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Streszczenie:
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

Streszczenie:
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

Streszczenie:
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

Streszczenie:
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

Streszczenie:
A density functional theory (DFT) calculation is carried out in this work to investigate the effect of vacancies on the behavior of Al(111)/6H SiC composites. Generally, DFT simulations with appropriate interface models can be an acceptable alternative to experimental methods. We developed two modes for Al/SiC superlattices: C-terminated and Si-terminated interface configurations. C and Si vacancies reduce interfacial adhesion near the interface, while Al vacancies have little effect. Supercells are stretched vertically along the z-direction to obtain tensile strength. Stress–strain diagrams illustrate that the tensile properties of the composite can be improved by the presence of a vacancy, particularly on the SiC side, compared to a composite without a vacancy. Determining the interfacial fracture toughness plays a pivotal role in evaluating the resistance of materials to failure. The fracture toughness of Al/SiC is calculated using the first principal calculations in this paper. Young’s modulus and dominant surface energy are calculated to obtain the fracture toughness. Young’s modulus is higher for C-terminated configurations than for Si-terminated configurations. Surface energy plays a dominant role in determining the fracture toughness process. Finally, to better understand the electronic properties of this system, the density of states (DOS) is calculated.

Słowa kluczowe:
DFT,interface,surface energy,young’s modulus,fracture toughness

Streszczenie:
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

Streszczenie:
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

Streszczenie:
The mechanical response of interpenetrating co-continuous composite Al-Si12/SiC3D was described for uniaxial tension
and compression. The internal structure of the IPC was examined by optical microscopy and micro-CT. The apparent density and
Young’s modulus were assessed theoretically and experimentally. Uniaxial tensile tests were performed using the prismatic samples
of dimensions 1 mm × 2 mm × 30 mm. Cylindrical samples of diameters ϕ = 5 mm and height h = 10 mm were subjected to quasistatic uniaxial compressive loading. During tests, the side surfaces of the specimen were observed using a digital image correlation system (DIC) to find strain fields and to monitor the surface cracks development in the complex internal microstructure of the IPC.
The analyzed two-phase ICP was manufactured using ceramic foam SiC infiltrated by alloy Al-Si12. This material finds application
in cosmic, airplane, or automobile industries, due to their excellent tribological, heat distribution, and ballistic properties.
Obtained results show different modes of microcracking and fracture of cylindrical and prismatic samples. They indicate the
substantial influence of the ceramic skeleton on the behavior of the IPC under uniaxial states of loading. Different modes of damage related to the tension or compression loading were described in detail. The results can find application in the designing process of modern co-continuous IPCs and further development of the numerical models of degradation processes.

Słowa kluczowe:
Co-continuous composite, Al-Si12/SiC , interpenetrating composite, tension and compression tests

Streszczenie:
Silicon carbide foam is a material that can be used as reinforcement of interpenetrated composites. This paper presents an analysis of such a foam subjected to low and fast compression. The analysis is performed using the peridynamics (PD) method. This approach allows for an evaluation of failure modes and such effects of microcracks nucleation, their growth, and, finally, fragmentation. Furthermore, the material appears to behave qualitatively and quantitatively differently while subjected to low- and high-speed steel piston movement. Under slow compression case, damage appears in the entire specimen, but the shape of the structure is not changing significantly, whereas during the fast compression the sample is dynamically fragmented.

Słowa kluczowe:
silicon carbide foam,impact,compression,peridynamics

Streszczenie:
The infiltrated phase composites (IPCs) widely applied in aviation, aerospace, and energy industries are often exposed to extreme loading conditions like impacts. The analyzed IPC consists of two components: (1) SiC skeleton in the form of open-cell foam and (2) an Al-Si12 matrix introduced into the foam by the squeeze casting process. Both IPC components have different material properties, i.e., the SiC is elastic-brittle, and the Al-Si12 matrix is elastic-brittle-plastic. The gradual degradation under the impact of the IPC is described numerically using the peridynamics method. It has been found that the smeared damage prevails during the failure process. The damage is concentrated in the interfaces between the SiC skeleton and the Al-Si12 matrix, and thin layers of damaged material appear at the beginning of the impact process.

