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Crystals
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Micromechanical Modelling and Its Applications to Polycrystals
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Micromechanical Modelling and Its Applications to Polycrystals

A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Inorganic Crystalline Materials".

Deadline for manuscript submissions: closed (30 November 2021) | Viewed by 20157

Special Issue Editors

Dr. Napat Vajragupta

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Guest Editor
Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Bochum, Germany
Interests: micromechanical modelling; microstructure digitalisation; crystal plasticity; nanoindentation; parameterisation by an inverse method; homogenization method; in-depth analysis of microstructure deformation; property-based design of microstructure; machine learning models; damage mechanics; integrated computational materials engineering (ICME)
Prof. Dr. Junhe Lian

E-Mail Website
Guest Editor
Department of Mechanical Engineering, Aalto University, Puumiehenkuja 3, 02150 Espoo, Finland
Interests: plasticity; damage and fracture; material modeling; crystal plasticity; microstructure-property relationship
Prof. Sebastian Münstermann

E-Mail Website
Guest Editor
Rheinisch-Westfalische Technische Hochschule Aachen, Aachen, Germany
Interests: damage mechanics; damage tolerant microstructures; fracture mechanics; material mechanics; structural integrity

Special Issue Information

Dear Colleagues,

The microstructure of a material influences its mechanical properties. It is hence desirable for the materials science and engineering (MSE) community to elucidate the relationships between microstructural features and mechanical properties. One of the promising ways to achieve this goal is to apply micromechanical modelling, which explicitly takes into account key microstructural features such as crystallographic texture and grain morphology. To promote this modelling technique to the research community and to exchange the latest findings from the experts, this Special Issue will focus on modelling methods and their applications, which are not restricted solving scientific problems but can also be applied to industry-related problems. In terms of modelling techniques and methods, the following topics are welcomed:

  • Microstructure digitalisation: methods for generate realistic microstructure model for micromechanical simulations
  • Constitutive models for describing deformation of crystalline materials e.g. crystal plasticity model
  • Parameterization of a material model by an inverse method
  • Homogenisation technique and prediction of mechanical properties
  • In-depth analysis of microstructure deformation
  • Assessment of damage, fatigue, and fracture by micromechanical modelling
  • Property-based design of microstructures

Furthermore, applications of micromechanical modelling on advanced materials like additively manufactured metals are accepted as well.

Dr. Napat Vajragupta
Dr. Junhe Lian
Prof. Sebastian Münstermann
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Crystals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Integrated computational materials engineering (ICME)
  • Micromechanical modelling
  • Microstructure digitalisation
  • Synthetic microstructure
  • Crystal plasticity
  • Damage mechanics

Published Papers (10 papers)

