An Overview of Phase Field Approach to Fracture

ZHANG Hao; YU Jidong; PEI Xiaoyang; PENG Hui; LI Ping; CAI Lingcang; TANG Tiegang

doi:10.11858/gywlxb.20190777

Volume 33 Issue 3

Jun 2019

Turn off MathJax

Article Contents

Chinese Journal of High Pressure Physics > 2019 > 33(3): 030109.

ZHANG Hao, YU Jidong, PEI Xiaoyang, PENG Hui, LI Ping, CAI Lingcang, TANG Tiegang. An Overview of Phase Field Approach to Fracture[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030109. doi: 10.11858/gywlxb.20190777

Citation:

ZHANG Hao, YU Jidong, PEI Xiaoyang, PENG Hui, LI Ping, CAI Lingcang, TANG Tiegang. An Overview of Phase Field Approach to Fracture[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030109. doi: 10.11858/gywlxb.20190777

Citation:

PDF( 29652 KB)

An Overview of Phase Field Approach to Fracture

doi: 10.11858/gywlxb.20190777

Institute of Fluid Physics, CAEP, Mianyang 621999, China

Received Date: 15 May 2019
Rev Recd Date: 22 May 2019
Publish Date: 25 May 2019

Abstract

Abstract

Phase field modeling to fracture has received much attention since the beginning of this century, which exhibits an advantage in fracture propagation simulation. In this work, we compare the phase field approach to fracture with other simulation methods, and show an overview and development of phase field approach to fracture. Up to now, the phase field method has been successfully applied to the brittle fracture and could simulate some classical crack problems. Based on this, the multi-fields problem coupled with the fracture is currently pursued. Furthermore, we introduce the study situation of the phase field simulation to the ductile fracture and put forward its development in the future.
- phase field approach to fracture,
- simulation,
- brittle fracture,
- ductile fracture

FullText(HTML)

References(46)

