A power-based approach to assess the barrelling test's weak solution

© 2019 Physical simulation of forming is an analytical-experimental branch of mechanical science. Carefully formulated models and their solutions are essential to interpret the simulation data meaningfully and to understand its underlying phenomena. Oversimplified models of deformation and their associated non-unique closed-form solutions are widespread due to the complex and path dependence nature of plastic deformation, its multi-layered governing equations and boundary conditions. Therefore, it is vital to critically evaluate these models at the kinematic level to ensure a reliable outcome. Incremental Profile Modelling (IPM) is proposed as a technique to integrate free surface geometrical data into the solution to address the path dependence issue. IPM also allows quantification of the solution's worthiness without making a reference to the mass or acting forces involved. The technique relies on calculating an equivalent area for a given solution. The area is estimated simply based on the deforming body's geometry and is compared with that of a numerical solution as the reference. The comparison provides a quick and quantitative assessment of the closed-form solution. To demonstrate the technique, the “Barrelling Compression Test” (BCT) is chosen here as a key example. Three kinematic models of the test are considered and their closed-form solutions are obtained and evaluated using IPM. Also, two reference solutions of the test are presented including those of a finite element model and the conventional Cylindrical Profile Model (CPM). The equivalent areas for the first two models and that of the finite element were in good agreement. The third model rendered an “equivalent area singularity” at the sample's centre, and was concluded to be unsuitable to study BCT. The conclusion was not evident purely based on the model's kinematic solution.