Dr.-Ing. Napat Vajragupta

Micromechanical and Macroscopic Modelling at ICAMS
Ruhr-Universität Bochum

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  • Deformation and damage assessments of two dp1000 steels using a micromechanical modelling method
    Habibi, N. and Vajragupta, N. and Münstermann, S.
    Crystals 11 (2021)
    Damage characterization and micromechanical modelling in dual-phase (DP) steels have recently drawn attention, since any changes in the alloying elements or process route strongly influence the microstructural features, deformation behavior of the phases, and damage to the micro-mechanisms, and subsequently the particular mechanical properties of the material. This approach can be used to stablish microstructure–properties relationships. For instance, the effects of local damage from shear cutting on edge crack sensitivity in the following deformation process can be studied. This work evaluated the deformation and damage behaviors of two DP1000 steels using a microstructure-based approach to estimate the edge cracking resistance. Phase fraction, grain size, phase distribution, and texture were analyzed using electron backscatter diffraction and secondary electron detectors of a scanning electron microscope and employed in 3D representative volume elements. The deformation behavior of the ferrite phase was defined using a crystal plasticity model, which was calibrated through nanoindentation tests. Various loading conditions, including uniaxial tension, equi-biaxial tension, plane strain tension, and shearing, along with the maximum shear stress criterion were applied to investigate the damage initiation and describe the edge cracking sensitivity of the studied steels. The results revealed that a homogenous microstructure leads to homogenous stress–strain partitioning, delayed damage initiation, and high edge cracking resistance. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/cryst11070805
  • Influence of temperature on void collapse in single crystal nickel under hydrostatic compression
    Prasad, M.R.G. and Neogi, A. and Vajragupta, N. and Janisch, R. and Hartmaier, A.
    Materials 14 (2021)
    Employing atomistic simulations, we investigated the void collapse mechanisms in single crystal Ni during hydrostatic compression and explored how the atomistic mechanisms of void collapse are influenced by temperature. Our results suggest that the emission and associated mutual interactions of dislocation loops around the void is the primary mechanism of void collapse, irrespective of the temperature. The rate of void collapse is almost insensitive to the temperature, and the process is not thermally activated until a high temperature (1200-1500 K) is reached. Our simulations reveal that, at elevated temperatures, dislocation motion is assisted by vacancy diffusion and consequently the void is observed to collapse continuously without showing appreciable strain hardening around it. In contrast, at low and ambient temperatures (1 and 300 K), void collapse is delayed after an initial stage of closure due to significant strain hardening around the void. Furthermore, we observe that the dislocation network produced during void collapse remains the sample even after complete void collapse, as was observed in a recent experiment of nickel-base superalloy after hot isostatic pressing. © 2021 by the authors.
    view abstract10.3390/ma14092369
  • The influence of post-weld tempering temperatures on microstructure and strength in the stir zone of friction stir welded reduced activation ferritic/martensitic steel
    Li, S. and Yang, X. and Vajragupta, N. and Tang, W. and Hartmaier, A. and Li, H.
    Materials Science and Engineering A 814 (2021)
    Reduced activation ferritic/martensitic (RAFM) steels are among the most competitive candidates of structural materials for nuclear fusion reactors, due to their superior comprehensive properties. Friction stir welding (FSW) was investigated in joining RAFM steel, considering its potential advantages in obtaining an optimal microstructure and mechanical properties of welded joint. To evaluate the feasibility of FSW in joining RAFM steel, an in-depth understanding of the microstructure-property relationships for friction stir welded joints of RAFM steel is necessary. In this research, the quantitative relationships between microstructural evolution and tensile properties in the stir zone (SZ) of friction stir welded RAFM steel after post-weld tempering treatment (PWTT) were systematically studied. Three different post-weld tempering temperatures namely 720 °C, 760 °C, and 800 °C were adopted. Then the uniaxial tensile properties were tested at room temperature and 550 °C, respectively. Electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and the Thermo-Calc Calphad software were adopted to systematically investigate the microstructural evolution. Martensite lath width, precipitate number density, equilibrium solid solubility of alloying elements in the matrix, and geometrically necessary dislocation (GND) density were analyzed quantitatively. With the results obtained, we assessed the contribution of each strengthening mechanism to the 0.2% offset yield strength. According to the effective inter-barrier spacing theory, a microstructure-sensitive yield strength model was obtained to well predict the change in yield strength at different conditions. Finally, the results calculated by equivalent strengthening effect indicated that the crucial microstructure determining the yield strength of the SZ for RAFM steel after PWTT is the high density of dislocation substructures. © 2021 Elsevier B.V.
    view abstract10.1016/j.msea.2021.141224
  • Effect of Grain Statistics on Micromechanical Modeling: The Example of Additively Manufactured Materials Examined by Electron Backscatter Diffraction
    Biswas, A. and Prasad, M.R.G. and Vajragupta, N. and Kostka, A. and Niendorf, T. and Hartmaier, A.