References

[1]	钱学森. 物理力学讲义[M]. 上海: 上海交通大学出版社, 2007.
[2]	BECKER R. How metals fail [R]. Metal Fracture-Lawrence Livermore Nation Laboratory, 2002: 13–30.
[3]	FAN R, FISH J. The rs-method for material failure simulations [J]. International Journal for Numerical Methods in Engineering, 2008, 73(11): 1607–1623. doi: 10.1002/nme.2134
[4]	HALLQUIST J O. LS-DYNA theoretical manual [M]. USA: Livemore Software Technology Corporation, 1998.
[5]	XU X P, NEEDLEMAN A. Numerical simulations of fast crack growth in brittle solids [J]. Journal of the Mechanics and Physics of Solids, 1994, 42(9): 1397–1434. doi: 10.1016/0022-5096(94)90003-5
[6]	CAMACHO G T, ORTIZ M. Computational modelling of impact damage in brittle materials [J]. International Journal of Solids and Structures, 1996, 33(20/21/22): 2899–2938.
[7]	BELYTSCHKO T, BLACK T. Elastic crack growth in finite elements with minimal remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620. doi: 10.1002/(sici)1097-0207(19990620)45:5<601::aid-nme598>3.0.co;2-s
[8]	MOËS N, DOLBOW J, BELYTSCHKO T. A finite element method for crack growth without remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150. doi: 10.1002/(SICI)1097-0207(19990910)46:13.0.CO;2-J
[9]	庄茁, 成斌斌. 发展基于CB壳单元的扩展有限元模拟三维任意扩展裂纹 [J]. 工程力学, 2012, 29(6): 12–21. doi: 10.6052/j.issn.1000-4750.2010.08.0616 ZHUANG Z, CHENG B B. Development of X-FEM on CB shell element for simulating 3D arbitrary crack growth [J]. Engineering Mechanics, 2012, 29(6): 12–21. doi: 10.6052/j.issn.1000-4750.2010.08.0616
[10]	PROVATAS N, ELDER K. Book-phase-field methods in materials science and engineering [M]. Wiley-VCH Press, 2010.
[11]	SONG J H, WANG H, BELYTSCHKO T. A comparative study on finite element methods for dynamic fracture [J]. Computational Mechanics, 2008, 42(2): 239–250. doi: 10.1007/s00466-007-0210-x
[12]	BORDEN M J, VERHOOSEL C V, SCOTT M A, et al. A phase-field description of dynamic brittle fracture [J]. Computer Methods in Applied Mechanics and Engineering, 2012, 217(220): 77–95.
[13]	RAMULU M, KOBAYASHI A S. Mechanics of crack curving and branching-a dynamic fracture analysis [J]. International Journal of Fracture, 1985, 27(3/4): 187–201.
[14]	KALTHOFF J F, WINKLER S. In failure mode transition at high rates of shear loading [C]//Impact Loading and Dynamic Behavioavior of Materials. FRG, 1987: 185–195.
[15]	BOURDIN B, FRANCFORT G A, MARIGO J J. Numerical experiments in revisited brittle fracture [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(4): 797–826. doi: 10.1016/S0022-5096(99)00028-9
[16]	GIACOMINI A, PONSIGLIONE M. A Γ-convergence approach to stability of unilateral minimality properties in fracture mechanics and applications [J]. Archive for Rational Mechanics and Analysis, 2006, 180(3): 399–447. doi: 10.1007/s00205-005-0392-3
[17]	GRAVOUIL A, MOËS N, BELYTSCHKO T. Non-planar 3D crack growth by the extended finite element and level sets-Part II: level set update [J]. International Journal for Numerical Methods in Engineering, 2002, 53(11): 2569–2586. doi: 10.1002/nme.v53:11
[18]	SUKUMAR N, CHOPP D L, BÉCHET E, et al. Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method [J]. International Journal for Numerical Methods in Engineering, 2008, 76(5): 727–748. doi: 10.1002/nme.v76:5
[19]	MIEHE C, SCHÄNZEL L M, ULMER H. Phase field modeling of fracture in multi-physics problems. Part I. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids [J]. Computer Methods in Applied Mechanics and Engineering, 2015, 294(1): 449–485.
[20]	HAKIM V, KARMA A. Laws of crack motion and phase-field models of fracture [J]. Journal of the Mechanics and Physics of Solids, 2009, 57(2): 342–368. doi: 10.1016/j.jmps.2008.10.012
[21]	PONS A J, KARMA A. Helical crack-front instability in mixed-mode fracture [J]. Nature, 2010, 464(7285): 85–89. doi: 10.1038/nature08862
[22]	FRANCFORT G A, MARIGO J J. Revisiting brittle fracture as an energy minimization problem [J]. Journal of the Mechanics and Physics of Solids, 1998, 46(8): 1319–1342. doi: 10.1016/S0022-5096(98)00034-9
[23]	SPATSCHEK R, BRENER E, KARMA A. Phase field modeling of crack propagation [J]. Philosophical Magazine, 2011, 91(1): 75–95. doi: 10.1080/14786431003773015
[24]	GRIFFITH A A. The phenomena of rupture and flow in solid [J]. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1920, 221: 163–198.
[25]	Bourdin B, Francfort G A, Marigo J J. The variational approach to fracture[M]. Springer Science+Business Media B. V., 2008.
[26]	AMOR H, MARIGO J J, MAURINI C. Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments [J]. Journal of the Mechanics and Physics of Solids, 2009, 57(8): 1209–1229. doi: 10.1016/j.jmps.2009.04.011
