THEORETICAL DETERMINATION OF THE TEMPERATURE-DEPENDENCE OF ELASTIC PROPERTIES IN CUBIC POLYCRYSTALS

This paper presents theoretical expressions giving the effective elast ic moduli of a cubic or isotropic homogeneous solid under hydrostatic stress as functions of strain and temperature. The temperature depende nce of these expressions is derived within the fourth-order quasi-harm onic approximation of lattice dynamics. General fourth-order finite st rain equations are then deduced for the bulk modulus and shear modulus of a cubic polycrystal which is subjected to a hydrostatic pressure. It is shown that the isotropic polycrystalline parameters entering the se equations may be found from the pressure and temperature derivative s of the effective single-crystal elastic moduli by means of the Voigt -Reuss-Hill averaging procedure. Finally, the temperature variations o f the effective polycrystalline moduli of aluminium are calculated and compared with available experimental measurements at high temperature s. (C) 1997 Published by Elsevier Science Ltd.