Junhe Lian

Design of damage tolerance in high-strength steels

Abstract With the extensive application of advanced high-strength steels in various fields due to their excellent mechanical properties, industrial interest in the damage of advanced high-strength steels has increased in recent years. For these modern steels, due to their multiphase microstructure and different deformation mechanisms, the concept of damage must be re-examined. In this paper, the definition, length scale and different mechanisms of damage are introduced. Both the experimental evaluation of damage and the numerical damage models are briefly reviewed and compared. The approaches to improving damage tolerance are given in the framework of the damage tolerance design principle.

Exploiting the Property Profile of High Strength Steels by Damage Mechanics Approaches

Abstract Although high strength low alloy steels offer the potential for lightweight design, their application is often rather limited due to existing design rules. A further development of these standards requires precise prediction of realistic limit states. The damage model of Bai and Wierzbicki has been extended in order to improve the description of the ductile failure behaviour of steels, especially when crack initiation in dynamic loading is to be simulated. Application examples of the extended model are given in order to show that it can be used for limit state analysis. An outlook presents the application of the model to derive improved safety factors for probabilistic safety concepts.

Crystal plasticity assisted prediction on the yield locus evolution and forming limit curves

The aim of this study is to predict the plastic anisotropy evolution and its associated forming limit curves of bcc steels purely based on their microstructural features by establishing an integrated multiscale modelling approach. Crystal plasticity models are employed to describe the micro deformation mechanism and correlate the microstructure with mechanical behaviour on micro and mesoscale. Virtual laboratory is performed considering the statistical information of the microstructure, which serves as the input for the phenomenological plasticity model on the macroscale. For both scales, the microstructure evolution induced evolving features, such as the anisotropic hardening, r-value and yield locus evolution are seamlessly integrated. The predicted plasticity behaviour by the numerical simulations are compared with experiments. These evolutionary features of the material deformation behaviour are eventually considered for the prediction of formability.

The Second Blind Sandia Fracture Challenge: improved MBW model predictions for different strain rates

Sandia National Laboratories have carried out the Sandia Fracture Challenge in order to evaluate ductile damage mechanics models under conditions which are similar to those in the industrial practice. In this challenge, the prediction of load-deformation behavior and crack path of a sample that is designed for the competition under two loading rates is required with given data: the material Ti–6Al–4V, and raw data of tensile tests and V-notch tests under two loading rates. Within the stipulated time frame 14 teams from USA and Europe gave their predictions to the organizer. In this work, the approach applied by Team Aachen is presented in detail. The modified Bai–Wierzbicki (MBW) model is used in the framework of the Second Blind Sandia Fracture Challenge (SFC2). The model is made up by a stress-state dependent plasticity core that is extended to cope with strain rate and temperature effects under adiabatic conditions. It belongs to the group of coupled phenomenological ductile damage mechanics models, but it assumes a strain threshold value for the instant of ductile damage initiation. The initial guess of material parameters for the selected material Ti–6Al–4V was taken from an in-house database available at the authors’ institutes, but parameters are optimized in order to meet the validation data provided. This paper reveals that the model predictions can be improved significantly compared to the original submission of results at the end of SFC2 by two simple measures. On the one hand, the function to express the critical damage as well as the amount of energy dissipation between ductile damage initiation and complete ductile fracture were derived more carefully from the data provided by the challenge’s organizer. On the other hand, the experimental set-up of the challenge experiment was better described in the geometrical representation used for the numerical simulations. These two simple modifications allowed for a precise prediction of crack path and estimation of force–displacement behavior. The improved results show the general ability of the MBW model to predict the strain rate sensitivity of ductile fracture at various states of stress.

Evaluation of the Cold Formability of Multiphase Steels by Damage Mechanics Approaches

Abstract During sheet metal forming of multiphase steel for automotive application, more and more often failure happens prior to necking, so that the forming limit diagram is not an appropriate measure for cold formability anymore. Alternatively, the modified Bai Wierzbicki (MBW) model can be applied since it belongs to the group of coupled continuum damage mechanics models. It considers all invariants of the stress tensor both in the yield potential and in the crack initiation criterion. In this publication the model is successfully applied to characterize the cold formability of a dual phase steel of the grade DP600. Additionally, a procedure is described which delivers the parameters of the macroscopic MBW models damage initiation criterion by simulations of representative volume elements. In these simulations, the underlying physical mechanisms of crack initiation and propagation are quantitatively described.

