Research on nail-sheet joining by multi-plate extrusion via the three-quadrant method

•A new plastic joining process is proposed in nail-sheet joining.•Nail forming, nail cutting and joining are completed in one press stroke.•The method of fracture control in simulation is precisely applied.•An irrelevant term is added to build functions of the three-quadrant method.

In this paper, in-plane nail-sheet joints were created by multi-plate extrusion, a plastic joining method that is an alternative to traditional mechanical joining methods. Nail forming, nail cutting, nail-sheet joining and optional assembling are combined in a single press stroke in multi-plate extrusion, which can be divided into three processing periods that includes two separations. Practical experiments were performed in which compressive forces were dynamically measured at different extrusion depths. An axisymmetric model was created to simulate the process, and its results were compared with the experimental results, where both separation actions were presented. The three-quadrant method was used to estimate the exceeded length of the nail, in which an irrelevant term was required to be added to make up a four-term system which is able to create correspondence to a coordinate system with four quadrants.