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Research

17 pages, 16201 KiB  
Article
Crystal Plasticity Modeling of Grey Cast Irons under Tension, Compression and Fatigue Loadings
by Viacheslav Balobanov, Matti Lindroos, Tom Andersson and Anssi Laukkanen
Crystals 2022, 12(2), 238; https://doi.org/10.3390/cryst12020238 - 09 Feb 2022
Cited by 3 | Viewed by 1540
Abstract
The study of the micromechanical performance of materials is important in explaining their macrostructural behavior, such as fracture and fatigue. This paper is aimed, among other things, at reducing the deficiency of microstructural models of grey cast irons in the literature. For this [...] Read more.
The study of the micromechanical performance of materials is important in explaining their macrostructural behavior, such as fracture and fatigue. This paper is aimed, among other things, at reducing the deficiency of microstructural models of grey cast irons in the literature. For this purpose, a numerical modeling approach based on the crystal plasticity (CP) theory is used. Both synthetic models and models based on scanning electron microscope (SEM) electron backscatter diffraction (EBSD) imaging finite element are utilized. For the metal phase, a CP model for body-centered cubic (BCC) crystals is adopted. A cleavage damage model is introduced as a strain-like variable; it accounts for crack closure in a smeared manner as the load reverses, which is especially important for fatigue modeling. A temperature dependence is included in some material parameters. The graphite phase is modeled using the CP model for hexagonal close-packed (HCP) crystal and has a significant difference in tensile and compressive behavior, which determines a similar macro-level behavior for cast iron. The numerical simulation results are compared with experimental tensile and compression tests at different temperatures, as well as with fatigue experiments. The comparison revealed a good performance of the modeling approach. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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17 pages, 9739 KiB  
Article
Microstructure-Based Fatigue Modeling with Residual Stresses: Effect of Inclusion Shape on Very High Cycle Fatigue Life
by Chao Gu, Junhe Lian, Ziyu Lv and Yanping Bao
Crystals 2022, 12(2), 200; https://doi.org/10.3390/cryst12020200 - 29 Jan 2022
Cited by 4 | Viewed by 2178
Abstract
When considering the effect of inclusions on fatigue life, the size effect of inclusions is well recognized. However, many of these studies overlooked or decoupled the size effect from the shape features. Therefore, in this study, the influence of the shape characteristics of [...] Read more.
When considering the effect of inclusions on fatigue life, the size effect of inclusions is well recognized. However, many of these studies overlooked or decoupled the size effect from the shape features. Therefore, in this study, the influence of the shape characteristics of inclusions with 3 equivalent sizes of 26.6 μm, 13.3 μm, and 4.2 μm on the very high cycle fatigue life of high-strength steels is investigated based on a microstructure-sensitive modeling approach, considering residual stresses. A shape parameter, unifying the aspect ratio and tilting angle of inclusion, is introduced. Based on this parameter, a new formulation of fatigue life with respect to inclusions is also proposed, extending the former one to consider the shape effect of inclusions. It is concluded that the general trend that the fatigue life increases with the decrease in inclusion size is still valid, while the shape features in terms of aspect ratio and tilting angle complicate the quantitative influence of inclusions size significantly. Even for a constant inclusion size, the combination of shape factor and tilting angle could change the fatigue life with one order of magnitude compared with the commonly assumed round shape. These findings would enhance the precision for the fatigue life estimation based on pre-inclusion analysis and also eventually provide new dimensions for inclusion engineering to improve fatigue resistance, as size will not be the only design parameter for fatigue life. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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18 pages, 6765 KiB  
Article
Influence of Crystal Plasticity Parameters on the Strain Hardening Behavior of Polycrystals
by Mahdieh Shahmardani, Napat Vajragupta and Alexander Hartmaier
Crystals 2021, 11(12), 1473; https://doi.org/10.3390/cryst11121473 - 27 Nov 2021
Cited by 2 | Viewed by 2095
Abstract
The effective mechanical properties of a polycrystal depend directly on the single-crystal properties of each grain and its crystallographic orientation with respect to the load axis. While the micromechanical approach has been used quite extensively to study the influence of grain shape and [...] Read more.
The effective mechanical properties of a polycrystal depend directly on the single-crystal properties of each grain and its crystallographic orientation with respect to the load axis. While the micromechanical approach has been used quite extensively to study the influence of grain shape and crystallographic texture on the resulting mechanical behavior of a polycrystal, the influence of the crystal plasticity parameters, which describe the constitutive behavior of the single crystal, requires to be investigated systemically because, typically, these parameters are fitted to describe a given material behavior. In the current research, this gap is filled by systemically studying the effect of changes in crystal plasticity parameters on the effective mechanical properties of polycrystals. The numerical model employed here consists of a representative volume element of 100 grains, and the material properties are described by using a non-local crystal plasticity model. A proper homogenization technique was used to homogenize the micromechanical results to an effective macroscopic material response. The equivalent stress versus equivalent plastic strain curve was obtained numerically by introducing the Voce-type hardening law, mimicking the material behavior in uniaxial tensile tests. The four parameters of the Voce-type hardening law were fitted to the macroscopic stress-strain curves, and the correlation between the crystal plasticity parameters and the Voce parameters has been studied, which is an efficient way to study the influence of microscopic material descriptions on the macroscopic behavior of polycrystals. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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16 pages, 2488 KiB  
Article
Finite Element Modeling of Brittle and Ductile Modes in Cutting of 3C-SiC
