2023-Sustainable Industrial Processing Summit
Intl. Symp on Physics, Mathematics and Multiscale Mechanics
| Editors: | F. Kongoli, A. B. Bhattacharya, A.C. Pandey, G. Sandhu, F. Quattrocchi, L. Sajo-Bohus, S. Singh, H.S. Virk, R.M. Santilli, M. Mikalajunas, E. Aifantis, T. Vougiouklis, P. Mandell, E. Suhir, D. Bammann, J. Baumgardner, M. Horstemeyer, N. Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2023 |
| Pages: | 298 pages |
| ISBN: | 978-1-989820-96-4 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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PORTVIN - LE CHATELIER EFFECT
Alexander Filonov1; Lyudmila Kveglis2; Artur Abkaryan2; Evgeniy Artemyev2;1INSTITUTE OF NONFERROUS METALS AND MATERIALS SCIENCE SIBERIAN FEDERAL UNIVERSITY KRASNOYARSK PR. IMENI GAZETY KRASNOYARSKII RABOCHII 95 RUSSIAN FEDERATION, Красноярск, Russian Federation; 2INSTITUTE OF ENGINEERING PHYSICS AND RADIOELECTRONICS, SIBERIAN FEDERAL UNIVERSITY, Krasnoyarsk, Russian Federation;
Type of Paper: Regular
Id Paper: 475
Topic: 38
Abstract:
Quote from [1,2]: -“Many experiments measuring the deformation of solids under static loads have revealed sudden yielding and other deviations from normal behavior, now known as the “Portvin-Le Chatelier effect.” If we follow historical truth, then the honor of the discovery of this phenomenon should be associated with the names of Felix Savard (1837) and Antoine Philibert Masson (1841). Masson described a steep, almost vertical (σ-ε diagram) increase in stress, accompanied by very little deformation, up to a value at which there was a sudden sharp increase in deformation at constant stress. In experiments of this type with dead loads used in testing machines in the 19th century, this phenomenon took on the form that later led to the use of the term "staircase effect."
For small and large deformations, this effect has been studied by many over the past two centuries, but a satisfactory explanation has not yet been achieved.
It makes sense to compare the experimental ladders of the Portvin-Le Chatelier effect [1,2] with the already existing theoretical ladders [3,4].
In [1,2], in experiments on stretching Al with a purity of 99.99% shows several detailed graphs of the σ-ε dependence, for example, [9, p. 74] and [10, p. 288].
If you compare the staircase [1, p. 74] with the staircases [3,4], then their similarities are revealed - they almost coincide. But if you look at [1, p. 74] more carefully, especially at the initial stretching section, then qualitative differences are noticeable. First of all, this is the absence of strictly vertical segments in the experimental graphs. Consequently, the FK model is not enough to explain the EPLC, so it needs to be modified and replaced with the DFK model.
From the point of view of the DFK model, the initial stretching segment is associated with the general stretching of two CHs united by the potential Vlj. Further, at a certain critical force Fc, failure occurs with compression of CH2 and abrupt stretching of CH1 followed by interchain capture. The process is repeated until the sample breaks.
The first prediction of the new model is that when stretched, the sample becomes chemically inhomogeneous in length and composition of m and M atoms.
The most important question for the EPLC within the framework of the DFK model arises - the nature of Hooke's chains.
If stretchable CH1 is logically associated with an AL crystal, then the nature of CH2 may be associated with metal impurities. Let's follow this hypothesis.
In metals with a small amount of impurities, for example, in ALR%, the metal impurity R% is capable of being ordered into a cubic crystal at high temperatures. Impurity period CH2 – one-dimensional projection of the crystal R%,
, where % is the number of impurities in the main matrix. Suppose that in our case % = 10-6, then the period CH2
Comparing the number of steps [1, p. 74] with R=100, we find an approximate match.
As a result of stretching, the period of the R-sublattice changes from r=100 to r=1.
From the temperature graphs of the EPLC [2] it is clear that the EPLC disappears at T> Tc.
EPLC is a special case of phenomena in metal alloys AxB1-x.
Keywords:
FK model; Development; Portven - Le Chatelier effectReferences:
[1] Bell J.F. Experimental foundations of the mechanics of deformable solids. Part 1. Small deformations. Moscow, “Science”, 1984[2] Bell J.F. Experimental foundations of the mechanics of deformable solids. Part 2. Finite deformations. Moscow, “Science”, 1984, translation ENCYCLOPEDIA OF PHYSICS Chief Editor S. FLUGGE volume VIa/1 MECHANICS OF SOLIDS I Editor WITH TRUESDELL SPR1NGER-VERLAG BERLIN-HEIDELBERG-NEW YORK 1973
[3] A.K. Abkaryan, A.Yu. Babushkin, B.S. Dobronets, V.S. Krasikov, A.N. Filonov FTT, 2, (2016)
[4] A.Yu. Babushkin, A.K. Abkaryan, B.S. Dobronets, V.S. Krasikov, A.N. Filonov FTT, 9, (2016)