The lattice strain ratio in characterizing the grain-to-grain interaction effect and its specific insight on the plastic deformation of polycrystalline materials

A single grain can contract or expand in the transverse direction when it is stretched. It becomes complex when the single grain is embedded in a stretched polycrystal, due to the grain neighborhood effect, which can outweigh the lateral contraction/expansion of that grain itself. Here, we performed numerical simulations to elucidate such grain-to-grain interaction effects on the lattice strain behavior. For individual grains in a polycrystal, pseudo Poisson’s ratio is defined. Ratios of Poisson’s ratio over pseudo Poisson’s ratio were employed to indicate the difference between the cases of the grain deformation with and without the constraint imposed from the neighboring grains. The high-stress spots and the sense of the stress components can be identified with a high possibility according to the proposed ratios. Most of the identified high-stress spots feature tensile stresses in three directions, while some of them feature the compressive stress in one transverse direction and a negative Poisson’s ratio. For the latter, a strong grain-to-grain interaction during the plastic stage of deformation is found. These grains induce the reversal of the lattice strain evolution curve for the measured <002>//TD, which is often found in the literature and in the data of neutron diffraction.

Modeling of plasticity and fracture behavior of X65 steels: seam weld and seamless pipes

A non-associated/associated flow rule coupled with an anisotropic/isotropic quadratic yield function is presented to describe the mechanical responses of two distinct X65 pipeline steels. The first as a product of the cold-rolling forming (UOE) process also known as seam weld pipes and the second as a result of high temperature piercing process called seamless tube manufacturing. The experimental settings consist of a wide range of sample types, whose geometric characteristics represent different state of stresses and loading modes. For low to intermediate stress triaxiality levels, flat specimens are extracted at different material orientations along with notched round bar samples for high stress triaxialities. The results indicate that despite the existing differences in plasticity between materials due to anisotropy induced processes, material failure can be characterized by an isotropic weighting function based on the modified Mohr–Coulomb (MMC) criterion. The non-associated flow rule allows for inclusion of strain directional dependence in the definition of equivalent plastic strain by means of scalar anisotropy (Lankford) coefficients and thus keeping the original capabilities of the MMC model.

Forming limit prediction by an evolving non-quadratic yield criterion considering the anisotropic hardening and r-value evolution

The constitutive model development has been driven to a very accurate and fine-resolution description of the material behaviour responding to various environmental variable changes. The evolving features of the anisotropic behaviour during deformation, therefore, has drawn particular attention due to its possible impacts on the sheet metal forming industry. An evolving non-associated Hill48 (enHill48) model was recently proposed and applied to the forming limit prediction by coupling with the modified maximum force criterion. On the one hand, the study showed the significance to include the anisotropic evolution for accurate forming limit prediction. On the other hand, it also illustrated that the enHill48 model introduced an instability region that suddenly decreases the formability. Therefore, in this study, an alternative model that is based on the associated flow rule and provides similar anisotropic predictive capability is extended to chapter the evolving effects and further applied to the forming limit prediction. The final results are compared with experimental data as well as the results by enHill48 model.The constitutive model development has been driven to a very accurate and fine-resolution description of the material behaviour responding to various environmental variable changes. The evolving features of the anisotropic behaviour during deformation, therefore, has drawn particular attention due to its possible impacts on the sheet metal forming industry. An evolving non-associated Hill48 (enHill48) model was recently proposed and applied to the forming limit prediction by coupling with the modified maximum force criterion. On the one hand, the study showed the significance to include the anisotropic evolution for accurate forming limit prediction. On the other hand, it also illustrated that the enHill48 model introduced an instability region that suddenly decreases the formability. Therefore, in this study, an alternative model that is based on the associated flow rule and provides similar anisotropic predictive capability is extended to chapter the evolving effects and further applied to the forming l...

