An implicit gradient type of static failure criterion for mixed-mode loading

International Journal of Fracture

Volumn 141, Issue 3-4, 2006, Pages 497-511

  Tovo, R ^a   Livieri, P ^a   Benvenuti, E ^a  

^a UNIVERSITY OF FERRARA   (Italy)

Author keywords

Brittle fracture; Implicit gradient; Non local failure criterion; NSIF; V notches

Indexed keywords

BOUNDARY CONDITIONS; BRITTLE FRACTURE; BRITTLENESS; DIFFERENTIAL EQUATIONS; ELASTICITY; FINITE ELEMENT METHOD; FRACTURE TOUGHNESS; LAPLACE TRANSFORMS; STRESS CONCENTRATION; TENSILE STRESS;

IMPLICIT GRADIENT; MIXED-MODE LOADING; NON-LOCAL FAILURE CRITERION; STATIC FAILURE LOAD;

FAILURE ANALYSIS;

EID: 33751103665     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-006-9011-z     Document Type: Article

References (33)

1. Aifantis EC (2003) Update on a class of gradient theories. Mech Mater 35:259-280
2. Barenblatt GI (2004) Scaling phenomena in fatigue and fracture. Lawrence Berkeley National Laboratory, paper LBNL 56765 University of California
3. Bažant Z (1987) Why continuum damage is nonlocal: Justification by quasiperiodic microcrack array. Mech Res Commun 14:407-419
4. Benvenuti E, Tralli A (2006) The fast Gauss transform for non-local integral models. Commun Numer Methods Eng 22:505-533
5. Benvenuti E, Loret B, Tralli A (2004) A unified multifield formulation in nonlocal damage. Eur J Mech A/Solids 23:539-559
6. Carpinteri A (1987) Stress-singularity and generalized fracture toughness at the vertex of re-entrant corners. Eng Fract Mech 26:143-155
7. Carpinteri A, Pugno N (2005) Fracture instability and limit strength conditions in structures with reentrant corners. Eng Fract Mech 72:1254-1267
8. Ciarlet PG (1988) Mathematical elasticity, vol 1: Three dimensional elasticity. North-Holland
9. De Borst R, Mühlhaus HB (1992) Gradient dependent plasticity: formulation and algorithmic aspect. Int J Numer Methods Eng 35:521-539
10. Edelen DGB (1976) Continuum physics, vol IV. Academic Press, New York, pp 75-204
11. Eringen CA, Edelen DGB (1972) On nonlocal elasticity. Int J Eng Sci 10:233-248
12. Geers MGD, de Borst R, Brekelmans WAM, Peerlings RHJ (1998) Strain-based trasient-gradient damage model for failure analyses. Comput Methods Appl Mech Eng 160:133-153
13. Gómez FJ, Elices M (2003) Fracture of components with V-shaped notches. Eng Fract Mech 70:1913-1927
14. Gross B, Mendelson A (1972) Plane elastostatic analysis of V-notched plates. Int J Fract Mech 8:267-276
15. Kröner E (1967) Elasticity theory with long-range cohesive forces. Int J Solids Struct 3:731-742
16. Lasry D, Belytschko T (1988) Localization limiters in transient problems. Int J Solids Struct 24:581-597
17. Lazzarin P, Tovo R (1996) A unified approach to the evaluation of linear elastic fields in the neighbourhood of cracks and notches. Int J Fract 78:3-19
18. Lazzarin P, Zambardi R (2001) A finite-volume-energy based approach to predict the static and fatigue behaviour of components with sharp V-shaped notches. Int J Fract 112:275-298
19. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A/Solids 21:61-72
20. Livieri P, Tovo R (2004) Fatigue limit evaluation of notches, small cracks and defects: An engineering approach. Fatigue Fract Eng Mater Struct 27:1037-1050
21. Mühlhaus HBM, Aifantis EC (1991) A variational principle for gradient plasticity. Int J Solids Struct 7:845-857
22. Neuber H (1968) Über die Berücksichtigung der Spannungskonzentration bei Festigkeitsberechnungen. Konstruktion 20:245-251
23. Novozhilov VV (1969) On the foundations of the theory of equilibrium cracks in elastic bodies. Prikl Matem i Mekhan 33:797-812
24. Peerlings RHJ (1999) Enhanced damage modelling for fracture and fatigue. Ph.D. Dissertation, T.U. Eindhoven
25. Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi- brittle material. Int J Numer Methods Eng 39: 3391-3403
26. Picu RC (2002) On the functional form of non-local elasticity kernels. J Mech Phys Solids 50:1923-1939
27. Pijaudier-Cabot G, Bažant ZP (1987) Nonlocal damage theory. J Eng Mech 10:1512-1533
28. Polizzotto C (2001) Non-local elasticity and related variation principles. Int J Solids Struct 38:7359-7380
29. Seweryn A (1994) Brittle fracture criterion for structures with sharp notches. Eng Fract Mech 47:673-681
30. Seweryn A, Mroz Z (1995) A non-local stress failure condition for structural elements under multiaxial loading. Eng Fract Mech 51:955-973
31. Seweryn A, Poskrobko S, Mroz Z (1997) Brittle fracture in plane elements with sharp notches under mixed-mode loading. ASCE J Eng Mech 123:535-543
32. Taylor D (1999) Geometric effects in fatigue: A unifying theoretical model. Int J Fatigue 21:413-420
33. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension.ASME J Appl Mech 19:526-528