Design and application of experimental methods for steel sheet shearing

Shearing is the process where sheet metal is mechanically cut between two tools. Various shearing technologies are commonly used in the sheet metal industry, for example, in cut to length lines, slitting lines, end cropping etc. Shearing has speed and cost advantages over competing cutting methods like laser and plasma cutting, but involves large forces on the equipment and large strains in the sheet material. The constant development of sheet metals toward higher strength and formability leads to increased forces on the shearing equipment and tools. Shearing of new sheet materials imply new suitable shearing parameters. Investigations of the shearing parameters through live tests in the production are expensive and separate experiments are time consuming and requires specialized equipment. Studies involving a large number of parameters and coupled effects are therefore preferably performed by finite element based simulations. Accurate experimental data is still a prerequisite to validate such simulations. There is, however, a shortage of accurate experimental data to validate such simulations. In industrial shearing processes, measured forces are always larger than the actual forces acting on the sheet, due to friction losses. Shearing also generates a force that attempts to separate the two tools with changed shearing conditions through increased clearance between the tools as result. Tool clearance is also the most common shearing parameter to adjust, depending on material grade and sheet thickness, to moderate the required force and to control the final sheared edge geometry. In this work, an experimental procedure that provides a stable tool clearance together with accurate measurements of tool forces and tool displacements, was designed, built and evaluated. Important shearing parameters and demands on the experimental set-up were identified in a sensitivity analysis performed with finite element simulations under the assumption of plane strain. With respect to large tool clearance stability and accurate force measurements, a symmetric experiment with two simultaneous shears and internal balancing of forces attempting to separate the tools was constructed. Steel sheets of different strength levels were sheared using the above mentioned experimental set-up, with various tool clearances, sheet clamping and rake angles. Results showed that tool penetration before fracture decreased with increased material strength. When one side of the sheet was left unclamped and free to move, the required shearing force decreased but instead the force attempting to separate the two tools increased. Further, the maximum shearing force decreased and the rollover increased with increased tool clearance. Digital image correlation was applied to measure strains on the sheet surface. The obtained strain fields, together with a material model, were used to compute the stress state in the sheet. A comparison, up to crack initiation, of these experimental results with corresponding results from finite element simulations in three dimensions and at a plane strain approximation showed that effective strains on the surface are representative also for the bulk material. A simple model was successfully applied to calculate the tool forces in shearing with angled tools from forces measured with parallel tools. These results suggest that, with respect to tool forces, a plane strain approximation is valid also at angled tools, at least for small rake angles. In general terms, this study provide a stable symmetric experimental set-up with internal balancing of lateral forces, for accurate measurements of tool forces, tool displacements, and sheet deformations, to study the effects of important shearing parameters. The results give further insight to the strain and stress conditions at crack initiation during shearing, and can also be used to validate models of the shearing process.

Experimental study of strain fields during shearing of medium and high-strength steel sheet

There is a shortage of experimentally determined strains during sheet metal shearing. These kinds of data are a requisite to validate shearing models and to simulate the shearing process. In this work, strain fields were continuously measured during shearing of a medium and a high strength steel sheet, using digital image correlation. Preliminary studies based on finite element simulations, suggested that the effective surface strains are a good approximation of the bulk strains below the surface. The experiments were performed in a symmetric set-up with large stiffness and stable tool clearances, using various combinations of tool clearance and clamping configuration. Due to large deformations, strains were measured from images captured in a series of steps from shearing start to final fracture. Both the Cauchy and Hencky strain measures were considered, but the difference between these were found negligible with the number of increments used (about 20 to 50). Force-displacement curves were also determined for the various experimental conditions. The measured strain fields displayed a thin band of large strain between the tool edges. Shearing with two clamps resulted in a symmetric strain band whereas there was an extended area with large strains around the tool at the unclamped side when shearing with one clamp. Furthermore, one or two cracks were visible on most of the samples close to the tool edges well before final fracture. The fracture strain was larger for the medium strength material compared with the high-strength material and increased with increasing clearance.

Phase-field analysis of finite-strain plates and shells including element subdivision

With the theme of fracture of finite-strain plates and shells based on a phase-field model of crack regularization, we introduce a new staggered algorithm for elastic and elasto-plastic materials. To account for correct fracture behavior in bending, two independent phase-fields are used, corresponding to the lower and upper faces of the shell. This is shown to provide a realistic behavior in bending-dominated problems, here illustrated in classical beam and plate problems. Finite strain behavior for both elastic and elasto-plastic constitutive laws is made compatible with the phase-field model by use of a consistent updated-Lagrangian algorithm. To guarantee sufficient resolution in the definition of the crack paths, a local remeshing algorithm based on the phase- field values at the lower and upper shell faces is introduced. In this local remeshing algorithm, two stages are used: edge-based element subdivision and node repositioning. Five representative numerical examples are shown, consisting of a bi-clamped beam, two versions of a square plate, the Keesecker pressurized cylinder problem, the Hexcan problem and the Muscat-Fenech and Atkins plate. All problems were successfully solved and the proposed solution was found to be robust and efficient.

Acoustic Propagation over Periodic and Quasi-Period Rough Surfaces Proceedings

Numerical techniques such as the Boundary Element Method, Finite Element Method and Finite Difference Time Domain have been used widely to investigate plane and curved wave-front scattering by rough surfaces. For certain shapes of roughness elements (cylinders, semi-cylinders and ellipsoids) there are semi-analytical alternatives. Here, we present a theory for multiple scattering by cylinders on a hard surface to investigate effects due to different roughness shape, the effects of vacancies and variation of roughness element size on the excess attenuation due to a periodically rough surfaces.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.