Słowa kluczowe:
infiltrated phase composites, SiC skeleton, Al-Si12 matrix, impact load, damage, plasticity, peridynamics

Streszczenie:
Silicon carbide foam is a promising material for high-temperature use because it has excellent thermal shock resistance and strength, low thermal conductivity, and excellent chemical resistance. Up till now SiC foam was analyzed under quasi-static compression and 4- and 3-point bending. This paper attempts for the first time to numerically analyze the SiC foam properties under impact conditions. Using the peridynamical approach it was possible to describe damage initiation, its dynamical growth, and the final fragmentation of the foam. The major conclusions resulting from the analysis are that for high impact velocities damage initiates much earlier compared to low-velocity impact, and the modes of failure are qualitatively different.

Słowa kluczowe:
silicon carbide, skeleton, impact, fragmentation, simulation, peridynamical approach

Streszczenie:
Ceramic composites (CCs) are mixtures of different phases, and their development is often regarded as a milestone in technological progress. They are used in practically all significant industries. Frequently, CCs are exposed to variable dynamic loads, impacts or high temperatures. In this paper, the impact of thin plates fabricated from Al2O3/ZrO2 is analyzed. The plates are made of the above CC with different proportions of its components. Damage progression is analyzed using peridynamics, similarly to quasi‐static tension. The purpose of the study is to describe the impact damage development in the CC plates and determine the role of phase contents. It has been found that phase ratios in the tested CC are vital for the behavior of the plates. In conclusion, it can be claimed that the employed peridynamic approach is suitable for solving the problems under study and that the impacting plates should be treated as real three‐dimensional structures.

Słowa kluczowe:
Al2O3/ZrO2, brittle composite, peridynamics, impact loading

Streszczenie:
Ceramic composites are used in such industries as the armaments industry, aviation, automotive, nuclear power, and space exploration. In several areas, they stand as the source of technological progress. The material is often subjected to extreme loads, such as variable dynamic loads and high temperatures. Peridynamics is a non-local, meshless, quite recently formulated method of stress analysis. The methods appear to be useful in the analysis of brittle materials. In the paper, an impact model of an Al2O3/ZrO2 thin plate is investigated. A brittle damage model is used for both phases of the composite. The attention is focused on damage initiation and distribution in the impacting sample.

Słowa kluczowe:
brittle composites, Al2O3/ZrO2, impact, peridynamics

Streszczenie:
WC/Co metal-matrix ceramic composites (MMCs) are used for manufacturing cutting and drilling tools, surgical tools, mill inserts, jet engines, and other high-responsibility structures. The combination of a phase of hard wolfram carbide (WC) grains with a metallic ductile interface of cobalt (Co) yields a complex microstructure with significantly different mechanical properties of the phases. The aim of this study is to investigate the thermomechanical behavior of the MMC polycrystalline material with ductile binders under impact conditions. An adiabatic and coupled thermomechanical analysis of the WC/Co composite under impact loading is performed using FEM. The heat conduction is considered in the analysis in order to capture heat transfer in the polycrystalline structure, i.e. between the grains and the grain boundaries (GBs). The Johnson-Cook yield function is used in the constitutive model of the ductile Co interface, while the WC phase is linear elastic. The motivation comes from the observation that the heat conductivity effect is often omitted, even in recent papers **[75]. Significant differences between temperatures and plastic strains in the adiabatic and coupled solutions are observed, which leads to the main conclusion that the adiabatic solution should not be used for assessing the impact response of the composite material.

Słowa kluczowe:
metal-ceramic composite, impact, coupled problem, thermomechanics, ductile interface

Streszczenie:
2-phase composites are often used for high demanding parts that can undergo impact loads. However, most of the papers on dynamic loading concerns layered composites. In our opinion, the impact loads are not considered thoroughly enough. Good examples of 2-phase composites are: (1) a WC/Co cermet or (2) a monolithic ceramic Al2O3/ZrO2. The WC/Co cermet is often modelled as having ductile elasto-plastic Co matrix and ideally elastic WC grains. It is because of very high crushing resistivity of the WC. In this paper, we present an extension to earlier elaborated models ([44]) with the assumption of ideal elasticity of the grains. The new and general numerical model for high-velocity impact of the 2-phase composites is proposed. The idea of this novelty relies on the introduction of crushability of grains in the composite and thermo-mechanical coupling. The model allows for description of the dynamic response both composite polycrystals made of: (1) 2 different purely elastic phases (e.g. Al2O3/ZrO2) or (2) one elastic phase and the second one plastic (e.g. cermet WC/Co), or (3) 2 elasto-plastic phases with different material properties and damage processes. In particular, the analysis was limited to the to the cases (2) and (3), i.e. we investigated the WC/Co polycrystal that impacted a rigid wall with the initial velocity equal to 50 m/s.

