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Advanced Approaches Applied to Materials Development and Design Predictions

A special issue of Materials (ISSN 1996-1944).

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 39828

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Guest Editor
Department of Civil Engineering, University of Porto, 4200-465 Porto, Portugal
Interests: numerical modeling of engineering structures and structural components (offshore applications, steel bridges, pressure vessels, pipelines, wind turbine towers, etc.); mathematical problems in fatigue and fracture; mechanics of solids and structures; metals materials and structures; numerical fracture mechanics and crack growth; local approaches; finite element methods in structural mechanics applications; computer-aided structural integrity
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Guest Editor
Key Laboratory of Pressure Systems and Safety, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China
Interests: multi-physics damage modeling; high temperature fatigue; fatigue-creep interaction; life design and prediction; structural integrity; damage tolerance
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Guest Editor
School of Energy and Power Engineering, Beihang University, Beijing 100083, China
Interests: additive manufacturing; fatigue; fracture; multiscale modeling; in-situ experiments
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Special Issue Information

Dear Colleagues,

Fatigue damage represents one of the most important types of damage to which structural materials are subjected to in normal industrial services, which can finally result in a sudden and unexpected abrupt fracture. Since metal alloys are still the most used materials in designing a majority of components and structures able to carry the highest service loads, the study of the different aspects of metals fatigue attracts the permanent attention of scientists, engineers and designers.

The first International Colloquium on Mechanical Fatigue of Metals (ICMFM) was organized in Brno, Czech Republic in 1968. Afterwards, regular Colloquia on Mechanical Fatigue of Metals started in 1972 also in Brno and were originally limited to participants form the countries of the former “Eastern Block”. They continued until the 12th Colloquium in 1994 (Miskolc, Hungary) every two years. After a break twelve years long, the Colloquia restarted in 2006 (Ternopil, Ukraine), followed by the ones in 2008 (Varna, Bulgaria), 2010 (Opole, Poland), 2012 (Brno, Czech Republic), 2014 (Verbania, Italy), until the last one, which was organized in 2016 in Gijón (Asturias), Spain, with the aim of opening the Colloquium to participants from all countries interested in the subject of fatigue of metallic materials.

The XIX International Colloquium on Mechanical Fatigue of Metals (ICMFM XIX) will be organized in 5­–7 September 2018, at the Faculty of Engineering of the University of Porto, in Porto City, located at seaside in the northwest region of Portugal. This International Colloquium is intended to facilitate and encourage the exchange of knowledge and experiences among the different communities involved in both basic and applied research in this field, the fatigue of metals, looking at the problem of fatigue from a multiscale perspective, and exploring analytical and numerical simulative approaches, without losing the applications perspectives.

The limits of current generation materials are continuously reached according to the frontier of hostile environments, whether in the aerospace, nuclear or petro chemistry industry, or in the design of gas turbines where efficiency of energy production and transformation demands increased temperatures and pressures. At the same time, increase the reliability and performance, in particular by the control and understanding of early failures is one key point for the future materials. Moreover, increasing of material lifetimes in service and the extension of recycling time are expected. Accordingly, continued improvements on “materials by design” have been possible through accurate modeling of failure mechanisms by introducing advanced theoretical and simulation approaches/tools. Based on this, researches on failure mechanisms can provide assurance for new materials at the design stage and ensure the integrity in the construction at the fabrication phase. Specifically, material failure in hostile environments occurs under multi-sources of variability, resulting from load environments, material properties, geometry variations within tolerances, and other uncontrolled variations. Thus, advanced methods and applications for theoretical, numerical, and experimental contributions that address these issues on failure mechanism modeling and simulation of materials are desired and expected.

