On the accurate determination of contact compliance for impact test modelling

To model the specimen interaction with supports during an impact test, simple formulas for indentation–contact force relation between a beam specimen and a rigid cylindrical indenter have been derived using a mixed analytical/numerical approach. Two types of boundary conditions for the specimen (i) support by a frictionless rigid foundation and (ii) conventional threepoint bending have been considered. The first scheme of loading (the compression indentation test, CIT) is sometimes used for quasi-static estimation of the specimen–striker or specimen–support contact compliance instead of the second scheme, which more closely corresponds to the real loading conditions of the specimen during an impact test. It has been found that the indentation (and, therefore, the contact compliance) of the specimen loaded according to the first scheme is up to 19% higher than for the second one. A simple correction of the results of CIT, which allows to estimate the contact compliance accurately has been proposed. Approximate formulas for the linearized contact compliance have been derived for both schemes of loading using three different methods of linearization. The best result has been obtained by the method of the equality of work done by nonlinear and linearized contact forces. An example of modelling of the three-point-bending test using the computed contact stiffness of the anvil is presented.