Słowa kluczowe:
2-phase composites, cermet, Johnson-Cook plasticity, impact, numerical modelling

Streszczenie:
Metal-ceramic composite (MCC) materials can be used for manufacturing high-responsibility structures such as jet engines or cutting tools. One example of these materials is a two-phase wolfram carbide (WC) and cobalt (Co) composite. This MCC is a combination of hard WC grains with a Co metallic ductile binder. The resulting microstructure is a combination of two phases with significantly different mechanical behaviors. In this study, we investigate impact conditions, starting with an illustrative example of the Taylor impact bar where—although the process is very rapid—the equivalent plastic strain and temperature are higher in the adiabatic solution than those in the coupled solution. On exposing the WC/Co composite with a metallic binder to impact loading, heat is generated by plastic deformation. If the process is fast enough, the problem can be treated as adiabatic. However, a more common situation is that the process is slower, and the heat is generated in the ductile metallic binders. As a result, the associated grains are heated due to the conduction effect. Consequently, the process should be treated as coupled. When the impact is applied over a short time period, maximum temperatures are significantly lower if the process is analyzed as coupled rather than as adiabatic. The grains are immediately affected by temperature increase in the binders. Therefore, the heat conduction effect should not be omitted.

Słowa kluczowe:
metal-ceramic composite, impact, coupled problem, thermomechanics

Streszczenie:
WC/Co composite is a standard hard material used for the production of cutting tools. It has both very good thermo-mechanical and wear properties. During the cutting, process tools are subjected to impact loading and gradual degradation due to high-stress concentrations. This loading induced deterioration is complex process still not well investigated and explained. Up till now the dynamic response of the WC/Co composite was analysed under dynamic impulse compressive loading [1]. However, the behaviour of the above two-phase composite under impacts conditions was not investigated in details. In the presented micromechanical approach the real material structure geometry of the internal structure can be performed including spatial distribution of: (1) WC grains and their dimensions, (2) volume content of plastic Co binder with their thickness, (3) system of grain/binder interfaces and (4) cracks initiated and developed during impulse loading, (5) possible brittle grains rotation. The results reveal the dependence of the microcracking processes and the stress distribution on impact velocity and presence of discontinuities in the Co binder and the interface zone between the binders and the grains. The microcracks system was evaluated by the damage parameter according to Kachanov, 1986 [62].

Słowa kluczowe:
cermet, impact load, microcracking, cohesive elements, numerical modelling

Streszczenie:
Cutting tools are manufactured among others from cermet (e.g. WC/Co) having excellent mechanical properties. Geometry of the internal microstructure is complex and mechanical response due to quasi-static or dynamic loading is difficult to be described. Particularly, the dynamic loading is not investigated enough precise up till now.
Experimental evidences, e.g. Siegl and Fischmester (1988), Ravichandran (1994), indicate that the fracture energy of WC/Co is expended through ductile failure of the Co: (1) near the binder/tungsten carbide interface or by (2) dimple rupture across the interphase. Concentrations of stresses around grain boundaries lead to initiation of microcrack system, which is dispersed for dynamic loading.
The aim of the paper is to extend the previously formulated models (Sadowski et al., 2005, 2006, 2007, Dębski and Sadowski, 2014, 2017) of the polycrystalline composite towards more advanced finite element formulation, applicable for description of the cermet behavior under dynamic pulses. The model takes into account: (1) spatial distribution of the cermet constituents, (2) system of grain boundaries/binder interfaces modeled by interface elements, (3) rotation of brittle grains.
The obtained results show that stress distributions and gradual microcracking processes are quite different for quasi-static and dynamic loadings. It was revealed by damage parameter indicating concentration of microcracks.