    Advanced Engineering Materials 22 (2020)
    Micromechanical modeling is one of the prominent numerical tools for the prediction of mechanical properties and the understanding of deformation mechanisms of metals. As input parameters, it uses data obtained from microstructure characterization techniques, among which the electron backscatter diffraction (EBSD) technique allows us to understand the nature of microstructural features, that are usually described by statistics. Because of these advantages, the EBSD dataset is widely used for synthetic microstructure generation. However, for the statistical description of microstructural features, the population of input data must be considered. Preferably, the EBSD measurement area must be sufficiently large to cover an adequate number of grains. However, a comprehensive study of this measurement area with a crystal plasticity finite element method (CPFEM) framework is still missing although it would considerably facilitate information exchange between experimentalists and simulation experts. Herein, the influence of the EBSD measurement area and the number of grains on the statistical description of the microstructural features and studying the corresponding micromechanical simulation results for 316L stainless steel samples produced by selective laser melting is investigated. © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    view abstract10.1002/adem.201901416
  • Influence of Pore Characteristics on Anisotropic Mechanical Behavior of Laser Powder Bed Fusion–Manufactured Metal by Micromechanical Modeling
    R. G. Prasad, M. and Biswas, A. and Geenen, K. and Amin, W. and Gao, S. and Lian, J. and Röttger, A. and Vajragupta, N. and Hartmaier, A.
    Advanced Engineering Materials 22 (2020)
    In recent times, additive manufacturing (AM) has proven to be an indispensable technique for processing complex 3D parts because of the versatility and ease of fabrication it offers. However, the generated microstructures show a high degree of complexity due to the complex solidification process of the melt pool. In this study, micromechanical modeling is applied to gain deeper insight into the influence of defects on plasticity and damage of 316L stainless steel specimens produced by a laser powder bed fusion (L-PBF) process. With the statistical data obtained from microstructure characterization, the complex AM microstructures are modeled by a synthetic microstructure generation tool. A damage model in combination with an element deletion technique is implemented into a nonlocal crystal plasticity model to describe anisotropic mechanical behavior, including damage evolution. The element deletion technique is applied to effectively model the growth and coalescence of microstructural pores as described by a damage parameter. Numerical simulations show that the shape of the pores not only affects the yielding and hardening behavior but also influences the porosity evolution itself. © 2020 The Authors. Published by Wiley-VCH GmbH
    view abstract10.1002/adem.202000641
  • Influence of trapped gas on pore healing under hot isostatic pressing in nickel-base superalloys
    Prasad, M.R.G. and Gao, S. and Vajragupta, N. and Hartmaier, A.
    Crystals 10 (2020)
    Under the typical hot isostatic pressing (HIP) processing conditions, plastic deformation by dislocation slip is considered the primary mechanism for pore shrinkage, according to experimental observations and deformation mechanism maps. In the present work, a crystal plasticity model has been used to investigate the influence of applied pressure and holding time on porosity reduction in a nickel-base single crystal superalloy. The influence of trapped gas on pore shrinkage is modeled by coupling mechanical deformation with pore–gas interaction. In qualitative agreement with experimental investigations, we observe that increasing the applied pressure or the holding time can effectively reduce porosity. Furthermore, the effect of pore shape on the shrinkage is observed to depend on a combination of elastic anisotropy and the complex distribution of stresses around the pore. Simulation results also reveal that, for pores of the same shape, smaller pores (radius < 0.1 µm) have a higher shrinkage rate in comparison to larger pores (radius ≥ 0.1 µm), which is attributed to the increasing pore surface energies with decreasing pore sizes. It is also found that, for smaller initial gas-filled pores (radius < 0.1 µm), HIP can result in very high gas pressures (on the order of GPa). Such high pressures either act as a driving force for argon to diffuse into the surrounding metal during HIP itself, or it can result in pore re-opening during subsequent annealing or mechanical loading. These results demonstrate that the micromechanical model can quantitatively evaluate the individual influences of HIP processing conditions and pore characteristics on pore annihilation, which can help optimize the HIP process parameters in the future. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/cryst10121147
  • Micromechanical modeling of DP600 steel: From microstructure to the sheet metal forming process
    Vajragupta, N. and Maassen, S. and Clausmeyer, T. and Brands, D. and Schröder, J. and Hartmaier, A.
