TY - JOUR
T1 - A new form of exact solutions for mode I, II, III crack problems and implications
AU - Aifantis, E. C.
AU - Gerberich, William W
PY - 1978
Y1 - 1978
N2 - 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.
AB - 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.
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U2 - 10.1016/0013-7944(78)90053-X
DO - 10.1016/0013-7944(78)90053-X
M3 - Article
AN - SCOPUS:0018057749
VL - 10
SP - 95
EP - 108
JO - Engineering Fracture Mechanics
JF - Engineering Fracture Mechanics
SN - 0013-7944
IS - 1
ER -