PSI - Issue 39

O.N. Belova et al. / Procedia Structural Integrity 39 (2022) 770–785 Author name / Structural Integrity Procedia 00 (2021) 000–000

775

6

fringes is shown in figs. 4 and 5. The skeleton is shown by green points. Finally, the chosen points are shown in fig.4 and 5. It should be noted that, as it is revealed in the process of the experimental data processing, in order to produce theoretically the isochromatic fringe shown in figs. 4 and 5 it is indispensable to held at least sixteen-twenty terms in the Williams series expansion (1). 3. The over-deterministic method and the Broyden – Fletcher – Goldfarb – Shanno algorithm The relation between the optical and stress effects is linear and is given in photoelasticity as

1 2 / Nf h σ σ σ = −

(4)

where f σ is the material stress fringe value, N is the order of the generated interference fringes (or fringe order) and h is the thickness of the model. For a plane stress problem, the stress components are related to the principal stresses as

(

)

(

) 2

2

1 2 σ σ σ σ = + 11 22 ,

/ 2

/ 4

(5)

± −

11 σ σ

+

σ

.

22

12

Substituting Eq. (5) in (4) one can define an error function for m th data point

Fig. 4. Fringe skeletons - fringe thinned images for 80 kg (left) and 90 kg (right).