Justification of paris-type fatigue laws from cohesive forces model via a variational approach

Continuum Mechanics and Thermodynamics

Volumn 18, Issue 1-2, 2006, Pages 23-45

  Jaubert, A ^a   Marigo, J J ^b  

^a UNIVERSITÉ PARIS 13   (France)

^b INSTITUT JEAN LE ROND D ALEMBERT   (France)

Author keywords

Calculus of Variations; Fatigue; Fracture Mechanics; Paris law; Surface energy

Indexed keywords

CYCLIC LOADS; DEBONDING; FRACTURE MECHANICS; INTERFACIAL ENERGY; MATHEMATICAL MODELS; THIN FILMS;

CALCULUS OF VARIATIONS; FATIGUE; MONOTONE LOADING; PARIS LAW;

THEOREM PROVING;

EID: 33746037617     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-006-0023-8     Document Type: Article

References (35)

1. Abdul-Baqi. A., Schreurs, P.J.G.. Geers. M.G.D.: Fatigue damage modeling in solder interconnects using a cohesive zone approach. Tnt. J. Sol. Struct., 42, 927-942 (2005)
2. Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 55-129 (1962)
3. Bourdin, B., Francfort, G.A., Marigo, J.-J.: Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48, 797-826 (2000)
4. Braides, A.: Γ-convergence for Beginners, volume 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford: Oxford University Press 2002
5. Charlotte, M., Francfort, G.A., Marigo, J.-J., Truskinovsky, L.: Revisting brittle fracture as an energy minimization problem: comparison of griffith and barenblatt surface energy models. In. dans: Cachan, A.B. (Ed.), Proceedings of the Symposium on "Continuous Damage and Fracture", dans: The Data Science Library. Paris: Elsevier, 7-12 (2000)
6. Cherepanov, G.P.: Mechanics of brittle fracture. New York: McGraw-Hill International Book Company 1979
7. Dacorogna, B.: Direct methods in the calculus of variations. Berlin Heidelberg New york: Springer 1989
8. Dacorogna, B.: Introduction au calcul des variations. Cahiers Mathématiques de l'École Polytechnique Fédérale de Lausanne. Editions Presses Polytechniques et Universitaires Romandes, 1992
9. Dal Maso. G., Toader, R.: A model for the quasi-static growth of brittle fractures based on local minimization Models Methods App. Sci. 12, 1773-1799 (2002)
10. Darque-Ceretti, E., Felder, E.: Adhésion et adhérence. Sciences et Techniques de l'ingénieur. CNRS Editions, 2003
11. Del Piero. G.: One-dimensional ductile-brittle transition, yielding and structured deformations. In: Argoul, P., Frémond M.: (Eds.), Proceedings of IUTAM Symposium "Variations de domaines et frontières libres en mécanique", Paris, 1997. Dordrecht: Kluwer 1999
12. Del Piero, G., Truskinovsky, L.: Macro and micro-cracking in one-dimensional elasticity. Int. J. Solids Structs. 38(6), 1135-1138(2001)
13. Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100-108 (1960)
14. Ferriero, A.: Quasi-static evolution for fatigue debonding. Preprint
15. Francfort, G.A., Larsen, C.J.: Existence and convergence for quasi-static evolution in brittle fracture. Comm. Pure. Appl. Math. 56(10), 1465-1500 (2003)
16. Francfort, G.A., Marigo, J.-J.: Stable damage evolution in a brittle continuous medium. Eur. J. Mech. A/Solids A/Solids 12, 149-189 (1993)
17. Francfort. G.A., Marigo, J.-J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids. 46(8), 1319-1342 (1998)
18. Griffith, A.: The phenomena of rupture and flow in solids. Philos Trans Roy Soc Lond CCXXI(A), 163-198 (1920)
19. Halphen, B., Nguyen, Q.S.: Sur les matériaux standards généralisés. J. Mec. 14(1), 39-63 (1975)
20. Jaubert, A.: Approche variationnelle de la fatigue. Thèse de doctorat, Université Paris-Nord, Paris, 2006
21. Laverne, J., Marigo, J.-J.: Approche globale, minima relatifs et critère d'amorçage en mécanique de la rupture. Comptes Rendus Mécanique 332(4), 313-318 (2004)
22. Leblond, J.-B.: Mécanique de la rupture fragile et ductile. Collection Études en mécanique des matériaux et des structures. Editions Lavoisier, 2000
23. Maiti, S., Geubelle. P.: A cohesive model for fatigue failure of polymers. Eng. Fract. Mech. 72(5), 691-708 (2005)
24. Marigo, J.-J., Truskinovsky, L.: Initiation and propagation of fracture in the models of Griffith and Barenblatt. Continuum Mech. Thermodyn. 16(4), 391-409 (2004)
25. Mielke, A.: Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Contin Mech Thermodyn 15(4), 351-382 (2003)
26. Needleman, A.: Micromechanical modelling of interface decohesion. Ultramicroscopy, 40, 203-214 (1992)
27. Nguyen, O., Repetto, E. A., Ortiz, M., Radovitzki, R. A.: A cohesive model of fatigue crack growth. Int. J. Fract. 110, 351-369(2001)
28. Obreimoff, J. W.: The splitting strength of mica. Proc. Roy. Soc. Lond. A 127(805), 290-297 (1930)
29. Paris, P.C., Erdogan, F.: A critical analysis of crack propagation laws. J. Basic. Eng. 85, 528-534 (1963)
30. Paris, P.C., Gomez, M.P., Anderson, W. E.: A rational analytic theory of fatigue. Trend Eng 13(8), 9-14 (1961)
31. Roe, K.L., Siegmund, T.: An irreversible cohesive zone model for interface fatigue crack growth simulation. Eng. Fract. Mech. 70, 209-232(2002)
32. Serebrinsky, S., Ortiz, M.: A hysteretic cohesive-law model of fatigue-crack nucleation. Scripta. Materialia 53, 1193-1196 (2005)
33. Siegmund, T.: A numerical study of transient fatigue crack growth by use of an irreversible cohesive zone model. Int. J. Fatigue. 26(9), 929-939 (2004)
34. Suresh, S.: Fatigue of materials. Cambridge: Cambridge University press 1998
35. Yang, B., Mall, S., Ravi-Chandar, K.: A cohesive zone model for fatigue crack growth in quasibrittle materials. Int. J. Sol. Struct. 38, 3927-3944 (1999)