Issue34

A. Satoh et alii, Frattura ed Integrità Strutturale, 34 (2015) 397-405; DOI: 10.3221/IGF-ESIS.34.44 400 (a) Model R and M (b) Model S-N (c) Model S-A (d) Model W-N (e) Model W-A Figure 4 : FEM models with a dimension of 5.6 x 6.4 mm which consists of triangle elements sized 0.2 mm (bottom) and 0.1 mm (height). At the top and bottom they have notches of 0.4 mm depth. The aggregate is sized in 0.4 x 0.4 mm. A NALYSIS OF MODEL R AND M he authors analyzed Model R and M. Tab. 4 and Fig. 5 exhibit the material properties of the elements, which were obtained from the reference [8]. Aggregate in Tab. 4 has three different material properties from void to iron. The authors assumed that void is made with resin bead, then the material property for it is rather large not zero. Tab. 5 shows the features of the models, where one can see each model has a different modulus from 10 GPa to 70.4 GPa. The analyzed stress-deformation response is depicted in Fig. 6. Reflecting the brittle nature of the mortar matrix, the response for Model M is brittle compared to the response for Model R. The important point is that strength for Model M is dependent to the Young’s modulus in the case of Model M (Fig. 6(a)). But in the case of ductile matrix (Model R), Model R-I and R-S have almost the same strength. Though tensile strength of mortar is 7.21 MPa, the response even for M-I is far below it (5.32 MPa). In the case of Model R, the response for R-I and R-S is almost the same for the tensile strength of matrix. These facts derives from the ductility of the matrix. It means that the brittle matrix fractures when small part of the ligament reaches its tensile strength, whereas the ductile one fractures when almost all part of the ligament reaches its tensile strength with the help of ductility. Then the high modulus aggregates are effective in the case of brittle matrix, and not effective for the ductile matrix. It is worthy to note that 28.6% of void decreases the strength about 50% ( 42% for M-V and 53% for R-V). The reason for it derives from the fact that length of the matrix part is 2.4 mm in the total length of crack path (4.8 mm). Young's modulus Poisson ratio Name (GPa) ( - ) Matrix: Mortar 14.0 0.2 Repair material 18.7 0.2 Aggregate: Iron 200.0 0.3 Sand 39.0 0.2 Void 0.08 0.35 Table 4 : Material properties of the elements. Figure 5 : Tension softening diagram of mortar and repair. Model Matrix Aggregate Volume fraction (%) Averaged Young's modulus Matrix Aggregate Notch (GPa) M-I Mortar Iron 71.0 28.6 0.4 67.1 M-S Sand 21.1 M-V Void 10.0 M None 14.0 R-I Repair material Iron 70.4 R-S Sand 24.4 R-V Void 13.3 R None 18.7 Table 5 : Features of the monolithic models for FEM analysis. T 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0 0.01 0.02 0.03 0.04 0.05 σt (MPa) ε Repair material Mortar