Irreversible thermodynamics of ideal plastic deformation

Abstract

Thermodynamics for ideal plastic deformation causing no disorganization of the structure in the deformed body, which was discussed by P. W. Bridgman studied (1950), revealed that the concept of entropy was still applicable to its irreversible process. Noting that the structural invariability in an ideal plastic body is physically equivalent to the prerequisite of thermodynamics, namely, thermodynamic quantities must be independent of the macroscopic body shape, the generalized concept of entropy can be extended to the other thermodynamic potentials such as internal energy, free energies and so on. Here the extended generalization for ideal plastic deformation is theoretically justified on the basis of the irreversible thermodynamics constructed by Prigogine and his discipline. Thermodynamic state of the ideally deformed body is found to be specified both by the generalized thermodynamic potential (S, U, F, H or G) and by the irreversible potential energy J which drives the plastic deformation.

Keywords:

• ideal plastic deformation
• irreversible thermodynamics
• generalized state
• generalized thermodynamic potentials

PUBLIC INTEREST STATEMENT

“When a piece of straight wire of metal is subjected to bending force, the wire deforms plastically into a bent state. Once bent, the wire never returns to its original shape by itself. This one way process is called irreversible. The irreversible process is qualitatively understood by the second law of thermodynamics, namely by the law of entropy increase. Since thermodynamics deals with the equilibrium state, at first glance no entropy is defined for the irreversible process. A bulk body deforms irreversibly similar to the wire and therefore no entropy appears to be defined either. When no disorder is observed in the structure of the deformed body, however, the entropy can be defined and is found constant through the process of deformation. This type of plastic deformation is named ideal. On the basis of the ideal deformation, thermodynamics of the deformed body with disordered structures will be studied in future.”

Acknowledgements

We thank Dr. Masahiro Koiwa for encouraging us to complete the present work. One of us (K.O.) thanks Dr. Masaharu Kato for letting him know Kestin’s work.

Additional information

Funding

This work was supported by the Tohoku University [operational expenses].

Notes on contributors

Keiichi Ogawa

“The first author was impressed by the pioneering work of Bridgman (1950), the thermodynamics of ideal plastic deformation and generalized entropy in his graduate school days. It was only recently reconsidered when he came across the book, Modern Thermodynamics by Kondenpudi and Prigogine (1998). He noted that their argument on the falling of an object to the bottom of a viscous fluid was closely parallel to the ideal plastic deformation. We then find that not only entropy but also all the other thermodynamic potentials are generalized for the irreversible process of ideal plastic deformation. Application of equilibrium thermodynamics to the irreversible process is a tricky issue. It takes more than half a year of serious and frequent discussions among us to elucidate the thermodynamics of ideal plastic deformation. We hope that the present result plays a role similar to that of ideal gases.”