This Special Issue selects excellent papers from ICMFM 19 that are related to materials development. Potential topics include, but are not limited to:

  • Environmental assisted fatigue
  • Multi damage/degradation
  • Multi-scale modeling and simulation
  • Micromechanics of fracture
  • Material defects evolution
  • Interactions of extreme environments
  • Microstructure-based modeling and simulation
  • Fracture in extreme environments
  • Probabilistic Physics of Failure modeling and simulation
  • Advanced testing and simulation
  • Life prediction and extension
  • Stochastic degradation modeling and analysis
  • Ultra-low, low-, high- and giga-cycle fatigue
  • Fatigue in biomaterials
  • Cyclic plasticity and internal structure

Prof. Dr. Abílio M.P. De Jesus
Dr. José A.F.O. Correia
Assoc. Prof. Dr. Shun-Peng Zhu
Prof. Dr. Xiancheng Zhang
Prof. Dr. Dianyin Hu
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. Materials is an international peer-reviewed open access semimonthly 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

  • Wind/gas/steam turbine technologies
  • Power plant technologies
  • Failure mechanisms
  • Damage/degradation
  • Probabilistic Physics of Failure
  • Advanced testing and statistics

Published Papers (11 papers)

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Editorial

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4 pages, 195 KiB  
Editorial
Advanced Simulation Tools Applied to Materials Development and Design Predictions
by José Correia, Abílio De Jesus, Shun-Peng Zhu, Xiancheng Zhang and Dianyin Hu
Materials 2020, 13(1), 147; https://doi.org/10.3390/ma13010147 - 30 Dec 2019
Cited by 6 | Viewed by 2144
Abstract
This thematic issue on advanced simulation tools applied to materials development and design predictions gathers selected extended papers related to power generation systems, presented at the XIX International Colloquium on Mechanical Fatigue of Metals (ICMFM XIX) organized at University of Porto, Portugal, in [...] Read more.
This thematic issue on advanced simulation tools applied to materials development and design predictions gathers selected extended papers related to power generation systems, presented at the XIX International Colloquium on Mechanical Fatigue of Metals (ICMFM XIX) organized at University of Porto, Portugal, in 2018. Guest editors express special thanks to all contributors for the success of this special issue—authors, reviewers, and journal staff. Full article

