C B Silbermann

Ductile damage model for metal forming simulations including refined description of void nucleation

Abstract We address the prediction of ductile damage and material anisotropy accumulated during plastic deformation of metals. A new model of phenomenological metal plasticity is proposed which is suitable for applications involving large deformations of workpiece material. The model takes combined nonlinear isotropic/kinematic hardening, strain-driven damage and rate-dependence of the stress response into account. Within this model, the work hardening and the damage evolution are fully coupled. The description of the kinematics is based on the double multiplicative decomposition of the deformation gradient proposed by Lion. An additional multiplicative decomposition is introduced in order to account for the damage-induced volume increase of the material. The model is formulated in a thermodynamically admissible manner. Within a simple example of the proposed framework, the material porosity is adopted as a rough measure of damage. A new simple void nucleation rule is formulated based on the consideration of various nucleation mechanisms. In particular, this rule is suitable for materials which exhibit a higher void nucleation rate under torsion than in case of tension. The material model is implemented into the FEM code Abaqus and a simulation of a deep drawing process is presented. The robustness of the algorithm and the performance of the formulation is demonstrated.

Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

FE-simulation of the Presta joining process for assembled camshafts - local widening of shafts through rolling

Considerable weight benefits and the option to combine various steel alloys of the single parts are the major advantages of assembled over conventional camshafts. The Presta joining process is the leading manufacturing method of assembled camshafts in the global market. The process is divided into two substeps. At first, the outer diameter of the shaft is widened with a profile oriented orthogonal to the shaft axis at the intended cam seat. At this position the shaft is subsequently joined with a cam with an internal profile oriented parallel to the shaft axis. As a result, these perpendicular profiles form a tight fit due to plastic deformations. Consequently the simulation of the manufacturing process has to start with the simulation of the rolling of the shaft. The resulting profile requested in this step is axisymmetric, but the arrangement of tools is not. Thus a three-dimensional model is required, which is presented in this work. Furthermore, the infeed of the rolling tool is unknown and controlled by the stiffness of the holders of the rolling tool. This work shows the modeling of this behavior. To predict realistic results for the underlying process, the use of precise material models is essential in order to take several hardening mechanisms into account. However, the use of complex material models implies additional effort, which is shown in this work.

FE-simulation of the Presta joining process for assembled camshafts – modelling of the joining process

The Presta joining process is based on the separate manufacturing of internal profiled cams and shafts with previously widened diameters at the intended cam seat through rolling. With regard to further optimization and enhancement, the two substeps are modelled and simulated using FEM. The results of the rolling process simulation are employed as the starting point for the simulation of the joining step, which is presented in this contribution. First, the shaft is widened with a profile oriented orthogonal to the shaft axis at the intended cam seat. Subsequently, the shaft is joined with a cam that has an internal profile oriented parallel to the shaft axis. Due to plastic deformations these perpendicular profiles form a tight fit. Because of these complex plastic deformations, that are related to large local forming degrees, the use of precise material models is essential. Moreover, it is necessary to maintain the deformation history of the rolling simulation in the joining step with regard to effects like kinematic or isotropic hardening. For that purpose, the applied material models invariance under change of the reference configuration is used by transferring its internal state variables from one simulation step to another. Finally, the results of the simulation are compared to measurements of series production.

Analogies between continuum dislocation theory, continuum mechanics and fluid mechanics

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Interestingly, CDT shows striking analogies to other branches of continuum mechanics. The present contribution demonstrates this on two essential kinematical quantities which reflect tensorial dislocation properties: the (resultant) Burgers vector and the dislocation density tensor. First, the limiting process for the (resultant) Burgers vector from an integral to a local quantity is performed analogously to the limiting process from the force vector to the traction vector. By evaluating the balance of forces on a tetrahedral volume element, Cauchy found his famous formula relating traction vector and stress tensor. It is shown how this procedure may be adopted to a continuously dislocated tetrahedron. Here, the conservation of Burgers vector implicates the introduction of the dislocation density tensor. Second, analogies between the plastic flow of a continuously dislocated solid and the liquid flow of a fluid are highlighted: the resultant Burgers vector of a dislocation ensemble plays a similar role as the (resultant) circulation of a vortex tube. Moreover, both vortices within flowing fluids and dislocations within deforming solids induce discontinuities in the velocity field and the plastic distortion field, respectively. Beyond the analogies, some peculiar properties of the dislocation density tensor are presented as well.