Issue 69

S. Eleonsky et alii, Frattura ed Integrità Strutturale, 69 (2024) 192-209; DOI: 10.3221/IGF-ESIS.69.14

   Δ u  



   Δ v  







u

v





(14)

N

N

Δ

,

Δ





2sin

2sin

The approach presented in this paper is based on experimental determination of two exclusive parameters, namely, the two differences between fringe orders on external face of the specimen. These values are derived for a single fringe pattern between a pair of basic points located at the hole edge. In this work, the required fringe counts were obtained manually via “naked-eye” observations performed by an operator. Quantitative uncertainty analysis based on inequality (8) employs i d  parameter. The first step in this way resides in obtaining   Δ u  and   Δ v  values from inequalities (14). The accuracy analysis of all experimental results assumes determination the fringe order differences with an absolute error   Δ 0.5 N   of the fringe width, which implies the distance between neighboring bright and dark fringes. Thus, the following estimations are valid:     3 Δ Δ 0.19 10 u v mm      



  2 



2



3

.

(15)









 

i d

u

v

mm

Δ

Δ

0.27 10

R ESULTS

P

ractical implementation of uncertainty analysis, presented in Section 4, needs real residual stress values inherent in investigated structures. Required data follow below.

Residual stress components in Sample 1 The mesh of probe holes drilled at the external surface of T-shaped stringer part is shown in Fig. 1 (b). The measurement points were positioned along x -direction (Line A) and along y -direction (Line B). Whole set of initial experimental data and corresponding results of residual stress determination are presented in Tab. 1. Configuration of the probe hole mesh, shown in Fig. 1 (b), indicates that locations of hole #1 and hole #6 with respect to adjacent assemblage holes are very close. Moreover, the values of hole diameter increments and principal residual stress completely coincide. Practically the same situation takes place for hole pairs #2, #7 and #3, #8. Data, which are related to the probe holes equivalently located with respect to assemblage holes, were averaged for constructing residual stress distributions. This was purposefully undertaken in order to decrease the uncertainties of residual stress components determination. The obtained results are listed in Tab.2 and Tab. 3.

Point number

1 σ , MPa

2 σ , MPa

u N , fringes

Δ v N , fringes

Δ u , μ m

Δ v , μ m

Δ

1 2 3 4 5 6 7 8 9

–19.0 –18.0 –9.5 –4.0 +1.0 –19.0 –16.0 –7.5 +1.0 –3.0

0

–7.22 –6.84 –3.61 –1.52 –7.22 –6.08 –2.85 +0.38 –1.14 0.38

0

–158.0 –147.0 –106.0

–53.0 –42.0

+1.0 –9.5 –7.5 –17.5 +1.0 –10.5 –15.0 –18.5 0

0.38

–3.61 –2.85 –6.65

–106.0

–54.0 –41.0

–77.0

–143.0

0

–158.0 –131.0

–53.0 –36.0

0.38

–3.99 –5.70 –7.03

–92.0 –34.0 –77.0

–108.0 –122.0 –163.0

10

Table 1: Initial experimental information and values of principal residual stress components.

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