Identification of strength and toughness of quasi-brittle materials from spall tests: a Sigma-point Kalman filter approach

Under impacts, monolithic quasi-brittle specimens fail by cracking if the magnitude of the induced stress waves exceeds their tensile strength. In spall tests, depending on the velocity of the striker hitting the specimen, either a partial damage or a whole crack formation can be induced. Since cracking occurs almost instantaneously in this dynamic process, experimental data need to be accurately and reliably filtered to identify the material strength and toughness ruling a cohesive law that describes the damaging/cracking event. To this aim, a Sigma-point Kalman filter approach is here discussed. The performance of the proposed methodology, in terms of constitutive parameter estimation and tracked specimen state, especially crack opening, is first quantitatively assessed through pseudo-experimental testing. It is shown that, if the stress pulse leads to a complete failure of the specimen and if the out-of-plane velocity is measured at the back surface of the impacted specimen, a noteworthy accurate and (almost) initialization-independent calibration of the cohesive model is obtained. Next, some results are provided by processing real experimental data relevant to two ceramic materials: SiC and BC.