Semi-analytical approaches to assess the crack driving force in periodically heterogeneous elastic materials

International Journal of Fracture

Volumn 173, Issue 1, 2012, Pages 57-70

  Fischer, F D ^a   Predan, J ^b   Fratzl, P ^c   Kolednik, O ^d  

^a INSTITUTE OF MECHANICS   (Austria)

^b UNIVERSITY OF MARIBOR   (Slovenia)

^c MAX PLANCK INSTITUTE OF COLLOIDS AND INTERFACES   (Germany)

^d ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

Author keywords

Configurational forces; Crack tip shielding and anti shielding; Finite element modelling; Inhomogeneous materials; Moduli perturbation concept

Indexed keywords

CONFIGURATIONAL FORCE; CRACK TIP SHIELDING AND ANTI-SHIELDING; FINITE ELEMENT MODELLING; INHOMOGENEOUS MATERIALS; MODULI PERTURBATION CONCEPT;

CRACK TIPS; ELASTIC MODULI; ELASTICITY; SHIELDING;

CRACKS;

EID: 84857356303     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-011-9657-z     Document Type: Article

References (36)

1. TL Becker Jr RM Cannon RO Ritchie 2000 An approximate method for residual stress calculation in functionally graded materials Mech Mater 32 85 97 10.1016/S0167-6636(99)00042-3 (Pubitemid 32211903)
2. TL Becker Jr RM Cannon RO Ritchie 2002 Statistical fracture modeling: crack path and fracture criteria with application to homogeneous and functionally graded materials Eng Fract Mech 69 1521 1555 10.1016/S0013-7944(02) 00047-4 (Pubitemid 35022358)
3. A Carpinteri M Paggi 2005 On the asymptotic stress field in angularly nonhomogeneous materials Int J Fract 135 267 283 10.1007/s10704-005-4087-4 (Pubitemid 41794366)
4. F Delale F Erdogan 1983 The crack problem for a nonhomogeneous plane ASME J Appl Mech 50 609 614 10.1115/1.3167098
5. JW Eischen 1987 Fracture of nonhomogenous materials Int J Fract 34 3 22
6. F Erdogan 1995 Fracture mechanics of functionally graded materials Compos Eng 5 753 770 10.1016/0961-9526(95)00029-M
7. Fischer FD, Predan J, Kolednik O, Simha NK (2007) Application of material forces to fracture of inhomogeneous materials: illustrative examples. Arch Appl Mech 77:95-112 (Corrections: Arch Appl Mech 78:835) (Pubitemid 46207130)
8. P Fratzl HS Gupta FD Fischer O Kolednik 2007 Hindered crack propagation in materials with periodically varying Young's modulus-lessons from biological materials Adv Mater 19 2657 2661 10.1002/adma.200602394 1:CAS:528: DC%2BD2sXhtFGhurrI (Pubitemid 47481832)
9. P Fratzl R Weinkamer 2007 Nature's hierarchical materials Prog Mater Sci 52 1263 1334 10.1016/j.pmatsci.2007.06.001 1:CAS:528:DC%2BD2sXhtVGisLnM (Pubitemid 47374755)
10. P Fratzl 2008 When the cracks begin to show Nat Mater 7 610 612 10.1038/nmat2240 1:CAS:528:DC%2BD1cXovFWrtbs%3D
11. H Gao 1991 Fracture analysis of nonhomogeneous materials via a moduli perturbation approach Int J Solids Struct 27 1663 1682 10.1016/0020-7683(91) 90068-Q
12. H Gao 2006 Application of fracture mechanics concepts to hierarchical biomechanics of bone and bone-like materials Int J Fract 138 101 137 10.1007/s10704-006-7156-4
13. Gross D, Seelig T (2001) Bruchmechanik. edn 3. Springer, Berlin
14. L-Ch Guo N Noda 2007 Modeling method for a crack problem of functionally graded materials with arbitrary properties-piecewise-exponential model Int J Solids Struct 44 6768 6790 10.1016/j.ijsolstr.2007.03.012 (Pubitemid 47361138)
15. Hamamoto Y, Okumura K (2008) Analytical solution to a fracture problem in a tough layered structure. Phys Rev E 78.026118(5)
16. JW Hutchinson 1987 Crack tip shielding by micro-cracking in brittle solids Acta metal 35 1605 1619 10.1016/0001-6160(87)90108-8 1:CAS:528: DyaL2sXkvVamtbw%3D (Pubitemid 17618686)
