Kjell Mattiasson

Implicit and dynamic explicit solutions of blade forging using the finite element method

Abstract Blade forging has been studied and solved by two elastic-plastic finite element codes, NIKE2D and DYNA2D, as a two-dimensional plane-strain problem. The main difference between the two codes is that the first one is implicit while the second is dynamic explicit. The efficiency of implicit and explicit solutions regarding blade forging has been studied. The initial position of the circular preform was optimized so that the corner spaces of the dies become filled and the pressure on the dies become as small as possible thus satisfying the design condition of flashless forging. The grading of the finite element mesh for the perform has been studied and been found to be of great importance.

Three-dimensional simulation of hemming with the explicit FE-method

Abstract This paper is dedicated to three-dimensional simulation of hemming of an automotive hood. The results from the simulations are compared with measurements on hoods manufactured in the production line, both with and without adhesives, in order to check the validity of the FE-model. Both the ordinary serial version as well as the massively parallel processing (MPP)-version of the code LS-DYNA have been applied in the simulations, in order to verify that the two versions are giving the same results, and thereby ensuring that the MPP-version can be used for this type of simulations. Four different types of under-integrated shell elements, three of them based on the Mindlin shell theory and one based on a degenerated solid element, have been used in order to determine which of them is showing the best agreement with test results. Furthermore, results from a transversely anisotropic material model are compared to results from a model with full anisotropy in order to study if anisotropy is a crucial issue in these simulations. One simulation was performed of the case with adhesives between the parts. The effects on the roll-in of the adhesives were in this simulation modelled as a smaller friction coefficient in the contacts between the two parts. Finally, the effect on roll-in from the preceding stamping is studied in an FE-model with pre-strained outer and inner parts.

Solution of quasi‐static, force‐driven problems by means of a dynamic‐explicit approach and an adaptive loading procedure

Argues that the dynamic‐explicit approach has in recent years been successfully applied to the solution of various quasi‐static, elastic‐plastic problems, especially in the metal forming area. A condition for the success has, however, been that the problems have been displacement‐driven. The solution of similar force‐driven problems, using this approach, has been shown to be much more complicated and computationally time consuming because of the difficulties in controlling the unphysical dynamic forces. Describes a project aiming to develop a methodology by which a force‐driven problem can be analysed with similar computational effort as a corresponding displacement‐driven one. To this end an adaptive loading procedure has been developed, in which the loading rate is controlled by a prescribed velocity norm. Presents several examples in order to exhibit the merits of the proposed procedure.

A Phenomenological Model for the Hysteresis Behavior of Metal Sheets Subjected to Unloading/Reloading Cycles

The springback phenomenon is defined as elastic recovery of the stresses produced during the forming of a material. An accurate prediction of the springback puts high demands on the material modeling during the forming simulation, as well as during the unloading simulation. In classic plasticity theory, the unloading of a material after plastic deformation is assumed to be linearly elastic with the stiffness equal to Youngs modulus. However, several experimental investigations have revealed that this is an incorrect assumption. The unloading and reloading stress-strain curves are in fact not even linear, but slightly curved, and the secant modulus of this nonlinear curve deviates from the initial Youngs modulus. More precisely, the secant modulus is degraded with increased plastic straining of the material. The main purpose of the present work has been to formulate a constitutive model that can accurately predict the unloading of a material. The new model is based on the classic elastic-plastic framework, and works together with any yield criterion and hardening evolution law. To determine the parameters of the new model, two different tests have been performed: unloading/reloading tests of uniaxially stretched specimens, and vibrometric tests of prestrained sheet strips. The performance of the model has been evaluated in simulations of the springback of simple U-bends and a drawbead example. Four different steel grades have been studied in the present investigation.

