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| Keywords: Plastic zone estimation using VON MISSES criteria in Fracture Mechanics.jpg Uploaded with en wp UW marker 2013 04 10 In fracture mechanics we estimate plastic zone size with the help of The Irwin Approach and The Strip Yeild Model here did it using different criteria of VON MISSES FAILURE CRITERIA and did the analysis which found to be consistent with results obtained with The Irwin Approach we use different criteria such as in The Irwin Approach we use Maximum Normal Stress Theory here i used VON MISSES STRESS failure criteria 2013-04-08 Alybaka ;Other information plastic zone estimation is very important in fracture mechanics so i tried to do this by different method this is self made and will be helpful cc-by-3 0 Fracture Mechanics 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/ 2 r cos θ/2 1-sin θ/2 sin 3θ/2 3 σ_yy K_1/ 2 r cos θ/2 1+sin θ/2 sin 3θ/2 4 τ_xy K_1/ 2 r 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/ 2 r 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/ 2 r cos θ/2 2 2 sin θ/2 sin 3θ/2 2+ K_1/ 2 r cos θ/2 1- 2 sin θ/2 sin 3θ/2 2+ K_1/ 2 r cos θ/2 1+ 2 sin θ/2 sin 3θ/2 2 σ_e 1/ 2 K_1/ 2 r 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/ 2 r σ_ys K_1/ 2 r On solving further we get r 1/2 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 Uncategorized 2015 March 10 | ||||
