Calculate the length of plastic deformation, Mechanical Engineering

Calculate the length of plastic deformation:

Calculate the length of plastic deformation along 45o in case the applied stress is

63.25% of yield stress in the plate of above Example

Solution

In this case (referring to Eq. (1)) q = 45o.

So that q/2= 22.5, 3q/2 = 67.5o  and cos  q/2=0.924, sin q /2 = 0.383, cos 3q /2 = 0.383, sin 3q/2 = 0.924 .

1595_Calculate the length of plastic deformation1.png

1522_Calculate the length of plastic deformation.png

The condition of plasticity istmax  = tY =  sY /2

798_Calculate the length of plastic deformation2.png

∴          r/a1 =[0.22(s/sY]2 = [0.22´0.6325]2

or, r = 0.0194 a1 or 1.94% of crack length.

Compare that under a stress which is 63.25% of yield stress the plastic zone extends 10% of crack length in the direction of crack length but 1.94% of crack length at 45o.

Posted Date: 1/22/2013 2:12:44 AM | Location : United States







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