An efficient inverse approach for material hardening parameter identification from a three-point bending test

The cyclic three-point bending test has been frequently used for the determination of material hardening parameters. The advantage of this test is that it is simple to perform, and standard test equipment can be used. The disadvantage is that the material parameter identification requires some kind of inverse approach. The current authors have previously, successfully been utilizing a method, in which computed force–displacement relations have been fitted to corresponding experimental results. The test has been simulated by means of the Finite Element code LS-DYNA, and the material parameters have been determined by finding a best fit to the experimental results by means of the optimization tool LS-OPT, based on a response surface methodology. A problem is, however, that such simulations can be quite time consuming, since the Finite Element model has to be analyzed numerous times. In the current paper, an alternative numerical methodology will be described, in which instead calculated moment–curvature relations are fitted to experimental ones. This optimization procedure does not involve any solution of the FE problem. The Finite Element problem needs only to be solved a limited number of times in an outer iteration loop. This fact results in a considerable reduced computational cost. It is also demonstrated that the parameters determined by this new method correspond excellently to the ones determined by the conventional method.

Oriented damage in ductile sheets: Constitutive modeling and numerical integration

Thermodynamics with internal variables provides a framework for constitutive modeling of elasto-plastic deformations. Within the scope of the theory, constitutive and evolution equations for ductile, elasto-plastic materials with mixed (isotropic and kinematic) hardening and anisotropic damage have been developed. Postulates within continuum damage mechanics were used in order to incorporate damage as an internal variable. Owing to this, and to a simplified definition of the inverted damage effect tensor, a general expression for degradation of the elastic properties in materials has been obtained. The corresponding numerical algorithm for integration of the constitutive equations is based on an elastic predictor – plastic/damage corrector procedure. The plastic/damage corrector is uncoupled, which further simplifies and expedites the corrector procedure.

Boundary element formulation in finite deformation plasticity using implicit integration

Abstract A Boundary Element Method is developed for the solution of large strain problems. Bettis reciprocal theorem relevant to an Updated Lagrangian formulation is established as the basis for the boundary element formulation. Fully implicit integration of the constitutive relations leads to a nonlinear virtual work equation in each increment, which is solved by iteration. In each such equilibrium equation the elastic operator is isolated, and so the Boundary Element Method can be conveniently used. A system of equations is solved with all nonlinear terms assembled on the right hand side. A numerical example shows application to the stretching of a metal sheet. Elastic and plastic cross-anisotropy (the stressed plane is isotropic) and complete incompressibility are assumed. Hills yield criterion is adopted together with isotropic hardening.

Material Characterization and Modeling for Industrial Sheet Forming Simulations

In the present paper a project carried out at Volvo Cars Corp. and Chalmers University of Technology, with the purpose of improving material characterization and modeling for sheet forming simulation, is described. One of the primary targets has been to identify a material testing procedure, which is capable of providing effective stress‐strain data at considerably larger strains than what can be achieved in a standard uniaxial tensile test. Another objective has been to advance from the common Hill ’48 material model to a more flexible one, and, furthermore, to identify suitable test procedures for determining the parameters of such a model. A third objective has been to find practical examples, in which the importance of a careful material modeling can be clearly demonstrated.

On The Influence Of The Yield Locus Shape In The Simulation Of Sheet Stretch Forming

In the present paper results from an ongoing project at Volvo Cars and Chalmers University will be presented. The object of this project is to reduce the gap between the research frontier and the industrial practice concerning material modeling. One of the targets of the project is to identify a yield function, which can fulfill the special industrial demands concerning accuracy, easy parameter identification, and computational efficiency. Lately, some new yield functions have been presented, which seem to satisfy these demands. These yield functions belong to a group of non‐quadratic yield criteria, sometimes referred to as “the Hosford family”. These criteria are characterized by a stress exponent, which has been shown to have a strong coupling to the crystallographic structure of the material. The present paper addresses the issue of how the main parameters controlling the shape of the yield locus are influencing the material flow in sheet forming simulations. Since it is a well established fact that t...

On The Prediction Of Plastic Instability In Metal Sheets

The current report presents some results from a study on the prediction of necking failure in ductile metal sheets. In particular methods for creating Forming Limit Curves (FLCs) are discussed in the present report. Three groups of methods are treated: Experimental methods, Theoretical/analytical methods, and the Finite Element Method (FEM). The various methods are applied to two different materials: An aluminum alloy and a high strength steel. These materials do both exhibit a distinct necking behavior before fracture, and they do both exhibit only a small strain rate dependence. As can be expected, the resulting FLCs from the various experimental, theoretical, and numerical methods show a substantial scatter. The reasons for these deviating results are analyzed, and some conclusions are drawn regarding the applicability of the different methods.