13th International Conference on Fracture June 16–21, 2013, Beijing, China 5 (a) Overall FEM model (b) Details of each phase Figure 5. 2D micro-scale FEM model of MRAC 4.2. Modeling implementation In this paper, ABAQUS/explicit quasi-static analyses were applied for the numerical simulation [19, 20, 21]. The ABAQUS/explicit quasi-static solver used an analysis time of 0.1 second (period time). A displacement-controlled loading scheme was adopted in this simulation. In order to obtain complete stress-strain curves, after trial and comparison, all the analyses for uniaxial tension and compression were ended at a displacement d=0.09 mm (ultimate strain 0.0006) and 0.9 mm (ultimate strain 0.006), respectively. The FEM numerical response depends on two sets of parameters. The first set is relevant to the tensile and compressive stress data which are provided as a tabular function of strain, which is directly obtained from the constitutive relation of each phase in MRAC. These mechanical properties are provided by experimental study and mix design. The other one is the definition of the damage variable as a tabular function of the inelastic strain for both the tensile and compression. If the damage variable is specified, ABAQUS automatically calculates the inelastic and plastic strain values. Generally, the maximum tensile stress (S11) tends to concentrate mainly in the ITZs in Figure 6. These stress concentrations could lead to the development of microcracks along these regions, which in turn could lead to the failure of the MRAC. As the properties of the ITZs are weaker than those of other phases in the MRAC, the stress concentrations mainly occur in these regions and may lead to or promote the failure. Experimental results also proved that bond cracks firstly appeared around the weak ITZs, and then propagated into the mortar by connecting with each other [5, 14]. 0 15 30 45 60 75 90 105 120 135 150 -2 -1 0 1 2 3 4 5 Stress S11 (MPa) Horizontal Distance (mm) (a) Cross section in MRAC (b) Tensile stress S11 distribution Figure 6. Stress distribution for section A-A 4.3. Simulation results A Section A-A A
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