PSI - Issue 28

Stylianos Anastopoulos et al. / Procedia Structural Integrity 28 (2020) 2132–2141 S. Anastopoulos et al. / Structural Integrity Procedia 00 (2019) 000–000

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This paper focuses on the specimens with short multi walled carbon nano tubes (MWCNTS). These were acquired from Cheap Tubes and had purity higher than 95 % and a specific surface 110 m 2 /g. With a length of 10 to 30 μm and a diameter of 20 to 40 nm, the aspect ratio was of 700. In all experiments the crack mouth opening displacement was measured. The test results were plotted into graphs such as that of Fig. 11.

Fig. 11 Plot of experimental results for the short fibers – 6‰ combination.

The unreinforced matrix was found to be of an E = 4000 MPa. Characteristic values for the CNTs were gathered from the work of Min-Feng Yu, Rodney S. Ruoff, et al. (2000), with E CNT taking the values of 274, 335 and 470 GPa and a Poisson’s ratio of the order of 0.10 to 0.35. Thus for a cement paste modulus of elasticity of 4000MPa, for volume fractions used in the experimental data of 6‰ and 20‰ for both short fibers of the aforementioned characteristics, the process began with selecting the lowest E and highest ν for the CNTs. Then followed calculation of the Homogenized Material Stiffness Matrix for combinations of multistep Mori Tanaka homogenization + random orientation tensor and finite element + fixed angles. Next stage was the modelling of the pre-cracked specimens using the aforementioned Homogenized Matrix and Simulation of the experiment (FE) and then the measurement of the Crack Mouth Opening Displacement (CMOD) in the CAE models. The latter was compared with CMOD values of the experimental results, and if so required the procedure was repeated starting with higher E and lower ν . 4. Results Results for the multi-step homogenization / random orientation tensor method (Fig. 12) showed that the CMOD of our simulations came closer to the experimental results as the E CNT was raised for each Poisson’s ratio, ending at 470 GPa and a v of 0.17. Lower Poisson’s ratio values up to 0.1 allowed by literature was possible but gains were minimal beyond that value, meaning the rate at which the simulation CMOD/Load curve came closer to the experimental one was low. Same pattern was observed with the results of the fixed angles – RVE combination. (Fig. 13). When both combinations were compared the multi-step / random orientation tensor combination was the one closer to the experimental results (Fig. 14).

Fig. 3 Plot of the load against CMOD values for the multistep method using random orientation tensor versus experimental results