Fracture simulation of ferroelectrics based on the phase field continuum and a damage variable

International Journal of Fracture

Volumn 166, Issue 1-2, 2010, Pages 163-172

  Xu, Bai Xiang ^a   Schrade, David ^b   Gross, Dietmar ^b   Mueller, Ralf ^a  

^a University of Koblenz Landau   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Continuum fracture model; Crack propagation; Ferroelectric domain structure; Phase field simulation

Indexed keywords

2-D FINITE ELEMENT METHOD; CONTINUUM FRACTURE; CRACK GROWTH; CRACK PATHS; DAMAGE VARIABLES; DOMAIN STRUCTURE; DOMAIN SWITCHINGS; EDGE CRACKS; ENERGY DENSITY; FERROELECTRIC DOMAIN STRUCTURE; FERROELECTRIC SINGLE CRYSTALS; FRACTURE BEHAVIOR; FRACTURE CRITERIA; FRACTURE MODEL; FRACTURE SIMULATIONS; GINZBURG-LANDAU; IMPLICIT TIME INTEGRATION; NEWTON ITERATIONS; NON-LINEAR; NONLINEAR BEHAVIOR; ORDER PARAMETER; PHASE FIELDS; PHASE-FIELD SIMULATION; SPONTANEOUS POLARIZATIONS; SYSTEM OF EQUATIONS;

CRACK PROPAGATION; CRACK TIPS; FERROELECTRIC MATERIALS; FERROELECTRICITY; FINITE ELEMENT METHOD; SINGLE CRYSTALS;

COMPUTER SIMULATION;

EID: 77956394830     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-010-9520-7     Document Type: Conference Paper

References (22)

1. IS Aranson VA Kalatsky VM Vinokur 2000 Continuum field description of crack propagation Phys Rev Lett 85 1 118 121 1:CAS:528:DC%2BD3cXksV2nsrk%3D 10.1103/PhysRevLett.85.118 2000PhRvL..85..118A 10991173
2. B Bourdin GA Francfort JJ Marigo 2000 Numerical experiments in revisited brittle fracture J Mech Phys Solids 48 797 826 0995.74057 10.1016/S0022-5096(99) 00028-9 1745759 2000JMPSo..48..797B
3. YH Chen N Hasebe 2005 Current understanding on fracture behaviors of ferroelectric/piezoelectric materials J Intell Mater Sys Struc 16 7-8 673 687 1:CAS:528:DC%2BD2MXmsVamu7g%3D 10.1177/1045389X05054330
4. LO Eastgate JP Sethna M Rauscher T Cretegny 2002 Fracture in mode i using a conserved phase-field model Phys Rev E71 036117 2002PhRvE..65c6117E
5. GA Francfort J Marigo 1998 Revising brittle fracture as an energy minimization problem J Mech Phys Solids 35 7 1319 1342 10.1016/S0022-5096(98) 00034-9 1633984
6. Hughes T (2000) The finite element method. Dover, Mineola, New York
7. M Kamlah 2001 Ferroelectric and ferroelastic piezoceramics-modeling of electromechanical hysteresis phenomena Cont Mech Thermodyn 13 219 268 1049.74021 1:CAS:528:DC%2BD3MXnsFSmsbs%3D
8. C Kuhn R Mueller 2008 A phase field model for fracture PAMM 8 1 10223 10224 10.1002/pamm.200810223
9. Kuhn C, Mueller R, A continuum phase field model for fracture. Eng Fract Mech, (Special Issue on CMFD, submitted)
10. R Mueller D Gross D Schrade BX Xu 2007 Phase field simulation of domain structure in ferroelectric materials within the context of inhomogeneity evolution Int J Frac 147 1-4 173 180 05302915 10.1007/s10704-007-9153-7
11. Mueller R, Xu BX, Schrade D, Gross D Modelling of domain structure evolution in ferroelectric materials. Int J Fract, (Special Issue on IUTAM2009, accepted)
12. GA Schneider 2007 Influence of electric field and mechanical stresses on the fracture of ferroelectrics Ann Rev Mater Res 37 491 538 1:CAS:528: DC%2BD2sXptlSlsLw%3D 10.1146/annurev.matsci.37.052506.084213 2007AnRMS..37..491S
13. D Schrade R Mueller BX Xu D Gross 2007 Domain evolution in ferroelectric materials: a continuum phase field model and finite element implementation Comput Meth Appl Mech Eng 196 4365 4374 1173.74329 10.1016/j.cma.2007.05.010
14. Schrade D, Xu BX, Mueller R, Gross D (2009) On phase field simulations of ferroelectrics: Parameter identification and verification. Proceedings of the ASME 2008 smart materials, adaptive structures and intelligent systems (SMASIS2008), pp 301-308
15. D Schrade R Mueller D Gross 2010 Parameter identification in phase field models for ferroelectrics Proc Appl Math Mech 9 1 369 370 10.1002/pamm.200910158
16. YC Song AK Soh Y Ni 2007 Phase field simulation of crack tip domain switching in ferroelectrics J Phys D Appl Phys 40 1175 1182 1:CAS:528: DC%2BD2sXisFCls74%3D 10.1088/0022-3727/40/4/040 2007JPhD...40.1175S
17. R Spatschek M Hartmann EA Brener H Mueller-Krumbhaar 2006 Phase field modeling of fast crack propagation Phys Rev Lett 96 015502 10.1103/PhysRevLett. 96.015502 2006PhRvL..96a5502S 16486473
18. BX Xu D Schrade R Mueller D Gross 2009 Micromechanical analysis of ferroelectric structures by a phase field method Comput Mater Sci 45 832 836 1:CAS:528:DC%2BD1MXkvFCjurg%3D 10.1016/j.commatsci.2008.07.010
19. Xu BX, Schrade D, Gross D, Mueller R (2010) Phase field simulation of domain structures in cracked ferroelectrics. Int J Fract. Special Issue: Broberg symposium. doi: 10.1007/s10704-010-9471-z
20. J Wang TY Zhang 2007 Simulations of polarization switching-induced toughening in ferroelectric ceramics Acta Mate 55 2465 2477 1:CAS:528: DC%2BD2sXjtl2ht7Y%3D 10.1016/j.actamat.2006.11.041
21. TY Zhang M Zhao P Tong 2002 Fracture of piezoelectric ceramics Adv Appl Mech 38 147 289 10.1016/S0065-2156(02)80104-1
22. TY Zhang CF Gao 2004 Fracture behaviors of piezoelectric materials Theor Appl Frac Mech 41 339 379 1:CAS:528:DC%2BD2cXisVymt70%3D 10.1016/j.tafmec.2003. 11.019 2067096