Volume 8, Issue 3
Brittle and Ductile Character of Amorphous Solids

Adv. Appl. Math. Mech., 8 (2016), pp. 485-498.

Published online: 2018-05

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• Abstract

Common silicate glasses are among the most brittle of the materials. However, on warming beyond the glass transition temperature $T_g$ glass transforms into one of the most plastic known materials. Bulk metallic glasses exhibit similar phenomenology, indicating that it rests on the disordered structure instead on the nature of the chemical bonds. The micromechanics of a solid with bulk amorphous structure is examined in order to determine the most basic conditions the system must satisfy to be able of plastic flow. The equations for the macroscopic flow, consistent with the constrictions imposed at the atomic scale, prove that a randomly structured bulk material must be either a brittle solid or a liquid, but not a ductile solid. The theory permits to identify a single parameter determining the difference between the brittle solid and the liquid. However, the system is able of perfect ductility if the plastic flow proceeds in two dimensional plane layers that concentrate the strain. Insight is gained on the nature of the glass transition, and the phase occurring between glass transition and melting.

• Keywords

Glasses, bulk metallic glass, shear bands, ductility, micromechanical modelling.

74A45, 74A60, 74A20

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@Article{AAMM-8-485, author = {Miguel and Lagos and and 19688 and and Miguel Lagos and Raj and Das and and 19689 and and Raj Das}, title = {Brittle and Ductile Character of Amorphous Solids}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {3}, pages = {485--498}, abstract = {

Common silicate glasses are among the most brittle of the materials. However, on warming beyond the glass transition temperature $T_g$ glass transforms into one of the most plastic known materials. Bulk metallic glasses exhibit similar phenomenology, indicating that it rests on the disordered structure instead on the nature of the chemical bonds. The micromechanics of a solid with bulk amorphous structure is examined in order to determine the most basic conditions the system must satisfy to be able of plastic flow. The equations for the macroscopic flow, consistent with the constrictions imposed at the atomic scale, prove that a randomly structured bulk material must be either a brittle solid or a liquid, but not a ductile solid. The theory permits to identify a single parameter determining the difference between the brittle solid and the liquid. However, the system is able of perfect ductility if the plastic flow proceeds in two dimensional plane layers that concentrate the strain. Insight is gained on the nature of the glass transition, and the phase occurring between glass transition and melting.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m439}, url = {http://global-sci.org/intro/article_detail/aamm/12099.html} }
TY - JOUR T1 - Brittle and Ductile Character of Amorphous Solids AU - Lagos , Miguel AU - Das , Raj JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 485 EP - 498 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2013.m439 UR - https://global-sci.org/intro/article_detail/aamm/12099.html KW - Glasses, bulk metallic glass, shear bands, ductility, micromechanical modelling. AB -

Common silicate glasses are among the most brittle of the materials. However, on warming beyond the glass transition temperature $T_g$ glass transforms into one of the most plastic known materials. Bulk metallic glasses exhibit similar phenomenology, indicating that it rests on the disordered structure instead on the nature of the chemical bonds. The micromechanics of a solid with bulk amorphous structure is examined in order to determine the most basic conditions the system must satisfy to be able of plastic flow. The equations for the macroscopic flow, consistent with the constrictions imposed at the atomic scale, prove that a randomly structured bulk material must be either a brittle solid or a liquid, but not a ductile solid. The theory permits to identify a single parameter determining the difference between the brittle solid and the liquid. However, the system is able of perfect ductility if the plastic flow proceeds in two dimensional plane layers that concentrate the strain. Insight is gained on the nature of the glass transition, and the phase occurring between glass transition and melting.

Miguel Lagos & Raj Das. (2020). Brittle and Ductile Character of Amorphous Solids. Advances in Applied Mathematics and Mechanics. 8 (3). 485-498. doi:10.4208/aamm.2013.m439
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