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Keywords = inelastic strain energy density

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16 pages, 6813 KiB  
Article
Creep–Fatigue Behavior and Life Prediction of Medium-Si-Mo Ductile Iron
by Mucheng Liu, Huihua Feng and Peirong Ren
Appl. Sci. 2025, 15(10), 5406; https://doi.org/10.3390/app15105406 - 12 May 2025
Viewed by 520
Abstract
Exhaust manifolds accumulate creep and fatigue damage under cyclic thermal loading, leading to localized failure. Understanding a material’s mechanical behavior is crucial for accurate life assessment. This study systematically investigated the low-cycle fatigue (LCF) and creep–fatigue interaction behaviors of medium-silicon molybdenum ductile iron. [...] Read more.
Exhaust manifolds accumulate creep and fatigue damage under cyclic thermal loading, leading to localized failure. Understanding a material’s mechanical behavior is crucial for accurate life assessment. This study systematically investigated the low-cycle fatigue (LCF) and creep–fatigue interaction behaviors of medium-silicon molybdenum ductile iron. It was found that QTRSi4Mo exhibited cyclic hardening at room temperature and 400 °C, whereas it exhibited cyclic softening at 600 °C and 700 °C for low-cycle stress–strain responses. During creep–fatigue tests with hold time, variations in the strain amplitude did not alter the hysteresis loop shape or the hardening/softening characteristics of the material. They only induced a slight upward shift in the yield center. Additionally, stress relaxation primarily occurred in the initial phase of the hold period, so the hold duration had little effect on the final stress value. The investigation of creep–fatigue life models highlighted that accurately characterizing the damage induced by stress relaxation during the hold stage is critical for creep damage evaluation. The calculated creep damage results differed greatly from the experimental results of the time fraction model (TF). A combined approach using the strain energy density dissipation model (T-SEDE) and the Ostergren method demonstrated excellent predictive capability for creep–fatigue life. Full article
(This article belongs to the Special Issue Advances and Applications in Mechanical Fatigue and Life Assessment)
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23 pages, 5371 KiB  
Article
Low-Cycle Fatigue Properties of Bimetallic Steel Bar with Buckling: Energy-Based Numerical and Experimental Investigations
by Xuanyi Xue, Fei Wang, Neng Wang, Jianmin Hua and Wenjie Deng
Materials 2024, 17(16), 3974; https://doi.org/10.3390/ma17163974 - 9 Aug 2024
Cited by 3 | Viewed by 1065
Abstract
A bimetallic steel bar (BSB) consisting of stainless-steel cladding and carbon steel substrate exhibits excellent corrosion resistance and good mechanical properties. The bimetallic structure of BSBs may affect their low-cycle fatigue performance, and current investigations on the above issue are limited. In this [...] Read more.
A bimetallic steel bar (BSB) consisting of stainless-steel cladding and carbon steel substrate exhibits excellent corrosion resistance and good mechanical properties. The bimetallic structure of BSBs may affect their low-cycle fatigue performance, and current investigations on the above issue are limited. In this study, the low-cycle fatigue properties of bimetallic steel bars (BSBs) with inelastic buckling were investigated. Experiments and numerical studies were conducted to investigate the low-cycle fatigue capacity for BSBs, considering buckling. The buckling mode of BSBs is discussed. The hysteretic loops and energy properties of BSBs with various slenderness ratios (L/D) and fatigue strain amplitudes (εa) are investigated. With increases in the L/D and εa, the original symmetry for hysteresis loops disappears gradually, which is caused by the buckling. A predictive equation revealing the relation between the εa and fatigue life is suggested, which considers the effects of the L/D. A numerical modelling method is suggested to predict the hysteretic curves of BSBs. The effect of buckling on the stress and energy properties of BSBs is discussed through the numerical analysis of 44 models including the effects of the L/D, εa, and cladding ratios. The numerical analysis results illustrate that the hysteresis loops of BSBs with various εa values exhibit similar shapes. The increase in the cladding ratio reduces the peak stress and the dissipated energy properties of BSBs. The hysteresis loop energy density decreases by about 3% with an increase of 0.1 in the cladding ratio. It is recommended that the proportion of stainless steel inBSBs should be minimized once the corrosion resistance requirements are met. Full article
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24 pages, 20879 KiB  
Article
Creep-Fatigue Life Evaluation for Grade 91 Steels with Various Origins and Service Histories
by Haruhisa Shigeyama, Yukio Takahashi, John Siefert and Jonathan Parker
Metals 2024, 14(2), 148; https://doi.org/10.3390/met14020148 - 25 Jan 2024
Cited by 3 | Viewed by 2178
Abstract
Grade 91 steel is widely used in the boilers and piping of thermal power plants. There has been significant research interest in understanding the variations in creep characteristics among different heats of this steel for effective plant management. In recent years, thermal power [...] Read more.
