PSI - Issue 33

Jesús Toribio et al. / Procedia Structural Integrity 33 (2021) 1131–1138 Jesús Toribio / Porcedia Structural Integrity 00 (2021) 000–000

1133

3

L/2

x = a - r

R

r

a

A

D/2

Fig. 1. Axisymmetric notched geometries used in the experiments.

3. Weakest link fracture criterion In a previous paper (Toribio, 1996) a fracture criterion was formulated for high-strength pearlitic steel bars as described above. The criterion was established on the basis of the experimental results and a numerical analysis (by an elastic-plastic finite element method) of the stress-strain state in the vicinity of the notch tip at the moment of fracture (Fig. 2). The fracture criterion was formulated as follows: "fracture will take place when the distortional part of the strain energy density (or, accordingly, the effective or equivalent stress in the von Mises sense) reaches a critical value over a critical region characteristic of the microstructure of the material". The effective or equivalent stress in the von Mises sense may be defined as follows:  eff = (3 • / 2) ½ (1) where is the stress deviatoric tensor. This variable is a direct function of the distortional part of the strain energy density, i.e., the component associated with shape changes in the material. The critical equivalent stress —closely related to the fracture toughness of the material— may be obtained by computer analysis, whereas the critical distance is a (constant) characteristic microstructural length of the material (the size of two cleavage facets). For the analyzed pearlitic steel, the characteristics of strength and microstructure (parameters of the material) are:  eff c = 1270 ± 10 MPa (2) x c = 2 x CL = 150  m (3) where  eff c is the critical equivalent stress and x c the characteristic length (depth measured from the notch tip).