applied fracture mechanics

Evaluating the Integrity of Pressure Pipelines by Fracture Mechanics 2872.3. Engineering methods for determining the J integral2.3.1. The FC methodThis method was proposed as the Js method in Addendum A16 of the French nuclear code(RCC-MR, 1985). It stems from the second option for describing the transition state betweenideally elastic and fully plastic behaviour of a material, i.e. from the function f2(Lr) of the R6method (Milne et al., 1986). This function takes the form:wheref2Lr E LR3ref Lr Re2Er e ref12(6)Lr = σ/σL (σ – applied stress, σL – stress at the limit load)Re is the yield stressE is Young´s modulusεref is the reference strain corresponding to the reference (nominal) stress σrefIf we identify function f2(Lr) with function f L3 r J J e 12and express Lr as σref / Re and theelastic J integral Je as K 2 / E´, where E´ =E for plane stress state and E´ =E / (1−ν 2 ) for planestrain state, we have:2K E.J (7)E 3refref2ref 2 ER .e. refThe stress σref in the above equation is a nominal stress – i.e. a stress acting in the planewhere the crack occurs. Taking into consideration the description of the stress-straindependence by the Ramberg-Osgood relation (8) and adjusting Eq. (7), we obtain the J-integral in the form (9).whereJ 0 0 0 2 K 0.5 AE n 2A0 (8)(9) A 1 0 n1(10)