Michael P. Pietryga

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.

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 new FE-model for the investigation of bond formation and failure in roll bonding processes

Roll bonding is a process to join two or more different materials permanently in a rolling process. A typical industrial application is the manufacturing of aluminum sheets for heat exchangers in cars where the solder is joined onto a base layer by roll bonding. From a modelling point of view the challenge is to describe the bond formation and failure of the different material layers within a FE-process model. Most methods established today either tie the different layers together or treat them as completely separate. The problem for both assumptions is that they are not applicable to describe the influence of tangential stresses that can cause layer shifting and occur in addition to the normal stresses within the roll gap. To overcome these restrictions in this paper a 2D FE-model is presented that integrates an adapted contact formulation being able to join two bodies that are completely separated at the start of the simulation. The contact formulation is contained in a user subroutine that models bond formation by adhesion in dependence of material flow and load. Additionally if the deformation conditions are detrimental already established bonds can fail. This FE-model is then used to investigate the process boundaries of the first passes of a typical rolling schedule in terms of achievable height reductions. The results show that passes with unfavorable height reduction introduce tensile and shear stresses that can lead to incomplete bonding or can even destroy the bond entirely. It is expected that, with adequate calibration, the developed FE-model can be used to identify conditions that are profitable for bond formation in roll bonding prior to production and hence can lead to shorter rolling schedules with higher robustness.

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

Finite Element Implementation of a Bonding Model and Application to Roll Bonding of Aluminum Sheets of Largely Different Yield Strength

Roll bonding is a joining-by-forming operation, in which two or more metallic strips or plates are bonded permanently through the pressure and plastic deformation in the roll gap. Although roll bonding has been successfully used in industrial production over many years, difficulties occur especially when materials of largely different yield strength are roll-bonded, e.g. when hard aluminum alloys are clad with soft commercially pure aluminum. Examples are AA2024 sheets used in wing and fuselage structures of aircrafts, which are clad with AA1050 to improve the corrosion resistance. Likewise, aluminum sheets for heat exchangers consist of a hard base material that is clad with a soft solderable aluminum alloy. In these cases, the strength difference may influence the bonding behavior since the softer face sheet has to transmit the deformation to the harder core material. To analyze and optimize such cases, a bonding model integrated into a numerical framework for the simulation of the roll bonding process is required. In this paper, a finite element model is presented, in which the development of bond strength is simulated using a cohesive contact formulation. The model is used to study the bonding behavior of laboratory-scale roll bonding trials of two aluminum alloys with a large difference in yield strength. It is found that shear stresses are generated towards the end of the roll gap that may exceed the shear bond strength created earlier in the roll gap such that no firm bond is obtained. The conditions under which bonding is successful are analyzed using a finite element simulation study with varying yield stress differences and pass reductions and summarized in a map.

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.

On the Modeling of Evolving Elastic and Plastic Anisotropy in the Finite Strain Regime – Application to Deep Drawing Processes

In this work, we discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been used for the simulation of the phenomenon of earing during cylindrical deep drawing.

Constitutive modelling of evolving flow anisotropy including distortional hardening

The paper presents a new constitutive model for anisotropic metal plasticity that takes into account the expansion or contraction (isotropic hardening), translation (kinematic hardening) and change of shape (distortional hardening) of the yield surface. The experimentally observed region of high curvature (“nose”) on the yield surface in the loading direction and flattened shape in the reverse loading direction are modelled here by means of the concept of directional distortional hardening. The modelling of directional distortional hardening is accomplished by means of an evolving fourth‐order tensor. The applicability of the model is illustrated by fitting experimental subsequent yield surfaces at finite plastic deformation. Comparisons with test data for aluminium low and high work hardening alloys display a good agreement between the simulation results and the experimental data.