17. MY Kashtalayan JJ Rushchitsky 2010 Love's general representation of solution in linear isotropic inhomogeneous theory of elasticity for dependence of elastic properties on radius Int Appl Mech 46 56 3 13
18. O Kolednik J Predan GX Shan NK Simha FD Fischer 2004 On the fracture behavior of inhomogeneous materials - A case study for elastically inhomogeneous bimaterials Int J Solids Struct 42 605 620 10.1016/j.ijsolstr.2004.06.064
19. O Kolednik J Predan FD Fischer 2010 Cracks in inhomogeneous materials: Comprehensive assessment using the configurational forces concept Eng Fract Mech 77 2698 2711 10.1016/j.engfracmech.2010.07.002
20. O Kolednik J Predan FD Fischer P Fratzl 2011 Bio-inspired design criteria for damage-resistant materials with periodically varying microstructure Adv Funct Mater 21 3634 3641 10.1002/adfm.201100443 1:CAS:528:DC%2BC3MXpvVantLs%3D
21. S Kumar WA Curtin 2007 Crack interaction with microstructure Mater Today 10 34 44 10.1016/S1369-7021(07)70207-9 (Pubitemid 47223793)
22. SJ Matysiak DM Perkowski 2008 Crack normal to layered elastic periodically stratified space Theor Appl Fract Mech 50 220 225 10.1016/j.tafmec.2008.07.009 1:CAS:528:DC%2BD1cXhsVGltb7N
23. SA Meguid XD Wang LY Jiang 2002 On the dynamic propagation of a finite crack in functionally graded materials Eng Fract Mech 69 1753 1768 10.1016/S0013-7944(02)00046-2 (Pubitemid 35016264)
24. MA Meyers P-Y Chen AY-M Lin Y Seki 2008 Biological materials: structure and mechanical properties Prog Mater Sci 53 1 206 10.1016/j.pmatsci.2007.05.002 1:CAS:528:DC%2BD2sXht1KmtrzJ (Pubitemid 350017839)
25. S Muju PM Anderson DA Mendelsohn 1998 Microcrack toughening in two-phase multilayered media Acta mater 46 5385 5397 10.1016/S1359-6454(98)00195-5 1:CAS:528:DyaK1cXmsFWlu74%3D (Pubitemid 128410486)
26. S Muju 2000 Crack propagation in bimaterial multilayered periodically microcracking composite media Compos Sci Technol 60 2213 2221 10.1016/S0266-3538(00)00016-6
27. E Munch ME Launey DH Alsem E Saiz AP Tomsia RO Ritchie 2008 Tough, bio-inspired hybrid materials Science 322 1516 1520 10.1126/science.1164865 1:CAS:528:DC%2BD1cXhsVGltb%2FE
28. K Okumura P-G de Gennes 2001 Why is nacre strong? Elastic theory and fracture mechanics for biocomposites with stratified structures Eur Phys J E 4 121 127 10.1007/s101890170150 1:CAS:528:DC%2BD3MXhsFegsLw%3D
29. K Okumura 2002 Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets Eur Phys J E 7 303 310 1:CAS:528: DC%2BD38Xls1Shurc%3D (Pubitemid 36185037)
30. R Pippan P Weinert 1998 The effective threshold of fatigue crack propagation in aluminium alloys. II. The influence of particle reinforcement Philos Mag A 77 875 886 10.1080/01418619808221217 1:CAS:528:DyaK1cXitV2kt7k%3D
31. Rice JR (1968) Mathematical analysis in the Mechanics of Fracture. In: Liebowitz H (ed) Fracture, vol II. Academic Press, New York, pp 379-386
32. OM Sallah LJ Gray SN Fata 2010 Evaluation of Green's function derivatives for exponentially graded elasticity Int J Numer Methods Eng 83 693 708
33. NK Simha FD Fischer O Kolednik CR Chen 2003 Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials J Mech Phys Solids 51 209 240 10.1016/S0022-5096(02)00025-X (Pubitemid 35282046)
34. NK Simha J Predan O Kolednik FD Fischer GX Shan 2005 Crack tip shielding or anti-shielding due to smooth and discontinuous material inhomogeneities Int J Fract 135 73 93 10.1007/s10704-005-3944-5 (Pubitemid 41794357)
35. NK Simha FD Fischer GX Shan CR Chen O Kolednik 2008 J-integral and crack driving force in elastic-plastic materials J Mech Phys Solids 56 2876 2895 10.1016/j.jmps.2008.04.003 1:CAS:528:DC%2BD1cXpt1SmurY%3D
36. PS Steif 1987 A semi-infinite crack partially penetrating a circular inclusion ASME J Appl Mech 54 87 92 10.1115/1.3172999 (Pubitemid 17555085)