Thermomechanics of creep equation proposed by le Gac and Duval

Mathematical modelling of deformation of construction steels at elevated temperatures was in- vestigated 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 thermomechanical 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 was given, and some improvements were also 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'. 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 values of the material parameters for the power plant material 10 CrMo 9 10 were given. The material model was implemented into the ABAQUS finite element method program. The computed examples showed that even a 27-year-long creep response can be predicted.