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Published in: Journal of Materials Science 10/2017

24-01-2017 | Original Paper

Phase-field-crystal study on the evolution behavior of microcracks initiated on grain boundaries under constant strain

Authors: Shi Hu, Zheng Chen, Wen Xi, Ying-Ying Peng

Published in: Journal of Materials Science | Issue 10/2017

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Abstract

The initiation and propagation behavior of microcracks is closely associated with the cleavage of crystalline materials. We use phase-field-crystal method to explore the evolution process and mechanism of microcracks initiated on grain boundaries (GBs). Constant biaxial strain is applied to the (0001) crystal plane of hexagonal close-packed bicrystal. Under applied strain, cracks are initiated at the end of semi-boundaries between grains. Following this crack initiation (CIN) mechanism, grain boundary misorientation angle (GBMA) can greatly affect the process of crack initiation and propagation (CINPR) in normal GB system. Along with the increase in GBMA, CIN is promoted and the type of subsequent crack propagation changes from trans-granular propagation into inter-granular propagation. System temperature and applied strain also have influence on CINPR. Associated with fracture mechanics theory, the effects of GBMA, temperature and strain on the behavior of CINPR are investigated. Additionally, we give curves of change in free energy to illustrate these effects from energy perspective. Crack arrestment mechanism, especially the plastic relaxation mechanism, is also discussed. The simulation results acquired in this work are in good agreement with theoretical analyses and experimental results.

