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Research Papers

Application of Multiscale Cohesive Zone Model to Simulate Fracture in Polycrystalline Solids

[+] Author and Article Information
Jing Qian

Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720

Shaofan Li1

Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720; School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, P.R. Chinashaofan@berkeley.edu

1

Corresponding author.

J. Eng. Mater. Technol 133(1), 011010 (Dec 02, 2010) (10 pages) doi:10.1115/1.4002647 History: Received February 21, 2010; Revised May 14, 2010; Published December 02, 2010; Online December 02, 2010

In this work, we apply the multiscale cohesive method (Zeng and Li, 2010, “A Multiscale Cohesive Zone Model and Simulations of Fracture,” Comput. Methods Appl. Mech. Eng., 199, pp. 547–556) to simulate fracture and crack propagations in polycrystalline solids. The multiscale cohesive method uses fundamental principles of colloidal physics and micromechanics homogenization techniques to link the atomistic binding potential with the mesoscale material properties of the cohesive zone and hence, the method can provide an effective means to describe heterogeneous material properties at a small scale by taking into account the effect of inhomogeneities such as grain boundaries, bimaterial interfaces, slip lines, and inclusions. In particular, the depletion potential of the cohesive interface is made consistent with the atomistic potential inside the bulk material and it provides microstructure-based interface potentials in both normal and tangential directions with respect to finite element boundary separations. Voronoi tessellations have been utilized to generate different randomly shaped microstructure in studying the effect of polycrystalline grain morphology. Numerical simulations on crack propagation for various cohesive strengths are presented and it demonstrates the ability to capture the transition from the intergranular fracture to the transgranular fracture. A convergence test is conducted to study the possible size-effect of the method. Finally, a high-speed impact example is reported. The example demonstrates the advantages of multiscale cohesive method in simulating the spall fracture under high-speed impact loads.

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Figures

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Figure 1

Multiscale cohesive zone model: (a) triangular bulk element and cohesive zone and (b) hexagonal lattice used in this paper

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Figure 2

Effected Fc in deformed cohesive zone

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Figure 3

Mesh generation: (a) Voronoi cell and (b) triangular bulk elements over grains

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Figure 4

Orientation of grains and grain boundary.

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Figure 5

Example of unilateral tension: (a) sketch of unilateral tension model and (b) mesh of the plate

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Figure 6

Intergranular crack propagates through grains: (a) t=1.5 μs, (b) t=2.5 μs, (c) t=3.5 μs, and (d) t=4.5 μs

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Figure 7

Transgranular crack propagates along grain boundaries: (a) t=1.5 μs, (b) t=2.5 μs, (c) t=3.5 μs, and (d) t=4.5 μs

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Figure 8

Different meshes over grains: (a) case 1 ρ=0.5, (b) case 2 ρ=0.2, (c) case 3 ρ=0.1, and (d) case 4 ρ=0.05

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Figure 9

Crack surfaces calculated by different meshes: (a) case 1 ρ=0.5, (b) case 2 ρ=0.2, (c) case 3 ρ=0.1, and (d) case 4 ρ=0.05

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Figure 10

Reaction force varies along time

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Figure 11

Examples of high-speed impact: (a) sketch of impact model and (b) mesh of the plate

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Figure 12

Intergranular spall fracture propagates through grains: (a) t=1.0 μs, (b) t=1.2 μs, (c) t=1.3 μs, and (d) t=1.5 μs

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Figure 13

Transgranular spall fracture propagates along grain boundaries: (a) t=1.0 μs, (b) t=1.2 μs, (c) t=1.3 μs, and (d) t=1.5 μs

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