A theoretical study of steady-state wedge cutting through metal plates

Abstract

The process of steady-state wedge cutting through steel plates is investigated by analyzing experimental data and developing a simple and realistic model of the problem. Kinematics of the cutting process is discussed and three characteristic deformation zones are identified: (i) plastic zone at wedge tip, (ii) transient bent flap, and (iii) transition zone. Deformation energies are calculated for each zone, and the upper bound theorem in plasticity is applied to derive a closed-form solution for the cutting force. Frictional effects were considered including machining friction near the wedge tip and sliding friction between the transient flap and the wedge surface. Prediction of the steady-state cutting model is compared with experiments conducted at Cambridge University, MIT, and Det norske Veritas. Good correlation with the test data is reported. A parametric study is performed and on that basis a simple approximate solution is developed. An interesting association was discovered with previous empirical formulas proposed by Minorsky, Vaughan, and Kuroiwa.

Extension of the super-elements method to the analysis of oblique collision between two ships

“…Some references are also available to evaluate the resistance of metal plates after rupture, when they are submitted to tearing and cutting. For example, these phenomena have been studied by Wang [10], Zhang [11], Wierzbicki [12] and Zheng [13].…”

Axial cutting of AA6061-T6 circular extrusions under impact using single- and dual-cutter configurations

“…Another important characteristic of an ideal energy absorber is that it activates at a pre-defined load under both dynamic and quasi-static loading conditions. The cutting process in reference [13] was identified as a clean cut due to the observed load/displacement response and similar energy dissipating mechanisms as reported in references [11,12] except for the far-field petalled sidewall outward bending. Fair agreements on the predictions of the steady-state cutting force using the analytical models developed in references [11,12] were presented.…”

“…The cutting process in reference [13] was identified as a clean cut due to the observed load/displacement response and similar energy dissipating mechanisms as reported in references [11,12] except for the far-field petalled sidewall outward bending. Fair agreements on the predictions of the steady-state cutting force using the analytical models developed in references [11,12] were presented. Majumder et al [14] experimentally investigated the cutting deformation behaviour of circular AA6061-T6 and -T4 extrusions with two different extrusion wall thicknesses (t) of 3.175 mm and 1.587 mm using cutters from reference [13] under quasi-static loading conditions.…”

“…The analysis of the cutting deformation involves two stages: the initial wedge penetration (transient) stage and the steady-state cutting stage. Analytical models were developed by Simonsen and Wierzbicki [11], and Zheng and Wierzbicki [12] to predict the cutting resistance force considering the contribution of a finite shoulder width (2 $ B) of the wedge for the steady-state cutting process under a stable cut. Three major energy dissipation mechanisms [11,12] were considered in the development of the analytical models, namely, crack tip zone in front of the wedge (ductile fracture and moving hinge line), membrane deformation, and friction.…”

“…Depending on the deformation behaviour, three categories of the cutting process were identified in references [11,12], namely a stable (or clean) cut, braided cut, and concertina tearing. The mechanics of the cutting process are complicated because they involve plastic flow, fracture of the plate in the vicinity of the wedge tip, membrane deformation of the plate, and friction between the wedge and plate.…”