Instytut Podstawowych Problemów Techniki

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This study comprehensively investigates Al2O3’s mechanical properties, focusing on fracture toughness, surface energy, Young’s modulus, and crack propagation. The density functional
theory (DFT) is employed to model the vacancies in Al2O3, providing essential insights into this material’s structural stability and defect formation. The DFT simulations reveal a deep understanding of vacancy-related properties and their impact on mechanical behavior. In conjunction with molecular dynamics (MD) simulations, the fracture toughness and crack propagation in Al2O3 are explored, offering valuable information on material strength and durability. The surface energy of Al2O3 is also assessed using DFT, shedding light on its interactions with the surrounding environment.
The results of this investigation highlight the significant impact of oxygen vacancies on mechanical characteristics such as ultimate strength and fracture toughness, drawing comparisons with the effects observed in the presence of aluminum vacancies. Additionally, the research underscores the validation of fracture toughness outcomes derived from both DFT and MD simulations, which align well with findings from established experimental studies. Additionally, the research underscores the validation of fracture toughness outcomes derived from DFT and MD simulations, aligning well with findings from established experimental studies. The combination of DFT and MD simulations provides a robust framework for a comprehensive understanding of Al2O3’s mechanical properties, with implications for material science and engineering applications.

Słowa kluczowe:

Al2O3, fracture toughness, density functional theory, molecular dynamics

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Metal matrix composites (MMCs) combine metal with ceramic reinforcement, offering high strength, stiffness, corrosion resistance, and low weight for diverse applications. Al-SiC, a common MMC, consists of an aluminum matrix reinforced with silicon carbide, making it ideal for the aerospace and automotive industries. In this work, molecular dynamics simulations are performed to investigate the mechanical properties of the complex-shaped models of Al-SiC. Three different volume fractions of SiC particles, precisely 10%, 15%, and 25%, are investigated in a composite under uniaxial tensile loading. The tensile behavior of Al-SiC composites is evaluated under two loading directions, considering both cases with and without diffusion effects. The results show that diffusion increases the ultimate tensile strength of the Al-SiC composite, particularly for the 15% SiC volume fraction. Regarding the shape of the SiC particles considered in this research, the strength of the composite varies in different directions. Specifically, the ultimate strength of the Al-SiC composite with 25% SiC reached 11.29 GPa in one direction, and 6.63 GPa in another, demonstrating the material’s anisotropic mechanical behavior when diffusion effects are considered. Young’s modulus shows negligible change in the presence of diffusion. Furthermore, diffusion improves toughness in Al-SiC composites, resulting in higher values compared to those without diffusion, as evidenced by the 25% SiC volume fraction composite (2.086 GPa) versus 15% (0.863 GPa) and 10% (1.296 GPa) SiC volume fractions.

Słowa kluczowe:

Molecular dynamics, Al-SiC composites, Diffusion, SiC particle

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In this paper, the effective elastic properties of hexagonal monolayers such as graphene, boron nitride, silicon carbide, and aluminum nitride are evaluated using the asymptotic homogenization method taking into account temperature changes. The effective properties are determined analytically by considering temperature, force constants, bond lengths, and thickness, using atomic interactions within the context of the unit cell problem. The relationship between environmental temperature and the coefficient of thermal expansion is established by considering changes in the values ​​of bond stretching, bond angle bending, and torsion resistance constants at different temperatures from 0 to 1800 K. The results provided by the proposed homogeneous model are consistent with the valid findings of other researchers in the literature. It is found that these different hexagonal nanosheets exhibit isotropic temperature-dependent properties and their Young's and shear modulus decrease almost linearly as the temperature rises, considering a constant coefficient of thermal expansion. However, Poisson's ratio is found to be independent of temperature. Furthermore, the temperature-dependent elastic properties of these nanosheets become nonlinear when the variation of the coefficient of thermal expansion with temperature is taken into account. The Young and shear moduli of the nanosheets increase as the coefficient of thermal expansion decreases and vice versa. The highest elastic modulus values are obtained when the thermal expansion is close to its minimum threshold. However, it is recognized that the elastic modulus of graphene and boron nitride nanosheets is higher than that of silicon carbide and aluminum nitride at any temperature. As an alternative to lengthy computer modeling or rigorous testing, the homogeneous models provided can be used to simulate nanosheets.