Research

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16 pages, 10470 KiB  
Article
Study of the Fatigue Crack Growth in Long-Term Operated Mild Steel under Mixed-Mode (I + II, I + III) Loading Conditions
by Grzegorz Lesiuk, Michał Smolnicki, Dariusz Rozumek, Halyna Krechkovska, Oleksandra Student, José Correia, Rafał Mech and Abílio De Jesus
Materials 2020, 13(1), 160; https://doi.org/10.3390/ma13010160 - 01 Jan 2020
Cited by 24 | Viewed by 3292
Abstract
The paper presents an analysis of mixed-mode fatigue crack growth in bridge steel after 100-years operating time. Experiments were carried out under mode I + II configuration on Compact Tension Shear (CTS) specimens and mode I + III on rectangular specimens with lateral [...] Read more.
The paper presents an analysis of mixed-mode fatigue crack growth in bridge steel after 100-years operating time. Experiments were carried out under mode I + II configuration on Compact Tension Shear (CTS) specimens and mode I + III on rectangular specimens with lateral stress concentrator under bending and torsion loading type. Due to the lack of accurate Stress Intensity Factor (SIF) solutions, the crack path was modelled with the finite element method according to its experimental observation. As a result, the Kinetic Fatigue Fracture Diagrams (KFFD) were constructed. Due to the change in the tendency of higher fatigue crack growth rates from KI towards KIII dominance for the samples subjected to bending and torsion, it was decided to analyze this phenomenon in detail using electron-scanning microscopy. The fractographic analysis was carried out for specimens subjected to I + III crack loading mode. The mechanism of crack growth in old bridge steel at complex loads was determined and analyzed. Full article
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14 pages, 3736 KiB  
Article
Probabilistic Fatigue/Creep Optimization of Turbine Bladed Disk with Fuzzy Multi-Extremum Response Surface Method
by Chun-Yi Zhang, Zhe-Shan Yuan, Ze Wang, Cheng-Wei Fei and Cheng Lu
Materials 2019, 12(20), 3367; https://doi.org/10.3390/ma12203367 - 15 Oct 2019
Cited by 18 | Viewed by 2309
Abstract
To effectively perform the probabilistic fatigue/creep coupling optimization of a turbine bladed disk, this paper develops the fuzzy multi-extremum response surface method (FMERSM) for the comprehensive probabilistic optimization of multi-failure/multi-component structures, which absorbs the ideas of the extremum response surface method, hierarchical strategy, [...] Read more.
To effectively perform the probabilistic fatigue/creep coupling optimization of a turbine bladed disk, this paper develops the fuzzy multi-extremum response surface method (FMERSM) for the comprehensive probabilistic optimization of multi-failure/multi-component structures, which absorbs the ideas of the extremum response surface method, hierarchical strategy, and fuzzy theory. We studied the approaches of FMERSM modeling and fatigue/creep damage evaluation of turbine bladed disks, and gave the procedure for the fuzzy probabilistic fatigue/creep optimization of a multi-component structure with FMERSM. The probabilistic fatigue/creep coupling optimization of turbine bladed disks was implemented by regarding the rotor speed, temperature, and density as optimization parameters; the creep stress, creep strain, fatigue damage, and creep damage as optimization objectives; and the reliability and GH4133B fatigue/creep damages as constraint functions. The results show that gas temperature T and rotor speed ω are the key parameters that should be controlled in bladed disk optimization, and respectively reduce by 85 K and 113 rad/s after optimization, which is promising to extend bladed disk life and decrease failure damages. The simulation results show that this method has a higher modeling accuracy and computational efficiency than the Monte Carlo method (MCM). The efforts of this study provide a new useful method for overall probabilistic multi-failure optimization and enrich mechanical reliability theory. Full article
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13 pages, 10741 KiB  
Article
Influence of Polyurea Composite Coating on Selected Mechanical Properties of AISI 304 Steel
by Monika Duda, Joanna Pach and Grzegorz Lesiuk
Materials 2019, 12(19), 3137; https://doi.org/10.3390/ma12193137 - 26 Sep 2019
Cited by 18 | Viewed by 2936
Abstract
This paper contains experimental results of mechanical testing of the AISI 304 steel with composite coatings. The main goal was to investigate the impact of the applied polyurea composite coating on selected mechanical properties: Adhesion, impact resistance, static behavior, and, finally, fatigue lifetime [...] Read more.
This paper contains experimental results of mechanical testing of the AISI 304 steel with composite coatings. The main goal was to investigate the impact of the applied polyurea composite coating on selected mechanical properties: Adhesion, impact resistance, static behavior, and, finally, fatigue lifetime of notched specimens. In the paper the following configurations of coatings were tested: EP (epoxy resin), EP_GF (epoxy resin + glass fabric), EP_GF_HF (epoxy resin + glass fabric hemp fiber), EP_PUA (epoxy resin + polyurea) resin, EP_GF_PUA (epoxy resin + glass fabric + polyurea) resin, and EP_GF_HF_PUA (epoxy resin + glass fabric + hemp fiber + polyurea) resin. The highest value of force required to break adhesive bonds was observed for the EP_PUA coating, the smallest for the single EP coating. A tendency of polyurea to increase the adhesion of the coating to the base was noticed. The largest area of delamination during the impact test was observed for the EP_GF_HF coating and the smallest for the EP-coated sample. In all tested samples, observed delamination damage during the pull-off test was located between the coating and the metallic base of the sample. Full article