    Procedia Manufacturing 47 (2020)
    This study proposes a micromechanical modeling scheme to predict relevant mechanical behavior of DP600 steel for the sheet metal forming process. This study can be divided into two parts which are the prediction of the advanced anisotropic initial yield function by means of microstructure-based simulations and the investigation of microstructure changes during the sheet metal forming process. Firstly, based on the quantitative microstructure characterization of DP600 steel by EBSD analysis, the obtained statistical information of important microstructural features is used to generate a microstructure model with the help of an advanced dynamic microstructure generator (ADMG), which combines a particle simulation method with radical Voronoi tessellation. In the next step, finite element simulations with a non-local crystal plasticity model for the individual grains are conducted. With the help of these simulations, the crystal plasticity parameters are adapted to match the experiments. The resulting parameterized microstructure model of DP600 steel is then applied to various loading conditions to investigate the corresponding mechanical responses. For the second part, macroscopic simulations of the bending process are performed and local deformation fields of the location of interest are captured and imposed as boundary conditions on the microstructure model to study the changes in the microstructural features. © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 23rd International Conference on Material Forming.
    view abstract10.1016/j.promfg.2020.04.347
  • Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations Reconstruction of the orientation density function
    Biswas, A. and Vajragupta, N. and Hielscher, R. and Hartmaier, A.
    Journal of Applied Crystallography 53 (2020)
    Crystallographic textures, as they develop for example during cold forming, can have a significant influence on the mechanical properties of metals, such as plastic anisotropy. Textures are typically characterized by a non-uniform distribution of crystallographic orientations that can be measured by diffraction experiments like electron backscatter diffraction (EBSD). Such experimental data usually contain a large number of data points, which must be significantly reduced to be used for numerical modeling. However, the challenge in such data reduction is to preserve the important characteristics of the experimental data, while reducing the volume and preserving the computational efficiency of the numerical model. For example, in micromechanical modeling, representative volume elements (RVEs) of the real microstructure are generated and the mechanical properties of these RVEs are studied by the crystal plasticity finite element method. In this work, a new method is developed for extracting a reduced set of orientations from EBSD data containing a large number of orientations. This approach is based on the established integer approximation method and it minimizes its shortcomings. Furthermore, the L 1 norm is applied as an error function; this is commonly used in texture analysis for quantitative assessment of the degree of approximation and can be used to control the convergence behavior. The method is tested on four experimental data sets to demonstrate its capabilities. This new method for the purposeful reduction of a set of orientations into equally weighted orientations is not only suitable for numerical simulation but also shows improvement in results in comparison with other available methods. © 2020 Abhishek Biswas et al.
    view abstract10.1107/S1600576719017138
  • Robust optimization scheme for inverse method for crystal plasticity model parametrization
    Shahmardani, M. and Vajragupta, N. and Hartmaier, A.
    Materials 13 (2020)
    A bottom-up material modeling based on a nonlocal crystal plasticity model requires information of a large set of physical and phenomenological parameters. Because of the many material parameters, it is inherently difficult to determine the nonlocal crystal plasticity parameters. Therefore, a robust method is proposed to parameterize the nonlocal crystal plasticity model of a body-centered cubic (BCC) material by combining a nanoindentation test and inverse analysis. Nanoindentation tests returned the load-displacement curve and surface imprint of the considered sample. The inverse analysis is developed based on trust-region-reflective algorithm, which is the most robust optimization algorithm for the considered non-convex problem. The discrepancy function is defined to minimize both the load-displacement curves and the surface topologies of the considered material under applying varied indentation forces obtained from numerical models and experimental output. The numerical model results based on the identified material properties show good agreement with the experimental output. Finally, a sensitivity analysis performed changing the nonlocal crystal plasticity parameters in a predefined range emphasized that the geometrical factor has the most significant influence on the load-displacement curve and surface imprint parameters. © 2020 by the authors.
    view abstract10.3390/ma13030735
  • Influence of Microstructural Features on the Strain Hardening Behavior of Additively Manufactured Metallic Components
    Biswas, A. and Prasad, M.R.G. and Vajragupta, N. and ul Hassan, H. and Brenne, F. and Niendorf, T. and Hartmaier, A.
    Advanced Engineering Materials 21 (2019)
    Additive manufacturing (AM) has recently become one of the key manufacturing processes in the era of Industry 4.0 because of its highly flexible production scheme. Due to complex thermal cycles during the manufacturing process itself and special solidification conditions, the microstructure of AM components often exhibits elongated grains together with a pronounced texture. These microstructural features significantly contribute to an anisotropic mechanical behavior. In this work, the microstructure and mechanical properties of additively manufactured samples of 316L stainless steel are characterized experimentally and a micromechanical modeling approach is employed to predict the macroscopic properties. The objective of this work is to study the effects of texture and microstructural morphology on yield strength and strain hardening behavior of face-centered cubic additively manufactured metallic components. To incorporate the texture in synthetic representative volume elements (RVE), the proposed approach considers both the crystallographic and grain boundary textures. The mechanical behavior of these RVEs is modeled using crystal plasticity finite element method, which incorporates size effects through the implementation of strain gradients. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    view abstract10.1002/adem.201900275
  • Modeling Macroscopic Material Behavior With Machine Learning Algorithms Trained by Micromechanical Simulations
    Reimann, D. and Nidadavolu, K. and ul Hassan, H. and Vajragupta, N. and Glasmachers, T. and Junker, P. and Hartmaier, A.
