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Dynamic Fracture of Shells Subjected to Impulsive Loads

[+] Author and Article Information
Jeong-Hoon Song1

Theoretical and Applied Mechanics, Northwestern University, Evanston, IL 60208-3111j-song2@northwestern.edu

Ted Belytschko

Theoretical and Applied Mechanics, Northwestern University, Evanston, IL 60208-3111

1

Corresponding author.

J. Appl. Mech 76(5), 051301 (Jun 12, 2009) (9 pages) doi:10.1115/1.3129711 History: Received November 30, 2007; Revised September 16, 2008; Published June 12, 2009

A finite element method for the simulation of dynamic cracks in thin shells and its applications to quasibrittle fracture problem are presented. Discontinuities in the translational and angular velocity fields are introduced to model cracks by the extended finite element method. The proposed method is implemented for the Belytschko–Lin–Tsay shell element, which has high computational efficiency because of its use of a one-point integration scheme. Comparisons with elastoplastic crack propagation experiments involving quasibrittle fracture show that the method is able to reproduce experimental fracture patterns quite well.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 5

The decomposition of an element into three elements e1, e2, and e3 to model crack branching; solid and hollow circles denote the original nodes and the added phantom nodes, respectively

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Figure 6

Schematic of averaging domain: averaging domain, which has averaging size of rc

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Figure 7

Schematic showing of a linear cohesive law: the area under curve is the fracture energy, Gf

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Figure 8

Setup for the notched cylinder fracture under internal detonation pressure (16): (a) total experiment assembly, (b) notched thin-walled specimen for shot 7, and (c) notched thin-walled specimen for shot 4

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Figure 9

Evolution of crack paths and distributions of effective plastic stress at different time steps: (a) t=213.55 μs, (b) t=228.61 μs, and (c) t=238.01 μs. Note that finite element nodes are plotted and crack paths are explicitly marked.

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Figure 10

Evolution of crack opening at time t=256.86 μs along with distribution of effective plastic stress: (a) side view and (b) top view

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Figure 11

Comparison of the final deformed shape between (a) the simulation result and (b) the experimental result (shot 7) (16,25)

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Figure 12

Comparison propagation speeds of two crack tips for the cylinder with the notch size of L=5.08 cm (shot 7)

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Figure 13

Evolution of crack and distributions of effective plastic stress at time times (a) t=231.41 μs and (b) t=239.05 μs. Note that finite element nodes are plotted and crack paths are explicitly marked.

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Figure 14

Comparison propagation speeds of two crack tips for the cylinder with the notch size of L=2.54 cm (shot 4)

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Figure 15

Evolution of crack and distributions of effective plastic stress at time t=261.98 μs: (a) top view and (b) side view

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Figure 16

Comparison of the final deformed shape between (a) the simulation result and (b) the experimental result (shot 4) (16,25)

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Figure 17

Setup for cylinder fracture with an initial weak spot: (a) only half of the cylinder is modeled due to the twofold symmetry, (b) cylinder with an initial weak spot at the center of the cylinder, and (c) cylinder with an initial weak spot close to the end cap

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Figure 18

The computed final deformed shape along with marked opened crack surfaces: (a) perspective view and (b) axial view

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Figure 19

Evolution of crack opening and effective plastic strain distributions at different times: (a) t=187.0 μs and (b) t=252.0 μs. For a clear representation of crack opening, finite element nodes are plotted: (c) top view and (d) side view.

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Figure 1

The nomenclature of a continuum shell description

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Figure 2

Representation of discontinuity in the reference configuration by a level set implicit function f(ξ) in the shell midsurface

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Figure 3

Nomenclature of a fractured shell descriptions: incompatible material overlaps occurred at the bottom surface due to crack opening

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Figure 4

The decomposition of a cracked element with generic nodes 1–4 into two elements e1 and e2; solid and hollow circles denote the original nodes and the added phantom nodes, respectively

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