Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval

Kari Santaoja

Research output: Book/ReportReport

Abstract

Mathematical modelling of deformation of construction steels at elevated temperatures was investigated in the present work. Special attention was paid to the derivation of constitutive equations using irreversible thermodynamics. As a practical example the creep equation proposed by Le Gac and Duval was studied from the thermodynamical point of view. Physical and mathematical modelling of creep processes were briefly considered. Two different physical interpretations, found in literature, together with their mathematical formulations for the constitutive equations proposed by Le Gac and Duval were examined in detail. A detailed critique on the interpretations and their mathematical formulations were given and also some improvements were suggested. The meaning of a 'correct set' of state variables was discussed. The consequences of the second law of thermodynamics found by studying 'constitutive processes' were also considered. The significant role of the 'constitutive processes' in the derivation of the Clausius-Duhem inequality was pointed out. The author suggested that scientists should examine the reality of the 'constitutive processes' i.e. that the material under consideration can actually follow the 'constitutive process'. Based on Zieglei's principle of maximal rate of entropy production and its consequence which is the normality rule, the specific dissipation function was shown to be a homogeneous function. The explicit forms of the specific Helmholz free energy and the specific dissipation function (or their Legendre transformations) were set out. Using the above-mentioned functions the constitutive equation proposed by Le Gac and Duval was derived. The mutual dependence of the internal state variables was noticed and its consequence was briefly discussed. Although it forces one to change the treatment of the problem, it does not cause any insurmountable obstacles to the application of the derived theory.
Original languageEnglish
Place of PublicationEspoo
PublisherVTT Technical Research Centre of Finland
Number of pages109
ISBN (Print)951-38-3978-8
Publication statusPublished - 1991
MoE publication typeD4 Published development or research report or study

Publication series

SeriesValtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports
Number731
ISSN0358-5077

Fingerprint

constitutive equations
derivation
dissipation
normality
formulations
thermodynamics
Legendre functions
free energy
steels
entropy
causes
temperature

Keywords

  • creep properties
  • construction materials
  • steels
  • mechanical properties
  • deformation
  • temperature
  • heat
  • constitutive equations
  • thermodynamics
  • irreversible processes
  • mathematical models
  • ice
  • Duval

Cite this

Santaoja, K. (1991). Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval. Espoo: VTT Technical Research Centre of Finland. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, No. 731
Santaoja, Kari. / Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval. Espoo : VTT Technical Research Centre of Finland, 1991. 109 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 731).
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Santaoja, K 1991, Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, no. 731, VTT Technical Research Centre of Finland, Espoo.

Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval. / Santaoja, Kari.

Espoo : VTT Technical Research Centre of Finland, 1991. 109 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 731).

Research output: Book/ReportReport

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AB - Mathematical modelling of deformation of construction steels at elevated temperatures was investigated in the present work. Special attention was paid to the derivation of constitutive equations using irreversible thermodynamics. As a practical example the creep equation proposed by Le Gac and Duval was studied from the thermodynamical point of view. Physical and mathematical modelling of creep processes were briefly considered. Two different physical interpretations, found in literature, together with their mathematical formulations for the constitutive equations proposed by Le Gac and Duval were examined in detail. A detailed critique on the interpretations and their mathematical formulations were given and also some improvements were suggested. The meaning of a 'correct set' of state variables was discussed. The consequences of the second law of thermodynamics found by studying 'constitutive processes' were also considered. The significant role of the 'constitutive processes' in the derivation of the Clausius-Duhem inequality was pointed out. The author suggested that scientists should examine the reality of the 'constitutive processes' i.e. that the material under consideration can actually follow the 'constitutive process'. Based on Zieglei's principle of maximal rate of entropy production and its consequence which is the normality rule, the specific dissipation function was shown to be a homogeneous function. The explicit forms of the specific Helmholz free energy and the specific dissipation function (or their Legendre transformations) were set out. Using the above-mentioned functions the constitutive equation proposed by Le Gac and Duval was derived. The mutual dependence of the internal state variables was noticed and its consequence was briefly discussed. Although it forces one to change the treatment of the problem, it does not cause any insurmountable obstacles to the application of the derived theory.

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KW - construction materials

KW - steels

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KW - deformation

KW - temperature

KW - heat

KW - constitutive equations

KW - thermodynamics

KW - irreversible processes

KW - mathematical models

KW - ice

KW - Duval

M3 - Report

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T3 - Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports

BT - Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval

PB - VTT Technical Research Centre of Finland

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ER -

Santaoja K. Thermodynamical considerations on the material model for creep proposed by Le Gac and Duval. Espoo: VTT Technical Research Centre of Finland, 1991. 109 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 731).