PSI - Issue 14

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

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2. Fracture toughness and elastic-plastic fracture mechanics approach Fracture mechanics is a part of the mechanics of deformed solids dealing with the strength of flaw-containing structures and making provisions based on the results of fracture toughness tests obtained with cracked specimens. As a crack has a sharp tip (radius R  0), if we suppose an elastic behaviour of material, we get a stress singularity at its tip, but actually a plastic strain arises at the crack tip. Real flaw-containing structures exist and have some strength reserve. Why? First, any load changes a crack tip to some finite radius, so stress singularity is avoided. Second, structural materials consist of microstructural elements of a finite size and a crack extension possibility might be related to structural barriers. This is a necessary condition of fracture. Alan Arnold Griffith in 1921 suggested the second, sufficient “energy” condition of fracture: a crack propagates if the change of elastic energy of the body dU corresponding to crack extension da is not less than a specific energy spent to form two new surfaces 2  :    / 2 G dU da . (1) 2  is a parameter of material, G is an elastic energy release rate. For a through crack of the length 2 a in an infinite plate E a G 2 2    , where E is an elastic modulus, so the fracture condition is const a   . In 1955 Egon Orowan amended the Griffith idea and told that specific fracture energy  combines the energies of plastic deformation  pl and forming new surfaces  f , where  pl >>  f for metals. Formula (1) seems to be hardly suitable for metals however it appears applicable in conditions of small scale yielding (SSY), i.e., when the plastic area at the crack tip is much less than all other sizes of the body. In 1957 George Rankin Irwin presented another approach dividing any loading to three main types of which type I is the most dangerous as the principal stress is normal to the crack plane. Stress near a crack tip is determined by a single parameter, stress intensity factor (SIF) K playing the role of stress from classical theory of elasticity. It is valid in terms of Linear-Elastic Fracture Mechanics (LEFM), in other words, when the stress is much more than the nominal stress, and SSY condition is met. a geometry K Y    ) ( I . (2) E.g. for a single edge notch bend specimen (SENB) of the dimensions shown in Fig.1, 4 3 2 14.57 14.18 ( ) 1.09 1.735 8.20           Y , a W /   .

Figure 1 – SENB specimen

LEFM fracture condition (local “force” condition) is c K K I I  .

(3) This condition coincides with Griffith “energy” condition in case of elastic deformation of material. When a plastic strain arises at a crack tip and the “force” condition is met in a microvolume much less than the plastic strain area, the “energy” condition of fracture shall not be met and a stable crack extension under applied load is observed. A difference of fracture conditions is illustrated by Fig. 2 obtained in an earlier study of Ilyin and Filin (2014). SENB specimens of low-alloyed steel grade F690 were unloaded before fracture; a crack tip region at mid-thickness was examined. When the test temperature was low (-40°C), Fig. 2, a , cleavage fracture was to be realized. Cleavage microcracks are seen ahead the main crack, however crack tip blunting is also observed, it is close to critical crack