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Estimating 3-D SE(B) Fracture Parameters using 2-D Equations

Last modified: 2013-02-10

#### Abstract

The present study was conducted to assess the accuracy of plane-stress orplane-strain approximations when used to assess the state of three-dimensional samples.SE(B) samples were modelled by 2-D and 3-D finite elements and load/CMOD complianceand elastic J-integrals were calculated for elastic deformations; no attempt was made tostudy the effects of plasticity. The calculated 2-D and 3-D results were compared with thoseestimated using the equations given in ASTM E 1820. For a standard B×2B SE(B) samplewith a/W = 0.5, the crack front is in a near-plane-strain state over most of the specimenthickness, although the specimen as a whole is in a mixed plane-strain/plane-stress state.The stress state changes continuously from plane strain to plane stress as the distance fromcrack tip (r) increases, and is close to plane stress when r/b = 0.6 to 0.8 where b is thewidth of the ligament. Near the point of load application (r/b = 1), the stress state is closeto plane strain. In general, the out-of-plane stress state is closest to plane strain in theregions of highest in-plane stress gradient. The crack length calculated from CMODcompliance is approximated better by a 2-D plane-stress equation than by a plane-strainone. Experimental results are reported which substantiate this conclusion. Also, therelation between the elastic J-integral (calculated by the virtual crack extension method)and the stress intensity factor is in closer agreement to a 2-D plane-stress equation than aplane-strain one.

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