Issue 32

I. Telichev, Frattura ed Integrità Strutturale, 32 (2015) 24-34; DOI: 10.3221/IGF-ESIS.32.03 29 Figure 5 : Steps of the fracture analysis. Calculation of length of the plastic zones Modules 8-9: Once a solution of the linearized system of equations is obtained, the stress intensity factor (SIF) at the end of the plastic strip can be evaluated by 2 2 2 ( ) ( 1) I K l l u     . Modules 8-9-10: The stress at the crack tips is considered to be finite. The unknown length of the plastic zones is determined from the condition that the stress intensity factor is equal to zero at the end of the plastic strip:   2 0 I K l  . The search is performed by golden section method. Calculation of crack tip opening displacement/angle Module 11: Once a numerical solution of the singular integral equation is obtained, the displacement can be calculated at any point on the crack faces. For the arbitrary point * 2 2 2 / x x l  of the segment L 2 we have the following expression:         2 * 2 2 1 ' 2 * * * 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ( ) (1)  1 l x x u g x g l g t dt l d l g x l g              (5) Building the system of singular integral equations Chebyshev’s nodes generation Applying the method of mechanical quadratures 5 6 Solution of normalized and linearized system of equations Initial data:  structure  material  damage 2 7 Start of analysis 1 Applying the boundary conditions 4 3 A End of analysis Plastic zone length search Calculation of stress intensity factor (SIF) Yes No SIF =0 at the end of plastic zone Calculation of CTOD/CTOA CTOD or CTOA > critical value NO crack propagation Pressure wall rupture (“unzipping”) 8 9 10 11 12 13 14 15 No Yes A