Słowa kluczowe:

Asymptotic homogenization method, Hexagonal nanosheets, Effective mechanical properties, Coefficient of thermal expansion

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The equivalent characteristics of the materials’ interfaces are known to impact the overall mechanical properties of ceramic–metal composites significantly. One technological method that has been suggested is raising the temperature of the liquid metal to improve the weak wettability of ceramic particles with liquid metals. Therefore, as the first step, it is necessary to produce the diffusion zone at the interface by heating the system and maintaining it at a preset temperature to develop the cohesive zone model of the interface using mode I and mode II fracture tests. This study uses the molecular dynamics method to study the interdiffusion at the interface of α-Al2O3/AlSi12. The hexagonal crystal structure of aluminum oxide with the Al- and O-terminated interfaces with AlSi12 are considered. A single diffusion couple is used for each system to determine the average main and cross ternary interdiffusion coefficients. In addition, the effect of temperature and the termination type on the interdiffusion coefficients is examined. The results demonstrate that the thickness of the interdiffusion zone is proportional to the annealing temperature and time, and Al- and O-terminated interfaces exhibit similar interdiffusion properties.

Słowa kluczowe:

self-diffusion , interdiffusion, diffusion coefficient, Al2O3/AlSi12 interface, molecular dynamics

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The mechanical properties of ceramic–metal nanocomposites are greatly affected by the equivalent properties of the interface of materials. In this study, the effect of vacancy in SiC on the
interdiffusion of SiC/Al interfaces is investigated using the molecular dynamics method. The SiC reinforcements exist in the whisker and particulate forms. To this end, cubic and hexagonal SiC lattice polytypes with the Si- and C-terminated interfaces with Al are considered as two samples of metal matrix nanocomposites. The average main and cross-interdiffusion coefficients are determined using a single diffusion couple for each system. The interdiffusion coefficients of the defective
SiC/Al are compared with the defect-free SiC/Al system. The effects of temperature, annealing time, and vacancy on the self- and interdiffusion coefficients are investigated. It is found that the interdiffusion of Al in SiC increases with the increase in temperature, annealing time, and vacancy.

Słowa kluczowe:

Interdiffusion,Diffusion coefficient,SiC/Al interface,Vacancy,Molecular dynamics

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Modeling metal matrix composites in finite element software requires incorporating a cohesive zone model (CZM) to represent the interface between the constituent materials. The CZM deter-mines the behavior of traction–separation (T–S) in this region. Specifically, when a diffusion zone is formed due to heat treatment, it becomes challenging to determine experimentally the equiva-lent mechanical properties of the interface. Additionally, understanding the influence of heat treatment and the creation of a diffusion zone on the T–S law is crucial. In this study, the molecular dynamics approach was employed to investigate the effect of the diffusion region formation, re-sulting from heat treatment, on the T–S law at the interface of a SiC/Al composite in tensile, shear, and mixed-mode loadings. It was found that the formation of a diffusion layer led to an increase in tensile and shear strengths and work of separation compared with the interfaces without heat treatment. However, the elastic and shear moduli were not significantly affected by the creation of the diffusion layer. Moreover, the numerical findings indicated that the shear strength in the diffu-sion region was higher when compared with the shear strength of the slip plane within the fcc aluminum component of the composite material. Therefore, in the diffusion region, crack propagation did not occur in the pure shear loading case; however, shear sliding was observed at the aluminum atomic layers.

