Numerical modelling of SHPB splitting tests

Abstract
The Splitting or Brazi1ian test of disks is a useful method to measure tensile strength on brittle materials. When the tensile stress reaches the tensile strength, the disk fails on the loading plane. Nevertheless, the stress state is not uniaxial and the material undergoes compressive stresses, normal to the tensile ones. On materials with a high compressive/tensile strength ratio as ceramics or concrete, the failure of the material is produced by the tensile stress, whereas no damage is caused by compressive stresses. This is the reason why splitting tests of disks have been proved to be an excellent solution to measure tensile strength on brittle materials like ceramics or concrete. This technique bas been used for years to test brittle materials on static conditions, and more recently, it has been brought into use on dynamic tests, as Hopkinson bar experiments. The results obtained on these experiments have been useful and fully accepted by the materials researchers. The loading process has been modelled by different authors and tests results have been justified when loading conditions remain static or in a low strain rate. In this paper, a numerical modelling of the splitting test is extended to high strain rates in 3D. Numerical results are compared with actual tests carried out in a Hopkinson bar published in previous papers. Results show that the specimen is under equilibrium only if the initial slope of the incident pulse is not very abrupt. A 3D effect has been noticed showing that tensile stress levels are higher on the specimen surfaces than inside the material, and it bas a direct influence on the tensile strength measured by means of the maximum load achieved and has to be taken into account. Finally, the crack patterns of the failure on the specimen are compared with actual tests showing a good agreement.