PSI - Issue 28

Vedernikova Alena et al. / Procedia Structural Integrity 28 (2020) 1160–1166 Author name / Structural Integrity Procedia 00 (2019) 000–000

1164

5

It was concluded from analysis of data on the Fig. 3 that the analytical assessment gives an overestimation of the localization scale. The estimation of the fundamental length by the results of numerical simulation gives the exact ratio corresponding to the result of the Theory of Critical Distances: the critical stress must be achieved at the half of the fundamental length of the dissipative structure:

1 L 2

.

(8)

l



c

TN



5. Numerical results in the three-dimensional case Consider the tension test of the Grade 2 specimen with U-shaped stress concentrator (notch root radius 1 mm) in the framework of the proposed theory. Geometry and finite-element mesh of the specimen are presented in Fig. 4. Specimen have following material parameters: Young’s modulus 11 E 1.12 10   Pa, Poisson ration 0.32   , ultimate tensile stress UTS 27.2   kN, applied load 500 MPa. Parameters of statistical thermodynamical model of defect evolution: s 1  , 2   , a 9.1  , q 50.9  , 7 k 4.7 10    m 2 .

Fig. 4. Geometry and finite-element mesh of the Grade2 specimen.

Fig. 5 and Fig. 6 show the values of the components y p of the defect density tensor at the notch tip for two cases:

y 0    and

y 0    ,

TN/ 2 l L  respectively. In both cases, there is a stable situation with an equilibrium

concentration of defects in the notched area. (a)

(b)

Fig. 5. (a) Values of y p versus distance from the notch ( y

0    ) at different times of evolution; (b) Spatial distribution of y p component in the

cross-sectional area perpendicular to the loading direction at the end-point to evolution