Experimental Investigation on Crack Growth in Pre-Notched Concrete Beams †

Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy; gianfranco.piana@polito.it (G.P.); federico.accornero@polito.it (F.A.); alberto.carpinteri@polito.it (A.C.) * Correspondence: giuseppe.lacidogna@polito.it; Tel.: +39-011-090-4871 † Presented at the 18th International Conference on Experimental Mechanics (ICEM18), Brussels, Belgium, 1–5 July 2018.


Introduction
In the present work, three-point bending tests were performed on plain concrete pre-notched specimens of different sizes, investigating the damage process that takes place when the dimensional scale is increased, maintaining all the remaining parameters unchanged [1].RILEM Recommendation [2,3] was followed for the testing procedure and for the evaluation of Fracture Energy and bending strength.During the tests, two non-destructive techniques for damage monitoring were used: Acoustic Emission (AE) analysis and 2D Digital Image Correlation (DIC).
As is well-known, the AE technique is based on the acquisition of the ultrasonic signals generated by crack formation and extension in the bulk of the material [4][5][6].Unlike Fracture Energy, that is dissipated in an invasive fractal domain, AE energy seems to be emitted in a lacunar fractal domain: this difference in the fractal physical dimensions indicates the un-correlation between dissipated and emitted energies [7][8][9].
On the other hand, DIC is an innovative non-contact optical technique for measuring displacement and strain based on accurate 2D and 3D tracking and registration of changes in images [10,11].
For three-point bending testing, specimen sizes prescribed by [2,3] were taken into account (Table 1).Specimens were tested by servo-hydraulic universal testing machines: an MTS with a maximum loading capacity of 100 kN was used for testing the smaller beams (depth = 100 mm); the tests on the beams of larger sizes were conducted-for convenience in terms of experimental set-up-using a Baldwin testing machine with maximum loading capacity of 500 kN (Figure 1).Table 1.Specimen sizes considered in the experimental campaign according to [2,3].All the specimens were tested until the final failure was reached.During the tests, Crack Mouth Opening Displacement (CMOD) was measured using a clip-on strain gage applied to the notch mouth; the vertical displacement of the beam mid-section was taken equal to the stroke of the machine hydraulic jack.Piezoelectric resonant AE sensors were applied on the specimen surface in order to capture AE signals [5].The data were acquired by an 8-channel national instruments digitizer, setting the acquisition threshold to 2 mV, and adopting a sampling frequency of 1 Msample/s.The registered signals were amplified by 60 dB before processing.
On the other hand, DIC measurements were performed on two beams, one with d = 300 mm and the other with d = 400 mm, by means of VIC-2D system by Correlated Solutions.Figure 2a shows the set-up of a test with the DIC apparatus, whereas Figure 2b shows a detail around the mid-span section, cracked after final collapse.
In the following, we briefly report on some of the results obtained.More details will be given in future contributions.

Results
In order to define scale-invariant material properties, the fractal nature of the damaged microstructure in quasi-brittle and disordered materials must be considered [12][13][14].It is known that: for tensile (bending) strength, the actual dimension of material ligament at peak stress is Figure 3 shows the renormalized load-deflection curves.The load F is nondimensionalised as: , where u   is the renormalized tensile (bending) strength and d  is the corresponding fractal exponent.The deflection  is nondimensionalised as: . The value of d  is, in this case, equal to 0.36, as will be shown hereafter.  (-) In Figure 4, the bending strength vs. specimen size (beam depth) values, corresponding to all the tests, are reported in a bi-logarithmic diagram.The relevant fractal scaling law reads: Figure 5 shows the fracture energy vs. beam depth diagram.The corresponding fractal scaling law is ln ln ln Figure 6 shows the AE energy per unit area vs. beam depth diagram.The fractal scaling law is ln ln ln   Lastly, the time evolution of strains at several points around the pre-notched section, and in particular along the crack, was obtained from DIC results.An example of data is shown in Figure 8, where principal strain values at five points (P0-P4) are superimposed to the relevant strain contour plot (along principal direction 1), for a test made on a beam with d = 400 mm.In future works, the damage progress monitored by DIC will be correlated with RA (AE signal rise time/the peak amplitude), AF (AE ringdown counts/the duration time), b-value, and other AE parameters.Cumulated AE events F (kN) t (s)

Conclusions
Scale effects on fracture energy, bending strength and AE energy unit area were observed by performing three-point bending tests on plain concrete specimens of four different sizes.The fractal model was applied to define scaling laws and renormalized scale-invariant values for the above-mentioned parameters.Results indicate the absence of correlation between dissipated (fracture) and emitted (AE) energies.The damage process around the pre-notched section was monitored by AE and DIC techniques, thus offering the possibility to correlate the two sets of data.Deeper investigations on the latter point will be the objective of future contributions.

Figure 1 .
Figure 1.Experimental set-up for three-point bending tests on universal testing machines: (a) specimen with d = 100 mm on MTS machine after final failure; (b) testing set-up on Baldwin machine for specimens with d = 200, 300, and 400 mm.

2  2 G
 (lacunar domain); for fracture energy, the actual dimension of fracture surface at failure is   (invasive domain).An interesting result is obtained here for AE energy per unit area, i.e., it is dissipated on a lacunar fractal domain (

Figure 4 .
Figure 4. Bending strength vs. beam depth diagram (R is the Pearson correlation coefficient).

Figure 5 .
Figure 5. Fracture energy vs. beam depth diagram (R is the Pearson correlation coefficient).

Figure 6 .In Figure 7 ,Figure 7 .
Figure 6.AE energy per unit area vs. beam depth diagram (R is the Pearson correlation coefficient).

Figure 8 .
Figure 8. Example of contour plot and strain values along principal direction 1 obtained by DIC.