Słowa kluczowe:

metal matrix composite, diffusion, cohesive zone law, interface, molecular dynamics

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The current investigation deals with an analytical formulation and solution procedure for the thermal stability characteristics of piezomagnetic nano-sensors and nano-actuators considering the flexomagnetic effects and geometrical imperfection. Piezo-flexomagnetic nano-plate strips with the mid-plane initial rise are subjected to external uniform, linear, and nonlinear temperature rise loading across the thickness. The nonlinear size-dependent governing equations are derived within the framework of the first-order shear deformation plate theory, nonlocal strain gradient theory and considering the nonlinear von- Kármán strains. The proposed closed-form solutions and the obtained results are validated with the available data in the literature. The calculated buckling and post-buckling temperatures of piezo-flexomagnetic nano-plate strips are shown to be dependent on several factors including the scaling parameters, plate slenderness ratio, mid-plane initial rise, different temperature distributions, and scalar magnetic potential. The presented closed-form solutions and numerical results can serve as benchmarks for future analyses of piezo-flexomagnetic nano-sensors and nano-actuators.

Słowa kluczowe:

Thermal buckling and post-buckling, Closed-form solution, Piezo-flexomagnetic plate strip, Size-dependent theories, Mid-plane initial rise

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The mechanical properties of the SiC/Al interface are crucial in estimating the overall strength of this ceramic-metal composite. The present work investigates the interdiffusion at the SiC/Al in-terface using molecular dynamics simulations. One cubic and one hexagonal SiC with a higher probability of orientations in contact with Al are examined as two samples of metal-matrix nanocomposites with whisker and particulate reinforcements. These reinforcements with the Si- and C-terminated surfaces of the SiC/Al interfaces are also studied. The average main and cross-interdiffusion coefficients are evaluated using a single diffusion couple for each system. The effect of temperature and annealing time are analysed on the self- and interdiffusion coeffi-cients. It is found that the diffusion of Al in SiC is similar in cubic and hexagonal SiC and as ex-pected, the interdiffusion coefficient increases as the temperature and annealing time increase. The model after diffusion can be used to evaluate the overall mechanical properties of the inter-face region in future studies.

Słowa kluczowe:

Interdiffusion, Metal-matrix composites, Silicon carbide/aluminium interface, Molecular dynamics

Afiliacje autorów:

Słowa kluczowe:

Cr-doped SnO2, sol–gel, Williamson–Hall models, Halder–Wagner method, microstrains

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Introduction: In the early stage of fracture fixation, the aim of a unilateral external fixator (UEF) to stimulate healing and maintain stability may be suppressed by using inadequate number of pins. Cortical thinning due to age or osteoporosis endangers a successful fracture fixation.
Materials and methods: This study evaluates the initial strength and stability of the fracture fixation and tissue differentiation under the influences of variable cortical thickness (5 mm to 1 mm) and variable number of pins (1 to 4 in each bone fragment). A finite element program was utilised to develop 20 three-dimensional models of simplified diaphyseal tibia with fracture callus fixed with UEF. A mechano-regulation code based on the deviatoric strain theory was written and applied to simulate tissue differentiation. The values of von Mises stress, interfragmentary strain (IFS), and fibrocartilage index (FCI) were evaluated.
Results: Cortical thinning from 5 mm to 1 mm increased IFS and FCI by an average of 30.3% and 18.7%, respectively, and resulted in higher stresses in the UEF and bone. Using 1 pin in each bone fragment produced excessive IFS in the models with 1 mm, 2 mm and 3 mm cortical thickness. Inserting the second pin into the bone fragment could considerably reduce the IFS and fibrocartilaginous tissue formation in the fracture site and improve load transmission to the fixator. Whereas inserting the fourth pin could minimally affect the mechano-biological environment of healing.
Conclusions
This study suggests that initial instability due to cortical thinning can be efficiently alleviated by adding the number of pins up to 3 in a UEF; additionally, it may improve the knowledge about applying UEFs adequately stable, whilst promoting inclination toward endochondral ossification, simultaneously.

