Abstract
To explore constraint effects on fully plastic crakc-tip fields, analytical solutions are examined for mode-I, II and III loading in non-hardening materials under plane strain conditions. The results reveal that under mode-II and III loading the crack-tip stress fields are unique, and thus can be characterized by a `single parameter'. Under mode-I loading, however, the crack-tip stress field is non-unique but can be characterized by two sets of solutions or `two parameters'. One set of the solutions is the well-known Prandtl field and the other is a plastic T-stress field. This conclusion corroborates the observation of McClintock (1971) that the slip-line field is non-unique for plane strain tensile cracks. A two-term plastic solution which combines the Prandtl field and the plastic T-stress field with two parameters B 1 and B 2 can then characterize the crack-tip stress field of plane strain mode-I crack over the plastic region and quantify the magnitude of crack-tip constraints. These characters are similar to those for hardening materials. Analyses and examples show that the two-term plastic solution can match well with the slip-line field or finite element results over plastic region. Thus the parameters B 1 and B 2 can be used to characterize the constraint level for mode-I finite-sized crack specimens in non-hardening materials under plane strain conditions.
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Chao, Y., Zhu, X. Constraint effects on plastic crack-tip fields for plane strain mode-I, II and III cracks in non-hardening materials. International Journal of Fracture 105, 187–207 (2000). https://doi.org/10.1023/A:1007643127900
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DOI: https://doi.org/10.1023/A:1007643127900