PSI - Issue 2_B

Chernyatin A.S. et al. / Procedia Structural Integrity 2 (2016) 2650–2658 Chernyatin A.S., MatvienkoYu.G., Lopez-Crespo P. / Structural Integrity Procedia 00 (2016) 000–000

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The following geometric relationships can be deduced from Fig. 3:             sin cos ; sin cos 0 0 0 0 X X y Y Y Y Y x X X         . (1) It is possible to establish the relationship between the geometric and kinematic parameters. It provide to recalculation of the fields around the crack-tip to the displacement data registered by means of DIC:         B y x v V u A y x v U u                           cos cos sin sin cos sin ; sin sin cos cos sin cos , (2) where      .

Fig. 2. The geometric and kinematic formulation of the problem of the displacement fields definition

The displacements u and v occurred around the crack-tip can be calculated by using of the singular problem equations with T-stress in the LCS: , (3)   ...; cos 1 sin cos , 2      r M T r M K u r    

  

2 4    

2 

G

2

G



K

T

2 4     

    M

  , 



 ... 2

2

sin

cos

sin

r

M

v r

r





 

2

G

2

G



where r , θ are the polar coordinates in plane x0y attached to the crack tip, T is so called T xx -streess (the amplitudes of the second order terms in the three-dimensional series expansion of the crack-front stress field [7]) and . The equation (3) is right for plane stress state implemented at the points on the body surface. So, the determination of the K and T on the basis of experimental data can be lead in conjunction with the definition of the following parameters: X 0 , Y 0 , α , A , B , φ , which (with K and T ) will be called as state parameters. Solution of the problem can be representing as a multiparameter problem of minimizing the objective function I . The objective function shows the deviation between experimentally obtained displacements U *, V * in registration points         1 2 , 2 1 G E M