The elastic stress field produced by a point force in a cubic crystal

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Abstract
Fredholm in 1900 gave a solution in principle for the displacements generated by a point force at the origin in an infinite elastic solid. Eshelby in 1955 gave an approximate solution of the dilation for the triple force at the origin with no moment. Eshelby and Leibried gave expressions which converge only when The present calculation uses Fredholm's work to provide a Fourier expansion of displacement which converges for all stable cubic crystals. The convergence of the series giving the displacement due to a point force is very slow for lithium which is on the verge of a phase change Detailed calculations of stress fields have been made for aluminium and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshelby appears in the angular dependence of dilatation for the triple double force but for Al the dilatation is in close agreement with Eshelby's result. The elastic interaction energies of two triple double force interstitials and of two single double force interstitials with no moment are calculated. The calculated stresses are accurate to about 15 and 8% of their value for Cu and Al, respectively. Fifteen terms for Cu and six terms for Al were used in the series for stresses. Better accuracy could be obtained by including higher order terms in the expansions.