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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

Benedetti, I. , and Aliabadi, M. H. , 2013, “ A Three-Dimensional Cohesive-Frictional Grain-Boundary Micromechanical Model for Intergranular Degradation and Failure in Polycrystalline Materials,” Comput. Methods Appl. Mech. Eng., 265, pp. 36–62. [CrossRef]
Herbig, M. , King, A. , Reischig, P. , Proudhon, H. , Lauridsen, E. M. , Marrow, J. , Buffire, J. Y. , and Ludwig, W. , 2011, “ 3D Growth of a Short Fatigue Crack Within a Polycrystalline Microstructure Studied Using Combined Diffraction and Phase-Contrast X-Ray Tomography,” Acta Mater., 59(2), pp. 590–601. [CrossRef]
Ludwig, W. , King, A. , Reischig, P. , Herbig, M. , Lauridsen, E. M. , Schmidt, S. , Proudhon, H. , Forest, S. , Cloetens, P. , Du Roscoat, S. R. , Buffière, J. Y. , Marrow, T. J. , and Poulsen, H. F. , 2009, “ New Opportunities for 3D Materials Science of Polycrystalline Materials at the Micrometre Lengthscale by Combined Use of X-Ray Diffraction and X-Ray Imaging,” Mater. Sci. Eng. A, 524(1–2), pp. 69–76. [CrossRef]
Groeber, M. A. , Haley, B. K. , Uchic, M. D. , Dimiduk, D. M. , and Ghosh, S. , 2006, “ 3D Reconstruction and Characterization of Polycrystalline Microstructures Using a FIB-SEM System,” Mater. Charact., 57(4–5), pp. 259–273. [CrossRef]
Paggi, M. , and Wriggers, P. , 2012, “ Stiffness and Strength of Hierarchical Polycrystalline Materials With Imperfect Interfaces,” J. Mech. Phys. Solids, 60(4), pp. 557–572. [CrossRef]
Espinosa, H. D. , and Zavattieri, P. D. , 2003, “ A Grain Level Model for the Study of Failure Initiation and Evolution in Polycrystalline Brittle Materials. Part I: Theory and Numerical Implementation,” Mech. Mater., 35(3–6), pp. 333–364. [CrossRef]
Espinosa, H. D. , and Zavattieri, P. D. , 2003, “ A Grain Level Model for the Study of Failure Initiation and Evolution in Polycrystalline Brittle Materials. Part II: Numerical Examples,” Mech. Mater., 35(3–6), pp. 365–394. [CrossRef]
Zhai, J. , Tomar, V. , and Zhou, M. , 2004, “ Micromechanical Simulation of Dynamic Fracture Using the Cohesive Finite Element Method,” ASME J. Eng. Mater. Technol., 126(2), pp. 179–191. [CrossRef]
Sukumar, N. , Srolovitz, D. J. , Baker, T. J. , and Prévost, J. H. , 2003, “ Brittle Fracture in Polycrystalline Microstructures With the Extended Finite Element Method,” Int. J. Numer. Methods Eng., 56(14), pp. 2015–2037. [CrossRef]
Sfantos, G. K. , and Aliabadi, M. H. , 2007, “ Multi-Scale Boundary Element Modelling of Material Degradation and Fracture,” Comput. Methods Appl. Mech. Eng., 196(7), pp. 1310–1329. [CrossRef]
Sfantos, G. K. , and Aliabadi, M. H. , 2007, “ A Boundary Cohesive Grain Element Formulation for Modelling Intergranular Microfracture in Polycrystalline Brittle Materials,” Int. J. Numer. Methods Eng., 69(8), pp. 1590–1626. [CrossRef]
Benedetti, I. , and Aliabadi, M. H. , 2012, “ A Grain Boundary Formulation for the Analysis of Three-Dimensional Polycrystalline Microstructures,” Key Eng. Mater., 525–526, pp. 1–4. [CrossRef]
Benedetti, I. , and Aliabadi, M. H. , 2013, “ A Three-Dimensional Grain Boundary Formulation for Microstructural Modeling of Polycrystalline Materials,” Comput. Mater. Sci., 67, pp. 249–260. [CrossRef]
Crocker, A. G. , Flewitt, P. E. J. , and Smith, G. E. , 2005, “ Computational Modelling of Fracture in Polycrystalline Materials,” Int. Mater. Rev., 50(2), pp. 99–125. [CrossRef]
Madenci, E. , and Oterkus, E. , 2014, Peridynamic Theory and Its Applications, Springer, New York.
Zi, G. , Rabczuk, T. , and Wall, W. , 2007, “ Extended Meshfree Methods Without Branch Enrichment for Cohesive Cracks,” Comput. Mech., 40(2), pp. 367–382. [CrossRef]
Anderson, T. L. , 2005, Fracture Mechanics—Fundamentals and Applications, 3rd ed., Taylor & Francis, Boca Raton, FL.