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17 pages, 5468 KiB  
Article
Computed Tomography-Based Characterization of the Fatigue Behavior and Damage Development of Extruded Profiles Made from Recycled AW6060 Aluminum Chips
by Alexander Koch, Philipp Wittke and Frank Walther
Materials 2019, 12(15), 2372; https://doi.org/10.3390/ma12152372 - 25 Jul 2019
Cited by 13 | Viewed by 2615
Abstract
The possibility of producing profiles directly by hot extrusion of aluminum chips, normally considered as scrap, is a promising alternative to the energy-intensive remelting process. It has to be taken into account that the mechanical properties depend on the quality of the weld [...] Read more.
The possibility of producing profiles directly by hot extrusion of aluminum chips, normally considered as scrap, is a promising alternative to the energy-intensive remelting process. It has to be taken into account that the mechanical properties depend on the quality of the weld seams between the chips, which arise during the extrusion process. To estimate the influence of the weld seams, quasistatic and cyclic investigations were performed on chip-based profiles and finally compared with cast-based extruded profiles. In order to gain comprehensive information about the fatigue progress, different measurement techniques like alternating current potential drop (ACPD)-technique, hysteresis measurements, and temperature measurements were used during the fatigue tests. The weld seams and voids were investigated using computed tomography and metallographic techniques. Results show that quasistatic properties of chip-based specimens are only reduced by about 5%, whereas the lifetime is reduced by about a decade. The development of the fatigue cracks, which propagate between the chip boundaries, was characterized by an intermittent testing strategy, where an initiation of two separate cracks was observed. Full article
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15 pages, 6628 KiB  
Article
PSO-BP Neural Network-Based Strain Prediction of Wind Turbine Blades
by Xin Liu, Zheng Liu, Zhongwei Liang, Shun-Peng Zhu, José A. F. O. Correia and Abílio M. P. De Jesus
Materials 2019, 12(12), 1889; https://doi.org/10.3390/ma12121889 - 12 Jun 2019
Cited by 48 | Viewed by 3817
Abstract
The full-scale static testing of wind turbine blades is an effective means to verify the accuracy and rationality of the blade design, and it is an indispensable part in the blade certification process. In the full-scale static experiments, the strain of the wind [...] Read more.
The full-scale static testing of wind turbine blades is an effective means to verify the accuracy and rationality of the blade design, and it is an indispensable part in the blade certification process. In the full-scale static experiments, the strain of the wind turbine blade is related to the applied loads, loading positions, stiffness, deflection, and other factors. At present, researches focus on the analysis of blade failure causes, blade load-bearing capacity, and parameter measurement methods in addition to the correlation analysis between the strain and the applied loads primarily. However, they neglect the loading positions and blade displacements. The correlation among the strain and applied loads, loading positions, displacements, etc. is nonlinear; besides that, the number of design variables is numerous, and thus the calculation and prediction of the blade strain are quite complicated and difficult using traditional numerical methods. Moreover, in full-scale static testing, the number of measuring points and strain gauges are limited, so the test data have insufficient significance to the calibration of the blade design. This paper has performed a study on the new strain prediction method by introducing intelligent algorithms. Back propagation neural network (BPNN) improved by Particle Swarm Optimization (PSO) has significant advantages in dealing with non-linear fitting and multi-input parameters. Models based on BPNN improved by PSO (PSO-BPNN) have better robustness and accuracy. Based on the advantages of the neural network in dealing with complex problems, a strain-predictive PSO-BPNN model for full-scale static experiment of a certain wind turbine blade was established. In addition, the strain values for the unmeasured points were predicted. The accuracy of the PSO-BPNN prediction model was verified by comparing with the BPNN model and the simulation test. Both the applicability and usability of strain-predictive neural network models were verified by comparing the prediction results with simulation outcomes. The comparison results show that PSO-BPNN can be utilized to predict the strain of unmeasured points of wind turbine blades during static testing, and this provides more data for characteristic structural parameters calculation. Full article
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15 pages, 2453 KiB  
Article
