On the numerical evaluation of the anvil force for accurate dynamic stress intensity factor determination

To evaluate precisely the dynamic fracture toughness of a brittle material in the tests with short time-to-fracture, both tup and anvil forces have to be known. Unfortunately, the anvil force is rarely registered by the standard impact testing equipment. The method for numerical evaluation of the support reactions by using registered tup force and the calculated specimen modal parameters is proposed. It assumes that the contact between the specimen and the supports can be described by the quasi-static Hertz’s theory. Both linearized and nonlinear relations for the specimen–support contact compliance are considered. The efficiency of the method has been verified by processing the results of two three-point-bend impact tests reported by Böhme and Kalthoff. The influence of the various calculation parameters (number of eigenmodes taken into account, time step size) and the specimen geometry (length of the specimen overhangs) on the accuracy of determination of the anvil force and dynamic stress intensity factor variation with time is investigated.