    Frontiers in Materials 6 (2019)
    Micromechanical modeling of material behavior has become an accepted approach to describe the macroscopic mechanical properties of polycrystalline materials in a microstructure-sensitive way. The microstructure is modeled by a representative volume element (RVE), and the anisotropic mechanical behavior of individual grains is described by a crystal plasticity model. Such micromechanical models are subjected to mechanical loads in a finite element (FE) simulation and their macroscopic behavior is obtained from a homogenization procedure. However, such micromechanical simulations with a discrete representation of the material microstructure are computationally very expensive, in particular when conducted for 3D models, such that it is prohibitive to apply them for process simulations of macroscopic components. In this work, we suggest a new approach to develop microstructure-sensitive, yet flexible and numerically efficient macroscopic material models by using micromechanical simulations for training Machine Learning (ML) algorithms to capture the mechanical response of various microstructures under different loads. In this way, the trained ML algorithms represent a new macroscopic constitutive relation, which is demonstrated here for the case of damage modeling. In a second application of the combination of ML algorithms and micromechanical modeling, a proof of concept is presented for the application of trained ML algorithms for microstructure design with respect to desired mechanical properties. The input data consist of different stress-strain curves obtained from micromechanical simulations of uniaxial testing of a wide range of microstructures. The trained ML algorithm is then used to suggest grain size distributions, grain morphologies and crystallographic textures, which yield the desired mechanical response for a given application. For validation purposes, the resulting grain microstructure parameters are used to generate RVEs, accordingly and the macroscopic stress-strain curves for those microstructures are calculated and compared with the target quantities. The two examples presented in this work, demonstrate clearly that ML methods can be trained by micromechanical simulations, which capture material behavior and its relation to microstructural mechanisms in a physically sound way. Since the quality of the ML algorithms is only as good as that of the micromechanical model, it is essential to validate these models properly. Furthermore, this approach allows a hybridization of experimental and numerical data. © Copyright © 2019 Reimann, Nidadavolu, ul Hassan, Vajragupta, Glasmachers, Junker and Hartmaier.
    view abstract10.3389/fmats.2019.00181
  • Parameterization of a Non-local Crystal Plasticity Model for Tempered Lath Martensite Using Nanoindentation and Inverse Method
    Engels, J.K. and Vajragupta, N. and Hartmaier, A.
    Frontiers in Materials 6 (2019)
    Crystal plasticity (CP) models have proven to accurately describe elasto-plastic behavior on micro- and nanometer length scales in numerous applications. However, their parameterization requires a series of experiments and inverse analysis of the results. In this regard, nanoindentation promises to be a well-suited tool for realizing a parameterization approach to determine all model parameters. The objective of this work is to develop a parameterization technique for a non-local CP model by means of an accessible and reproducible workflow. To determine its feasibility, tempered lath martensite with two different carbon contents is used as testing material. The workflow combines nanoindentation tests with finite element simulations. First, indentation into single packets of tempered lath martensitic specimen is yielding the load-displacement curves and the residual imprint topology on the surface with the help of atomic force microscopy. In a second step, a finite element simulation of the indentation using non-local crystal plasticity as constitutive model is performed with estimated model parameters. In the next step, non-local CP parameters are systematically adapted in an optimization scheme to reach optimal agreement with experiments. As a final validation step, it is successfully demonstrated that the CP model parameterized by nanoindentation is able to determine the macroscopic stress-strain response of polycrystals. Two observations are made: on the one hand, the material properties locally scatter very strongly, which is caused by fluctuations in microstructure and chemistry. On the other hand, a novel method has been demonstrated, were an inverse analysis is used to parameterize a non-local CP model for highly complex microstructures as those of tempered lath martensite. The novelty of this study is the application of nanoindentation and optimization scheme to parameterize a higher-order CP model of oligocrystals with a complex microstructure like the tempered lath martensite as well as the topology identification method developed and employed for both experiment and numerics. © Copyright © 2019 Engels, Vajragupta and Hartmaier.
    view abstract10.3389/fmats.2019.00247
  • Studying grain boundary strengthening by dislocation-based strain gradient crystal plasticity coupled with a multi-phase-field model
    Amin, W. and Ali, M.A. and Vajragupta, N. and Hartmaier, A.
