Question

1. Invoke the Mises yield criterion to show that the approximate plastic zone around the tip of a Mode III crack is a circle of radius 3 km 2

Answer 1

Solution:

The step-wise solution is given below in the fig.

Solution- Diagram- Step I'- length of the plastic zone 'o' can be caleweted by 52 koys -CI) Step II!- Ķ in the ean-ci) depends upon whether it is plane - Stoess case or plene strain case • We know that G2z = k/ (2007) - ciil Step tur! - Equating eqn-ci) and Cit), we get K Eys = kl Squaring both sides, en K2 5752 1,2/2009 JE kist22 am Steptu - svaluating Ķ for plane stressed delane strain, psuincip al stressed 6 = 62.27 52= 622,6 = 6420 (plane stress). 6 = 2v 622 cplane stein) Step 5!- putting in mises yield coniterion, we get - (G-6212 + (62-612+ (6-6) 27 25ys² We get Rs I Cplane stress), K- 7 -2) Cplane storin) step viPutting the values in ean-Clin), we get step wit - for mode s prack Mgo 920 Charts {41 = 341}

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