Abstract
With ε = 1/2 − ν (ν - Poisson's ratio) as a small parameter, perturbation expansion is made, based upon the generally accepted solution for near-tip fields of cracks growing in elastic perfectly-plastic incompressible materials under plane strain. Asymptotic solutions up to the order ε2 are obtained for near-tip fields of cracks growing quasi-statically and steadily in elastic perfectly-plastic compressible materials. The near-tip field has a 5-sector structure. As ν → 1/2 the 5-sector solution degenerates to the 4-sector solution for the case of incompressible materials. The perturbation expansion provides deeper insight into the process of degeneration of the 5-sector solution to the 4-sector one, and also gives approximate analytical solutions for the case of compressible materials.
Résumé
On réalise l'expansion d'une perturbation en faisant légèrement varier le paramètre ε = 1/2 − ν (ν = Module de Poisson) et en se basant sur la solution g'enéralement admise pour des champs au voisinage de l'extrémité de fissures en croissance dans des matériaux incompressibles parfaitement élastiques-plastiques soumis á déformation plane.
On obtient des solutions asymptotiques jusqu'à l'ordre ε2 pour des champs au voisinage de l'extrémité de fissures qui croissent de manière quasi-statique et stable dans des matériaux compressibles élastiques-parfaitement plastiques. Ce type de champ a une structure comportant cinq secteurs. Lorsque ν tend vers 1/2, la solution à cinq secteurs dégénère en la solution à quatre secteurs relative au cas des matériaux imcompressibles.
L'expansion de la perturbation procure une vision plus profonde de ce processus de dégénérescence, et donne des solutions analytiques approchèes pour le cas des matériaux compressibles.
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Hwang, KC., Luo, XF. Perturbation solution for near-tip fields of cracks growing in elastic perfectly-plastic compressible materials. Int J Fract 42, 323–340 (1990). https://doi.org/10.1007/BF01185955
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DOI: https://doi.org/10.1007/BF01185955