PSI - Issue 78

Han Liu et al. / Procedia Structural Integrity 78 (2026) 1759–1766

1763

where δ represents the midpoint deflection, taken as the maximum vertical displacement recorded at mid-span; h is the height of the beam; and L is the span length between the two supports. Assuming a linear strain profile across the beam depth, with maximum strain occurring at the extreme fibers and zero strain at the neutral axis, the average bending strain ε avg at the middle of the sensing layer, the third printed layer located 11 mm from the base of the 55 mm specimen’s overall height, can be approximated using geometric scaling as:

24 · δ · h 5 L 2

44 · ε max 55

(4)

ε avg =

=

By applying logarithmic di ff erentiation to equation 1, the FCR reflecting geometric strain e ff ects that account for strain-dependent changes in resistivity, can be expressed as a function of the average bending strain ε avg :

∆ e

∆ A A

∆ ρ ρ

∆ ρ ρ

+ (1 + 2 ν ) ε avg

(5)

FCR =

e −

+

=

where ν is the Poisson’s ratio of the material, and ∆ ρ/ρ is the piezoresistive e ff ect that often dominates when at electrical percolation. Therefore, the gauge factor λ bend of the self-sensing beam under bending can be written:

1 ε avg

FCR ε avg

∆ ρ ρ

= (1 + 2 ν ) +

(6)

λ bend =

3. Experiments

The strain sensing performance of the self-sensing Sikacrete beam was characterized and evaluated through a series of three-point bending test. Figure 3(a) shows the overall experimental setup. Flexural testing was carried out using an Instron 5944 universal testing machine equipped with a 1 kN load cell (2580 series). Each beam specimen was horizontally supported on a three-point bending fixture with a span length of 200 mm along its longitudinal axis. A loading nose was positioned at the midpoint of the span to apply a vertically concentrated force, and fiberglass plates were placed between the specimen and both the loading nose and support rollers to provide electrical insulation, as illustrated in Figure 3(b). The loading protocol consisted of five triangular waveform cycles. The first two cycles were applied with a peak load of 150 N at a rate of 30 N / s, followed by two additional cycles with a peak load of 300 N at 60N / s. The final cycle reached a maximum load of 600 N with a loading rate of 120 N / s. A preload of 20 N was applied prior to testing to ensure full contact between the specimen and supports and to eliminate minor mechanical slack or seating e ff ects in the test setup. Load and displacement data were captured at a sampling frequency of 100 Hz, while electrical resistance was measured independently between each set of adjacent electrodes, AB, BC, CD, DE, and EF, at 10 Hz using a resistance-reactance (R–X) model of an LCR meter implemented through LabVIEW.