by Masud Alam, Liang Zhao, Napat Vajragupta, Junjie Zhang and Alexander Hartmaier
Crystals 2021, 11(11), 1286; https://doi.org/10.3390/cryst11111286 - 24 Oct 2021
Cited by 5 | Viewed by 1885
Abstract
Machining of brittle ceramics is a challenging task because the requirements on the cutting tools are extremely high and the quality of the machined surface strongly depends on the chosen process parameters. Typically, the efficiency of a machining process increases with the depth [...] Read more.
Machining of brittle ceramics is a challenging task because the requirements on the cutting tools are extremely high and the quality of the machined surface strongly depends on the chosen process parameters. Typically, the efficiency of a machining process increases with the depth of cut or the feed rate of the tool. However, for brittle ceramics, this easily results in very rough surfaces or even in crack formation. The transition from a smooth surface obtained for small depths of cut to a rough surface for larger depths of cut is called a brittle-to-ductile transition in machining. In this work, we investigate the mechanisms of this brittle-to-ductile transition for diamond cutting of an intrinsically brittle 3C-SiC ceramic with finite element modeling. The Drucker–Prager model has been used to describe plastic deformation of the material and the material parameters have been determined by an inverse method to match the deformation behavior of the material under nanoindentation, which is a similar loading state as the one occurring during cutting. Furthermore, a damage model has been introduced to describe material separation during the machining process and also crack initiation in subsurface regions. With this model, grooving simulations of 3C-SiC with a diamond tool have been performed and the deformation and damage mechanisms have been analyzed. Our results reveal a distinct transition between ductile and brittle cutting modes as a function of the depth of cut. The critical depth of cut for this transition is found to be independent of rake angle; however, the surface roughness strongly depends on the rake angle of the tool. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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20 pages, 22309 KiB  
Article
On Sampling Discrete Orientations from XRD for Texture Representation in Aggregates with Varying Grain Size
by Aditya Vuppala, Alexander Krämer and Johannes Lohmar
Crystals 2021, 11(9), 1021; https://doi.org/10.3390/cryst11091021 - 25 Aug 2021
Cited by 3 | Viewed by 2178
Abstract
The amount of orientation difference of crystallites, i.e., the texture in a metallic polycrystal governs, plastic anisotropy, electrical and magnetic properties of the material. For simulating the microstructure and texture evolution during forming processes, representative volume elements (RVEs) often generated based on experimental [...] Read more.
The amount of orientation difference of crystallites, i.e., the texture in a metallic polycrystal governs, plastic anisotropy, electrical and magnetic properties of the material. For simulating the microstructure and texture evolution during forming processes, representative volume elements (RVEs) often generated based on experimental measurements are commonly used. While the grain size and morphology of polycrystals are often determined via light-optical microscopy, their texture is conventionally analyzed through diffraction experiments. Data from these different experiments must be correlated such that a representative set of sampled orientations is assigned to the grains in the RVE. Here, the concept Texture Sampling through Orientation Optimization (TSOO) is introduced, where based on the intensity the required number of orientations is first assigned to the grains of the RVE directly. Then the Bunge–Euler angles of all orientations are optimized in turn with respect to the experimental measurements. As orientations are assigned to grains of variable size during optimization, the compatibility between inhomogeneity in the microstructure and texture is inherently addressed. This method was tested for different microstructures of non-oriented electrical steels and showed good accuracy for homogenous and inhomogeneous grain size distributions. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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12 pages, 3580 KiB  
Article
Crystal Plasticity with Micromorphic Regularization in Assessing Scale Dependent Deformation of Polycrystalline Doped Copper Alloys
by Matti Lindroos, Tom Andersson, Jarkko Metsäjoki and Anssi Laukkanen
Crystals 2021, 11(8), 994; https://doi.org/10.3390/cryst11080994 - 21 Aug 2021
Cited by 2 | Viewed by 1991
Abstract
It is planned that doped copper overpacks will be utilized in the spent nuclear fuel repositories in Finland and in Sweden. The assessment of long-term integrity of the material is a matter of importance. Grain structure variations, segregation and any possible manufacturing defects [...] Read more.
It is planned that doped copper overpacks will be utilized in the spent nuclear fuel repositories in Finland and in Sweden. The assessment of long-term integrity of the material is a matter of importance. Grain structure variations, segregation and any possible manufacturing defects in microstructure are relevant in terms of susceptibility to creep and damage from the loading evolution imposed by its operating environment. This work focuses on studying the microstructure level length-scale dependent deformation behavior of the material, of particular significance with respect to accumulation of plasticity over the extensive operational period of the overpacks. The reduced micromorphic crystal plasticity model, which is similar to strain gradient models, is used in this investigation. Firstly, the model’s size dependent plasticity effects are evaluated. Secondly, different microstructural aggregates presenting overpack sections are analyzed. Grain size dependent hardening responses, i.e., Hall-Petch like behavior, can be achieved with the enhanced hardening associated with the micromorphic model at polycrystalline level. It was found that the nominally large grain size in the base material of the overpack shows lower strain hardening potential than the fine grained region of the welded microstructure with stronger strain gradient related hardening effects. Size dependent regularization of strain localization networks is indicated as a desired characteristic of the model. The findings can be utilized to provide an improved basis for modeling the viscoplastic deformation behavior of the studied copper alloy and to assess the microstructural origins of any integrity concerns explicitly by way of full field modeling. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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9 pages, 3860 KiB  