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Appendix
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Literature
1.
go back to reference Kresse G, Hafner J (1994) Ab initio molecular-dynamics simulation of the liquid-metalamorphous-semiconductor transition in germanium. Phys Rev B 49:14251–14269CrossRef Kresse G, Hafner J (1994) Ab initio molecular-dynamics simulation of the liquid-metalamorphous-semiconductor transition in germanium. Phys Rev B 49:14251–14269CrossRef
2.
go back to reference Rappé AK, Casewit CJ, Colwell KS, Goddard WA III, Skiff WM (1992) UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J Am Chem Soc 114:10024–10035CrossRef Rappé AK, Casewit CJ, Colwell KS, Goddard WA III, Skiff WM (1992) UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J Am Chem Soc 114:10024–10035CrossRef
3.
4.
go back to reference Rappé AK, Goddard WA III (1991) Charge equilibration for molecular dynamics simulations. J Phys Chem 95:3358–3363CrossRef Rappé AK, Goddard WA III (1991) Charge equilibration for molecular dynamics simulations. J Phys Chem 95:3358–3363CrossRef
5.
go back to reference Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Sci 32:113–140CrossRef Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Sci 32:113–140CrossRef
6.
go back to reference Karma A, Rappel WJ (1998) Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys Rev E 57:4323–4349CrossRef Karma A, Rappel WJ (1998) Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys Rev E 57:4323–4349CrossRef
7.
go back to reference Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys Rev A 45:7424–7439CrossRef Wheeler AA, Boettinger WJ, McFadden GB (1992) Phase-field model for isothermal phase transitions in binary alloys. Phys Rev A 45:7424–7439CrossRef
8.
go back to reference Zaeem MA, Yin H, Felicelli SD (2012) Comparison of cellular automaton and phase field models to simulate dendrite growth in hexagonal crystals. J Mater Sci Technol 28:137–146CrossRef Zaeem MA, Yin H, Felicelli SD (2012) Comparison of cellular automaton and phase field models to simulate dendrite growth in hexagonal crystals. J Mater Sci Technol 28:137–146CrossRef
9.
go back to reference Elder KR, Grant M (2004) Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. Phys Rev E 70:51605CrossRef Elder KR, Grant M (2004) Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. Phys Rev E 70:51605CrossRef
10.
go back to reference Elder KR, Katakowski M, Haataja M, Grant M (2002) Modeling elasticity in crystal growth. Phys Rev Lett 88:2457011–2457014CrossRef Elder KR, Katakowski M, Haataja M, Grant M (2002) Modeling elasticity in crystal growth. Phys Rev Lett 88:2457011–2457014CrossRef
11.
go back to reference Elder KR, Provatas N, Berry J, Stefanovic P, Grant M (2007) Phase-field crystal modeling and classical density functional theory of freezing. Phys Rev B 75:064107CrossRef Elder KR, Provatas N, Berry J, Stefanovic P, Grant M (2007) Phase-field crystal modeling and classical density functional theory of freezing. Phys Rev B 75:064107CrossRef
12.
go back to reference Stefanovic P, Haataja M, Provatas N (2006) Phase-field crystals with elastic interactions. Phys Rev Lett 96:225504CrossRef Stefanovic P, Haataja M, Provatas N (2006) Phase-field crystals with elastic interactions. Phys Rev Lett 96:225504CrossRef
13.
go back to reference Jaatinen A, Achim CV, Elder KR, Ala-Nissila T (2009) Thermodynamics of bcc metals in phase-field-crystal models. Phys Rev E 80:031602CrossRef Jaatinen A, Achim CV, Elder KR, Ala-Nissila T (2009) Thermodynamics of bcc metals in phase-field-crystal models. Phys Rev E 80:031602CrossRef
14.
go back to reference Greenwood M, Ofori-Opoku N, Rottler J, Provatas N (2011) Modeling structural transformations in binary alloys with phase field crystals. Phys Rev B 84:064104CrossRef Greenwood M, Ofori-Opoku N, Rottler J, Provatas N (2011) Modeling structural transformations in binary alloys with phase field crystals. Phys Rev B 84:064104CrossRef
15.
go back to reference Mellenthin J, Karma A, Plapp M (2008) Phase-field crystal study of grain-boundary premelting. Phys Rev B 78:184110CrossRef Mellenthin J, Karma A, Plapp M (2008) Phase-field crystal study of grain-boundary premelting. Phys Rev B 78:184110CrossRef
16.
go back to reference Goldenfeld N, Athreya BP, Dantzig JA (2005) Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model. Phys Rev E 72:020601CrossRef Goldenfeld N, Athreya BP, Dantzig JA (2005) Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model. Phys Rev E 72:020601CrossRef
17.
go back to reference Berry J, Elder KR, Grant M (2008) Melting at dislocations and grain boundaries: a phase field crystal study. Phys Rev B 77:22411CrossRef Berry J, Elder KR, Grant M (2008) Melting at dislocations and grain boundaries: a phase field crystal study. Phys Rev B 77:22411CrossRef
18.
go back to reference Stefanovic P, Haataja M, Provatas N (2009) Phase field crystal study of deformation and plasticity in nanocrystalline materials. Phys Rev E 80:046107CrossRef Stefanovic P, Haataja M, Provatas N (2009) Phase field crystal study of deformation and plasticity in nanocrystalline materials. Phys Rev E 80:046107CrossRef
19.
go back to reference Backofen R, Rätz A, Voigt A (2007) Nucleation and growth by a phase field crystal (PFC) model. Philos Mag Lett 87:813–820CrossRef Backofen R, Rätz A, Voigt A (2007) Nucleation and growth by a phase field crystal (PFC) model. Philos Mag Lett 87:813–820CrossRef
20.
go back to reference Trautt ZT, Adland A, Karma A, Mishin Y (2012) Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulations. Acta Mater 60:6528–6546CrossRef Trautt ZT, Adland A, Karma A, Mishin Y (2012) Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulations. Acta Mater 60:6528–6546CrossRef
21.
