Issue 50

I. Stavrakas et alii, Frattura ed Integrità Strutturale, 50 (2019) 573-583; DOI: 10.3221/IGF-ESIS.50.48 576 lubrication technique was used by van Vliet & van Mier [28] with excellent results. It is mentioned here that the PTFE sheets provided also electrical insulation, a crucial parameter for the application of the PSC technique. The main experimental protocol and the loading scheme The specimens were subjected to sequential, load-control, loading-unloading-reloading loops, up to stress levels very closely approaching the compressive fracture strength of Dionysos marble. In fact, the stress level attained was equal to about 98% to 99% of the compressive strength, as it was determined during the preliminary tests. After the specific stress level (equal to about 62.7 MPa) was attained for the first time the externally applied compressive force was kept constant for a relatively long time interval equal to about t L =150 s. This step is considered necessary in order for the PSC to return to its initial background level and also for the activity recorded by the AE sensors to be eliminated. After this time interval the mechanical load was removed and the specimen remained unloaded for a time interval equal to about t U =50 s. This pro- cedure was repeated until the fracture of the specimen, which usually occurred during the second or the third loop. A typical loading protocol is shown in Fig.2, in which the axial stress is plotted versus time in juxtaposition to the respective axial strain. The specific specimen collapsed suddenly during the second loading loop in its constant force branch. Figure 2 : The time variation of the applied stress and the corresponding axial strain during the whole experimental procedure. The respective axial stress - axial strain pairs, for the as above experiment, are plotted in Fig.3a. An almost perfectly linear region characterizes the first loading branch up to a stress level exceeding 50 MPa. The elastic modulus calculated from this branch is equal to about E 1 =76.2 GPa, in very good agreement with results of similar previous experimental projects [21, 24]. The non-reversible strain recorded after the load removal, equal to about 2x10 -4 , is, also, in good agreement with the respective results from previously published works with Dionysos marble [29, 30]. As it is expected, during the loading branch of the second loading loop, the linear region of the stress-strain curve extends at higher stress levels (approaching 85% of the maximum compressive stress attained). In addition, the corresponding value of the elastic modulus becomes lower, equal to about E 2 =61.8 GPa, again in good accordance with previously published data by Kourkoulis et al. [30], who have described the damage evolution in Dionysos marble in terms of the decrease of its elastic modulus versus the non-reversible portion of the strain, as recorded after successive loading-unloading-reloading loops. Taking advantage of their data, Fig.3b is plotted. In this figure the modulus of elasticity is plotted against the non-reversible part of the total strain, ε perm . On the same figure, the pair of ε perm and E 2 values obtained from Fig.3a (i.e., ε perm =2x10 -4 and E 2 =61.8 GPa) are indicated (see the red arrowed lines) clearly concluded that the damage level imposed during the first loading branch of the two-loops loading procedure approached very closely the terminal damage level that can be sustained by Dionysos marble. This close approach justifies the sudden collapse of the specific specimen during the second loading loop, even at its constant force branch. Concerning the fracture mode, it is interesting to note that all specimens failed by almost axial splitting rather than along inclined planes, as it is suggested by the classical Mohr-Coulomb theory. In other words, in the specific series of tests the familiar Mohr’s cones were almost totally suppressed. Although such behaviour is not common in standardized laboratory tests, it can be attributed to the excellent lubrication conditions achieved. The specific behaviour was long ago observed ex- perimentally by Vardoulakis et al. [31] (Fig.3c). To explain this observation the so-called “post-peak stress diffusion” theory was introduced, that is capable of describing fracture of brittle materials by axial splitting rather than along inclined (with respect to the load axis) planes [31]. The theory is based on an alternative normalization approach: Instead of normalizing the axial stress over the area of the specimen’s cross-section (which according to Van Vliet and van Mier [32] is inadequate for Compressive Stress (MPa) Axial Strain 0.0000 0.0005 0.0010 0.0015 0.0020 0 25 50 75 75 50 25 0 Axial stress [MPa] 0.20 0.15 0.10 0.05 0.00 0 100 200 300 400 500 t [s] Axial strain [mstrain] Stress Strain