Non-proportional deformation paths for sheet metal: experiments and models

For mild steel, after significant plastic deformation in one direction, a subsequent deformation in an orthogonal direction shows a typical stress overshoot compared to monotonic deformation. This phenomenon is investigated experimentally and numerically on a DC06 material. Two models that incorporate the observed overshoot are compared. In the Teodosiu-Hu model, pre-strain influences the rate of kinematic hardening by a rather complex set of evolution equations. The shape of the elastic domain is not changed. Another way to describe the observed overshoot is by distortional hardening, like in the model by Levkovitch et al. In this model, a deformation in one direction directly influences the shape of the yield locus, which is apparent even without additional plastic deformation in another direction. Both models can represent the experimental results well, but in the original implementations, the Teodosiu model performs better.\ud \ud KEYWORDS: non-proportional loading, plasticity, material model, distortional hardenin

Consistent plane stress-3D conversion of hardening models and yield criteria

Material models in FE-simulations are used both in 3D and plane stress situations. In this\ud paper it is shown that for models that include kinematic hardening, the conversion from a 3D to a plane\ud stress algorithm needs more adaptations than only eliminating the thickness components. An example\ud and a consistent conversion are presented. Secondly it is discussed how to convert a 2D plane stress\ud yield criterion into a full 3D yield criterion. This is essential for using solid-shell elements with 2D yield\ud criteria, typically used in sheet metal formin

Simulation of hydro-formability testing for tubes

With the development of dedicated tubular products for hydroforming, the need for a representative\ud test for these products evolves. Currently free expansion tests are used, but these tests only follow a more\ud or less plane strain deformation. In reality, hydroforming is used with end feeding and the plane strain deformation\ud is not representative. By performing a number of tests with different positive and negative end feeding a\ud forming limit curve can be constructed, dedicated to tubular hydroforming.\ud In the paper simulations are presented for the tests with different end feeding conditions, using shell elements.\ud The influence of material parameters is investigated. Results of the FEM analysis are comparable with results\ud from a Marciniak–Kuczynksi analysis. Some salient differences can be attributed to the more realistic incorporation\ud of boundary conditions in the FEM analysis. In the tensile/compression region, the M–K analysis requires\ud a free displacement perpendicular to the main principal strain to have a neck developed at a specific angle to the\ud loading direction. In a hydroforming test the lateral displacement of the sheet would result in a rotation along\ud the tube axis, which is prevented by the seals. The constraint displacement results in a higher forming limi

A material model for warm forming of aluminium sheet

A material model has been developed to simulate the warm forming of Al–Mg\ud sheet. Both the hardening behaviour, including temperature and strain rate effects, and the\ud biaxial stress–strain response of the sheet are considered. A physically-based hardening model\ud according to Bergström is used. This model incorporates the influence of the temperature\ud and strain rate on the flow stress and on the hardening rate based on dynamic recovery. For\ud deformations at constant temperature and strain rate, the Bergström model reduces to the well\ud known Voce hardening model. The Bergström/Voce models can be fitted quite well to the results\ud of monotonic tensile tests of an AA 5754-O alloy.\ud The biaxial stress–strain response of the material is experimentally determined by uniaxial,\ud plane strain, simple shear and equi-biaxial stress tests. It is demonstrated that the widely used\ud Hill ’48 yield locus is inappropriate for simulation of deformation of aluminium. The low Rvalues\ud for aluminium lead to a significant underestimation of the equi-biaxial yield stress. In\ud the simulation of the deep drawing of a cylindrical cup this results in a much too thin bottom of\ud the cup. The Vegter yield criterion is sufficiently flexible to accurately represent the shape of the\ud yield locus and the anisotropy.\ud

Formability created by the Bauschinger effect?

This paper describes tests to determine if the Bauschinger effect can act as an\ud additional source of formability, this may possibly explain the enhanced formability observed in incremental sheet forming Small cylindrical products have been made by deep drawing and wall ironing. The upper edges have been necked to various levels of reduction. Tensile test specimens have been cut from the necked upper edges and tested, causing an almost perfect stress/strain reversal. An increase of strain could be observed indeed. The results are discussed using the Considère condition as a guideline

Adaptive smoothed FEM for forming simulations

FEMsimulation of large deformations as occur in metal forming processes is usually accompanied with highly distorted meshes. This leads first to a reduction of accuracy and later to loss of convergence when implicit solvers are used. Remeshing can be used to reduce element distortion, but repeated remeshing will result in smoothing of data like equivalent plastic strain, due to averaging and interpolation. A meshless method circumvents the problem of mesh distortion, but depending on the integration of the weak formulation of equilibrium mapping of data and hence smoothing of data still remains unless a\ud nodal integration scheme is used. Starting with a LocalMaximum Entropy approach [1] with nodal integration, we end-up with a smoothed Finite Element formulation in the limit of local approximations [2]. It is straightforward to adapt the triangulation in every increment, yielding an Adaptive Smoothed Finite\ud Element Method, in which large deformations can be modelled with a Lagrangian description without the necessity to map data from one step to the other.\ud A cell based stabilized conforming nodal integration method (SCNI) [3] is used. Depending on the configuration of nodes, nodal integration can yield singular stiffness matrices, resulting in spurious displacement modes [4]. A stabilization is used, based on minimizing the difference between a ‘linear\ud assumed’ and the consistent strain field. The cells are based on the Delaunay triangulation, connecting mid-sides and centres of gravity of the triangles (Figure 1). Especially at the outer boundary, this yields a simpler formulation than using the dual Voronoi tesselatio

Efficient implicit simulation for incremental forming

Single Point Incremental Forming (SPIF) is a displacement controlled process performed on a CNC machine. A clamped blank is deformed by the movement of a small sized tool that follows a prescribed tool path. An extensive overview of the process has been given in [1]. The tool size plays a crucial role in the SPIF process. The small radius of the forming tool concentrates the strain at the zone of deformation in the sheet under the forming tool. The tool has to travel a lengthy forming path all over the blank to introduce the deformation. Numerically, this requires performing thousands of load increments on a relatively fine FE model resulting in enormous computing time. A typical computing time for implicit simulation of a small academic test is measured in by days. The focus of this paper is to efficiently use the implicit time integration method in order to reduce the required computing time for incremental forming implicit simulation drastically

Nodal integration of meshless methods

Meshless methods offer interesting properties for the simulation of bulk forming\ud processes. This research concerns the investigation of the stabilized conforming nodal integration scheme (SCNI) for use in metal-forming processes. Two tests are carried out. Firstly, the performance of SCNI is compared to a standard integration scheme. The performance seems problem specific. Secondly the footing of a piece of nearly incompressible material is used for testing the locking behavior of the method. No volumetric locking was found

Material characterization at high strain by adapted tensile tests

The strength of materials at high strain levels has\ud been determined using the so-called Continuous-Bendingunder-\ud Tension (CBT) test. This is a modified tensile test\ud where the specimen is subjected to repetitive bending at the\ud same time. This test enables to create high levels of uniform\ud strain. A wide variety of materials has been tested this way.\ud The strength of the material after CBT testing has been\ud measured in different ways: by secondary tensile tests, by\ud interrupted CBT tests, and directly from the fracture in the\ud CBT test. All methods yield similar results: the strength is\ud largely unaffected by the cyclic pre-deformation and mainly\ud depends on the overall increase in length. Only for multiphase\ud materials the strength shows a minor influence of\ud CBT test conditions. The hardening follows the extrapolated\ud hardening observed in a conventional tensile test, except for\ud brass. This test method can potentially be used for measuring\ud hardening curves at high strain levels