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Research Papers

Comparison of Concurrent Multiscale Methods in the Application of Fracture in Nickel

[+] Author and Article Information
Vincent Iacobellis

e-mail: vincent.iacobellis@mail.utoronto.ca

Kamran Behdinan

Professor
e-mail: behdinan@mie.utoronto.ca
Department of Mechanical and
Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada

1Corresponding author.

Manuscript received September 13, 2011; final manuscript received December 5, 2012; accepted manuscript posted January 22, 2013; published online July 12, 2013. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(5), 051003 (Jul 12, 2013) (8 pages) Paper No: JAM-11-1332; doi: 10.1115/1.4023477 History: Received June 28, 2012; Revised September 18, 2012; Accepted January 22, 2013

This paper presents a study of fracture in nickel using multiscale modeling. A comparison of six concurrent multiscale methods was performed in their application to a common problem using a common framework in order to evaluate each method relative to each other. Each method was compared in both a quasi-static case of crack tip deformation as well as a dynamic case in the study of crack growth. Each method was compared to the fully atomistic model with similarities and differences between the methods noted and reasons for these provided. The results showed a distinct difference between direct and handshake coupling methods. In general, for the quasi-static case, the direct coupling methods took longer to run compared to the handshake coupling methods but had less error with respect to displacement and energy. In the dynamic case, the handshake methods took longer to run, but had reduced error most notably when wave dissipation at the atomistic/continuum region was an issue. Comparing each method under common conditions showed that many similarities exist between each method that may be hidden by their original formulation. The comparison also showed the dependency on the application as well as the simulation techniques used in determining the performance of each method.

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Figures

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Fig. 1

Interface for (a) direct atomistic/continuum coupling. White circles are pad atoms and black circles are regular atoms, (b) handshake atomistic/continuum coupling. White circles are pad atoms, gray circles are handshake atoms, and black circles are regular atoms.

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Fig. 2

Dimensions and boundary conditions for fracture study

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Fig. 3

Mesh for fracture simulation: (a) model 1, (b) model 2, (c) model 3

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Fig. 4

(a) y-displacement plot for exact solution, (b) deformed crack with blunting and partial dislocations

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Fig. 5

Displacement error plots for direct coupling methods

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Fig. 6

Displacement error plots for handshake coupling methods

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Fig. 7

Mesh for fracture simulation: (a) model 1, (b) model 2, (c) model 3

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Fig. 8

(a) Final crack position, (b) stress around crack tip

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Fig. 9

Crack tip displacement versus simulation time for model 3

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Fig. 10

Crack tip displacement versus simulation time for three models of BDM

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