Issue 72

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

Testing machine experimental data

Experimental adherends displacements by DIC

Analytical J-integral evaluation

Numerical derivative of J -integral

TSL interpolations

CZM parameters

Figure 4: Flowchart of DIR1 approach.

The value of strain energy release rate, G , considering materials as linear elastic, can be obtained from the calculation of J , by using the simplified equation by Leffler et al. [24]:





2

 P a

 s



P

9

3 8

     

o

 

G J

(1)

s

2 3

Bh

16

EB h

where P is the applied load, a 0 is the pre-crack length,  s is the tangential displacement of adhesive layer at pre-crack tip, E is the adherend Young’s modulus, B and h are respectively the width and thickness of adherends.

30

1.6

DIR1 (Leffler et al.)

1.4

DIR1 (Leffler et al.)

25

Curve Fitting DIR1 (Leffler et al.)

1.2

20

1

15

0.8

0.6

J-integral [N/mm]

10

Cohesive stress [MPa]

0.4

5

0.2

0

0

0

0.04

0.08

0.12

0

0.04

0.08

0.12

Tangential slip displacement [mm]

a) b) Figure 5: a) Trend of J-integral vs tangential slip displacements  s ; b) Traction-separation law resulting from DIR1 method. Tangential slip displacement [mm]

   k s J was used for calculating the numerical derivative of    s J , see Fig. 5. The cohesive

The resulting set of points

shear stress is indeed expressed by analytical equation:

239