Abstract
First we recognize that the coherence of certain phase transformations in solids is most vividly expressed using the material manifold and within the kinematic continuum description based on the so-calledinverse motion. In this fully dynamical framework the equation of interest is theun-balance of pseudomomentum for thermoelastic conductors. On computing the power developed by the accompanying surface source of quasi-inhomogeneities at the phase-transition front, we show that this relates directly to the normal jump of the Eshelby stress — devoid of any kinetic energy, but computed from the free energy — a scalar quantity which may be referred to as theHugoniot-Gibbs configurational force at the front. The thermodynamic analysis also establishes that this power is dissipated as the material progresses at the front that ishomothermal. The jump relation including this dissipation is that associated with the heat propagation equation valid at regular points. In all, this approach is based on the theory of material uniformity and inhomogeneities as developed in recent years by M. Epstein and the authors. All reasonings are made in full dynamics, for finite strains, and any anisotropy in three dimensions.
Sommario
Si osserva preliminarmente che, per alcune trasformazioni di fase nei solidi, la più naturale descrizione del fenomeno nell'ambito del continuo sembra essere quella basata sul moto inverse in dinamica, o sulla deformazione inversa in statica. In tale quadro, la nozione di ‘coerenza di fase’, suggerita dalla congruenza geometricocinematica tra due distinti reticoli cristallini a contatto, trova la sua espressione più significativa nella condizione di continuità degli ‘spostamenti di siti’ nel riferimento cristalline. Sulla base di argomentazioni svolte in precedenti lavori dagli autori per il caso dinamico e da M. Epstein per il caso statico e termostatico, si presuppone valida un'equazione di bilancio ‘materiale’: quella dellapseudo-quantità di moto. Si richiede che tale bilancio sia soddisfatto attraverso una superficie di contatto tra le due fasi. Tale superficie o fronte, avanzando, determina la trasformazione del materiale da una fase nell'altra. Il fronte è suppostoomotermo ed il materiale termoelastico in ciascuna delle due fasi. Un ruolo chiave è svolto dal tensore degli sforzi materiali di Eshelby. Infatti, la potenza sviluppata dalle forze di disomogeneità attraverso il fronte che avanza è unicamente determinata dalla discontinuità del tensore di Eshelby lungo la normale al fronte. Inoltre, l'espressione che detta potenza assume permette di evidenziare una quantità scalare che proponiamo di denominareforza configurazionale di Hugoniot-Gibbs per le analogie che essa suggerisce. Si sviluppa infine una trattazione parallela sulla base di una formulazione termodinamica classica del continuo. Un confronto dei risultati permette di Stabilire che la potenza sviluppata dalla forza configurazionale viene dissipata mentre il fronte avanza.
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Maugin, G.A., Trimarco, C. The dynamics of configurational forces at phase-transition fronts. Meccanica 30, 605–619 (1995). https://doi.org/10.1007/BF01557088
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DOI: https://doi.org/10.1007/BF01557088