Słowa kluczowe:

Unilateral external fixator, Bone fracture healing, Osteoporosis, Interfragmentary strain, Mechanical stress, Endochondral ossification

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Streszczenie:

In this study, the size-dependent bistable behavior of a micro-electro-mechanical curved beam under the piezoelectric actuation is investigated. The system is modeled as a clamped slightly curved Euler–Bernoulli beam sandwiched with two piezoelectric layers along its length and suspended over a curved fixed electrode. Employing the strain gradient theory, the nonlinear governing equilibrium equation is derived using the principle of minimum total potential energy. A multi-mode Galerkin’s weighted residual method with the linear undamped mode-shapes of the straight beam as the approximating functions is then utilized to solve the higher-order governing equilibrium equation. The instability thresholds of the system are then obtained by vanishing the determinant of the Jacobian of the reduced equations. It is found that the present solutions are completely converged when three eigenmodes are included in the reduced order model (ROM), while hiring a single mode solution predicts the position of the snap-through and pull-in points with errors of at most 13% and 1.4%, respectively. The accuracy of the converged results is also validated by the available experimental observations in the literature. Moreover, snapping criteria which provide the required combination of the system properties for prompting snap-through instability is introduced in this study. A detailed parametric study is finally conducted to investigate the combined effects of the fixed electrode curvature and the piezoelectric actuation on the size-dependent bistability of electrically actuated curved micro-beams. Results reveal that the position of the snapping zone in the limit points map can be controlled by the input piezoelectric voltage as well as the initial rise of the fixed electrode.

Słowa kluczowe:

Bistability, Initially curved micro-beam, Curved fixed electrode, Piezoelectric actuation, Strain gradient theory

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This comparative study simulates bone remodeling outcome around titanium dental implants and compares the final bone configuration with the one around novel implants composed of radial functionally graded materials (FGMs) and the titanium implants with hydroxyapatite (HA) coating. A dental implant system embedded in 3D mandibular bone with masticatory loading was simulated by the finite element method. A bone remodeling algorithm was applied to cancellous and cortical bones. Young's modulus and von Mises stress were obtained to ensure bone homeostasis and evaluate the final bone configuration. Local stress distribution in the bone-implant interface was analyzed before and after bone remodeling. The average final Young's modulus of cancellous bone reached 2.68, 2.49, and 2.32 GPa for the FGM, HA-coated, and the titanium models, respectively. These values for cortical bone were 17.75, 16.86, and 17.20 GPa in the same order. Radial FGM implants generated the highest remodeling stimulus and bone density. Their superiority over the HA-coated models was confirmed by four implant surface stiffness values (10, 20, 30, and 40 GPa). Remodeling increased bone density around the implant, consistent with clinical data and reduced stress concentration in the cortical neck. The stress values were in the safe zone regarding overload-induced bone resorption. The findings of this study were substantiated by clinical images and bone density values from previous literature.

Słowa kluczowe:

Dental implants, Bone remodeling, Finite element, Radial functionally graded material (FGM), Hydroxyapatite (HA) coating, Stress analysis

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Streszczenie:

This exploration highlights the essential role of ceramics, nota bly aluminum oxide (Al2O3 ),
in various technological applications due to its remarkable properties, including high mecha-
nical strength and electrical insulation. It underscores the transformative impact of com-
putational approaches such as density functional theory (DFT) and molecular dynamics (MD)
simulations in unraveling Al2O3’s mechanical characteristics. The focus is on key attributes like
surface energy, Young’s modulus, and fracture toughness, providing insights into the atomic-scale mechanisms governing these features. Through the application of DFT and MD simulations,
a deeper understanding emerges regarding how cracks initiate, propagate, and influence overall
fracture behavior, contributing to the advancement of enhanced materials for diverse applica-
tions.