Słowa kluczowe:
Metal-ceramic composite, Interface elements, Crack propagation, Dynamic loading

Streszczenie:
Cermet Materials (CM), for example, WC/Co, have very good mechanical, thermal and wear properties. They are used for manufacturing of cutting tools. However, their behavior under dynamic loads is still not properly understood. Experiments, e.g. Siegl and Fischmester (1988) and Ravichandran (1994), indicate that the fracture energy of WC/Co is expended through ductile failure of the Co: (1) close to the binder/tungsten carbide interface (Liu et al., 2017) [64] or by (2) dimple rupture across the interphase (Sigl and Exner, 1987) [22]. Stress concentrations around grain boundaries lead to initiation of microcracks which are dispersed by dynamic loading. The main goal of the paper is to investigate the previously formulated models of the two-phase composite (Sadowski et al., 2005, 2006, 2007; Dębski and Sadowski, 2014, 2017) [47–51] in the case of dynamic compressive pulses that are common in the case of cutting tools. We have taken into account complex spatial distribution of cermet phases, grain/binder interfaces modeled by interface elements, possibility of cracks appearance within binders using interface elements as well, and rotation of brittle grains. The obtained results show that microcracking process and stress distributions are different for quasi-static and dynamic loadings. Early development of microcracks distribution revealed by damage parameter was observed.

Słowa kluczowe:
Cermet, Dynamic compressive impulse, Interface elements, Distributed microcracking process

Streszczenie:
Degradation of Cermet Materials (CM) under impact and pulse pressure is not thoroughly investigated. In this study, we qualitatively compare the behaviour of WC/Co samples under these types of loading.
The new models of impact and dynamic compressive load of a WC/Co plate were investigated. We developed two models of the composite plate, namely, a continuous model and a model with crack appearance possibility in the interfaces/binders.
We noted a qualitative difference of the shapes of the deformed structure due to different models and kind of loading. The differences also concern the Mises stress, equivalent plastic strains and damage parameter.
The proposed models are suitable for both impact and pressure load. The possibility of cracks appearance should not be neglected. In case of the model with discontinuities, for both kinds of loads, the grains rotation and sliding is more distinct than in case of the continuous model.

Słowa kluczowe:
Cermet, Impact, Pressure load, Interface elements, Distributed microcracking process, Numerical models

Streszczenie:
WC/Co ceramic metal-matrix composites are characterized by very high mechanical properties that allow for application of the composites mostly in production of different types of cutting tools. By combining in a composite structure a phase of brittle hard wolfram carbide (WC) grains with a metallic interface of cobalt (Co) that exhibits plastic properties, a geometrically complex microstructure with significantly different mechanical properties of the combined phases is created, see Fig. 1a. The presence of the elastic-plastic interface material, i.e. Co binder, in the composite structure is the reason for initiation of technological defects – mainly material porosity. During material loading pores start to coalesce and finally one can observe creation of microcracks system distributed along interfaces. The aim of the paper is to show the previously formulated model [1, 2] of the polycrystalline composite to be extended towards cracks development around the junctions of the interfaces. The obtained numerical results indicate that in the junctions high stress concentrations were observed, which leads to crack initiation and its further unstable propagation, and finally the composite failure. Results indicate that the first crack appears close to the junction and that the load carrying capacity of the sample is overestimated if a crack model in the interfaces is not assumed.

Słowa kluczowe:
metal-ceramic composite, interface elements, crack propagation at composite junctions

Streszczenie:
The aim of the paper is to develop the previously formulated model [19, 20] of the polycrystalline composite to include porosity growth at metallic interfaces of metal-ceramic composites (MCCs). Examples of this kind of MCCs are: (1) a two-phase material composed of brittle grains WC joined by the plastic binder Co, which can contain a small degree of porosity introduced during the cooling process [31], (2) TiC-Mo2C hard phase grains surrounded by tough binder phase Ni [12]. This work focuses on the description of the deformation of the MCC material including the modelling of a real material internal structure taking into account porosity growth during the loading. Experimental observations of the WC/Co composite [10] indicate that the majority of the fracture energy of MCC is expended through ductile failure of the plastic binder Co (dimple rupture across the binder or in the binder near the binder/carbide interface). This process is preceded by porosity growth at metallic interfaces and finally leads to inter-granular cracks propagation.

