PSI - Issue 77

Esteban Cadavid Gil et al. / Procedia Structural Integrity 77 (2026) 248–255 Cadavid et al. / Structural Integrity Procedia 00 (2026) 000–000

251

4

the mid-span (actuator position), hereby enabling the identification and quantification of the cable’s non-linear bending sti ff ness. This bending sti ff ness not only depends on the material properties and geometric configuration of the cable components but also on internal factors such as normal contact forces and inter-component friction, which together give rise to a slip-stick bending response. Overall, this approach provided a means to assess the mechanical behaviour of the power cable by monitoring the evolution of its non-linear bending sti ff ness throughout the test campaign. M ( x ) =   F 2 x , 0 ≤ x ≤ L / 2 F 2 x − F ⟨ x − L 2 ⟩ , L / 2 < x ≤ L (1)

y = f ( x ) = ax 3

2

+ bx

+ cx + d

(2)

ρ = − 

2  3 / 2

1 + 

dy dx 

(3)

d 2 y dx 2

3. Cyclic Bending Tests

In this study, approximately 40000 bending cycles were conducted using various settings of bending amplitude and frequency. During testing, the actuator operated at lower frequencies when higher bending amplitudes were applied, primarily due to limitations of the hydraulic system used in the bending rig. Four bending test series selected for post-processing are summarized in Table 1. To accurately capture the non-linear reciprocating bending response, a su ffi cient number of data points were sampled within each loading cycle using the 3D optical system. Sampling frequency, number of points per cycle, and total recorded cycles are reported in Table 1.

Table 1. Post-processed bending test series. Test block Vertical displacement ( mm )

Number of bending cycles

Actuator frequency ( Hz )

Sampling frequency ( Hz )

Number of sampling points per cycle

Total number of recorded bending cycles

5 6 7

0-125 0-225 0-350 0-600

5400 2400 1425

0.3

12

40 40 40 40

32 38 57 57

0.167 0.107 0.075

6.66 4.28

10

990

3

4. Results and Discussion

This section presents results from four selected bending test series reported in Table 1, chosen from the full set of tests conducted on the submarine power cable. Each test series is evaluated based on the characterised non-linear reciprocating bending behaviour at the mid-span (i.e., actuator position), where the maximum bending curvature and bending moment occur. In assessing the cable’s mechanical response to cyclic bending, particular focus is placed on the evolution of bending sti ff ness in the slip region, where relative motion between cable components—especially