Tensile behavior of concrete under high loading rates

• Tensile behavior of concrete under high loading rates is numerically investigated.
• 3D FE code for multi body dynamics with fragmentation capability is used.
• True strength due to material behavior and apparent strength due to inertia.
• Results of any indirect tension test such as SHB test, needs careful interpretation.
• Only true material strength should be accounted by the constitutive law.

The experimental and theoretical studies show that the influence of loading rate on tensile behavior of concrete is relatively strong. Dynamic tensile resistance of concrete is difficult to measure by direct tensile test. Therefore, the indirect tensile tests such as split Hopkinson bar tests are used. The evaluation of experimental measurements shows that after reaching a certain critical strain rate, tensile resistance progressively increases with increasing strain rate. In this paper, the authors attempt to investigate and discuss: (i) the reason for progressive increase of tensile resistance beyond a certain strain rate and (ii) whether the dynamic resistance can be attributed only to material strength or whether some other factors also contribute towards the same. To answer these questions, numerical analysis on two different types of examples is carried out: (i) Simple elastic-cohesive finite element (FE) model subjected to direct tension and (ii) FE model of indirect tension test on modified split Hopkinson bar. The results are evaluated in terms of apparent and true strength and compared with experimental results. It is found that under static loads, the true and apparent strengths are always equal, while under dynamic loads they are different. The true strength is controlled by the rate dependent constitutive law and the apparent strength is significantly influenced by the size of the fracture process zone and the size of the specimen. Evaluation of numerical results shows that concrete fracture energy is approximately a linear function of strain rate (semi-log scale) and is controlled by the rate dependent constitutive law. It is concluded that the results of any indirect tension test such as split Hopkinson bar test need careful interpretation, i.e. due to the fact that concrete specimen is damaged, and not elastic, the results of measurement need to be corrected.