go back to reference Gao Y, Luo Z, Huang L, Mao H, Huang C, Lin K (2016) Phase field crystal study of nano-crack growth and branch in materials. Model Simul Mater Sci Eng 24:055010CrossRef Gao Y, Luo Z, Huang L, Mao H, Huang C, Lin K (2016) Phase field crystal study of nano-crack growth and branch in materials. Model Simul Mater Sci Eng 24:055010CrossRef
22.
go back to reference Hu S, Chen Z, Peng YY, Liu YJ, Guo LY (2016) Modeling and simulation of microcrack behavior under shear stress using phase-field-crystal. Comput Mater Sci 121:143–150CrossRef Hu S, Chen Z, Peng YY, Liu YJ, Guo LY (2016) Modeling and simulation of microcrack behavior under shear stress using phase-field-crystal. Comput Mater Sci 121:143–150CrossRef
23.
24.
go back to reference Orowan E (1949) Fracture and strength of solids. Rep Prog Phys 12:185–232CrossRef Orowan E (1949) Fracture and strength of solids. Rep Prog Phys 12:185–232CrossRef
25.
go back to reference Saada G (2005) Stress concentration and crack nucleation at the end of a low-angle tilt boundary. Philos Mag Lett 85:481–490CrossRef Saada G (2005) Stress concentration and crack nucleation at the end of a low-angle tilt boundary. Philos Mag Lett 85:481–490CrossRef
26.
go back to reference Green AP, Sawkill J (1961) Plastic anisotropy and fracture in beryllium. J Nucl Mater 3:101–110CrossRef Green AP, Sawkill J (1961) Plastic anisotropy and fracture in beryllium. J Nucl Mater 3:101–110CrossRef
27.
go back to reference Jaatinen A, Ala-Nissila T (2010) Extended phase diagram of the three-dimensional phase field crystal model. J Phys Condens Matter 22:205402 Jaatinen A, Ala-Nissila T (2010) Extended phase diagram of the three-dimensional phase field crystal model. J Phys Condens Matter 22:205402
28.
go back to reference Stolle J, Provatas N (2014) Characterizing solute segregation and grain boundary energy in binary alloy phase field crystal models. Comput Mater Sci 81:493–502CrossRef Stolle J, Provatas N (2014) Characterizing solute segregation and grain boundary energy in binary alloy phase field crystal models. Comput Mater Sci 81:493–502CrossRef
29.
go back to reference Berry J, Rottler J, Sinclair CW, Provatas N (2015) Atomistic study of diffusion-mediated plasticity and creep using phase field crystal methods. Phys Rev B 92:134103CrossRef Berry J, Rottler J, Sinclair CW, Provatas N (2015) Atomistic study of diffusion-mediated plasticity and creep using phase field crystal methods. Phys Rev B 92:134103CrossRef
30.
go back to reference Hirouchi T, Takaki T, Tomita Y (2009) Development of numerical scheme for phase field crystal deformation simulation. Comput Mater Sci 44:1192–1197CrossRef Hirouchi T, Takaki T, Tomita Y (2009) Development of numerical scheme for phase field crystal deformation simulation. Comput Mater Sci 44:1192–1197CrossRef
31.
go back to reference Hu S, Chen Z, Yu GG, Xi W, Peng YY (2016) Phase-field-crystal study on the reaction mechanisms of opposite sign edge dislocations appearing in the deformation processes of asymmetric tilt sub-grain boundary system. Comput Mater Sci 124:195–203CrossRef Hu S, Chen Z, Yu GG, Xi W, Peng YY (2016) Phase-field-crystal study on the reaction mechanisms of opposite sign edge dislocations appearing in the deformation processes of asymmetric tilt sub-grain boundary system. Comput Mater Sci 124:195–203CrossRef
32.
go back to reference Long J, Zhang S, Zhao Y, Long Q, Yang T, Chen Z (2014) Deformation study of bicrystalline and nano-polycrystalline structures using phase field crystal method. Sci China Phys Mech Astron 57:1046–1056CrossRef Long J, Zhang S, Zhao Y, Long Q, Yang T, Chen Z (2014) Deformation study of bicrystalline and nano-polycrystalline structures using phase field crystal method. Sci China Phys Mech Astron 57:1046–1056CrossRef
33.
go back to reference Hakim V, Karma A (2009) Laws of crack motion and phase-field models of fracture. J Mech Phys Solids 57:342CrossRef Hakim V, Karma A (2009) Laws of crack motion and phase-field models of fracture. J Mech Phys Solids 57:342CrossRef
34.
go back to reference Cao L, Zhou Y, Jin T, Sun X (2014) Effect of grain boundary angle on stress rupture properties of a Ni-based bicrystal superalloy. Acta Metall Sin 50:11–18 Cao L, Zhou Y, Jin T, Sun X (2014) Effect of grain boundary angle on stress rupture properties of a Ni-based bicrystal superalloy. Acta Metall Sin 50:11–18
35.
go back to reference Li LL, Zhang ZJ, Zhang P, Zhang ZF (2011) Higher fatigue cracking resistance of twin boundaries than grain boundaries in Cu bicrystals. Scr Mater 65:505–508CrossRef Li LL, Zhang ZJ, Zhang P, Zhang ZF (2011) Higher fatigue cracking resistance of twin boundaries than grain boundaries in Cu bicrystals. Scr Mater 65:505–508CrossRef
36.
go back to reference Gilman JJ, Knudsen C, Walsh WP (1958) Cleavage cracks and dislocations in LiF crystals. J Appl Phys 29:601–607CrossRef Gilman JJ, Knudsen C, Walsh WP (1958) Cleavage cracks and dislocations in LiF crystals. J Appl Phys 29:601–607CrossRef
37.
go back to reference Zhao CW, Xing YM, Bai PC, Li JJ, Liu QL, Du YG, Liu MH (2011) Crack tip dislocation emission and nanoscale deformation fields in silicon. Appl Phys A 105:207–210CrossRef Zhao CW, Xing YM, Bai PC, Li JJ, Liu QL, Du YG, Liu MH (2011) Crack tip dislocation emission and nanoscale deformation fields in silicon. Appl Phys A 105:207–210CrossRef
Metadata
Title
Phase-field-crystal study on the evolution behavior of microcracks initiated on grain boundaries under constant strain
Authors
Shi Hu
Zheng Chen
Wen Xi
Ying-Ying Peng
Publication date
24-01-2017
Publisher
Springer US
Published in
Journal of Materials Science / Issue 10/2017
Print ISSN: 0022-2461
Electronic ISSN: 1573-4803
DOI
https://doi.org/10.1007/s10853-017-0799-x

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