User talk:Alybaka

ESTIMATION OF PLASTIC ZONE SIZE IN LINEAR ELASTIC MATERIAL

Abstract: We know because of plastic zone created in the vicinity of crack, crack behaves as if it were slightly longer. As stress in continuously applied plastic region goes on increasing and when it becomes comparable to specimens dimensions, linear elastic stress analysis becomes increasingly inaccurate. So it becomes necessary to estimate plastic zone size, in order to decide which parameters to be applied in fracture and crack growth estimation. Here I propose of using von misses stress criteria as basic criteria for evaluation of plastic zone size.

Introduction Earlier approaches include THE IRWIN APPROACH and THE STRIP YEILD MODEL in estimation of plastic zone and both of them leads to simple corrections for crack tip yielding. THE IRWIN APPROACH includes normal uniaxial failure criteria in evaluating plastic zone size, whereas THE STRIP YEILD MODEL assumes a central crack with slender plastic zoneand closure stress is assumed to be σ_y applied at each crack tip. We all know, von misses stress criteria is, σ_e = 1/√2 √((σ_1- σ_2 )^2+(σ_2- σ_3 )^2+(σ_3- σ_1 )^2 ) .................1 Where, σ_e = effective stress σ_1 = 1st principal stress 〖 σ〗_2 = 2nd principal stress σ_3 = 3rd principal stress Now here we are estimating plastic zone size for mode l type of fracture, σ_(1,) σ_2 = (σ_xx+σ_yy)/2 ± √(((σ_xx-σ_yy)/2)^2+(τ_xy )^2 )...................................................................................2

From stress intensity relations we can say, assuming plane stress condition, i.e.    σ_zz = 0 and also      τ_yz=0      τ_xz=0 Under the situation shown, σ_xx = K_1/√2πr cos⁡〖θ/2〗 [1-sin⁡〖θ/2〗  sin⁡〖3θ/2〗] .......................3 σ_yy = K_1/√2πr cos⁡〖θ/2〗 [1+sin⁡〖θ/2〗  sin⁡〖3θ/2〗]...................... 4     τ_xy =  K_1/√2πr  cos⁡〖θ/2〗  sin⁡〖θ/2〗  sin⁡〖3θ/2〗.................................5 Now putting back equations 3,4and 5 in equation 2 we get, σ_(2 ,) σ_1= K_1/√2πr  cos⁡〖θ/2〗 [1∓〖√2 sin〗⁡〖θ/2〗  sin⁡〖3θ/2〗] and σ_(3 )=0....................................................6 Substituting these values in equation 1.......we will have .......... σ_e= 1/√2 √((K_1/√2πr  cos⁡〖θ/2〗  〖2√2 sin〗⁡〖θ/2〗  sin⁡〖3θ/2〗 )^2+(K_1/√2πr  cos⁡〖θ/2〗  [1-〖√2 sin〗⁡〖θ/2〗  sin⁡〖3θ/2〗])^2+(K_1/√2πr  cos⁡〖θ/2〗  [1+〖√2 sin〗⁡〖θ/2〗  sin⁡〖3θ/2〗])^2 ) σ_e= 1/√2   K_1/√2πr   cos⁡〖θ/2〗   √(2+12 〖〖(sin〗⁡〖θ/2)〗〗^2  〖〖(sin〗⁡〖3θ/2)〗〗^2 ) For in plane crack we have, θ=0. σ_e= K_1/√2πr

σ_ys= K_1/√2πr

On solving further, we get

r= 1/2π (K_1/σ_ys )^2

Result: Result that we have obtained is also consistent with results obtained by irwin’s strip yield model that uses maximum normal stress theory.

Speedy deletion nomination of Plastic zone estimation


A tag has been placed on Plastic zone estimation, requesting that it be speedily deleted from Wikipedia. This has been done for the following reason:

appears to be a project report

Under the criteria for speedy deletion, articles that do not meet basic Wikipedia criteria may be deleted at any time.

If you think this page should not be deleted for this reason, you may contest the nomination by visiting the page and clicking the button labelled "Click here to contest this speedy deletion". This will give you the opportunity to explain why you believe the page should not be deleted. However, be aware that once a page is tagged for speedy deletion, it may be removed without delay. Please do not remove the speedy deletion tag from the page yourself, but do not hesitate to add information in line with Wikipedia's policies and guidelines. If the page is deleted, and you wish to retrieve the deleted material for future reference or improvement, you can place a request here. Vigyani (talk) 06:18, 16 April 2013 (UTC)