Issue 72

M. Perrella et alii, Fracture and Structural Integrity, 72 (2025) 236-246; DOI: 10.3221/IGF-ESIS.72.17

Experimental adherends displacements by DIC

Strain interpolation

Testing machine experimental data

Analytical energetic force evaluation

Numerical derivative of energetic

TSL interpolations

CZM parameters

Figure 6: Flowchart of DIR2 approach.

The bending moment at x b is function of the strain  b 2 measured on the bottom of the lower adherend         b b P a L EBh M h 3 2 4 8 (6) The measured strains were fitted with analytical function for reducing the noise related to DIC analysis. Alternatively, the measurement of  b 2 can be acquired by traditional strain gauge. An iterative algorithm was used for the estimation of    sa Q . Four iterations were necessary for achieving convergence, as shown in Fig. 7.a. The cohesive traction-separation relationship was then obtained by the derivative of the cohesive energy density at convergence:             s s s Q B 1 (7)

1.6

30

Q4 (convergent) Q3 Q2 Q1 Q0

DIR2 (Cricrì) Curve Fitting DIR2 (Cricrì)

1.4

25

1.2

20

1

0.8

15

0.6

10

Cohesive stress [MPa]

0.4

5

0.2 Cohesive energy density Q [N/mm]

0

0

0

0.04

0.08

0.12

0

0.04

0.08

0.12

a) b) Figure 7: a) Trend of cohesive energy density vs tangential slip displacements  s ; b) Traction separation law resulting from DIR2 method. Tangential slip displacement [mm] Tangential slip displacement [mm]

241