본 연구에서는 3차원 변형형상을 갖는 소재에서 상하금형면의 마찰이 다른 경우에, 작각주 소재와 비직각주 소재(non-prismatic block)에 대해서 적용할 수 있는 동적 가용 속도장(kinematically admissible velocity field)을 유도해 내고자 한다.이론계산에 있어서 가공경화를 고려하기 위해 소성변형 영역을 유한개의 요소들로 나누고 이들 각 요소에 대해서 유효변형도, 유효응력을 계산하여 에너지 소비율을 계산하였다.
Upsetting of non-circular blocks is characterized by the three-dimensional deformation with lateral sidewise spread as well as axial bulging along thickness. A kinematically admissible velocity field for the upsetting of prismatic or non-prismatic blocks is proposed which considers the different frictional conditions at the top and bottom surfaces of a billet. From the proposed velocity field the upper-bound load and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out with annealed SM 15C steel billets at room temperature for different billet shapes and frictional conditions. The theoretical predictions both in the forging load and the deformed configurations are shown to be in good agreement with the experimental observations. Therefore, the velocity field proposed in this work can be used for the prediction of forging load and deformation in upsetting of prismatic or non-prismatic blocks, considering the different frictional conditions at two flat dies.