Słowa kluczowe:

alumina, mechanical properties, crack development, density functional theory, molecular dynamics,

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Streszczenie:

Multiphase metal matrix composites are used in modern industries like energy, aerospace, and automotive. The materials are used in severe loading conditions like impact loads or thermal shocks. The presentation concerns a data-driven model of an interpenetrated composite. The geometry of the material phases is obtained using CT scanning. Further details, namely, the distribution of voids and inclusions are found with the scanning as well. Based on CT scans the 3D finite element and peridynamics models are derived from. Former analyses [1, 2] showed the importance of the existence of an interface zone in multiphase composites. In the current presentation, the diffusion-based mechanism of forming the interphase zone is shown. A constitutive law evaluated in [3] is considered. The constitutive law for the cohesive zone was obtained using molecular dynamics simulations. The effects of the MD-based law on mesoscale samples are presented. Acknowledgment: Grant from National Science Committee (PL) UMO-2019/33/B/ST8/01263; Polish National Agency for Academic Exchange (NAWA) [BPN/ULM/2021/1/00115/U/DRAFT/00001] Calculations: PL-GRID National Facilities: CYFRONET, Krakow, ICM at the University of Warsaw, TASK, Gdansk, Poland, and LUMI in Kajaani, Finland. References: [1] Felten, F., Schneider, G., and Sadowski T. Estimation of R-curve in WC/Co cermet by CT test. Int. J. Refract. Hard. Met., Vol. 26, pp. 55-60, 2008. [2] Postek, E. and Sadowski, T. Qualitative comparison of dynamic compressive pressure load and impact of WC/Co composite. Int. J. Refract. Hard. Met., Vol. 77, pp. 68-81, 2018. [3] Tahani, M., Postek, E., and Sadowski T., Investigating the Influence of Diffusion on the Cohesive ZoneModel of the SiC/Al Composite Interface, Molecules, Vol.28, No.19, pp. 6757-1-6757-19, 2023.

Słowa kluczowe:

Multiphase materials, Diffusion, Consitituve law, Molecular dynamics

Afiliacje autorów:

Streszczenie:

Metal matrix composites (MMCs) are materials consisting of a metal matrix reinforced often with ceramic to improve the properties of the base metal. MMCs are used in a wide range of applications due to their unique combination of high strength, stiffness, and wear resistance with relatively low weight.
It is well recognized that the interface in composites plays a crucial role in transferring the load efficiently from the matrix to the reinforcement. Hence, to predict the overall mechanical properties of MMCs, it is essential to evaluate the interface strength. In this study, the C- and Si-terminated hexagonal and cubic SiC/Al interfaces are studied. The molecular dynamics (MD) simulation is used as a virtual environment to obtain this relation because it is challenging to determine it from experimental results. The equivalent mechanical properties of the interface are characterized by a cohesive zone model based on the traction-separation relation obtained from MD simulations. SiC/Al composites are created using high-temperature techniques that result in a fuzzy interface due to the diffusion of atoms [1]. In this research, the effect of diffusion on the traction-separation relation in mode I fracture is examined. The systems are heated to 2000 K and then cooled to 300 K. Young's modulus of samples after atom diffusion is found to be about 25% lower than those before atom diffusion, but the work of separation is found to increase by at least 40% following the heating of the system and diffusion. This finding demonstrates that diffusion significantly increases the fracture energy of SiC/Al composites. Furthermore, following system heating and diffusion of atoms, the C-terminated samples are found to have higher work of separation than the Si-terminated ones.
Acknowledgments: We acknowledge the National Science Centre, grant No. UMO 2019/33/B/ST8/01263. The calculations were performed at the PLGrid – Academic Computer Centre Cyfronet in Krakow, Academic Computer Centre in Gdańsk, Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Poland.
REFERENCE
[1] Tahani M., Postek E., Sadowski T., Molecular dynamics study of interdiffusion for cubic and hexagonal SiC/Al interfaces, Crystals, Vol. 13 (1), 46, 2023.

