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

Fredholm in 1900 gave a solution in principle for the dis-placements generated by a point force at the origin in an infinite elastic solid. Eshe1by in 1955 gave an approximate solution of the dilatation for the triple force at the origin wi th no moment. Eshe1by and Leibried gave expressions which converge only when [equation] 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 apoint force is very slow for lithium which is on the verge of 2c:44 0 a phase change [equation] at 78. K Detailed calculations of stress fields have been made for aluminum and copper. It is noted that for Cu a contribution of additional terms besides that given by Eshe1by appears in the angular dependence of dilatation for the triple double force but for At the dilatation is in close agreement with Eshe1by's result. The elastic interaction energies of two triple double force interstitia1s and of two single double force interstitia1s with no moment are calculated. The calculated stresses are accurate to about 15 and 8 percent of their value for Cu and At, respectively. Fifteen terms for Cu and six terms for At were used in the series for stresses. Better accuracy could be obtained by including higher order terms in the expansions.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Lie, Kyoon-Haeng Choh

Contributors dc:contributor

• Koehler, James S.

• elastic stress field
• point force
• cubic crystal
• infinite elastic solid

Statement dc:rights

• 1967 Kyoon-Haeng Choh Lie

Language dc:language

en

Identifier

6086910

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/25691