Inverse parameter identification of an anisotropic plasticity model for sheet metal - Friedlein, J.; Wituschek, S.; Lechner, M.; Mergheim, J.; Steinmann, P. (IOP Conference Series: Materials Science and Engineering)
The increasing economic and ecological demands on the mobility sector require efforts to reduce resource consumption in both the production and utilization phases. The use of lightweight construction technologies can save material and increase energy efficiency during operation. Multi-material systems consisting of different materials and geometries are used to achieve weight reduction. Since conventional joining processes reach their limits in the connection of these components, new methods and technologies are necessary in order to be able to react versatilely to varying process and disturbance variables. For fundamental investigations of new possibilities in joining technology, numerical investigations are helpful to identify process parameters. To generate valid results, robust and efficient material models are developed which are adapted to the requirements of versatile joining technologies, for instance to the high plastic strains associated with self-piercing riveting. To describe the inherent strain-induced plastic orthotropy of sheet metal an anisotropic Hill-plasticity model is formulated. Tensile tests for different sheet orientations are conducted both experimentally and numerically to adjust the anisotropic material parameters by inverse parameter identification for aluminium EN AW-6014 and steel HCT590X. Then, the layer compression test is used to validate the model and the previously identified parameters.

Stochastic local FEM for computational homogenization of heterogeneous materials exhibiting large plastic deformations - Pivovarov, D.; Mergheim, J.; Willner, K.; Steinmann, P. (Computational Mechanics)
Computational homogenization is a powerful tool allowing to obtain homogenized properties of materials on the macroscale from simulations of the underlying microstructure. The response of the microstructure is, however, strongly affected by variations in the microstructure geometry. In particular, we consider heterogeneous materials with randomly distributed non-overlapping inclusions, which radii are also random. In this work we extend the earlier proposed non-deterministic computational homogenization framework to plastic materials, thereby increasing the model versatility and overall realism. We apply novel soft periodic boundary conditions and estimate their effect in case of non-periodic material microstructures. We study macroscopic plasticity signatures like the macroscopic von-Mises stress and make useful conclusions for further constitutive modeling. Simulations demonstrate the effect of the novel boundary conditions, which significantly differ from the standard periodic boundary conditions, and the large influence of parameter variations and hence the importance of the stochastic modeling.

Anisotropic plasticity‐damage material model for sheet metal — Regularised single surface formulation - Friedlein, J.; Mergheim, J.; Steinmann, P. (PAMM)
Sheet metal forming as well as mechanical joining demand increasingly accurate and efficient material modelling to capture large deformations, the inherent sheet orthotropy and even process-induced damage, which is expected to be influential. To account for large strains the additive logarithmic strain space is utilised that enables a straightforward incorporation of plastic anisotropy, herein modelled by a Hill48 yield function. A gradient-enhancement is used to equip the ductile damage model with an internal length scale curing the damage-induced localisation. An affine combination of the local and non-local softening variable is derived enabling a more efficient single surface formulation for the regularised plasticity-damage material model.

A finite plasticity gradient-damage model for sheet metals during forming and clinching - Friedlein, J.; Mergheim, J.; Steinmann, P. (Key Engineering Materials)
In recent years, clinching has gathered popularity to join sheets of different materials in industrial applications. The manufacturing process has some advantages, as reduced joining time, reduced costs, and the joints show good fatigue properties. To ensure the joint strength, reliable simulations of the material behaviour accounting for process-induced damage are expected to be beneficial to obtain credible values for the ultimate joint strength and its fatigue limit. A finite plasticity gradient-damage material model is outlined to describe the plastic and damage evolutions during the forming of sheet metals, later applied to clinching. The utilised gradient-enhancement cures the damage-induced localisation by introducing a global damage variable as an additional finite element field. Both, plasticity and damage are strongly coupled, but can, due to a dual-surface approach, evolve independently. The ability of the material model to predict damage in strongly deformed sheets, its flexibility and its regularization properties are illustrated by numerical examples.

Parametric FEM for computational homogenization of heterogeneous materials with random voids - Pivovarov, Dmytro; Mergheim, Julia; Willner, Kai; Steinmann, Paul (PAMM)
Computational homogenization is a powerful tool which allows to obtain homogenized properties of materials on the macroscale from the simulation of the underlying microstructure. The response of the microstructure is, however, strongly affected by variations in the microstructure geometry. The effect of geometry variations is even stronger in cases when the material exhibits plastic deformations. In this work we study a model of a steel alloy with arbitrary distributed elliptic voids. We model one single unit cell of the material containing one single void. The geometry of the void is not precisely known and is modeled as a variable orientation of an ellipse. Large deformations applied to the unit cell necessitate a finite elasto-plastic material model. Since the geometry variation is parameterized, we can utilize the method recently developed for stochastic problems but also applicable to all types of parametric problems — the isoparametric stochastic local FEM (SL-FEM). It is an ideal tool for problems with only a few parameters but strongly nonlinear dependency of the displacement fields on parameters. Simulations demonstrate a strong effect of parameter variation on the plastic strains and, thus, substantiate the use of the parametric computational homogenization approach.