    Materials 12 (2019)
    One ambitious objective of Integrated Computational Materials Engineering (ICME) is to shorten the materials development cycle by using computational materials simulation techniques at different length scales. In this regard, the most important aspects are the prediction of the microstructural evolution during material processing and the understanding of the contributions of microstructural features to the mechanical response of the materials. One possible solution to such a challenge is to apply the Phase Field (PF) method because it can predict the microstructural evolution under the influence of different internal or external stimuli, including deformation. To accomplish this, it is necessary to take into account plasticity or, specifically, non-homogeneous plastic deformation, which is particularly important for investigating the size effects in materials emerging at the micron length scale. In this work, we present quasi-2D simulations of plastic deformation in a face centred cubic system using a finite strain formulation. Our model consists of dislocation-based strain gradient crystal plasticity implemented into a PF code. We apply this model to study the influence of grain size on the mechanical behavior of polycrystals, which includes dislocation storage and annihilation. Furthermore, the initial state of the material before deformation is also considered. The results show that a dislocation-based strain gradient crystal plasticity model can capture the Hall-Petch effect in many aspects. The model reproduced the correct functional dependence of the flow stress of the polycrystal on grain size without assigning any special properties to the grain boundaries. However, the predicted Hall-Petch coefficients are significantly smaller than those found typically in experiments. In any case, we found a good qualitative agreement between our findings and experimental results. © 2019 by the authors.
    view abstract10.3390/ma12182977
  • Understanding of residual stresses in chain-die-formed dual-phase (DP) metallic components: predictive modelling and experimental validation
    Sun, Y. and Luzin, V. and Khan, S. and Vajragupta, N. and Meehan, P. and Daniel, B. and Yanagimoto, J. and Xiong, Z. and Ding, S.
    International Journal of Advanced Manufacturing Technology 103 (2019)
    Residual stresses in metallic components greatly affect the geometrical accuracy of advanced high-strength steels (AHSS) products used for automotive industry. Chain-die forming is a promising method to fabricate AHSS products which can minimize the residual stress induced. This paper aims to understand the residual stress in chain-die-formed dual-phase (DP) steels through analytical and numerical modelling together with experimental validation. Analytical and numerical models were firstly employed to predict the stress development and associated residual stresses induced by chain-die forming in consideration of an as-received residual stress field and a comprehensive material-hardening model. The residual stresses in different regions of formed parts were practically measured using the neutron diffraction method to verify the developed models. Same as the mesh size of the examining points of finite element analysis (FEA) models, the averaged over the same sampling size is measured to guarantee the accuracy. It seems to be consistent with the simulation and experimental results in consideration of both factors. However, compared with as-received residual stress, the kinematic factor has a more dominating impact on the final residual stress. The results presented should contribute to the prediction of geometric errors and minimize product defects caused by the residual stresses in chain-die forming or equivalent sheet metal-forming industry. © 2019, Springer-Verlag London Ltd., part of Springer Nature.
    view abstract10.1007/s00170-019-03671-9
  • Fracture properties of zinc coating layers in a galvannealed steel and an electrolytically galvanized steel
    He, J. and Lian, J. and Aretz, A. and Vajragupta, N. and Hangen, U. and Goodwin, F. and Münstermann, S.
    Materials Science and Engineering A 732 (2018)
    The zinc coating layer fracture properties of a galvannealed steel and an electrolytically galvanized steel are analyzed by conducting the in-situ bending test with newly designed samples. It is found that the fracture develops much earlier in the coating layers of the galvannealed steel than that of the electrolytically galvanized steel. Using transmission electron microscope and energy dispersive X-ray spectroscopy, the intermetallic phases of the coating layers are characterized and it is found that the early crack initiation in a galvannealed steel is mainly triggered in the gamma phase. Combining with nanoindentation tests and corresponding simulation, the deformability of intermetallic phases are analyzed to explain the failure behavior of coating layers in the two steels. © 2018 Elsevier B.V.
    view abstract10.1016/j.msea.2018.05.084
  • Micromechanical modeling approach to derive the yield surface for BCC and FCC steels using statistically informed microstructure models and nonlocal crystal plasticity
    Vajragupta, N. and Ahmed, S. and Boeff, M. and Ma, A. and Hartmaier, A.
    Physical Mesomechanics 20 (2017)
    In order to describe irreversible deformation during metal forming processes, the yield surface is one of the most important criteria. Because of their simplicity and efficiency, analytical yield functions along with experimental guidelines for parameterization become increasingly important for engineering applications. However, the relationship between most of these models and microstructural features are still limited. Hence, we propose to use micromechanical modeling, which considers important microstructural features, as a part of the solution to this missing link. This study aims at the development of a micromechanical modeling strategy to calibrate material parameters for the advanced analytical initial yield function Barlat YLD 2004-18p. To accomplish this, the representative volume element is firstly created based on a method making use of the statistical description of microstructure morphology as input parameter. Such method couples particle simulations to radical Voronoi tessellations to generate realistic virtual microstructures as representative volume elements. Afterwards, a nonlocal crystal plasticity model is applied to describe the plastic deformation of the representative volume element by crystal plasticity finite element simulation. Subsequently, an algorithm to construct the yield surface based on the crystal plasticity finite element simulation is developed. The primary objectives of this proposed algorithm are to automatically capture and extract the yield loci under various loading conditions. Finally, a nonlinear least square optimization is applied to determine the material parameters of Barlat YLD 2004-18p initial yield function of representative volume element, mimicking generic properties of bcc and fcc steels from the numerical simulations. © 2017, Pleiades Publishing, Ltd.
