A new form of exact solutions for mode I, II, III crack problems and implications

E. C. Aifantis, William W Gerberich

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A new form of an exact linear elastic solution is obtained for the problem of a crack in a semi-infinite plate subjected, at infinity, to antiplane stress (Mode III) loading. The use of the conformal mapping technique results in a convenient stress and displacement solution for each point of the semi-infinite domain. For completeness, the solution technique is extended to Mode I, II problems with center-cracks as well as the Mode III V-notch problem. It is shown that the limiting case of the V-notch collapses to the stress functions independently derived for the edge-cut. At distances equivalent to 10% of the crack length away from the crack tip, the exact solutions give stresses about 7.5% greater than the one-term results. Ramifications of the exact solutions to finite-element solutions, elastic-plastic and diffusion problems are discussed.

Original languageEnglish (US)
Pages (from-to)95-108
Number of pages14
JournalEngineering Fracture Mechanics
Issue number1
StatePublished - 1978


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