Experimental measurement of the near tip strain field in an iron-silicon single crystal

T. W. Shield, K. S. Kim

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Experimental results are presented for the plastic deformation field near a crack (200 μm wide notch) tip in an iron-3% silicon single crystal. The specimen was loaded in four point bending and the measurements were made at zero load after extensive plastic deformation had occurred. Results are given for a crack on the (011) plane with its tip along the [01|T] direction. The surface deformation field was measured using moire microscopy and a grating on the specimen surface. The in-plane Almansi strain components have been obtained by digitally processing the moire fringes. A well-structured asymptotic field has been found at a distance of 350-500 μm from the notch tip, where the maximum plastic strain is about 9%. The asymptotic field is observed to be composed of many distinct angular sectors. Three (six symmetric) of these sectors are found to have approximately constant strains. In a fourth (two symmetric) sector, the surface strains are approximately 1/r singular. Between these sectors there are interconnecting transition sectors. The location of the stress state on the yield surface and the active slip systems in each sector are identified by assuming that the plastic strain rates are normal to a Schmid law yield surface. The slip systems identified in this manner show excellent agreement with direct observations of the slip texture on the surface and dislocation etch pits in the interior of the specimen. The experimental strain measurements also show that the constant strain sectors are regions in which unloading occurs. Because of this unloading, the crack tip stress and deformation state is substantially different from an HRR type field which assumes proportional loading. This strong nonproportional loading is thought to be caused by the presence of material anisotropy. The nonproportional loading also provides a large amount of crack tip shielding that is evidence of a toughening mechanism that results from the presence of material anisotropy.

Original languageEnglish (US)
Pages (from-to)845-873
Number of pages29
JournalJournal of the Mechanics and Physics of Solids
Issue number5
StatePublished - May 1994

Bibliographical note

Funding Information:
TWS would like to acknowledge the National Science Foundation {through the NY1 program), the Office of Naval Research (grant No. NOOOl4-91-J-4034)a nd the McKnight Foun- dation for their support. Both authors would like to acknowledge the support of the Office of Naval Research (grant No. N00014-90-J-1295)a nd the National Science Foundation through the MRG at Brown University (grant Nos. DMR-8712665 and DMR-9002994). We would like to thank Professor J. R. Rice of Harvard University for providing the motivation to examine single crystal plasticity, T. Wei of Brown University for making the gratings and A. F. Bastawros for assistancew ith etching.


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