Grade 91 steel is widely used in the boilers and piping of thermal power plants. There has been significant research interest in understanding the variations in creep characteristics among different heats of this steel for effective plant management. In recent years, thermal power plants have been subjected to frequent load changes and startup/shutdown to adjust power supply and demand and stabilize frequencies. These operational shifts have raised concerns regarding the potential for creep-fatigue damage in high-temperature components. Therefore, this research focuses on creep-fatigue properties of Grade 91 steel and their predictability. Tensile, creep, strain-controlled fatigue, and strain-controlled creep-fatigue tests were performed on six Grade 91 steels with different heats and/or histories, and the characteristics in each test were compared. As a result, the variations in creep-fatigue life among the materials were found to be correlated with the difference in creep characteristics and stress level during stress relaxation. Furthermore, the study involved a comparative assessment of the predictive performance of creep-fatigue life using five different approaches: time fraction, classical ductility exhaustion, modified ductility exhaustion, energy-based, and hybrid approaches. Among these approaches, the hybrid approach, based on inelastic strain energy density at fracture formulated as a function of inelastic strain rate, exhibited the most accurate predictive performance. Full article
(This article belongs to the Special Issue Creep and Fatigue Behavior of Alloys)
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13 pages, 7797 KiB  
Article
Reliability Evaluation of Board-Level Flip-Chip Package under Coupled Mechanical Compression and Thermal Cycling Test Conditions
by Meng-Kai Shih, Yu-Hao Liu, Calvin Lee and C. P. Hung
Materials 2023, 16(12), 4291; https://doi.org/10.3390/ma16124291 - 9 Jun 2023
Cited by 5 | Viewed by 4393
Abstract
Flip Chip Ball Grid Array (FCBGA) packages, together with many other heterogeneous integration packages, are widely used in high I/O (Input/Output) density and high-performance computing applications. The thermal dissipation efficiency of such packages is often improved through the use of an external heat [...] Read more.
Flip Chip Ball Grid Array (FCBGA) packages, together with many other heterogeneous integration packages, are widely used in high I/O (Input/Output) density and high-performance computing applications. The thermal dissipation efficiency of such packages is often improved through the use of an external heat sink. However, the heat sink increases the solder joint inelastic strain energy density, and thus reduces the board-level thermal cycling test reliability. The present study constructs a three-dimensional (3D) numerical model to investigate the solder joint reliability of a lidless on-board FCBGA package with heat sink effects under thermal cycling testing, in accordance with JEDEC standard test condition G (a thermal range of −40 to 125 °C and a dwell/ramp time of 15/15 min). The validity of the numerical model is confirmed by comparing the predicted warpage of the FCBGA package with the experimental measurements obtained using a shadow moiré system. The effects of the heat sink and loading distance on the solder joint reliability performance are then examined. It is shown that the addition of the heat sink and a longer loading distance increase the solder ball creep strain energy density (CSED) and degrade the package reliability performance accordingly. Full article
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13 pages, 10434 KiB  
Article
High-Resolution Characterization of Deformation Induced Martensite in Large Areas of Fatigued Austenitic Stainless Steel Using Deep Learning
by Šárka Mikmeková, Jiří Man, Ondřej Ambrož, Patrik Jozefovič, Jan Čermák, Antti Järvenpää, Matias Jaskari, Jiří Materna and Tomáš Kruml
Metals 2023, 13(6), 1039; https://doi.org/10.3390/met13061039 - 29 May 2023
Cited by 1 | Viewed by 2654
Abstract
This paper aims to demonstrate a novel technique enabling the accurate visualization and fast mapping of deformation-induced α′-martensite produced during cyclic straining of a metastable austenitic stainless steel, refined by reversion annealing to different grain sizes. The technique is based on energy and [...] Read more.
