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

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.