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The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of alpha iron is investigated using ab initio density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic shear moduli. For the key slip planes in alpha-iron, $left[1overline{1}0right]$ and $left[11overline{2}right]$, we find a shear modulus reduction of approximately 1.6% per at.% H.