Advancing mechanics of Barrelling Compression Test

Abstract

Compression Test (CT) plays a fundamental role in our understanding of materials science and engineering. This is due to the test's capacity to physically simulate different deformation scenarios. Mechanics of CT is critical to model stored energy, microstructure and behaviours in a deforming material. To simulate “shear and heterogeneous” deformation, friction, constitutive behaviour, etc., new closed form solutions of CT are needed. Developing detailed solutions for the test is a fundamental priority to represent the deformation more reliably.Expressions for effective strain and the test sample's free surface were derived here to extend “Avitzur's solution” beyond a limit analysis. The extended Avitzur (EA) solution was employed in a “constant friction factor mode” to make it more comparable with other reference solutions such as the Cylindrical Profile Model (CPM) and the Finite Element (FE). Example EA and CPM solutions were obtained and compared to those of a FE model. Partial enforcement of incompressibility and a rough estimation of barrelling parameter in Avitzur solution were found to be responsible for unrealistic prediction of the sample's profile and friction factor. EA's effective strain and strain rate along the sample's centre line, particularly at its centre, agreed well with the FE predictions. Therefore, the sample centre was suggested as the representative point at which the deformation path can be traced for the constitutive modelling using EA solution.