This paper presents micromechanical modelling of the MCC response in the case of uniaxial tension of 3-D Representative Volume Element (RVE) with the application of the Finite Element Analysis (FEA). The MCC material includes: elastic grains and inter-granular metallic layers containing technological pores that create its real complex internal structure. The quasi-static deformation process of the material comprises elastic deformation of brittle grains, elasto-plastic deformation of inter-granular layers (of different thickness: 2-4 mu m) and additional deformation due to micro-porosity development in the layers. A micro-sample analysis leads to the conclusion that a small amount of technological porosity changes the qualitative behaviour of the MCC including deformation, rotation of grains, roughness, and level of plastic strains. (C) Koninklijke Brill NV, Leiden, 2011

Słowa kluczowe:
Interface porosity, Gurson-Tvergaard model, polycrystalline ceramic composites, INTER-GRANULAR LAYERS, POLYCRYSTALLINE CERAMICS, FRACTURE, GROWTH, PREDICTION, STRENGTH, BEHAVIOR, TENSION, CERMETS, MODEL

Streszczenie:
W pracy przedstawiono model polikrystalicznego materiału ceramicznego, w którym ziarna połączone są poprzez cienkie warstwy o innych własnościach mechanicznych. Powoduje to powstanie niejednorodnych rozkładów deformacji oraz koncentracje naprężeń inicjujące mikrouszkodzenia.

Słowa kluczowe:
ceramika, mikrouszkodzenia, polikryształy, modele numeryczne

Streszczenie:
Internal damage due to fissuration results in an overall anisotropic material behaviour. A scalar damage parameter does not allow one to model a direction dependent response of continuously damaging solids. Employing the idea that the scalar damage parameter can be associated with an appropriate strain a damage tensor related to strains is introduced. The overall elastic properties are determined using a simplified form of the sensor function representations and the stress-strain relations regarding the overall response are given. For combined stress states an uncoupled damage theory is derived for materials with no lateral deformability under axial stress. Both brittle-ductile and elastic-brittle cases are studied using circular plates, for the elastic-brittle case only the governing differential equation are presented.

Streszczenie:
Abstract. The WC/Co is one of broad class of cermet materials (CM) that are applied in fabrication of machining tools. It means that they are subjected to different kind of dynamic loadings. They have very good mechanical properties. However, the degradation of the CM material under dynamic load has not been enough thoroughly investigated. Experimental results yield that the dissipation of the fracture energy in WC/Co samples is due to Co ductile failure at the WC and Co interface [1] and/or dimple rupture mechanism [2]. Stress concentrations about stress raisers such as grain bounds cause microcracking that is further propagated by dynamic loading. However, there are no such predictions for impact conditions. The main goals of the presentation are to explore the formerly created models of the two-phase composite [3, 4] towards impact conditions impacts and give qualitative predictions of the crack and plastic strains initiation for such cases. It has been found that microcracks development process and stress fields depend on impact velocity and the existence of discontinuities: (1) inside the Co binder and (2) the interface between the binder and the grains. Estimation of the microcracks distribution by means of damage parameter is given.

Streszczenie:
The aim of this paper is to present a constitutive model in the case of an uniaxial tension of the polycrystalline materials including the inter-granular metallic layers, creating its internal structure. The paper is focused on the discussion of the elastic properties of a composite components influence on the overall material response. The effective continuum model was applied to get the constitutive relations. Representative Volume Element (RVE) was analysed taking into consideration an initial internal structure of the material obtained from SME photographs. Owing to a high complexity of the internal structure of the composite material, FEA technique was used to get macroscopic stress-strain correlations. They include gradual changes of the internal structure of the material due to porosity and cracks development under tension.

