2015-Sustainable Industrial Processing Summit
SIPS 2015 Volume 1: Aifantis Intl. Symp. / Multiscale Material Mechanics
| Editors: | Kongoli F, Bordas S, Estrin Y |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2015 |
| Pages: | 300 pages |
| ISBN: | 978-1-987820-24-9 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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On The Role of Strain Gradients in the Suppression of Material Instabilities at Small Length Scales
Ioannis Tsagrakis1;1ARISTOTLE UNIVERSITY OF THESSALONIKI, Thessaloniki, Greece;
Type of Paper: Regular
Id Paper: 522
Topic: 1
Abstract:
It is well known that the introduction of higher-order gradients in the constitutive equations for plasticity and elasticity provides the ability to capture size effects, i.e. the dependence of strength and other properties on the size of the specimen. This inherent ability of the gradient models is based on the interaction between intrinsic constitutive lengths associated with the gradient coefficients and a characteristic geometrical length of the specimen under consideration. Moreover, it has been shown that the gradient plasticity model proposed by Aifantis and co-workers is able to predict the thickness of shear bands which is directly related to the gradient coefficients. In this case, the problem remains well-posed upon the onset of softening and the numerical simulations do not exhibit the spurious discretization sensitivity of the classical theories. The rate-dependent (i.e. viscoplastic) counterpart of this model has been also used to provide estimates for the spacing of Portevin-Le Châtelier (PLC) bands and adiabatic shear bands.
The present work deals with a rather overlooked ability of the gradient theories, i.e. the suppression of instabilities at quite small length scales. Two benchmark problems are discussed concerning thermoviscoplastic and diffusional instabilities, respectively. In the former case, the competition of thermal and strain gradient terms on the onset of instability and its dependence on specimen size is illustrated. It is shown that heat conduction promotes the instability initiation in the hardening part of the homogeneous stress-strain graph, while the strain gradient term favors the occurrence of this initiation in the softening regime. This behavior is size dependent, i.e. small specimens can support stable homogeneous deformations even in the softening regime by suppressing the onset of the instability. In the latter case, a thermodynamically consistent model of gradient elastodiffusion is developed by coupling the standard Cahn-Hilliard-type of diffusion with a simple gradient elasticity model that includes the gradient of volumetric strain in the expression of the Helmholtz free energy density. Then, an initial-boundary-value problem is derived in terms of concentration and displacement fields and linear stability analysis is employed to determine the contribution of concentration and strain gradient terms on the instability that leads to spinodal decomposition. It is shown that the theoretical predictions are in accordance with the experimental trends in intercalation materials (as, for example, Li-ion battery material LiFePO4), i.e. the spinodal concentration range shrinks (i.e. the tendency for phase separation is reduced) as the crystal size decreases. Moreover, for crystals smaller than a critical size there is no spinodal region at all.