Ivaylo N. Vladimirov

Failure modelling in metal forming by means of an anisotropic hyperelastic-plasticity model with damage

In metal forming, formability is limited by the evolution of ductile damage in the work piece. The accurate prediction of material failure requires, in addition to the description of anisotropic plasticity, the inclusion of damage in the finite element simulation. This paper discusses the application of an anisotropic hyperelastic-plasticity model with isotropic damage to the numerical simulation of fracture limits in metal forming. The model incorporates plastic anisotropy, nonlinear kinematic and isotropic hardening and ductile damage. The constitutive equations of the proposed model are numerically integrated both implicitly and explicitly, and the model is implemented as a user material subroutine UMAT in the commercial solvers ABAQUS/Standard and LS-DYNA, respectively. The numerical examples investigate the potential of the constitutive framework regarding the prediction of failure in metal forming processes such as, e.g. cross-die deep drawing. In particular, simulations of the Nakazima stretching test with varying specimen geometry are utilized to simulate the forming limit diagram at fracture and the numerical results are compared to experimental data for aluminium alloy sheets.

Anisotropic Modelling of Metals in Forming Processes

The accuracy of sheet metal forming simulations crucially relies on the quality of the material description which involves the modelling of large strains, elastic and plastic anisotropy as well as isotropic and kinematic hardening. In the present paper we propose a hyperelasticity-based concept using structural tensors whose evolution is in contrast to previous works explicitly taken into account. In this way we consider the evolution of the elastic anisotropy (through the dependence of the Helmholtz free energy function on the evolving structural tensors) as well as of the plastic anisotropy (through the dependence of the yield locus on the structural tensors). Exploiting the dissipation inequality leads to the important result that the model includes only symmetric tensor-valued internal variables the integration of which can be performed very efficiently by means of the exponential map. Numerical examples are shown to qualitatively validate the model.

Constitutive Modelling of Anisotropy, Hardening and Failure of Sheet Metals

The paper discusses the application of a newly developed coupled material model of finite anisotropic multiplicative plasticity and continuum damage to the numerical prediction of the forming limit diagram at fracture (FLDF). The model incorporates Hill-type plastic anisotropy, nonlinear Armstrong-Frederick kinematic hardening and nonlinear isotropic hardening. The numerical examples investigate the simulation of forming limit diagrams at fracture by means of the so-called Nakajima stretching test. Comparisons with test data for aluminium sheets display a good agreement between the finite element results and the experimental data.

Characterization and Simulation of High-Speed-Deformation-Processes

The combination of the processes deep drawing and electromagnetic pulse forming is a promising way to cope with the ever higher complexity of new sheet metal designs. A cooperation between the Institute of Materials Science (IW) of the Leibniz Universitat Hannover and the Institute of Applied Mechanics (IFAM) of the RWTH Aachen is investigating these processes both experimental and in simulation. Aim is the characterization of the combined process. Therefore the material properties of the investigated aluminum alloy EN AW 6082 T6 have to be determined quasi-static as well as at high speed. These properties are then used as a basic for the simulations. Anisotropic behaviors as well as dynamic hardening effects are investigated in the quasi-static state. Several experiments for analyzing “Bauschinger” respectively “Ratcheting effects” have been conducted resulting in a new measuring set-up for thin sheets. For the determination of high speed forming limit diagrams a novel testing device on the basis of the Nakajima-test has been developed allowing for strain rates of approximately 103 s. Both testing methods are described in this paper; the results are then used to adapt the simulation models for the combined processes. The high speed deformation process is simulated by means of finite elements using a material model developed at the IFAM. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamic setting. It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening which is widely adopted as capable of representing the above metal hardening effects. To prevent locking * This work is based on the results of PAK 343 “Hochgeschwindigkeitsblechumformung”; the authors would like to thank the “Deutsche Forschungsgemeinschaft DFG” for its financial support

On the Improvement of Formability and the Prediction of Forming Limit Diagrams at Fracture by Means of Constitutive Modelling

Sheet metal forming processes are well-established in production technology for the manufacturing of large quantities. To increase the formability, the processing limit of a single forming process can be enhanced by a combination of quasi-static and high-speed forming process. The forming limits for both operations for the aluminum alloy EN AW 6082 T6 obtained via simulations and experiment are investigated in a research cooperation between the Institute of Materials Science (IW) and the Institute of Applied Mechanics (IFAM). Significant changes in forming limits with higher strain rates are indicated by the experimental results. Here, the forming limit curves move to the lower right hand side. The processes are simulated and the FLD at fracture are predicted by means of finite element analysis. The constitutive model is based on the multiplicative split of the deformation gradient. It is coupled with ductile damage and combines nonlinear kinematic and isotropic hardening. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. The coupling of damage and viscoplasticity is carried out following the well-known concept of effective stress and the principle of strain equivalence. Using these powerful tools the simulation of dynamic effects and the prediction of forming limit diagrams at fracture shows good correlation with the experiments.