Silling, S. A. , 2000, “ Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces,” J. Mech. Phys. Solids, 48(1), pp. 175–209. [CrossRef]
Askari, E. , Bobaru, F. , Lehoucq, R. B. , Parks, M. L. , Silling, S. A. , and Weckner, O. , 2008, “ Peridynamics for Multiscale Materials Modeling,” J. Phys. Conf. Ser., 125(1), p. 012078. [CrossRef]
Ghajari, M. , Iannucci, L. , and Curtis, P. , 2014, “ A Peridynamic Material Model for the Analysis of Dynamic Crack Propagation in Orthotropic Media,” Comput. Methods Appl. Mech. Eng., 276, pp. 431–452. [CrossRef]
Seleson, P. , and Parks, M. , 2011, “ On the Role of the Influence Function in the Peridynamic Theory,” Int. J. Multiscale Comput. Eng., 9(6), pp. 689–706. [CrossRef]
Oterkus, E. , and Madenci, E. , 2012, “ Peridynamic Analysis of Fiber-Reinforced Composite Materials,” J. Mech. Mater. Struct., 7(1), 2012. [CrossRef]
Hirose, Y. , and Mura, T. , 1984, “ Nucleation Mechanism of Stress Corrosion Cracking From Notches,” Eng. Fract. Mech., 19(2), pp. 317–329. [CrossRef]
Rimoli, J. J. , and Ortiz, M. , 2010, “ A Three-Dimensional Multiscale Model of Intergranular Hydrogen-Assisted Cracking,” Philos. Mag., 90(21), pp. 2939–2963, 2010. [CrossRef]
Hosford, W. F. , 1993, The Mechanics of Crystals and Textured Polycrystals, Oxford University Press, New York.
Rimoli, J. J. , 2009, “ A Computational Model for Intergranular Stress Corrosion Cracking,” Ph.D. dissertation, California Institute of Technology, Pasadena, CA.
Lawn, B. , 1993, Fracture of Brittle Solids, 2nd ed., Cambridge University Press, West Nyack, NY.
Shum, D. K. M. , and Hutchinson, J. W. , 1990, “ On Toughening by Microcracks,” Mech. Mater., 9(2), pp. 83–91. [CrossRef]
Hutchinson, J. W. , 1989, “ Mechanisms of Toughening in Ceramics,” Theoretical and Applied Mechanics, North Holland, Amsterdam, The Netherlands, pp. 139–144.
Ruhle, M. , Evans, A. G. , McMeeking, R. M. , Charalambides, P. G. , and Hutchinson, J. W. , 1987, “ Microcrack Toughening in Alumina/Zirconia,” Acta Met., 35(11), pp. 2701–2710. [CrossRef]
Toi, Y. , and Atluri, S. N. , 1990, “ Finite Element Analysis of Static and Dynamic Fracture of Brittle Microcracking Solids. Part 1: Formulation and Simple Numerical Examples,” Int. J. Plast., 6, pp. 166–188. [CrossRef]
Johnson, E. , 2001, “ Simulations of Microcracking in the Process Region of Ceramics With a Cell Model,” Int. J. Fract., 111(1978), pp. 361–380. [CrossRef]
Wang, H. , Liu, Z. , Xu, D. , Zeng, Q. , and Zhuang, Z. , 2016, “ Extended Finite Element Method Analysis for Shielding and Amplification Effect of a Main Crack Interacted With a Group A of Nearby Parallel Microcracks,” Int. J. Damage Mech., 25(1), pp. 4–25. [CrossRef]
Chandar, K. R. , and Knauss, W. G. , 1982, “ Dynamic Crack-Tip Stresses Under Stress Wave Loading—A Comparison of Theory and Experiment,” Int. J. Fract., 20(3), pp. 209–222. [CrossRef]
Bobaru, F. , and Hu, W. , 2012, “ The Meaning, Selection, and Use of the Peridynamic Horizon and Its Relation to Crack Branching in Brittle Materials,” Int. J. Fract., 176(2), pp. 215–222. [CrossRef]
Ha, Y. D. , and Bobaru, F. , 2010, “ Studies of Dynamic Crack Propagation and Crack Branching With Peridynamics,” Int. J. Fract., 162(1), pp. 229–244. [CrossRef]
Ha, Y. D. , and Bobaru, F. , 2011, “ Characteristics of Dynamic Brittle Fracture Captured With Peridynamics,” Eng. Fract. Mech., 78(6), pp. 1156–1168. [CrossRef]
Pouillier, E. , Gourgues, A. F. , Tanguy, D. , and Busso, E. P. , 2012, “ A Study of Intergranular Fracture in an Aluminium Alloy Due to Hydrogen Embrittlement,” Int. J. Plast., 34, pp. 139–153. [CrossRef]
Silling, S. A. , and Askari, E. , 2005, “ A Meshfree Method Based on the Peridynamic Model of Solid Mechanics,” Comput. Struct., 83(17–18), pp. 1526–1535. [CrossRef]

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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