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Fig. 8

Effect of imperfection, nominal hoop traction T/σ0 versus nominal hoop strain ΔR/R0, rate independent materials m = 0.0005 and ɛ·0 = 1385 s−1; the solid square represents the maximum value of T/σ0

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Fig. 9

Effect of imperfection, nominal minimum cross section Amin/A0 versus nominal hoop strain ΔR/R0, rate independent materials m = 0.0005 and ɛ·0 = 1385 s−1; the solid square is the diffuse necking point and the open circle is the localized necking point

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Fig. 10

Effect of the starting strain rate ɛ·0 on the diffused and localized necking strains, rate independent materials m = 0.0005 and ɛ·0 = 1385 s−1

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Fig. 11

Effective plastic strain contour plot, rate independent materials m = 0.0005 versus rate sensitive materials (m = 0.05) with imperfection δ = 0.002

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Fig. 12

Effect of rate sensitivity, ɛinside versus ɛoutside, materials with imperfection δ = 0.002 and ɛ·0 = 1385 s−1

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Fig. 13

Effect of rate sensitivity, localized necking strain ɛnecking versus rate sensitivity m, materials with imperfection δ = 0.002

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Fig. 14

Effect of rate sensitivity, localized necking strain ɛnecking versus starting strain rate ɛ·0, materials with imperfection δ = 0.002

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Fig. 15

Effect of rate sensitivity, ɛnecking/ɛnecking_min versus starting strain rate ɛ·0, materials with imperfection δ = 0.002

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Fig. 16

The sketch of the laminated composite system

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Fig. 17

Effect of clad percentage p* and rate sensitivity m on localized necking strain ɛnecking, materials with imperfection δ = 0.002 and ɛ·0 = 1385 s−1

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Fig. 18

Effect of clad percentage p* and rate sensitivity m on localized necking strain ɛnecking, materials with imperfection δ = 0.002 and ɛ·0 = 1385 s−1

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Fig. 19

Effect of rate sensitivity m on localized necking strain ɛnecking in the laminated composite system, materials with imperfection δ = 0.002

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