Analysis of damage and fracture formulations in cold extrusion

In forming processes, components generally undergo large deformations. This induces the evolution of damage, which can influence material and product properties. To capture these effects, a continuum damage mechanics (CDM) model, based on the work of Lemaitre [8] and Soyarslan [13, 14] as well as different fracture criteria according to Cockcroft and Latham [2], Freudenthal [4] and Oyane [10] are implemented and in- vestigated. While the CDM theory considers the evolution of damage and the associated softening, fracture criteria do not affect the results of the mechanical finite element (FE) analysis. However, a coupling is generally possible via element deletion, but material softening cannot be depicted in the simulation. Tensile tests with notched specimens are performed in order to obtain the material parameters associated with these models by inverse parameter identification processes. The optimized set of parameters is finally ap- plied to the damage and fracture models used for the FE simulations of a cold extrusion process, which are investigated in terms of damage evolution and material failure. It is demonstrated that the CDM model predicts the evolution of damage observed for differ- ent process parameters in cold extrusion quantitatively. The prediction of the failure by the fracture criteria does not agree well with the experiments

Comparison of gurson and lemaitre model in the context of blanking simulation of a high strength steel

The process of blanking takes place in a short band with high accumulated strain undergoing various stress triaxialities. Enhanced implementations for shear and compressive loads of Gurson’s and Lemaitre’s model are directly compared for the same blanking setup. For a dual phase steel DP600 the Lemaitre parameters are identified completely by an inverse strategy, while the parameters of the Gurson’s porous plasticity model are predominantly gained from analysis with a scanning electron microscopy (SEM). The models are validated by comparison of force-displacement curves, time point and location of crack initiation. Advantages and disadvantages of both approaches are discussed with respect to prediction accuracy and costs of parameter identification. Both of the models deliver an exact prediction for the location of the crack and a good prediction of the punch displacement at the onset of cracking

Testing of Formed Gear Wheels at Quasi-Static and Elevated Strain Rates

Geared components can be manufactured from sheet metals by sheet-bulk metal forming. One relevant load case in service are overload events, which might induce elevated strain rates. To determine the characteristic hardening and fracture behavior, specimens manufactured from the deep-drawing steel DC04 were tested with strain rates ranging from 0.0001 to 5 s−1. The gear wheels manufactured by sheet-bulk metal forming are tested at crosshead velocities of 0.08 mm/s and 175 mm/s. The tests are analyzed by measuring deformed geometry and hardness. While the tensile tests results show obvious strain-rate dependency, the hardness measurements show no strain-rate depended effect. The analyses are complemented by finite-element-simulations, which assess the homogeneity of deformation and point out the mechanisms of failure. Both coupled and uncoupled ductile damage models are able to predict the critical areas for crack initiation. The coupled damage model has slight advantages regarding deformed shape prediction

Phenomenological modeling of anisotropy induced by evolution of the dislocation structure on the macroscopic and microscopic scale \ud

This work focuses on the modeling of the evolution of anisotropy induced by the development of the dislocation microstructure. A model formulated at the engineering scale in the context of classical metal plasticity and a model formulated in the context of crystal plasticity are presented. Images obtained by transmission-electron microscopy (TEM) show the influence of the strain path on the evolution of anisotropy for the case of two common materials used in sheet metal forming, DC06 and AA6016-T4. Both models are capable of accounting for the transient behavior observed after changes in loading path for fcc and bcc metals. The evolution of the internal variables of the models is correlated with the evolution of the dislocation structure observed by TEM investigations

Characterization of flow induced anisotropy in sheet metal at large strain

Background: Many metals exhibit a stress overshoot, the so-called cross-hardening when subjected to a specific strain-path change. Existing tests for sheet metals are limited to an equivalent prestrain of 0.2 and show varying levels of cross-hardening for identical grades. Objective: The aim is to determine cross-hardening at large strains, relevant for forming processes. Mild steel grades (DC04, DC06, DX56) and high strength steel grades (BS600, DP600, ZE800) are investigated to quantify the level of cross-hardening between different grades and reveal which grades exhibit cross-hardening at all. Method: A novel test setup for large prestrain using hydraulic bulge test and torsion of curved sheets is developed to achieve an orthogonal strain-path change, i.e. the strain rate tensors for two subsequent loadings are orthogonal. The influence of strain rate differences between the tests and clamping of curved sheets on the determined cross-hardening are evaluated. The results are compared to experiments in literature. Results: Cross-hardening for sheet metal at prestrains up to 0.6 true plastic strain are obtained for the first time. For DX56 grade the maximum cross-hardening for all prestrains have a constant level of approximately 6%, while the maximum cross-hardening for DC04 and DC06 grades increases, with levels between 7 and 11%. The high strength grades BS600 and ZE800 do not show cross-hardening behavior, while, differencing from previous publications, cross-hardening is observed for dual phase steel DP600. Conclusion: Depending on the microstructure of the steel grade the cross-hardening increases with large prestrain or remains constant

Analytical model of the in-plane torsion test

In research and industry, the in-plane torsion test is applied to investigate the material behaviour at large plastic strains: a sheet is clamped in two concentric circles, the boundaries are twisted against each other applying a torque, and simple shear of the material arises. This deformation is analysed within the scope of finite elasto-plasticity. An additive decomposition of the Almansi strain tensor is derived, valid as an approximation for arbitrary large plastic strains and sufficiently small elastic strains and rotations. Constitutive assumptions are the von Mises yield criterion, an associative flow rule, isotropic hardening, and a physically linear elasticity relation. The incremental formulation of the elasticity relation applies covariant Oldroyd derivatives of the stress and the strain tensors. The assumptions combined with equilibrium conditions lead to evolution equations for the distribution of stresses and accumulated plastic strain. The nonzero circumferential stress must be determined from the equilibrium condition because no deformation is present in tangential direction. As a result, a differential-algebraic-equation (DAE) system is derived, consisting of three ordinary differential equations combined with one algebraic side condition. As an example material, properties of a dual phase steel DP600 are analysed numerically at an accumulated plastic strain of 3.0. Radial normal stresses of 3.1% and tangential normal stresses of 1.0% of the shear stresses are determined. The influence of the additional normal stresses on the determination of the flow curve is 0.024%, which is negligibly small in comparison with other experimental influences and measurement accuracies affecting the experimental flow curve determination

Advanced material model for shear cutting of metal sheets

A finite-element simulation of the shear cutting process is used to predict thegeometry of the cutting surface. A fully-coupled Lemaitre-type model is used in the process model for the description of the material behaviour. The extended Lemaitre model considers the influence of shear and compression-dominated stress states on the propagation of damage. Tensile tests with and without notches are used for the identification of material parameters. These methods are advantageous for the analysis of different blanking processes. Since damage parameters have a strong influence on the cutting surface quality, a numerical study isconducted to analyse their influence. The results of the simulations are compared with experimental data

Investigations of ductile damage in DP600 and DC04 deep drawing steel sheets during punching

The paper presents numerical and microstructural investigations on a punching process of 2 mm thick steel sheets. The dual phase steel DP600 and the mild steel DC04 exhibit different damage and fracture characteristics. To distinguish the void development and crack initiation for both materials, interrupted tests at varied punch displacements are analyzed. The void volume fractions in the shearing zone are identified by scanning electron microscopy (SEM). The Gurson model family, which is recently extended for shear fracture, is utilized to model the elastoplastic behavior with ductile damage. The effect of the shear governing void growth parameter, introduced by Nahshon and Hutchinson (2008), is discussed