    view abstract10.1134/S1029959917030109
  • Prediction of plasticity and damage initiation behaviour of C45E + N steel by micromechanical modelling
    Wu, B. and Vajragupta, N. and Lian, J. and Hangen, U. and Wechsuwanmanee, P. and Münstermann, S.
    Materials and Design 121 (2017)
    For large-scale engineering applications, macroscopic phenomenological damage mechanics models with less complexity are usually applied due to their high computational efficiency and simple implementation procedures in finite element simulations. Compared with micromechanical models, however, they also have a significant disadvantage, namely the lack of microstructure sensitivity. This work aims to develop a method to integrate the influence of microstructural features into the parameter calibration of a stress-state-dependent damage mechanics model (the modified Bai-Wierzbicki model) for a C45E + N steel. For this purpose, virtual experiments are performed on an artificial microstructure model to derive the plasticity and damage initiation behaviour for the investigated material. A crystal plasticity model for ferrite along with an empirical strain hardening law for pearlite are assigned to the corresponding constituents in the artificial microstructure model to define their material properties. Nanoindentation tests and numerical analysis are used to calibrate the parameters of the crystal plasticity model. By applying different boundary conditions to the artificial microstructure model, both the plasticity and the damage initiation behaviour under different stress states are calibrated by the virtual experiments. In addition, this approach is also applied to investigating the influence of microstructure on plasticity and damage initiation. © 2017 Elsevier Ltd
    view abstract10.1016/j.matdes.2017.02.032
  • Towards prediction of springback in deep drawing using a micromechanical modeling scheme
    Vajragupta, N. and Ul Hassan, H. and Hartmaier, A.
    Procedia Engineering 207 (2017)
    Deep drawing is one of the most commonly used sheet metal forming processes, which can produce metal parts at a high rate. One of the major problems in deep drawing is springback, which is mainly elastic deformation occurring when the tool is removed. The focus of this work is the prediction of springback in deep drawing for DC04 steel using a micromechanical modeling scheme. A novel method is used for the characterization of material that leads to cyclic stress-strain curve. Simulations are performed with the Yoshida Uemori (YU) model for the prediction of springback for a U draw-bend geometry. The maximum deviation between the geometries of experiment and the springback simulation for hat geometry is 2.2 mm. It is shown that this micromechanical modeling scheme allows us to relate the influence of the microstructure to the springback prediction. © 2017 The Authors. Published by Elsevier Ltd.
    view abstract10.1016/j.proeng.2017.10.739
  • The Second Blind Sandia Fracture Challenge: improved MBW model predictions for different strain rates
    Di, Y. and Lian, J. and Wu, B. and Vajragupta, N. and Novokshanov, D. and Brinnel, V. and Döbereiner, B. and Könemann, M. and Münstermann, S.
    International Journal of Fracture 198 (2016)
    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. © 2016, Springer Science+Business Media Dordrecht.
    view abstract10.1007/s10704-016-0097-7
  • The second Sandia Fracture Challenge: predictions of ductile failure under quasi-static and moderate-rate dynamic loading
    Boyce, B.L. and Kramer, S.L.B. and Bosiljevac, T.R. and Corona, E. and Moore, J.A. and Elkhodary, K. and Simha, C.H.M. and Williams, B.W. and Cerrone, A.R. and Nonn, A. and Hochhalter, J.D. and Bomarito, G.F. and Warner, J.E. and Carter, B.J. and Warner, D.H. and Ingraffea, A.R. and Zhang, T. and Fang, X. and Lua, J. and Chiaruttini, V. and Mazière, M. and Feld-Payet, S. and Yastrebov, V.A. and Besson, J. and Chaboche, J.-L. and Lian, J. and Di, Y. and Wu, B. and Novokshanov, D. and Vajragupta, N. and Kucharczyk, P. and Brinnel, V. and Döbereiner, B. and Münstermann, S. and Neilsen, M.K. and Dion, K. and Karlson, K.N. and Foulk, J.W., III and Brown, A.A. and Veilleux, M.G. and Bignell, J.L. and Sanborn, S.E. and Jones, C.A. and Mattie, P.D. and Pack, K. and Wierzbicki, T. and Chi, S.-W. and Lin, S.-P. and Mahdavi, A. and Predan, J. and Zadravec, J. and Gross, A.J. and Ravi-Chandar, K. and Xue, L.
