THE MODELING OF ELASTIC RESPONSE OF A 3-POINT BEND SPECIMEN UNDER IMPACT LOADING

The beam model of a 3PB specimen (3PBS) is proposed, according to whic h, the specimen has only two degrees of freedom, namely, a translation motion as a rigid unit, and an elastic rotation of the specimen's hal ves around its center, where the rotation compliance is found from sta tic considerations. The contact zones of 3PBS with the hammer and with anvils are presented as linear springs.The results are obtained for t wo cases (1) when the forces on the hammer and on the anvil vs time ar e known from an instrumented test; and (2) when they are unknown. (1) A simple formula for SIF calculation similar in appearance to Kishimot o's expression has been obtained. The differences between them are as follows: the suggested formula employs the combination of the hammer a nd anvil forces instead of only the former, the natural frequencies ar e different. The reason for this is a nonrealistic boundary condition employed in Kishimoto's analysis (a rigid hinge for the points of 3PBS which are in contact with the anvils). (2) A full analytical descript ion of the forces considered and the SIF vs time is obtained for both one-point and three-point bending. It is shown that, at early stages o f loading, the direction of motion of the specimen's points, at a dist ance from the specimen center of more then 2/3 of its half-length, is opposite to that of the hammer motion. That is why, in standard three- point impact testing a one-point impact takes place at the early stage s of loading. The comparison of experimental and analytical results re vealed a good predictive capability of the suggested model. (C) 1998 E lsevier Science Ltd. All rights reserved.