PSI - Issue 13

Tomasz Brynk et al. / Procedia Structural Integrity 13 (2018) 1267–1272 Tomasz Brynk/ Structural Integrity Procedia 00 (2018) 000 – 000

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Presented technique is believed to have advantages on the traditional method where tensometric rosettes are used instead of non-contact optical displacement measurements resulted from much more data point delivered from the latter. Developed methodology has been applied to determine residual stress components in steel sample loaded with 500 MPa stress in special grip.

Nomenclature A, B, C

hole geometry dependent coefficients for through hole case hole geometry dependent coefficients for blind hole case

A’, B’, C’

d E h

hole diameter Young’s modulus data point index polar coordinates hole depth

i

r, 

r 0 

hole radius

r/r 0

 xx ,  yy ,  xy

residual stress components rigid body movement and rotation

T x , T y , R

u

horizontal (parallel to sample length) displacement

u r

radial displacement angular displacement

u 

v 

vertical (perpendicular to sample length) displacement

Poisson’s ratio

2. Methodology 2.1. Digital image correlation and inverse method in residual stress calculation

Digital image correlation (DIC) is non- contact optical displacement fields measurement technique developed in 80’s of XX century and firstly reported by Peters (1982) and Chu (1982). The method utilizes digital gray scale images of specially prepared (with speckled pattern) object surface to trace centers of square subset of a few pixel size. One camera based method (2D DIC) allows to determine displacement field of flat objects surface and the camera should be mounted perpendicular to the observed surface. This method is sensitive to out of plane displacement movement. In experiments concerning displacement field determination near drilled hole of a few millimeter diameter in material loaded to a few hundreds MPa maximal displacement are expected to be at the level of a few thousandth of millimeter, therefore less sensitive to out of plane displacement 3D DIC method with two cameras is more suitable. Moreover, in 3D DIC method cameras do not have to be placed in right angle to the surface allowing to place driller between them which simplifies testing stand design. Application of 3D DIC in hole drilling based method for residual stress determination deliver much more data in comparison to standardized procedure where only 3 or 6 strain reading are available, depending on tensometric rossete used. Having this in mind overdeterministic inverse method procedures might be applied to calculate residual stress and hole eccentricity sensitivity of standardized method might be overcame (hole center coordinates inverse method parameters optimization could be treated in the same way as residual stress components). If analytical solutions relating displacement fields near the drilled hole of specified geometry and residual stress components are known inverse method calculations might be applied to determine residual stress from DIC displacement field data. The Newton-Raphson iterative algorithm in the form of Matlab code has been developed to determine optimized set of coefficients  xx ,  yy ,  xy , x 0 , y 0 , T x , T y , R by simultaneously minimizing functions: ℎ = ( , , , , , 0 , 0 ) − − − (1) ℎ = ( , , , , , 0 , 0 ) − + − (2)