Reliability-Based Low Fatigue Life Analysis of Turbine Blisk with Generalized Regression Extreme Neural Network Method
by Chunyi Zhang, Jingshan Wei, Huizhe Jing, Chengwei Fei and Wenzhong Tang
Materials 2019, 12(9), 1545; https://doi.org/10.3390/ma12091545 - 10 May 2019
Cited by 29 | Viewed by 3530
Abstract
Turbine blisk low cycle fatigue (LCF) is affected by various factors such as heat load, structural load, operation parameters and material parameters; it seriously influences the reliability and performance of the blisk and aeroengine. To study the influence of thermal-structural coupling on the [...] Read more.
Turbine blisk low cycle fatigue (LCF) is affected by various factors such as heat load, structural load, operation parameters and material parameters; it seriously influences the reliability and performance of the blisk and aeroengine. To study the influence of thermal-structural coupling on the reliability of blisk LCF life, the generalized regression extreme neural network (GRENN) method was proposed by integrating the basic thoughts of generalized regression neural network (GRNN) and the extreme response surface method (ERSM). The mathematical model of the developed GRENN method was first established in respect of the LCF life model and the ERSM model. The method and procedure for reliability and sensitivity analysis based on the GRENN model were discussed. Next, the reliability and sensitivity analyses of blisk LCF life were performed utilizing the GRENN method under a thermal-structural interaction by regarding the randomness of gas temperature, rotation speed, material parameters, LCF performance parameters and the minimum fatigue life point of the objective of study. The analytical results reveal that the reliability degree was 0.99848 and the fatigue life is 9419 cycles for blisk LCF life when the allowable value is 6000 cycles so that the blisk has some life margin relative to 4500 cycles in the deterministic analysis. In comparison with ERSM, the computing time and precision of the proposed GRENN under 10,000 simulations is 1.311 s and 99.95%. This is improved by 15.18% in computational efficiency and 1.39% in accuracy, respectively. Moreover, high efficiency and high precision of the developed GRENN become more obvious with the increasing number of simulations. In light of the sensitivity analysis, the fatigue ductility index and temperature are the key factors of determining blisk LCF life because their effect probabilities reach 41% and 26%, respectively. Material density, rotor speed, the fatigue ductility coefficient, the fatigue strength coefficient and the fatigue ductility index are also significant parameters for LCF life. Poisson’s ratio and elastic modulus of materials have little effect. The efforts of this paper validate the feasibility and validity of GRENN in the reliability analysis of blisk LCF life and give the influence degrees of various random parameters on blisk LCF life, which are promising to provide useful insights for the probabilistic optimization of turbine blisk LCF life. Full article
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13 pages, 2504 KiB  
Article
Application of a New, Energy-Based ΔS* Crack Driving Force for Fatigue Crack Growth Rate Description
by Grzegorz Lesiuk
Materials 2019, 12(3), 518; https://doi.org/10.3390/ma12030518 - 09 Feb 2019
Cited by 6 | Viewed by 5463
Abstract
This paper presents the problem of the description of fatigue cracking development in metallic constructional materials. Fatigue crack growth models (mostly empirical) are usually constructed using a stress intensity factor ΔK in linear-elastic fracture mechanics. Contrary to the kinetic fatigue fracture diagrams [...] Read more.
This paper presents the problem of the description of fatigue cracking development in metallic constructional materials. Fatigue crack growth models (mostly empirical) are usually constructed using a stress intensity factor ΔK in linear-elastic fracture mechanics. Contrary to the kinetic fatigue fracture diagrams (KFFDs) based on stress intensity factor K, new energy KFFDs show no sensitivity to mean stress effect expressed by the stress ratio R. However, in the literature there is a lack of analytical description and interpretation of this parameter in order to promote this approach in engineering practice. Therefore, based on a dimensional analysis approach, ΔH is replaced by elastic-plastic fracture mechanics parameter—the ΔJ-integral range. In this case, the invariance from stress is not clear. Hence, the main goal of this paper is the application of the new averaged (geometrically) strain energy density parameter ΔS* based on the relationship of the maximal value of J integral and its range ΔJ. The usefulness and invariance of this parameter have been confirmed for three different metallic materials, 10HNAP, 18G2A, and 19th century puddle iron from the Eiffel bridge. Full article
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11 pages, 3692 KiB  
Article
First-Principles Study on the Adsorption and Dissociation of Impurities on Copper Current Collector in Electrolyte for Lithium-Ion Batteries
by Jian Chen, Chao Li, Jian Zhang, Cong Li, Jianlin Chen and Yanjie Ren
Materials 2018, 11(7), 1256; https://doi.org/10.3390/ma11071256 - 21 Jul 2018
Cited by 9 | Viewed by 4490
Abstract
The copper current collector is an important component for lithium-ion batteries and its stability in electrolyte impacts their performance. The decomposition of LiPF6 in the electrolyte of lithium-ion batteries produces the reactive PF6, which reacts with the residual water and [...] Read more.
