Matches in DBpedia 2014 for { <http://dbpedia.org/resource/HRR_singularity> ?p ?o. }
Showing items 1 to 11 of
11
with 100 items per page.
- HRR_singularity abstract "Three scientists named Hutchinson, Rice and Rosengren independently evaluated the character of crack-tipstress fields in the case of power-law-hardening materials. Hutchinson evaluated both plane stressand plane strain, while Rice and Rosengren considered only plane-strain conditions. Both articles,which were published in the same issue of the Journal of the Mechanics and Physics of Solids,argued that stress times strain varies as 1/r near the crack tip, although only Hutchinson was ableto provide a mathematical proof of this relationship.Hutchinson began by defining a stress function Φ for the problem. The governing differentialequation for deformation plasticity theory for a plane problem in a Ramberg-Osgood material ismore complicated than the linear elastic case:where the function γ differs for plane stress and plane strain. For the Mode I crack problem,Hutchinson chose to represent Φ in terms of an asymptotic expansion in the following form:where A,B are constants that depend on θ, the angle from the crack plane. Equation (A2) isanalogous to the Williams expansion for the linear elastic case. If s < t, and t is lessthan all subsequent exponents on r, then the first term dominates as r →0. If the analysis isrestricted to the region near the crack tip, then the stress function can be expressed as follows:where k is the amplitude of the stress function and is a dimensionless function of Φ. AlthoughEquation (A1) is different from the linear elastic case, the stresses can still be derived. Thus the stresses, in polar coordinates, aregiven by The boundary conditions for the crack problem are as follows:In the region close to the crack tip where Equation (A3) applies, elastic strains are negligiblecompared to plastic strains; only the second term in Equation (A1) is relevant in this case.Hutchinson substituted the boundary conditions and Equation (A3) into Equation (A1) andobtained a nonlinear eigenvalue equation for s. He then solved this equation numerically for a rangeof n values. The numerical analysis indicated that s could be described quite accurately (for bothplane stress and plane strain) by a simple formula:which implies that the strain energy density varies as 1/r near the crack tip. This numerical analysisalso yielded relative values for the angular functions σ_ij. The amplitude, however, cannot beobtained without connecting the near-tip analysis with the remote boundary conditions. The Jcontour integral provides a simple means for making this connection in the case of small-scaleyielding. Moreover, by invoking the path-independent property of J, Hutchinson was able to obtaina direct proof of the validity of Equation (A5).".
- HRR_singularity wikiPageID "39072445".
- HRR_singularity wikiPageRevisionID "589468575".
- HRR_singularity subject Category:Mechanical_failure.
- HRR_singularity comment "Three scientists named Hutchinson, Rice and Rosengren independently evaluated the character of crack-tipstress fields in the case of power-law-hardening materials. Hutchinson evaluated both plane stressand plane strain, while Rice and Rosengren considered only plane-strain conditions.".
- HRR_singularity label "HRR singularity".
- HRR_singularity sameAs m.0swnwnd.
- HRR_singularity sameAs Q17092065.
- HRR_singularity sameAs Q17092065.
- HRR_singularity wasDerivedFrom HRR_singularity?oldid=589468575.
- HRR_singularity isPrimaryTopicOf HRR_singularity.