PSI - Issue 41

6

Umberto De Maio et al. / Procedia Structural Integrity 41 (2022) 598–609 Author name / Structural Integrity Procedia 00 (2019) 000–000

603

The elastic parameters of constituent materials are the following: Young’s modulus and Poisson’s ratio are respectively equal to 31.48 GPa c E  and 0.2 c   for concrete and 200 GPa s E  and 0.3 s   for steel of the reinforcement bar. The tensile and compressive strengths of the concrete phase are equal to 24.8 MPa ck f  and 1.96 MPa ct f  , respectively, while the yielding stress of the rebars is equal to 430 MPa y f  .

Fig. 3. (a) Geometric configuration and boundary conditions of the tested element (all dimensions are expressed in mm); (b) adopted computational discretization.

The cohesive parameters required by the traction-separation law, useful to describe the behavior of the cohesive tractions acting between the bulk elements, are reported in Table 1. The mode-II fracture parameters, in terms of stress ( c  ) and fracture energy ( IIc G ), are set equal to the mode-I counterparts (i.e. c  and Ic G ), thus allowing the mesh induced toughening effect associated with the activation of local mixed-mode conditions during the crack propagation, to be notably reduced. A plane stress state is assumed. Displacement-controlled loading conditions are imposed to conduct the following simulations adopting a displacement increment of 5e−3 mm.

Table 1. Cohesive parameters required by the adopted traction-separation law. c  (MPa) c  (MPa) Ic G (N/m) IIc G (N/m) 0 n K (N/m 3 ) 0 s K (N/m 3 ) 

1.96

1.96

85

85

1.70E14

1.70E14

5

The loading curve of the tested RC element predicted by the proposed model is reported in Fig. 4a together with that obtained by the experiment of (Lee and Kim, 2009). The load versus average steel strain curve of the tested specimen predicted by the proposed model result to be globally in good agreement with the experimental outcome, showing the well-known four loading stages of an RC element under tensile load, i.e. the elastic stage (1), the crack formation stage (2) and the stabilized cracking stage (3) before the branch associated with the rebar yielding (4) (see Fig. 4a). Moreover, the numerically predicted loading curve shows sudden load reductions associated with the crack nucleation. Fig. 4b shows the crack pattern predicted by the adopted model together with the concrete normal stresses at different load levels. We can note that the propagated transverse cracks are very similar to that obtained by the experiments and they are represented in a very realistic manner by the proposed model. To assess the effectiveness of the adopted model, a comparison, in terms of crack number and crack spacing, is reported in Table 2. It is worth specifying that, the primary cracks are defined as the cohesive elements having a damage variable value equal to D 1  at yielding load. Moreover, the crack spacing has been measured at the rebar level. A lack of convergence of the crack spacing occurs due to the fact that a different crack number with respect to the available experimental range is predicted by the model. However, this result is influenced by the random location of the cracks within the unstructured computational discretization predicted by the model.