This paper aims to demonstrate a novel technique enabling the accurate visualization and fast mapping of deformation-induced α′-martensite produced during cyclic straining of a metastable austenitic stainless steel, refined by reversion annealing to different grain sizes. The technique is based on energy and angular separation of the signal electrons in a scanning electron microscope (SEM). Collection of the inelastic backscattered electrons emitted under high take-off angles from a sample surface results in the acquisition of micrographs with high sensitivity to structural defects, such as dislocations, grain boundaries, and other imperfections. The areas with a high density of lattice imperfections reduce the penetration depth of the primary electrons, and simultaneously affect the signal electrons leaving the specimen. This results in an increase in the inelastic backscattered electrons yielded from the vicinity of α′-martensite, and a bright halo surrounds this phase. The α′-martensite phase can thus be separated from the austenitic matrix in SEM micrographs. In this work, we propose a deep learning method for a precise α′-martensite mapping within a large area. Various deep learning-based methods have been tested, and the best result measured by both Dice loss and IoU scores has been achieved using the U-Net architecture extended by the ResNet encoder. Full article
(This article belongs to the Special Issue Deformation and Failure Behavior of Metastable Metallic Materials)
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23 pages, 4766 KiB  
Article
Subgrain Coalescence Simulation by Means of an Advanced Statistical Model of Inelastic Deformation
by Nikita Kondratev, Peter Trusov, Andrej Podsedertsev and Matvej Baldin
Materials 2022, 15(15), 5406; https://doi.org/10.3390/ma15155406 - 5 Aug 2022
Cited by 3 | Viewed by 4179
Abstract
The development of technological methods for processing and manufacturing of functional (with a priori targeted properties) polycrystalline materials and products made of these materials still remains an acute problem. A multilevel modeling approach offers researchers the opportunity to describe inelastic deformation by applying [...] Read more.
The development of technological methods for processing and manufacturing of functional (with a priori targeted properties) polycrystalline materials and products made of these materials still remains an acute problem. A multilevel modeling approach offers researchers the opportunity to describe inelastic deformation by applying internal variables that give an effective characterization of the material structure at different structural scale levels. High temperature plastic deformation is accompanied by these processes, which leads to a significant rearrangement of the meso- and microstructure of the material. The most substantial contribution to changing the properties of polycrystals is made by the evolution of grain and defect structures at the expense of dynamic recrystallization, which significantly depends on dynamic recovery. In this paper, we consider the problem of the coalescence of subgrains undergoing rotation during inelastic hot deformation. This process is called subgrain coalescence, and it is one of the dynamic recovery mechanisms responsible for changes in the fine subgrain structure. Under applied thermomechanical loads, the coalescence process promotes the formation of recrystallization nuclei and their subsequent growth, which can greatly change the grain structure of a polycrystal. The problem was solved in terms of the advanced statistical model of inelastic deformation, modified to describe the subgrain coalescence process. The model takes into account the local interactions between contacting structural elements (subgrains). These have to be considered so that the grain coalescence caused by a decrease in subboundary energies during their progressive merging can be adequately analyzed. For this purpose, a subgrain structure quite similar to the real structure was modeled using Laguerre polyhedra. Subgrain rotations were investigated using the developed model, which relies on the consideration of the excess density edge component of the same sign dislocations on incidental subgrain boundaries. The results of modeling of a copper polycrystal are presented, and the effects of temperature and strain rate on the subgrain coalescence process is demonstrated. Full article
(This article belongs to the Section Mechanics of Materials)
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13 pages, 6000 KiB  
Article
Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
by Damian Sokołowski and Marcin Kamiński
Materials 2021, 14(21), 6676; https://doi.org/10.3390/ma14216676 - 5 Nov 2021
Viewed by 2306
Abstract
The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a [...] Read more.
The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain. Full article
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12 pages, 106 KiB  
Article
Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics
by Kuang-Dai Leng and Qiang Yang
Entropy 2011, 13(11), 1904-1915; https://doi.org/10.3390/e13111904 - 26 Oct 2011
Cited by 6 | Viewed by 5969
Abstract
Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative [...] Read more.
Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative external forces. Yet this general result holds true even without the Green-inelasticity presumption under a more general interpretation of the infinitesimal internal rearrangement. Three special cases are discussed following the generalized form: (a) the Green-elastic bodies whose free energy can be identified with the strain energy; (b) the Green-inelastic bodies composed of materials compliant with the additive decomposition of strain; and (c) the Green-inelastic bodies undergoing isothermal relaxation processes where the thermodynamic forces conjugate to internal variables, or the so-termed internal forces prove to be potential forces. This paper can be viewed as an extension of Yang et al. [1]. Full article
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