numero25

A.S. Chernyatin et alii, Frattura ed Integrità Strutturale, 25 (2013) 15-19 ; DOI: 10.3221/IGF-ESIS.25.03 16  creation so-called “response bank” which is mathematical analog of the FE model of the half-space with the surface crack. It allows calculating the values of the displacements in measurement points ( e i ) corresponding to e i * in case arbitrary values of the searching parameters ( b , σ x , σ y );  solution of a minimization problem. Variation of the searching parameters is carrying out for achievement of the minimum of objective function which describes a discrepancy between e i * and e i ;  assessment of e i * -scatter effect on determination accuracy of the searching parameters at different conditions of experimental measurements and minimization problem solution. The second step is connected with calculation of stress fields in the vicinity of the crack front at the parameters b , σ x , σ y which are defined by the first step. As results, distribution of the singular ( K I , K II ) and the non-singular ( T xx , T zz ) terms along the crack front are calculated. N UMERICAL SIMULATION he proposed method is realized in the case of a numerical experiment. Generation of the original data for the displacement fields is performed by numerical simulation of the probe hole in the vicinity of the surface crack. The finite element model of the elastic half-space under biaxial loading (Fig. 1a) is built in ANSYS software environment in the form of a prismatic body of finite dimensions, including the surface crack and volume of the probe hole (Fig. 1b). It should be noted that standard ANSYS procedure does not allow building a crack in this area, because its front is located over several volumes. Therefore, special multipurpose macros are created to build the planar crack with arbitrarily 3D-orientation and front geometry along which grid of singular elements is constructed in finite element model. Loading conditions are the following: σ x = 100 MPa, σ y = 200 MPa. The following sizes are also used in numerical simulation: the length of semi-elliptical crack 2 a =20 mm and the depth b =(2/3)a = 6.67 mm, the diameter and depth of the probe hole d = t = 2 mm. Figure 1 : The elastic half-space with a semi-elliptical crack and a probe hole (a) and finite element model of the output crack on the surface (b) . (a) (b) (c) Figure 2 : The displacement field u, v, w ( a , b , c , respectively) due to the to the formation of the hole in the vicinity of the surface crack tip. T