PSI - Issue 13

Lucie Malíková et al. / Procedia Structural Integrity 13 (2018) 1798–1803 Lucie Malíková & Jan Klusák / Structural Integrity Procedia 00 (2018) 000 – 000

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modulus of the MTX (cement paste) were defined as E MTX = 30 GPa based on the fracture tests performed, see Šimonová et al. (2017) and Young’s modulus of the AGG (quartz sand) E AGG = 60 GPa was taken from Acker (2001). Poisson’s ratio of all the materials applied in the numerical model was assumed  =  MTX =  AGG =  ITZ = 0.21, see Sorelli et al. (2008).

Fig. 1. Schema of the half model of the three-point bending test with a crack of the length a terminating at the MTX/ITZ interface.

The rest of the parameters of the numerical model were considered as variables and their influence on the value of the critical load was investigated: • the thickness of the ITZ layer, t ITZ , opted between 10, 50 and 100  m; • the radius of the AGG, r AGG , opted between 2, 4 and 6 mm; • the Young’s modulus of the ITZ, E ITZ , opted between 10, 15, 20, 30, 40, 50 and 60 GPa.

4. Results and their discussions

In the first step of the analysis, the values of the stress singularity exponents had to be determined for each case of the elastic mismatch between MTX and ITZ, the values can be found in Tab. 1.

Table 1. Values of the various Young’s modulus of ITZ and corresponding stress singularity exponents and g R functions. E ITZ [GPa] 10 15 20 30 40 50 60 E MTX / E ITZ [-] 3.00 2.00 1.50 1.00 0.75 0.60 0.50 p [-] 0.621075 0.576102 0.544371 0.500000 0.468901 0.445174 0.426187 g R [-] 0.729949 0.618544 0.558434 0.500000 0.475099 0.463608 0.458376

Then, the finite element analyses were performed for all the geometric configurations suggested (considering various ITZ thickness, AGG radius and ITZ Young’s modulus) to estimate the generalized stress intensity factor from the stress field ahead of the crack tip. The data of the stress distribution in the ITZ layer except for the data very close to the MTX/ITZ and ITZ/AGG interfaces were considered for application of the direct method to limit the results to a linear part for their extrapolation. Subsequently, the two selected fracture criteria were applied to determine the critical values of the generalized stress intensity factor. For their application, the critical distance d had to be chosen. The thickness of the ITZ layer seems to be a reasonable parameter ( d = t ITZ ). Results of the critical load calculated from Eq. 4 can be seen in Fig. 2 for the mean tangential stress value criterion and in Fig. 3 for the generalized strain energy density factor criterion. From the results presented in Fig. 2 and 3 the following conclusions can be stated for the fracture behavior of a crack terminating at a MTX/ITZ interface in a cement-based composite: • critical values of the applied force are higher for all the studied cases in comparison to the case of the purely homogeneous cement paste MTX, when the F crit ≐ 538 N; it means that the stiff aggregate enhance the fracture resistance of the system; • generalized strain energy factor fracture criterion gives generally slightly higher values of the critical load than the mean tangential stress value criterion;