[27]	MIEHE C, WELSCHINGER F, HOFACKER M. Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations [J]. International Journal for Numerical Methods in Engineering, 2010, 83(10): 1273–1311. doi: 10.1002/nme.v83:10
[28]	MIEHE C, HOFACKER M, WELSCHINGER F. A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits [J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199: 2765–2778. doi: 10.1016/j.cma.2010.04.011
[29]	MESGARNEJAD A, BOURDIN B, KHONSARI M M. Validation simulations for the variational approach to fracture [J]. Computer Methods in Applied Mechanics and Engineering, 2015, 290(1): 420–437.
[30]	BOURDIN B, LARSEN C J, RICHARDSON C L. A time-discrete model for dynamic fracture based on crack regularization [J]. International Journal of Fracture, 2011, 168(2): 133–143. doi: 10.1007/s10704-010-9562-x
[31]	LARSEN C J, ORTNER C, SÜLI E. Existence of solutions to a regularized model of dynamic fracture [J]. Mathematical Models and Methods in Applied Sciences, 2010, 20(7): 1021–1048. doi: 10.1142/S0218202510004520
[32]	HOFACKER M, MIEHE C. Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation [J]. International Journal of Fracture, 2012, 178(1): 113–129.
[33]	HOFACKER M, MIEHE C. A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns [J]. International Journal for Numerical Methods in Engineering, 2013, 93(3): 276–301. doi: 10.1002/nme.v93.3
[34]	SCHLÜTER A, WILLENBÜCHER A, KUHN C, et al. Phase field approximation of dynamic brittle fracture [J]. Computational Mechanics, 2014, 54(5): 1141–1161. doi: 10.1007/s00466-014-1045-x
[35]	MIEHE C, MAUTHE S. Phase field modeling of fracture in multi-physics problems. Part III. crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 304(1): 619–655.
[36]	MIEHE C, HOFACKER M, SCHÄNZEL L M, et al. Phase field modeling of fracture in multi-physics problems. Part II. coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids [J]. Computer Methods in Applied Mechanics and Engineering, 2015, 294(1): 486–522.
[37]	WILSON Z A, BORDEN M J, LANDIS C M. A phase-field model for fracture in piezoelectric ceramics [J]. International Journal of Fracture, 2013, 183(2): 135–153. doi: 10.1007/s10704-013-9881-9
[38]	ABDOLLAHI A, ARIAS I. Phase-field modeling of fracture in ferroelectric materials [J]. Archives of Computational Methods in Engineering, 2015, 22(2): 153–181. doi: 10.1007/s11831-014-9118-8
[39]	MIEHE C, SCHÄNZEL L M. Phase field modeling of fracture in rubbery polymers. Part I: finite elasticity coupled with brittle failure [J]. Journal of the Mechanics and Physics of Solids, 2014, 64: 93–113.
[40]	ZIAEI-RAD V, SHEN L, JIANG J, et al. Identifying the crack path for the phase field approach to fracture with non-maximum suppression [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 312(1): 304–321.
[41]	SANTILLÁN D, MOSQUERA J C, CUETO-FELGUEROSO L. Phase-field model for brittle fracture. validation with experimental results and extension to dam engineering problems [J]. Engineering Fracture Mechanics, 2017, 178: 109–125. doi: 10.1016/j.engfracmech.2017.04.020
[42]	DUDA F P, CIARBONETTI A, SÁNCHEZ P J, et al. A phase-field/gradient damage model for brittle fracture in elastic-plastic solids [J]. International Journal of Plasticity, 2015, 65: 269–296. doi: 10.1016/j.ijplas.2014.09.005
[43]	AMBATI M, GERASIMOV T, LORENZIS L D. Phase-field modeling of ductile fracture [J]. Computational Mechanics, 2015, 55(5): 1017–1040. doi: 10.1007/s00466-015-1151-4
[44]	AMBATI M, KRUSE R, LORENZIS L D. A phase-field model for ductile fracture at finite strains and its experimental verification [J]. Computational Mechanics, 2016, 57: 149–167. doi: 10.1007/s00466-015-1225-3
[45]	MCAULIFFE C, WAISMAN H. A coupled phase field shear band model for ductile-brittle transition in notched plate impacts [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 305: 173–195. doi: 10.1016/j.cma.2016.02.018
[46]	柳占立, 李想, 初东阳, 等. 多物理场耦合断裂的相场方法模拟及工程应用[C]//第十二届全国爆炸力学会议. 桐乡, 2018.

Relative Articles

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(10) / Tables(2)

Get Citation

PDF

XML

Article Metrics

Article views(8925) PDF downloads(186)

An Overview of Phase Field Approach to Fracture

doi: 10.11858/gywlxb.20190777

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Related

An Overview of Phase Field Approach to Fracture

doi: 10.11858/gywlxb.20190777

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Proportional views

Related

Export File

Citation

Format

Content