Article
Study on Microstructure and Mechanical Property in Mg-Gd-Y Alloy by Secondary Extrusion Process
by Jianhua Liu, Jie Sun, Qingqiang Chen, Laixiao Lu and Yanhua Zhao
Crystals 2021, 11(8), 939; https://doi.org/10.3390/cryst11080939 - 12 Aug 2021
Cited by 3 | Viewed by 1439
Abstract
Extruded Mg-Gd-Y alloy tubes were obtained by using cast ingot and extruded bar billets. Microstructure and mechanical properties were also studied with two different cooling methods: air cooling and water cooling. The result shows that by using an extruded bar as billet extruded [...] Read more.
Extruded Mg-Gd-Y alloy tubes were obtained by using cast ingot and extruded bar billets. Microstructure and mechanical properties were also studied with two different cooling methods: air cooling and water cooling. The result shows that by using an extruded bar as billet extruded tubes achieves higher elongation comparing to using cast ingots due to favored texture for the activation of basal slip. Using the water-cooling method, extruded tubes achieve a higher yield strength compared to the air cooling method due to their fine grain size. Using cast ingot billets and the water-cooling method, the elongation is only 6% due to large unrecrystallized grains caused by inhomogeneous deformation and unfavored texture for the activation of basal slip. Using the extruded bar billet and the water-cooling method, the tube has uniformed small grains and much more randomized texture caused by the inhibition of preferred grain growth process. The highest texture intensity is only 1.852 in this kind of tube. Both high yield strength (195.3 MPa) and high elongation (23.9%) are achieved in this tube. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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21 pages, 13836 KiB  
Article
Deformation and Damage Assessments of Two DP1000 Steels Using a Micromechanical Modelling Method
by Niloufar Habibi, Napat Vajragupta and Sebastian Münstermann
Crystals 2021, 11(7), 805; https://doi.org/10.3390/cryst11070805 - 10 Jul 2021
Cited by 5 | Viewed by 2321
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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23 pages, 12922 KiB  
Article
Spatial and Direction-Based Characterization of Microstructures and Microhardness of TA15 Titanium Alloy Produced by Electron Beam Melting
by Jiangtao Ran, Xiaojing Sun, Shiliang Wei, Zhuo Chen and Hong Zhao
Crystals 2021, 11(5), 495; https://doi.org/10.3390/cryst11050495 - 29 Apr 2021
Cited by 3 | Viewed by 1642
Abstract
The extracted position and characterization direction of specimens have an unignorable effect on the microstructural characteristics of materials produced by electron beam melting (EBM). This study focused on the effects of extracted position and characterization direction on the microstructure, defect distribution and Vickers [...] Read more.
The extracted position and characterization direction of specimens have an unignorable effect on the microstructural characteristics of materials produced by electron beam melting (EBM). This study focused on the effects of extracted position and characterization direction on the microstructure, defect distribution and Vickers hardness of TA15 titanium alloy fabricated by electron beam melting. Results show that the microstructure at the bottom end of TA15 specimens is coarser and hot cracks are visible at this end. Grain morphology in longitudinal direction is columnar while that in transversal direction is chessboard-like. The results of defect analysis show that gas pores are visible in transversal direction while lack of fusion exists in longitudinal direction. The average relative density of TA15 specimens in transversal direction is higher than that in longitudinal direction. The results of energy spectrum analysis show that there is evaporation of Al during the forming process, but no elements segregation and enrichment are observed. This study provides important insights on the microstructure analysis and defect evaluation of materials made by EBM technology. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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29 pages, 3223 KiB  
Article
A Numerical Method to Improve the Representativeness of Real Microstructure Cut-Outs Applied in Finite Element Simulations
by Yanling Schneider, Werner Wasserbäch, Siegfried Schmauder, Zhangjian Zhou, Reiner Zielke and Wolfgang Tillmann
Crystals 2021, 11(4), 382; https://doi.org/10.3390/cryst11040382 - 06 Apr 2021
Cited by 2 | Viewed by 1789
Abstract
To improve the representativeness of a real microstructural cut-out for modeling purposes, a numerical method named as “boundary pixel color alteration (BPCA)” is presented to modify measured 2D microstructure cut-outs. Its physical background is related to the phase growth. For the application, the [...] Read more.
To improve the representativeness of a real microstructural cut-out for modeling purposes, a numerical method named as “boundary pixel color alteration (BPCA)” is presented to modify measured 2D microstructure cut-outs. Its physical background is related to the phase growth. For the application, the precondition is that the representativeness of the microstructure is already satisfied to a certain extent. This method resolves the problem that the phase composition of a small cut-out can have a large discrepancy to the real one. The main idea is to change the pixel color among neighboring pixels belonging to different phases. Our process simultaneously maintains most of the characteristics of the original morphology and is applicable for nearly all kinds of multi-phase or polycrystalline metallic alloys, as well. From our axisymmetric finite element (FE) simulations (ABAQUS ) applied with 2D real microstructures, it shows that the volume ratios of microstructural phases, as a function of the structure position to the symmetric axis, converge to phase area ratios in the 2D cut-out, even though the axisymmetric element volume is position dependent. A mathematical proof provides the reason for the aforementioned convergence. As examples to achieve real compositions and to numerically prove the aforementioned convergence, four different materials including multiphase polycrystals are implemented. An improvement of the predicted FE result is presented for the application of a modified microstructure (with a higher representativeness) compared to the original one. Full article
(This article belongs to the Special Issue Micromechanical Modelling and Its Applications to Polycrystals)
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