A Cohesive Zone Model for Simulation of the Bonding and Debonding in Metallic Composite Structures - Experimental Validations

Flexible and economic production of composite structures which include functional layersrequires new manufacturing techniques. Joining by plastic deformation is a powerful technique whichis widely used in production processes to create metal composites [1]. The use of plastic deformationin joining processes offers improved accuracy, reliability and environmental safety [2]. The presentstudy deals with modeling of the bonding and debonding behavior in metallic composite structures.Therefore, a general cohesive zone element formulation in the framework of zero-thickness interfaceelements is developed. This enables the accurate and efficient modeling of the interface based on aninterfacial traction-separation law. The paper is concluded by a detailed description of the processsimulation and a comparison of its results with experimental data.

Comparison of Hyper- and Hypoelastic-Based Formulations of Elastoplasticity with Applications to Metal Forming

The aim of this work is to examine two specific finite strain elastoplasticity models in terms of their applicability in metal forming processes, namely a hyperelastic-based model which relies upon a multiplicative decomposition of the deformation gradient into elastic and plastic parts and a hypoelastic-based model which makes use of an additive elastic-plastic split of the rate of deformation tensor. Both models allow for nonlinear isotropic and kinematic hardening and were implemented as user material subroutines (UMAT) into ABAQUS/Standard. Various sample calculations were performed to assess the respective properties and capabilities of the models. The FE simulation of a deep drawing process produced nearly congruent results for both models which suggests that they are equally well-suited for modeling metallic materials in metal forming processes.

Lifetime Prediction of Rocket Combustion Chamber Wall by Means of Viscoplasticity Coupled With Ductile Isotropic Damage

This paper presents the application of a viscoplastic damage model for the lifetime prediction of a typical rocket combustion chamber structure. The material modeling is motivated by extension of the classical rheological model for elastoplasticity with Armstrong-Frederick kinematic hardening into a viscoplastic model. The coupling with damage is performed using the concept of effective stress and the principle of strain equivalence. The material parameters are identified based on experimental results for the high temperature copper alloy NARloy-Z, which is one of the typical combustion chamber wall materials. Finally the applicability of the model will be shown by means of sequentially coupled thermomechanical analyses.Copyright

Influence of Explicit and Implicit Integration of Hyperelastic-Plastic Combined Hardening Models on the Springback in Sheet Forming

In this paper, we investigate the computational efficiency of explicit and implicit integration schemes for hyperelastic-plastic combined hardening plasticity and examine the influence on the simulated springback in sheet metal forming. Due to the deviatoric character of the evolution equations, the finite strain combined hardening model discussed here is integrated by means of the exponential map algorithm in order to fulfil plastic incompressibility. We focus here on different possibilities of evaluating the exponential tensor functions of the material model. One option is to use the spectral decomposition to evaluate the exponential tensor functions in closed form. Alternatively, the latter functions can be evaluated by Taylor series expansion. Furthermore, we examine the potential of an explicit formulation of elasto-plasticity with combined hardening regarding accuracy and efficiency. The material model equations have been implemented as user material subroutines UMAT and VUMAT for use in the commercial solvers ABAQUS/Standard and ABAQUS/Explicit, respectively. The numerical models are applied to the finite element simulation of draw bending, where the forming step is simulated both in implicit and explicit manner, whereas the ensuing springback step is carried out only implicitly.Copyright

On the Use of Explicit and Implicit Exponential Map Algorithms of Finite Strain Combined Hardening Plasticity in the Simulation of Draw Bending

The paper investigates the computational efficiency of explicit and implicit integrationschemes for hyperelastic-plastic combined hardening plasticity and examines the influence on thesimulated springback in sheet metal forming. The finite strain combined hardening model discussedhere is integrated by means of the exponential map algorithm in order to fulfil plastic incompressibility.The focus is on different possibilities of evaluating the exponential tensor functions of thematerial model. One option is to use the spectral decomposition to evaluate the exponential tensorfunctions in closed form. Alternatively, the latter functions can be determined by Taylor series expansion.We examine the potential of an explicit formulation of elastoplasticity with combined hardeningwith respect to accuracy and efficiency. The material model equations have been implemented as usermaterial subroutines UMAT and VUMAT for use in the commercial solvers ABAQUS/Standard andABAQUS/Explicit, respectively, where the finite element simulation of draw bending is simulatedboth in implicit and explicit manner.