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Research Papers

Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

[+] Author and Article Information
Dennj De Meo, Ning Zhu, Erkan Oterkus

Department of Naval Architecture,
Ocean and Marine Engineering,
University of Strathclyde,
Glasgow, Lanarkshire G4 0LZ, UK

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received September 1, 2015; final manuscript received April 18, 2016; published online July 4, 2016. Assoc. Editor: Erdogan Madenci.

J. Eng. Mater. Technol 138(4), 041008 (Jul 04, 2016) (16 pages) Paper No: MATS-15-1210; doi: 10.1115/1.4033634 History: Received September 01, 2015; Revised April 18, 2016

A new peridynamic (PD) formulation is developed for cubic polycrystalline materials. The new approach can be a good alternative to traditional techniques such as finite element method (FEM) and boundary element method (BEM). The formulation is validated by considering a polycrystal subjected to tension-loading condition and comparing the displacement field obtained from both PDs and FEM. Both static and dynamic loading conditions for initially damaged and undamaged structures are considered and the results of plane stress and plane strain configurations are compared. Finally, the effect of grain boundary strength, grain size, fracture toughness, and grain orientation on time-to-failure, crack speed, fracture behavior, and fracture morphology are investigated and the expected transgranular and intergranular failure modes are successfully captured. To the best of the authors' knowledge, this is the first time that a PD material model for cubic crystals is given in detail.

Copyright © 2016 by ASME
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References

Figures

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Fig. 2

Definition of bond constant and critical stretch for linear elastic brittle material

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Fig. 3

Polycrystalline material model

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Fig. 4

Type-1 (dashed green lines) and type-2 (solid red lines) bonds for the PD micromechanical model

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Fig. 5

Iron crystal for static analysis

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Fig. 6

Displacement field comparison between FEM and PD for the iron crystal in plane stress configuration and 0 deg orientation

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Fig. 7

Displacement field comparison between FEM and PD for the iron crystal in plane stress configuration and 45 deg orientation

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Fig. 8

Displacement field comparison between FEM and PD for the iron crystal in plane strain configuration and 0 deg orientation

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Fig. 9

Displacement field comparison between FEM and PD for the iron crystal in plane strain configuration and 45 deg orientation

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Fig. 10

Iron polycrystal considered for static analysis

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Fig. 11

Displacement field comparison between FEM and PD for the iron polycrystal in plane stress configuration

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Fig. 12

Displacement field comparison between FEM and PD for the iron polycrystal in plane strain configuration

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Fig. 13

AISI 4340 polycrystal for convergence analysis (225 grains)

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Fig. 14

GBC = 0.5, time = 2.4 μs. Fracture pattern comparison of three polycrystals with different average grain size (333 μm, 416 μm, and 714 μm) and five different horizon values: from left to right, 202.7 μm (74 × 74 particles), 100 μm (150 × 150 particles), 50 μm (300 × 300 particles), 37.5 μm (400 × 400 particles), and 30 μm (500 × 500 particles).

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Fig. 15

GBC = 1, time = 2.4 μs. Fracture pattern comparison of three polycrystals with different average grain size (333 μm, 416 μm, and 714 μm) and five different horizon values: from left to right, 202.7 μm (74 × 74 particles), 100 μm (150 × 150 particles), 50 μm (300 × 300 particles), 37.5 μm (400 × 400 particles), and 30 μm (500 × 500 particles).

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Fig. 16

GBC = 2, time = 2.4 μs. Fracture pattern comparison of three polycrystals with different average grain size (333 μm, 416 μm, and 714 μm) and five different horizon values: from left to right, 202.7 μm (74 × 74 particles), 100 μm (150 × 150 particles), 50 μm (300 × 300 particles), 37.5 μm (400 × 400 particles), and 30 μm (500 × 500 particles).

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Fig. 17

Meaning of occurrence: occurrence (bottom notch), nonoccurrence (top notch)

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Fig. 18

Grain size effect on the number of occurrences

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Fig. 19

Microcrack cloud mechanism [27]

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Fig. 20

Grain size effect on time-to-failure

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Fig. 21

Top half of the polycrystal: crack tip in proximity to the grain boundary (lowest point of the blue curve in Fig. 21)

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Fig. 22

Bottom half of the polycrystal: crack tip embedded inside the grain (peak of the blue curve in Fig. 21)

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Fig. 23

Effect of GBC on damage map at time = 3.2 μs. From left to right: GBC = 0.7, GBC = 1, GBC = 5, and GBC = 10.

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Fig. 24

Effect of GBC on crack propagation speed

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Fig. 25

Effect of KIC on the morphology of damage (time = 3.2 μs). From left to right: ψ=0.2, ψ=0.35, ψ=0.5, ψ=1, and ψ=2.

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Fig. 26

Time evolution of damage in an initially damaged polycrystal in plane stress configuration when GBC = 0.5. From left to right: time = 1 μs, time = 2 μs, time = 3 μs, and time = 4 μs.

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Fig. 27

Time evolution of damage in an initially damaged polycrystal in plane stress configuration when GBC = 1.0. From left to right: time = 1 μs, time = 2 μs, time = 3 μs, and time = 4 μs.

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Fig. 28

Time evolution of damage in an initially damaged polycrystal in plane stress configuration when GBC = 2.0. From left to right: time = 1 μs, time = 2 μs, time = 3 μs, and time = 4 μs.

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Fig. 29

Time evolution of damage in an initially damaged polycrystal in plane strain configuration when GBC = 0.5. From left to right: time = 1 μs, time = 2 μs, time = 3 μs, and time = 4 μs.

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Fig. 30

Time evolution of damage in an initially damaged polycrystal in plane strain configuration when GBC = 1.0. From left to right: time = 1 μs, time = 2 μs, time = 3 μs, and time = 4 μs.

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Fig. 31

Time evolution of damage in an initially damaged polycrystal in plane strain configuration when GBC = 2.0. From left to right: time = 1 μs, time = 2 μs, time = 3 μs, and time = 4 μs.

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Fig. 32

First loading condition

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Fig. 33

Second loading condition

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Fig. 34

Third loading condition

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