    International Journal of Fracture 198 (2016)
    Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in (Formula presented.) 0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods. © 2016, The Author(s).
    view abstract10.1007/s10704-016-0089-7
  • A method to quantitatively upscale the damage initiation of dual-phase steels under various stress states from microscale to macroscale
    Lian, J. and Yang, H. and Vajragupta, N. and Münstermann, S. and Bleck, W.
    Computational Materials Science 94 (2014)
    The aim of this paper is to develop a micromechanical model to quantitatively upscale the damage initiation of dual-phase steels under various stress states from micro to macro and reveal the underlying mechanisms of the damage initiation dependency on stress states from a microstructural level. Finite element (FE) model based on the real microstructure of a DP600 steel sheet is employed by representative volume element (RVE) method. Several numerical aspects are also discussed, such as mesh size and discretisation feature of the phase boundary. The plastic strain localisation theory is applied to the RVE modelling without any other damage models or imperfections. Three typical stress states, uniaxial tension, plane-strain tension and equibiaxial tension, are considered to investigate the influence of the stress state on damage initiation. The quantitative evaluation of the damage initiation for three stress states obtained from the RVE simulation shows the dependency on both stress triaxiality and Lode angle. The results are further compared to the experimentally calibrated damage initiation locus (DIL) and a fairly good agreement is achieved. From this study, the general physical understanding of the effect of stress states on damage initiation is explored and the method for quantitative analysis of the damage initiation in a microstructural level is also established. The microstructure heterogeneity is considered as the key factor that contributes to the damage initiation behaviour of the dual-phase steel. © 2014 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.commatsci.2014.05.051
  • Modeling the microstructure influence on fatigue life variability in structural steels
    Sharaf, M. and Kucharczyk, P. and Vajragupta, N. and Münstermann, S. and Hartmaier, A. and Bleck, W.
    Computational Materials Science 94 (2014)
    The endurance and HCF lifetime of multiphase steel components depend mainly on the phase of fatigue microcrack initiation and early propagation. A numerical study, which quantitatively describes the influence of microstructural features on the initiation and growth of cyclic microcracks, is presented within the context of microstructure-sensitive modeling. The implementation of kinematic hardening on each slip system in a crystal plasticity model allows for capturing the local accumulation of plastic microdeformation representing slip irreversibility occurring in the crack incubation phase. A load increasing testing technique with continuous temperature measurement and interrupted cyclic bending experiments deliver information about the endurance strength of a structural steel and allow for metallographic observation of cyclic microcrack propagation and thereby provide the experimental basis for the numerical simulations. The material model is implemented in cyclic computations with statistically representative volume elements, which are based on experimental microstructure description using the electron backscatter diffraction technique (EBSD). The extreme value distributions of the computed accumulation of local dislocation slip are then correlated to the microstructure in an approach to assess and explore the validity extent of microstructure-sensitive modeling using fatigue indicator parameters (FIPs) to correlate to the endurance limit and fatigue life under high-cycle fatigue conditions. The eligibility of consideration of the stresses normal to the planes of localized plastic damage assisting fatigue crack formation into these FIPs is investigated. © 2014 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.commatsci.2014.05.059
  • The modeling scheme to evaluate the influence of microstructure features on microcrack formation of DP-steel: The artificial microstructure model and its application to predict the strain hardening behavior
    Vajragupta, N. and Wechsuwanmanee, P. and Lian, J. and Sharaf, M. and Münstermann, S. and Ma, A. and Hartmaier, A. and Bleck, W.
    Computational Materials Science 94 (2014)
    Due to the existence of constituents with strong distinction in mechanical properties, dual phase steels exhibit remarkably high-energy absorption along with excellent combination of strength and ductility. Furthermore, these constituents also affect deformation and microcrack formation in which various mechanisms can be observed. Thus, a reliable microstructure-based simulation approach for describing these deformations and microcrack initiation is needed. Under this framework of modeling scheme development, several work packages have been carried out. These work packages includes algorithm to generate the artificial microstructure model, a procedure to derive plasticity parameters for each constituent, and characterization of the microcrack formation and initiation criteria determination. However, due to the complexity of topic and in order to describe each work package in detail, this paper focused only on the approach to generate the artificial microstructure model and its application to predict the strain hardening behavior. The approach was based on the quantitative results of metallographic microstructure analysis and their statistical representation. The dual phase steel was first characterized by EBSD analysis to identify individual phase grain size distribution functions. The results were then input into a multiplicatively weighted Voronoi tessellation based algorithm to generate artificial microstructure geometry models. Afterwards, nanoindentation was performed to calibrate crystal plasticity parameters of ferrite and empirical approach based on local chemical composition was used to approximate flow curve of martensite. By assigning the artificial microstructure model with plasticity description of each constituent, strain-hardening behavior of DP-steel was then predicted. © 2014 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.commatsci.2014.04.011
  • Micromechanical modelling of damage and failure in dual phase steels
    Lian, J. and Vajragupta, N. and Münstermann, S.
