EUROPEAN CONGRESS AND EXHIBITION ON ADVANCED MATERIALS AND PROCESSES - EUROMAT 2021

The biaxial modulus is an important elastic property of thin films and coatings. A state of equi-biaxial strain does not generate equi-biaxial stresses in anisotropic materials and hence different biaxial moduli are defined under these cases. Thin films and coatings generally possess a fibre-texture. As the biaxial modulus is anisotropic, polycrystalline averages are used. The Voigt and Reuss averaging schemes are commonly used to estimate the upper and lower bounds respectively. The Voigt average is calculated assuming an iso-strain condition within the grains of the polycrystalline film while the Reuss average assumes an iso-stress condition. If the Voigt and Reuss bounds coincide, the assumptions of iso-strain and iso-stress conditions are both true and hence the polycrystal behaves like a single crystal. It is well known that these bounds coincide if the normal to the film plane possesses high symmetry (three, four or six-fold). However, in the present work, it is demonstrated that the bounds can coincide even in planes without symmetry. An analytical method has been developed to identify such planes in the general case of triclinic films. Specific cases of orthorhombic, tetragonal and hexagonal films have been analysed in detail with examples. Although anisotropic, the biaxial modulus is found to be isotropic along certain planes within a single crystal. If the fibre axis is normal to such planes, the film will have isotropic biaxial moduli at the polycrystalline and single crystalline scales. Methods to identify planes without symmetry having isotropic biaxial moduli under both equi-biaxial strain and stress states are presented in this study. Mathematical formalisms to identify planes with coinciding Voigt and Reuss bounds and planes with isotropic biaxial moduli and the relation between the two have been discussed in this study.