A nonlinear theory of thermochemical equilibrium of solids under stress
Abstract
A rigorous thermodynamic analysis permitting a constrained diffusional equilibration of a solid under nonuniform stress has been extended to large strains. The results can be expressed in terms of open-system stress-strain relations in which the diffusional equilibration requires that chemical potentials of interstitials and chemical potential differences of substitutional species be held constant.
[We construct an open-system elastic energy density from the knowledge of the elastic energy density at constant composition and the thermodynamic properties of hydrostatically stressed material. Second order open-system elastic coefficients can be expressed as functions of material properties at zero stress and display four distinct causes for nonlinear behavior.
Numerical examples on hypothetical ideal or regular solutions illustrate the contributions of the different factors in nonlinear behavior. A calculation on the Au-Ni system shows the predicted effect in a real case in which several factors contribute.
Résumé
On a étendu aux fortes déformations une analyse thermodynamique rigoureuse permettant la mise en équilibre par diffusion d'un solide soumis á une contrainte non uniforme. On peut exprimer les résultats sous la forme de relations contrainte-déformation d'un système ouvert, dans lequel la mise en équilibre par diffusion impose que les potentiels chimiques des atomes interstitiels et les différences de potentiel chimique des divers atomes substitutionnels soient maintenus constants.
Nous construisons une densité d'énergie élastique d'un système ouvert à partir de la densité d'énergie élastique à composition constante et des propriétés thermodynamiques d'un matériau soumis à une contrainte hydrostatique. On peut obtenir les coefficients élastiques du second order d'un système ouvert en fonction des propriétés du matériau sous contrainte nulle, et l'on obtient quatre causes différentes conduisant à un comportement non linéaire.
Des exemples numériques dans le cas de solutions hypothétiques idéales ou régulières illustrent les contributions des différents facteurs dans un comportement non linéaire. Les calculs effectués dans le système Au-Ni présentent dans un cas réel l'effet prévu auquel plusieurs facteurs contribuent.
Zusammenfassung
Eine strenge thermodynamische Analyse, die eine eingeschränkte Diffusions-Gleichgewichtseinstellung eines festen Körpers unter einer ungleichmäβigen Spannung erlaubt, wurde zu groβen Dehnungen erweitert. Die Ergebnisse können mit Spannungs-Dehnungsbeziehungen eines offenen Systèmes ausgedrückt werden, in denen die Diffusions-Gleichgewichtseinstellung erfordert, daβ die chemischen Potentiale der Zwischengitteratome und die Differenzen der chemischen Potentiale der Substitutionsatome konstant gehalten werden.
Wir konstruieren eine elastiche Energiedichte eines offenen Systems aus der Kenntnis der elastichen Energiedichte bei konstanter Zusammensetzung und der thermodynamischen Eigenschaften eines hydrostatisch belasteten Materials. Elastische Koeffizienten zweiter Ordnung des offenen Systems können als Funktionen der Materialeigeschaften bei Spannung Null geschrieben werden und lassen vier verschiedene Ursachen nichtlinearen Verhaltens erkennen.
Numerische Beispiele für hypothetische ideale oder regelmäβige Lösungen illustrieren die Beiträge der verschiedenen Faktoren zum nichtlinearen Verhalten. Eine Berechnung für das System Au-Ni zeigt den vorausgesagten Effekt in einem realen Fall, zu dem mehrere Faktoren beitragen.
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On leave-of-absence from the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.