Słowa kluczowe:

Metal Matrix Composite, Cohesive zone, Diffusion, Molecular dynamics

Afiliacje autorów:

Streszczenie:

Metal matrix composites (MMC) are used more and more in the aerospace, automotive, and bio-
-medical industries because of their high strength-to-weight ratio, high stiffness, and outstanding wear resistance. Aluminium, titanium, and magnesium are the most preferred matrix materials, whereas alumina and silicon carbide are the most used reinforcing elements for these composites. The overall mechanical and failure properties of MMCs depend on the mechanical properties of the constituents and the nature of the interface. The characteristics of the interface must be understood because they have the potential to significantly alter the properties of MMCs. The interface between phases is a fuzzy region because of diffusion. To this end, it is necessary to look into the diffusion between the two phases as the first step for determining the cohesive zone model of the interface.
In this study, AlSi12 metal alloy as matrix material reinforced with α-Al2O3 is considered. AlSi12
is an aluminium alloy that contains 12 wt.% silicon with excellent thermal conductivity, good corrosion resistance, and low density. The composite can be used in various high-temperature applications such as furnace linings, engine parts, and aerospace components. It is worth noting that the properties and performance of the composite will depend on the processing conditions, microstructure, the proportion of the components, and the interface’s characteristics.
The investigation carried out by Milas et al. [1] regarding the diffusion of Al, O, Pt, Hf, and Y atoms
on α-Al2O3(0001) can be mentioned as an illustration of research that has been published in the literature.
To the authors’ knowledge, no studies have been done on α-Al2O3/AlSi12 diffusion couple. To this end, the self-diffusion and interdiffusion at the interface are investigated in this research by heating the system to the desired temperature. The effect of annealing temperature and annealing time are studied on the diffusion zone and interdiffusion coefficients. The thickness of the diffusion zone and the interdiffusion coefficients are found to increase as expected with increasing annealing temperature and time.

Słowa kluczowe:

Self-diffusion, Interdiffusion, Metal-ceramic composite, Al2O3/AlSi12 interface, Molecular dynamics method

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Streszczenie:

Advanced multiphase ceramic composites (MCCs) are employed in several modern industrial sectors, for example, aerospace, automotive or energy. The composites are used when extreme conditions like variable loads, impact loads or thermal shocks are expected.
The presentation deals with examples of interpenetrated composites (IPCs). The previous analyses of the composite materials showed the significance of the interface between the phases for the loading resistance of the material [1,2]. The interface forming is affected by the diffusion of the materials. The effect of diffusion of the phases is presented in [3]. An attempt to include the mechanical properties of the interface based on atomistic simulations is given in the presentation.

An analysis of samples of IPC based on SiC ceramic skeleton and an aluminium alloy under impact is performed. The structure of the material is obtained with CT scans. The numerical model considers the properties of the interfaces between the phases. It has been noted that the interface properties are a significant feature of the materials.

Acknowledgement: Grant from National Scientific Committee (PL) UMO-2019/33/B/ST8; Polish National Agency for Academic Exchange (NAWA) [BPN/ULM/2021/1/00115/U/DRAFT/00001].
Calculations: PL-GRID: CYFRONET, Krakow, Poland. ICM at the University of Warsaw, Poland and TASK, Gdansk, Poland.
References
[1] Felten, F., Schneider, G. and Sadowski T. Estimation of R-curve in WC/Co cermet by CT
test. Int. J. Refract. Hard. Met. (2008) 26: 55-60.
[3] Postek, E. and Sadowski, T. Qualitative comparison of dynamic compressive pressure load
and impact of WC/Co composite. Int. J. Refract. Hard. Met. (2018) 77: 68-81.
[3] Tahani M., Postek E. and Sadowski T. Molecular Dynamics Study of Interdiffusion for Cubic and Hexagonal SiC/Al Interfaces, Crystals (2023) 13(1):1-15.

Słowa kluczowe:

Metal Matrix Composites, Cohesive law, Interface modelling, Diffusion, Molecular dynamics, Finite elements

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