PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 1013–1020 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

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2.2. On the fracture criterion The fracture criterion used in this work is that based on the stress intensity factor in the framework of LEFM principles, i.e., K I = K IC . However, two formulations will be used, one of them global ( energy-based ) and the other one local ( stress-based ) to ascertain which describes with more accuracy the fracture process in a 3D complex geometry like that of the cracked bar. These two approaches have been proposed in previous research, although no definitive conclusion has been drawn as to which is more adequate for describing the fracture process in cracked cylindrical bars. The global formulation was used by Athanassiadis (1979), Valiente (1980) and Athanassiadis et al. (1981) while the local one was proposed by D'Escatha and Labbens (1978), Bui and Dang Van (1979), Astiz et al. (1986) and Valiente and Elices (1998). In this paper both approaches are reviewed and applied to a broad range of fracture tests on prestressing steel bars. Firstly, a global fracture criterion may be formulated on the basis of energetic considerations, using either the strain energy release rate concept or the specimen compliance (related to the former by a one-to-one relationship). According to this criterion, fracture will take place when the energy release rate reaches a critical value. For a given geometry, it represents a single-parameter approach , since the energy release rate (or, accordingly, the compliance) for the considered geometry and loading mode (cf. Fig. 1) depends only on the crack depth a . Thus an average value of the energy release rate G * along the crack front may be computed (Athanassiadis, 1979; Athanassiadis et al., 1981) as follows: where E ' is the generalized Young's modulus, i.e., E ' = E in plane stress (bar surface) and E ' = E /(1 –  2 ) in plane strain (crack center). The single asterisk stands to emphasize that only one geometric parameter (the crack depth a ) is required. Another possibility is to evaluate the specimen compliance and calculate from it the energy release rate and thus the stress intensity factor. This procedure was employed by Valiente (1980), leading to the following one-parameter expression of it: (5) where  is the remote axial stress (far from the crack), a the crack depth, and Y* (a/D) a dimensionless function given by: Y * ( a / D ) = [0.473 – 3.286 ( a / D ) + 14.797 ( a / D ) 2 ] 1/2 [( a / D ) – ( a / D ) 2 ] – 1/4 (6) This function was obtained by a finite element computation of the compliance in a cracked cylinder with a straight fronted edge crack. Again a single asterisk is used to indicate that only one geometric parameter (the crack depth a ) is required, i.e., it is a simplified approach in which the aspect ratio a / b and the curvilinear coordinate s are not considered, the former because a representative geometry (the cylinder with a straight-fronted edge crack) is employed, and the latter due to the global character of the fracture criterion according to which failure takes place when a critical condition for the whole crack is achieved. From the results presented by Valiente (1980) using precracked rods of different materials, it may be concluded that global criteria seem to be more adequate in fracture situations with a certain degree of plasticity, i.e., when not purely brittle materials are involved and the microscopic fracture process develops by a micro-void coalescence over a certain area. K I * = Y * ( a / D )  ( ) (4)