The copper current collector is an important component for lithium-ion batteries and its stability in electrolyte impacts their performance. The decomposition of LiPF6 in the electrolyte of lithium-ion batteries produces the reactive PF6, which reacts with the residual water and generates HF. In this paper, the adsorption and dissociation of H2O, HF, and PF5 on the Cu(111) surface were studied using a first-principles method based on the density functional theory. The stable configurations of HF, H2O, and PF5 adsorbed on Cu(111) and the geometric parameters of the admolecules were confirmed after structure optimization. The results showed that PF5 can promote the dissociation reaction of HF. Meanwhile, PF5 also promoted the physical adsorption of H2O on the Cu(111) surface. The CuF2 molecule was identified by determining the bond length and the bond angle of the reaction product. The energy barriers of HF dissociation on clean and O-atom-preadsorbed Cu(111) surfaces revealed that the preadsorbed O atom can promote the dissociation of HF significantly. Full article
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12 pages, 2931 KiB  
Article
Surface Nanocrystallization and Amorphization of Dual-Phase TC11 Titanium Alloys under Laser Induced Ultrahigh Strain-Rate Plastic Deformation
by Sihai Luo, Liucheng Zhou, Xuede Wang, Xin Cao, Xiangfan Nie and Weifeng He
Materials 2018, 11(4), 563; https://doi.org/10.3390/ma11040563 - 06 Apr 2018
Cited by 22 | Viewed by 4029
Abstract
As an innovative surface technology for ultrahigh strain-rate plastic deformation, laser shock peening (LSP) was applied to the dual-phase TC11 titanium alloy to fabricate an amorphous and nanocrystalline surface layer at room temperature. X-ray diffraction, transmission electron microscopy, and high-resolution transmission electron microscopy [...] Read more.
As an innovative surface technology for ultrahigh strain-rate plastic deformation, laser shock peening (LSP) was applied to the dual-phase TC11 titanium alloy to fabricate an amorphous and nanocrystalline surface layer at room temperature. X-ray diffraction, transmission electron microscopy, and high-resolution transmission electron microscopy (HRTEM) were used to investigate the microstructural evolution, and the deformation mechanism was discussed. The results showed that a surface nanostructured surface layer was synthesized after LSP treatment with adequate laser parameters. Simultaneously, the behavior of dislocations was also studied for different laser parameters. The rapid slipping, accumulation, annihilation, and rearrangement of dislocations under the laser-induced shock waves contributed greatly to the surface nanocrystallization. In addition, a 10 nm-thick amorphous structure layer was found through HRTEM in the top surface and the formation mechanism was attributed to the local temperature rising to the melting point, followed by its subsequent fast cooling. Full article
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13 pages, 32816 KiB  
Article
Indentation Behavior and Mechanical Properties of Tungsten/Chromium co-Doped Bismuth Titanate Ceramics Sintered at Different Temperatures
by Shaoxiong Xie, Jiageng Xu, Yu Chen, Zhi Tan, Rui Nie, Qingyuan Wang and Jianguo Zhu
Materials 2018, 11(4), 503; https://doi.org/10.3390/ma11040503 - 27 Mar 2018
Cited by 18 | Viewed by 3791
Abstract
A sort of tungsten/chromium(W/Cr) co-doped bismuth titanate (BIT) ceramics (Bi4Ti2.95W0.05O12.05 + 0.2 wt % Cr2O3, abbreviate to BTWC) are ordinarily sintered between 1050 and 1150 °C, and the indentation behavior and mechanical [...] Read more.
A sort of tungsten/chromium(W/Cr) co-doped bismuth titanate (BIT) ceramics (Bi4Ti2.95W0.05O12.05 + 0.2 wt % Cr2O3, abbreviate to BTWC) are ordinarily sintered between 1050 and 1150 °C, and the indentation behavior and mechanical properties of ceramics sintered at different temperatures have been investigated by both nanoindentation and microindentation technology. Firstly, more or less Bi2Ti2O7 grains as the second phase were found in BTWC ceramics, and the grain size of ceramics increased with increase of sintering temperatures. A nanoindentation test for BTWC ceramics reveals that the testing hardness of ceramics decreased with increase of sintering temperatures, which could be explained by the Hall–Petch equation, and the true hardness could be calculated according to the pressure-state-response (PSR) model considering the indentation size effect, where the value of hardness depends on the magnitude of load. While, under the application of microsized Vickers, the sample sintered at a lower temperature (1050 °C) gained four linearly propagating cracks, however, they were observed to shorten in the sample sintered at a higher temperature (1125 °C). Moreover, both the crack deflection and the crack branching existed in the latter. The hardness and the fracture toughness of BTWC ceramics presented a contrary variational tendency with increase of sintering temperatures. A high sintering tends to get a lower hardness and a higher fracture toughness, which could be attributed to the easier plastic deformation and the stronger crack inhibition of coarse grains, respectively, as well as the toughening effect coming from the second phase. Full article
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