    Key Engineering Materials 554-557 (2013)
    Dual phase (DP) steels consisting of two phases, ferrite and dispersed martensite, offer an attractive combination of strength and stretchability, which is a result of the strong distinctions of these constituents in mechanical properties. However, the damage behaviour in DP steels exhibits a rather complex scenario: voids are generated by the debonding of the hard phase from the matrix and the inner cracking of the hard phase in addition to by inclusions. The target of this study is to describe the initiation and evolution of damage in DP steel and develop a microstructure-based model which is capable of reflecting the underlying damage mechanisms. Both uniaxial and biaxial tensile tests are performed and the subsequent metallographic investigations are executed to reveal the mechanisms of damage initiation and evolution under different stress state condition and attention will be paid on the influence of various microstructural features on the initiation of damage. In finite element (FE) simulations, the microstructural features are taken into account by the representative volume elements (RVE). Different treatments of the constitutive behaviour of each constituent including isotropic hardening rule and crystallographically dependent configuration with crystal plasticity finite element method are investigated. Several numerical aspects are also discussed, such as RVE size, mesh size, element type, and boundary connections. In the end, the study is attempting to achieve a quantitative assessment of the cold formability of the investigated steel in a microscopic level based on microstructure information of material as well as to understand the damage mechanisms under different stress states condition which cause the macroscopic failure during plastic deformation. Copyright © 2013 Trans Tech Publications Ltd.
    view abstract10.4028/www.scientific.net/KEM.554-557.2369
  • A micromechanical damage simulation of dual phase steels using XFEM
    Vajragupta, N. and Uthaisangsuk, V. and Schmaling, B. and Münstermann, S. and Hartmaier, A. and Bleck, W.
    Computational Materials Science 54 (2012)
    As a result of their microstructures being made up by constituents with strong distinctions in mechanical properties, multiphase steels exhibit high energy absorption as well as an excellent combination of strength and ductility. Furthermore, the microstructural composition influences the failure behaviour of such kind of steels because of the occurrence of different fracture mechanisms in parallel. When the failure behaviour of dual phase (DP) steels is investigated, several types of failures are typically observed, such as the ductile failure of ferrite, the brittle failure of martensite and the interface debonding between phases. Hence, a reliable microstructure-based simulation approach must be developed that describes material deformation and failure under any given loading condition. In this work, two different damage mechanics methods were employed to study the interaction between failure modes in DP steels by means of a representative volume element (RVE). In order to consider the characteristics of a real microstructure, all involved phases were modelled with a precise volume fraction. Firstly, the extended finite element method (XFEM) was used to study the damage onset and progression in martensitic regions without prescribing the crack path. Secondly, a damage curve was derived and employed for the ductile ferritic phase. By combining these two damage models in the RVE model on microscopic scale, development of different failures modes in DP steels could be investigated. © 2011 Elsevier B.V. All rights reserved.
    view abstract10.1016/j.commatsci.2011.10.035
  • Influence of Microstructural Features on the Propagation of Microstructurally Short Fatigue Cracks in Structural Steels
    Sharaf, M. and Lian, J. and Vajragupta, N. and Münstermann, S. and Bleck, W. and Schmaling, B. and Ma, A. and Hartmaier, A.
    Fatigue of Materials II: Advances and Emergences in Understanding (2012)
    Cyclically loaded structural steel components are usually designed to endure macroscopic stress amplitudes close to the material's endurance strength where microcracks initiate due to microstructural inhomogeneities and exhibit strong interactions with the various microstructural features in their neighborhood upon propagating. The current study presents a microstructural model with a capability to quantitatively describe the influence of microstructural features on the growth of cyclic cracks in the decisive, very early fatigue behavior stage. The FE model is based on the crystal plasticity theory and accounts for relative grain orientations. Both the extended finite element method (XFEM) and a coupled damage mechanics approach are used to describe crack opening behavior. The model is implemented to simulate real microcracking events produced in interrupted cyclic multiple-step tests under metallographic observation with temperature change measurements. Furthermore, the model is implemented on virtually created microstructures with altered grain sizes and orientations based on statistical EBSD analysis. © 2013 The Minerals, Metals, & Materials Society. All rights reserved.
    view abstract10.1002/9781118533383.ch18
  • crystal plasticity

  • finite element method

  • fracture

  • micromechanics

  • microstructure

  • modelling and simulation

  • representative volume element

  • steel

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