Propagation of cracks in ductile materials is well known to occur through two possible mechanisms: coalescence of cavities and formation of shear bands (‘void sheet mechanism’). The classical Gurson–Tvergaard–Needleman (GTN) homogenized model for such materials incorporates some phenomenological modelling of coalescence, but not of formation of shear bands assisted by the presence of microvoids, and this generates a number of shortcomings. In order to solve these difficulties, this paper presents a unified model of both coalescence and formation of shear bands in porous plastic solids, including the possible couplings between the two. Both phenomena are viewed as expressions of the same basic effect, namely strain localization within thin planar bands, the only difference being the mode of deformation. The model is first developed assuming a periodic distribution of cavities, then critically assessed through comparison with some micromechanical numerical simulations based on the same assumption, and finally extended to the case of a random distribution of voids.
Il est bien connu que la propagation de fissures dans les matériaux poreux ductiles s'effectue suivant deux mécanismes possibles : la coalescence des cavités et la formation de bandes de cisaillement. Le modèle homogénéisé classique de Gurson–Tvergaard–Needleman (GTN) pour ces matériaux contient une modélisation phénoménologique de la coalescence, mais pas de la formation de bandes de cisaillement assistée par la présence de microcavités, et ceci induit certains inconvénients. Afin de résoudre ces difficultés, cet article propose un modèle unifié de la coalescence des vides et de la formation de bandes de cisaillement dans les solides plastiques poreux, incluant les couplages possibles entre les deux phénomènes. Ces derniers sont considérés comme deux manifestations d'un même effet fondamental, à savoir la localisation de la déformation en minces couches planes, la seule différence résidant dans le mode de déformation. Le modèle est d'abord développé en faisant l'hypothèse d'une distribution périodique de cavités, puis validé par comparaison avec des simulations numériques micromécaniques fondées sur la même hypothèse, et finalement étendu au cas d'une distribution aléatoire de vides.
Mots-clés : Endommagement ductile, Coalescence, Bandes de cisaillement
Jean-Baptiste Leblond 1; Gérard Mottet 2
@article{CRMECA_2008__336_1-2_176_0, author = {Jean-Baptiste Leblond and G\'erard Mottet}, title = {A theoretical approach of strain localization within thin planar bands in porous ductile materials}, journal = {Comptes Rendus. M\'ecanique}, pages = {176--189}, publisher = {Elsevier}, volume = {336}, number = {1-2}, year = {2008}, doi = {10.1016/j.crme.2007.11.008}, language = {en}, }
TY - JOUR AU - Jean-Baptiste Leblond AU - Gérard Mottet TI - A theoretical approach of strain localization within thin planar bands in porous ductile materials JO - Comptes Rendus. Mécanique PY - 2008 SP - 176 EP - 189 VL - 336 IS - 1-2 PB - Elsevier DO - 10.1016/j.crme.2007.11.008 LA - en ID - CRMECA_2008__336_1-2_176_0 ER -
%0 Journal Article %A Jean-Baptiste Leblond %A Gérard Mottet %T A theoretical approach of strain localization within thin planar bands in porous ductile materials %J Comptes Rendus. Mécanique %D 2008 %P 176-189 %V 336 %N 1-2 %I Elsevier %R 10.1016/j.crme.2007.11.008 %G en %F CRMECA_2008__336_1-2_176_0
Jean-Baptiste Leblond; Gérard Mottet. A theoretical approach of strain localization within thin planar bands in porous ductile materials. Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 176-189. doi : 10.1016/j.crme.2007.11.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.008/
[1] Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media, ASME J. Engrg. Mater. Technol., Volume 99 (1977), pp. 2-15
[2] Analysis of cup-cone fracture in a round tensile bar, Acta Metallurgica, Volume 32 (1984), pp. 157-169
[3] J. Devaux, J.B. Leblond, G. Mottet, G. Perrin, Some new applications of damage models for ductile metals, in: Application of Local Fracture/Damage Models to Engineering Problems, Proceedings of the 1992 ASME Summer Mechanics Meeting, Tempe (USA), American Society of Mechanical Engineers
[4] Modelling of crack growth in round bars and plane strain specimens, Int. J. Solids Structures, Volume 38 (2001), pp. 8259-8284
[5] J. Kyong Lak, Rupture en mode mixte I + II de l'acier inoxydable austénitique 316L, PhD Thesis, Ecole Centrale de Paris, France, 1993
[6] J. Devaux, Etude de la rupture en mode mixte, action 2004—Application à la rupture d'un barreau de flexion 4 points, Note Interne ESI Group n° F/LE/04.5877/A, 2004
[7] M. Gologanu, Etude de quelques problèmes de rupture ductile des métaux, PhD thesis, Université Pierre et Marie Curie (Paris VI), France, 1997
[8] Theoretical models for void coalescence in porous ductile solids—I: Coalescence “in layers”, Int. J. Solids Structures, Volume 38 (2001), pp. 5581-5594
[9] Void growth and coalescence in porous plastic solids, Int. J. Solids Structures, Volume 24 (1988), pp. 835-853
[10] The continuum theory of plasticity on the macroscale and the microscale, J. Materials, Volume 1 (1966), pp. 873-910
[11] Second order estimates for nonlinear isotropic composites with spherical pores and rigid particles, C. R. Mécanique, Volume 333 (2005), pp. 147-154
[12] Influence of voids on shear band instabilities under plane strain conditions, Int. J. Fracture, Volume 17 (1981), pp. 389-407
[13] G. Perrin, Contribution à l'étude théorique et numérique de la rupture ductile des métaux, PhD thesis, Ecole Polytechnique, Palaiseau, France, 1992
[14] Analyzing ductile fracture using dual dilational constitutive equations, Fatigue Fract. Engrg. Mater. Struct., Volume 17 (1994), pp. 695-707
[15] An extended model for void growth and coalescence, J. Mech. Phys. Solids, Volume 48 (2000), pp. 2467-2512
[16] Micromechanics of coalescence in ductile fracture, J. Mech. Phys. Solids, Volume 50 (2002), pp. 1331-1362
[17] Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids, Acta Metallurgica, Volume 33 (1985), pp. 1079-1085
[18] A three-dimensional model for ductile fracture by the growth and coalescence of microvoids, Acta Metallurgica, Volume 33 (1985), pp. 1087-1095
[19] T. Pardoen, F. Scheyvaerts, private communication (2006)
[20] P. Suquet, Plasticité et homogénéisation, PhD thesis, Université Pierre et Marie Curie (Paris VI), France, 1982
[21] Analytical study of a hollow sphere made of porous plastic material and subjected to hydrostatic tension—Application to some problems in ductile fracture of metals, Int. J. Plasticity, Volume 6 (1990), pp. 677-699
[22] On the elastic plastic initial-boundary value problem and its numerical integration, Int. J. Numer. Meth. Engrg., Volume 11 (1977), pp. 817-832
Cited by Sources:
Comments - Policy