Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques

Martín I. Idiart; Juan E. Ramos Nervi

doi:10.1016/j.crme.2013.11.002

Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques

Martín I. Idiart ^1,² ; Juan E. Ramos Nervi ^1,³

¹ Departamento de Aeronáutica, Facultad de Ingeniería, Universidad Nacional de La Plata, Avda. 1 esq. 47, La Plata B1900TAG, Argentina
² Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), CCT La Plata, Calle 8 No. 1467, La Plata B1904CMC, Argentina
³ Nucleoeléctrica Argentina S.A., Arribeños 3619, Ciudad Autónoma de Buenos Aires C1429BKQ, Argentina

Comptes Rendus. Mécanique, Volume 342 (2014) no. 1, pp. 25-31.

Abstract
Résumé

A linear-comparison homogenization technique and its relaxed version are used to compute bounds of the Hashin–Shtrikman and the self-consistent types for the hydrostatic strength of ideally plastic voided polycrystals. Closed-form analytical results are derived for isotropic aggregates of various cubic symmetries (fcc, bcc, ionic). The impact of the variational relaxation on the bounds is found to be significantly larger than that previously observed in fully dense polycrystals. So much so that, quite surprisingly, relaxed self-consistent bounds are found to be weaker than non-relaxed Hashin–Shtrikman bounds in some of the material systems considered.

Une technique dʼhomogénéisation non linéaire et sa version relaxée sont utilisées pour calculer des bornes de types Hashin–Shtrikman et autocohérent pour la resistance hydrostatique de polycristaux poreux parfaitement plastiques. On en dérive des résultats analytiques pour des agrégats isotropes de différentes symétries cubiques (cfc, ccc, ionique). Lʼimpact sur les bornes de la relaxation variationnelle se révèle être beaucoup plus important que celui précédemment observé dans le cas de polycristaux denses, tant et si bien que des bornes relaxées de type autocohérent sʼavèrent être plus faibles que des bornes non relaxées de type Hashin–Shtrikman dans certains systèmes matériels considérés.

Received: 2013-10-07
Accepted: 2013-11-08
Published online: 2013-12-30

DOI: 10.1016/j.crme.2013.11.002

Keywords: Polycrystals, Plasticity, Homogenization, Bounds
Mots-clés : Polycrystaux, Plasticité, Homogenisation, Bornes

Author's affiliations:

Martín I. Idiart ^{1, 2}; Juan E. Ramos Nervi ^{1, 3}

¹ Departamento de Aeronáutica, Facultad de Ingeniería, Universidad Nacional de La Plata, Avda. 1 esq. 47, La Plata B1900TAG, Argentina
² Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), CCT La Plata, Calle 8 No. 1467, La Plata B1904CMC, Argentina
³ Nucleoeléctrica Argentina S.A., Arribeños 3619, Ciudad Autónoma de Buenos Aires C1429BKQ, Argentina

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     author = {Mart{\'\i}n I. Idiart and Juan E. Ramos Nervi},
     title = {Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {25--31},
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     year = {2014},
     doi = {10.1016/j.crme.2013.11.002},
     language = {en},
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Martín I. Idiart; Juan E. Ramos Nervi. Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques. Comptes Rendus. Mécanique, Volume 342 (2014) no. 1, pp. 25-31. doi : 10.1016/j.crme.2013.11.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.11.002/

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