Influence of Kinematic Hardening on Clinch Joining of Dual-Phase Steel HCT590X Sheet Metal - Friedlein, Johannes; Mergheim, Julia; Steinmann, Paul (The Minerals, Metals & Materials Series)
Nowadays, clinching is a widely used joining technique, where sheets are joined by pure deformation to create an interlock without the need for auxiliary parts. This leads to advantages such as reduced joining time and manufacturing costs. On the other hand, the joint strength solely relies on directed material deformation, which renders an accurate material modelling essential to reliably predict the joint forming. The formation of the joint locally involves large plastic strains and possibly complex non-proportional loading paths, as typical of many metal forming applications. Consequently, a finite plasticity formulation is utilised incorporating a Chaboche–Rousselier kinematic hardening law to capture the Bauschinger effect. Material parameters are identified from tension–compression tests on miniature spec- imens for the dual-phase steel HCT590X. The resulting material model is implemented in LS-Dyna to study the locally diverse loading paths and give a quantitative statement on the importance of kinematic hardening for clinching. It turns out that the Bauschinger effect mainly affects the springback of the sheets and has a smaller effect on the joint forming itself.
Keywords: Clinching; Material modelling; Kinematic hardening; Parameter identification; Bauschinger effect

Observations on additive plasticity in the logarithmic strain space at excessive strains - Friedlein, J.; Mergheim, J.; Steinmann, P. (International Journal of Solids and Structures)
Additive plasticity in the logarithmic strain space is compared to multiplicative plasticity for various loading cases including coaxial and non-coaxial plastic deformations. Even though both finite plasticity approaches are based on total Lagrangian descriptions, the former is popular due to its inherent similarity to the infinitesimal theory and its easy extensibility. However, since its introduction several limitations of additive plasticity in the logarithmic strain space have been discovered. In this study, these problems such as stress rotation and softening are considered, revealing that fundamental differences compared to multiplicative plasticity occur for non-coaxial plastic deformations. We focus in particular on the observed softer response of the additive based approach, which is analysed in depth using three numerical examples including two well-known benchmarks for finite plasticity. By means of these finite element simulations the softer and possibly even localising response of additive plasticity in the logarithmic strain space is confirmed.

A Review on the Modeling of the Clinching Process Chain - Part III: Operational Phase - Schramm, Britta; Harzheim, Sven; Weiß, Deborah; Joy, Tintu David; Hofmann, Martin; Mergheim, Julia; Wallmersperger, Thomas (Journal of Advanced Joining Processes)
Keywords: Mechanical Engineering; Mechanics of Materials; Engineering (miscellaneous); Chemical Engineering (miscellaneous)

A Review on the Modeling of the Clinching Process Chain - Part I: Design Phase - Schramm, Britta; Martin, Sven; Steinfelder, Christian; Bielak, Christian Roman; Brosius, Alexander; Meschut, Gerson; Tröster, Thomas; Wallmersperger, Thomas; Mergheim, Julia (Journal of Advanced Joining Processes)
Keywords: Mechanical Engineering; Mechanics of Materials; Engineering (miscellaneous); Chemical Engineering (miscellaneous)

A Review on the Modeling of the Clinching Process Chain - Part II: Joining Process - Schramm, Britta; Friedlein, Johannes; Gröger, Benjamin; Bielak, Christian Roman; Bobbert, Mathias; Gude, Maik; Meschut, Gerson; Wallmersperger, Thomas; Mergheim, Julia (Journal of Advanced Joining Processes)
Keywords: Mechanical Engineering; Mechanics of Materials; Engineering (miscellaneous); Chemical Engineering (miscellaneous)

Numerical analysis of failure modeling in clinching process chain simulation - Bielak, Christian Roman; Böhnke, Max; Friedlein, Johannes; Bobbert, Mathias; Mergheim, Julia; Steinmann, Paul; Meschut, Gerson (Materials Research Proceedings)
Abstract. The application of the mechanical joining process clinching allows the assembly of different sheet metal materials with a wide range of material thickness configurations, which is of interest for lightweight multi-material structures. In order to be able to predict the clinched joint properties as a function of the individual manufacturing steps, current studies focus on numerical modeling of the entire clinching process chain. It is essential to be able to take into account the influence of the joining process-induced damage on the load-bearing capacity of the joint during the loading phase. This study presents a numerical damage accumulation in the clinching process based on an implemented Hosford-Coulomb failure model using a 3D clinching process model applied on the aluminum alloy EN AW-6014 in temper T4. A correspondence of the experimentally determined failure location with the element of the highest numerically determined damage accumulation is shown. Moreover, the experimentally determined failure behavior is predicted to be in agreement in the numerical loading simulation with transferred pre-damage from the process simulation.

A calibration method for failure modeling in clinching process simulations - Böhnke, Max; Bielak, Christian Roman; Friedlein, Johannes; Bobbert, Mathias; Mergheim, Julia; Steinmann, Paul; Meschut, Gerson (Materials Research Proceedings)
Abstract. In the numerical simulation of mechanical joining technologies such as clinching, the material modeling of the joining parts is of major importance. This includes modeling the damage and failure behavior of the materials in accordance with varying occurring stress states. This paper presents a calibration method of three different fracture models. The calibration of the models is done by use of experimental data from a modified punch test, tensile test and bulge test in order to map the occurring stress states from clinching processes and to precisely model the resulting failure behavior. Experimental investigations were carried out for an aluminum alloy EN AW-6014 in temper T4 and compared with the simulative results generated in LS-DYNA. The comparison of force-displacement curves and failure initiation shows that the Hosford–Coulomb model predicts the failure behavior for the material used and the tests applied with the best accuracy.

Influence of plastic orthotropy on clinching of sheet metal - Friedlein, Johannes; Bielak, Christian Roman; Böhnke, Max; Bobbert, Mathias; Mergheim, Julia; Steinmann, Paul; Meschut, Gerson (Materials Research Proceedings)