A comparative study on the forming limit diagram prediction between Marciniak-Kuczynski model and modified maximum force criterion by using the evolving non-associated Hill48 plasticity model

Experimental and numerical investigations on the forming limit diagram (FLD) of a ferritic stainless steel were performed in this study. The FLD of this material was obtained by Nakajima tests. Both the Marciniak-Kuczynski (MK) model and the modified maximum force criterion (MMFC) were used for the theoretical prediction of the FLD. From the results of uniaxial tensile tests along different loading directions with respect to the rolling direction, strong anisotropic plastic behaviour was observed in the investigated steel. A recently proposed anisotropic evolving non-associated Hill48 (enHill48) plasticity model, which was developed from the conventional Hill48 model based on the non-associated flow rule with evolving anisotropic parameters, was adopted to describe the anisotropic hardening behaviour of the investigated material. In the previous study, the model was coupled with the MMFC for FLD prediction. In the current study, the enHill48 was further coupled with the MK model. By comparing the predicted forming limit curves with the experimental results, the influences of anisotropy in terms of flow rule and evolving features on the forming limit prediction were revealed and analysed. In addition, the forming limit predictive performances of the MK and the MMFC models in conjunction with the enHill48 plasticity model were compared and evaluated.Experimental and numerical investigations on the forming limit diagram (FLD) of a ferritic stainless steel were performed in this study. The FLD of this material was obtained by Nakajima tests. Both the Marciniak-Kuczynski (MK) model and the modified maximum force criterion (MMFC) were used for the theoretical prediction of the FLD. From the results of uniaxial tensile tests along different loading directions with respect to the rolling direction, strong anisotropic plastic behaviour was observed in the investigated steel. A recently proposed anisotropic evolving non-associated Hill48 (enHill48) plasticity model, which was developed from the conventional Hill48 model based on the non-associated flow rule with evolving anisotropic parameters, was adopted to describe the anisotropic hardening behaviour of the investigated material. In the previous study, the model was coupled with the MMFC for FLD prediction. In the current study, the enHill48 was further coupled with the MK model. By comparing the predicte...

Forming limit curves of DP600 determined in high-speed Nakajima tests and predicted by two different strain-rate-sensitive models

Determination of forming limit curves (FLC) to describe the multi-axial forming behaviour is possible via either experimental measurements or theoretical calculations. In case of theoretical determination, different models are available and some of them consider the influence of strain rate in the quasi-static and dynamic strain rate regime. Consideration of the strain rate effect is necessary as many material characteristics such as yield strength and failure strain are affected by loading speed. In addition, the start of instability and necking depends not only on the strain hardening coefficient but also on the strain rate sensitivity parameter. Therefore, the strain rate dependency of materials for both plasticity and the failure behaviour is taken into account in crash simulations for strain rates up to 1000 s−1 and FLC can be used for the description of the material’s instability behaviour at multi-axial loading. In this context, due to the strain rate dependency of the material behaviour, an extrapolation of the quasi-static FLC to dynamic loading condition is not reliable. Therefore, experimental high-speed Nakajima tests or theoretical models shall be used to determine the FLC at high strain rates. In this study, two theoretical models for determination of FLC at high strain rates and results of experimental high-speed Nakajima tests for a DP600 are presented. One of the theoretical models is the numerical algorithm CRACH as part of the modular material and failure model MF GenYld+CrachFEM 4.2, which is based on an initial imperfection. Furthermore, the extended modified maximum force criterion considering the strain rate effect is also used to predict the FLC. These two models are calibrated by the quasi-static and dynamic uniaxial tensile tests and bulge tests. The predictions for the quasi-static and dynamic FLC by both models are presented and compared with the experimental results.Determination of forming limit curves (FLC) to describe the multi-axial forming behaviour is possible via either experimental measurements or theoretical calculations. In case of theoretical determination, different models are available and some of them consider the influence of strain rate in the quasi-static and dynamic strain rate regime. Consideration of the strain rate effect is necessary as many material characteristics such as yield strength and failure strain are affected by loading speed. In addition, the start of instability and necking depends not only on the strain hardening coefficient but also on the strain rate sensitivity parameter. Therefore, the strain rate dependency of materials for both plasticity and the failure behaviour is taken into account in crash simulations for strain rates up to 1000 s−1 and FLC can be used for the description of the material’s instability behaviour at multi-axial loading. In this context, due to the strain rate dependency of the material behaviour, an extrap...