PSI - Issue 5

Anastasiia Kostina et al. / Procedia Structural Integrity 5 (2017) 302–309 Anastasiia Kostina et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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where 11 σ - value of the stress tensor component in the tension direction, c L - critical distance, r - distance to the notch, θ - angle locating the plane experiencing the maximum normal stress, 0 σ - ultimate strength. Fracture of the material induced by a sharp increase in concentration of defects takes place when stress exceeds critical value on the half of the critical distance. Let us consider quasistatic tension of a notched Grade 2 titanium specimen with a strain rate of 0.0078 1/s. Geometry of the specimen is presented in figure 1 (a). Figure 1 (b) shows elastic stress distribution along the line characterizing distance to the notch in the plane with the maximum normal stress. The critical distance value has been obtained from the condition of equality of the local stress to the ultimate strength of the material when applied load corresponds to the fracture of the specimen. Numerical analysis was carried out using the finite-element method. Results of the simulation have shown that for the considered specimen the half of the critical distance is equal to 0.85 mm. (a) (b)

Fig. 1. (a) geometry of the specimen (all sizes are in millimeters); (b) determination of the length scale parameter the critical distance theory.

4. Application of the proposed model to the static strength assessment of the quasi-brittle material

To explain physical meaning of the obtained critical distance we consider quasi-static tension of the same specimen using relations (11)-(14) with different values of the material parameters. Simulation results have shown that blow-up regime of the defect kinetics can be obtained when 11 σ is greater than critical value c σ (ultimate tensile strength) at some distance l from the stress concentrator and the value of this distance should be bigger than critical spatial scale which coincides with the half of the critical distance. Figure 2 shows values of 11 p component (in the direction of tension) for two cases: 11 σ < c σ (fig. 2(a)) and 11 σ > c σ , l < L c /2 (fig. 2(b)). In both cases we can observe stable situation without an abrupt change in the defect density.

(a)

(b) Fig. 2. Values of p 11 versus distance from the notch (a) 11 σ < c σ ; (b) 11 p < c / 2 L .