13th International Conference on Fracture June 16–21, 2013, Beijing, China 4 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Stress (MPa) Strain Mortar matrix ITZ 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0 5 10 15 20 25 30 35 40 45 50 Stress (MPa) Strain Mortar matrix ITZ (a) Uniaxial tension (b) Uniaxial compression Figure 4. Uniaxial stress-strain relation of ITZs and mortar matrix 3.3. Natural aggregate Granite cylinders are used as natural aggregate in the MRAC. Based on the experiment results [5], there were not cracks or damage observed in the natural aggregates during loading. In the current study, natural aggregate is modeled as linear-isotropic material. It behaves linearly throughout the analysis. For the numerical calibration validation, the materials parameters of each phase in MRAC, which were determined according to the experimental data, are listed in Table 1. However, the Poisson’s ratios of new ITZ and old ITZ were defined as 0.20 [18]. Table 1. Material properties of each phase in MRAC MRAC Thickness (m) Elastic modulus (GPa) Poisson's ratio () Strength (MPa) Compressive (fc) Tensile (ft) Natural aggregate Old mortar (OM) New mortar (NM) Old ITZ (OI) New ITZ (NI) — — — 50.0 60.0 80.0 25.0 23.0 20.0 18.0 0.16 0.22 0.22 0.20 0.20 — 45.0 41.4 36.0 33.1 — 3.00 2.76 2.40 2.21 4. FEM simulation and test verification 4.1. FEM model The software program (ABAQUS 6.11) was used for the FEM analyses. 4-node plane stress quadrilateral (CPS4R) elements were used to mesh the MRAC. The 2D micro-scale FEM model of MRAC is shown in Figure 5. The model was subjected to a uniformly distributed displacement at the top edge, as the displacement-controlled loading scheme was used. The Y degrees of freedom were fixed at the bottom edge, while the X degrees of freedom and rotation were not constrained. The FEM model has a total of 34240 elements in this simulation.
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