PSI - Issue 14

Filin V.Yu. et al. / Procedia Structural Integrity 14 (2019) 758–773 Author name / Structural Integrity Procedia 00 (2018) 000–000

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tip opening displacement (CTOD), about 0.08 mm. So the local fracture condition is met but unstable cleavage fracture has not started yet. At a higher test temperature, Fig. 2, b , stable crack extension and higher crack tip opening (0.8 mm) are seen typical for shear fracture. This case cannot be related to SSY as a shear crack starts at SIF about 300 MPa m and the plastic zone around crack tip exceeds 30 mm in radius. On the other hand, this case is only admissible for structural steel applied in critical structures. LEFM conditions cannot also be met due to heavy loading of structures up to 0.7...1.0  Y (yield strength). This means, no extended fracture shall be allowed even under emergency loads.

Figure 2 — Crack tip region at -40  C ( a ) and +20  C ( b ) (Ilyin and Filin, 2014). This needs fracture parameters and criteria applicable out of LEFM limits to be established. Such criteria were developed in terms of EPFM (elastic-plastic fracture mechanics) dealing with nonlinear-elastic bodies. An “energy” EPFM parameter is J-integral introduced in 1968 by James Robert Rice and independently by Gennady Cherepanov. J is a contour integral around a crack tip, it is defined in coordinates x , y ( x is ahead the crack tip) as        ds дx u д J w x y dy T / ( , ) . (4) The basis of J-integral applicability is its independence on the integration path. For a nonlinear-elastic material J-integral is an intensity of elastic energy release as a crack extends in a plate of unit thickness, a J    / . (5) In other words, it is supposed that an extending crack correspondingly shifts the stress-strain field at its tip. A “standard” solution for stress (  ij ) and strain ( e ij ) components in the plastic strain area around the crack tip (excluding a small area adjacent to this tip) unequivocally described by J was suggested by Hutchinson, Rice and Rosengren (HRR-solution): w J r e J r J r ij ij ; ~ / ; ~ ( / ) ~ ( / ) /( 1) 1/( 1)     . (6) When this plastic strain area is limited and J-integral can be taken on the contour involving it, for the case of plane strain SIF may be related to J-integral as E J K ) / (1 2 2 I    , (7) that allows to find K ( J ) when we are out of LEFM. Fracture condition is c J J  . (8)