Słowa kluczowe:
Polycrystalline ceramics, inter-granular layers, different elastic properties of components

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

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,

Streszczenie:
This study employs Density Functional Theory (DFT) simulations to explore the fracture toughness
(KIC), surface energy (γ), and Young's modulus (E) of α-Al2O3 (aluminum oxide) while investigating the impact of vacancies on these mechanical properties. Young's modulus and fracture toughness are determined for models with and without vacancies. Fracture toughness and Young's modulus are fundamental indicators of a material's ability to withstand crack propagation and its stiffness, respectively.
DFT, a computational approach, facilitates the analysis of atomic-level interactions within materials. Al2O3, a versatile ceramic with exceptional mechanical characteristics, serves as the subject of investigation.
Through DFT simulations, this research delves into the fracture mechanisms and crack propagation behavior of Al2O3, providing insights into its intrinsic fracture toughness. DFT can predict the formation and behavior of defects and dislocations in the material, which can affect its mechanical properties, including fracture toughness. By integrating DFT results with experimental data, a comprehensive understanding of both fracture toughness and Young's modulus is achieved. The research results provide useful information on the behavior of α-Al2O3 in the presence of vacancies. This study advances insights into Al2O3's crack behavior
and mechanical attributes, informing its application across aerospace, electronics, and manufacturing.
Demonstrating DFT's efficacy in uncovering complex mechanical phenomena, the research guides materials design strategies while forecasting employment opportunities in cutting-edge materials science.

Słowa kluczowe:
Crack, Al2O3, Fracture toughness, DFT

Streszczenie:

The interpenetrating composites consist of a scaffold and metallic matrix, which fills it being introduced under pressure. The scaffold is usually crushable. In our case, the SiC material stands for the skeleton, while the AlSi12 alloy is the matrix. Both materials are crushable. The SiC phase is brittle throughout the loading process, but the AlSi12 alloy is brittle during the elastic phase; then, its behaviour becomes viscous-plastic. The presentation concerns the experimental testing and simulations of the impact and fragmentation of metal matrix composite - AlSi12/SiC. The numerical model of the internal structure is created based on CT scanning. The microstructure of the composite is complex and consists of a metallic phase (85%), ceramic SiC skeleton, porosity, and a system of not perfect interfaces. The impacts are realized in the following few scenarios. The exemplary scenario is realized by imposing the initial conditions on the sample that hits a hard elastic barrier. The second one corresponds to SHPB experiments. The last one is the hitting of an elastic impactor against the sample. The influence of the impact velocities and material parameters of the phases on the failure modes is observed. Previously, analyses of the modes of loading application on the micromechanical failure of metal matrix composite were analysed in [1, 2]. An analysis of the empty SiC scaffolds is presented in [3]. The proposed finite element model of the AlSi12/SiC composite behaviour describing gradual degradation under impact loading was tested for different scenarios of hitting. In all cases, the growth of damage in the composite is very realistic. These results lead to the conclusion the proposed finite element model is very effective.

Acknowledgement: The results presented in this paper were obtained within the framework of research grant No. 2019/33/B/ST8/01263 financed by the National Science Centre, Poland. The numerical analyses were done in the ICM UW in Warsaw and in CI TASK in Gdańsk, Poland.

References:
[1] Postek, E. and Sadowski, T. Distributed microcracking process of WC/Co cermet under dynamic impulse compressive loading. Compos. Struct. (2018) 194: 494-508.
[2] 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] Postek, E., Sadowski, T. and Bieniaś, J. Simulation of impact and fragmentation of SiC skeleton, Phys. Letters (2021) 24:578-587.

Słowa kluczowe:
Cermets, Interpenetration, Impact, Viscoplasticity, Peridynamics

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

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

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

Streszczenie:
The interpenetrating composites consist of a scaffold and metallic matrix, which fills it being introduced under pressure. The scaffold is usually crushable. In our case, the SiC material stands for the skeleton, while the AlSi12 alloy is the matrix. Both materials are crushable. The SiC phase is brittle throughout the loading process, but the AlSi12 alloy is brittle during the elastic phase; then, its behaviour becomes viscous-plastic. The presentation concerns the simulations of impact and fragmentation of metal matrix composite - AlSi12/SiC. The numerical model of the internal structure is created based on CT scanning. The microstructure of the composite is complex and consists of metallic phase (85%), ceramic SiC skeleton, porosity, and system of not perfect interfaces. The impacts are realized in the following few scenarios. The exemplary scenario is realized by imposing the initial conditions on the sample that hits a hard elastic barrier. The second one corresponds to SHPB experiments. The last one is the hitting of an elastic impactor against the sample. The influence of the impact velocities and material parameters of the phases on the failure modes is observed. Previously, analyses of the modes of loading application on the micromechanical failure of metal matrix composite were analysed in [1, 2]. An analysis of the empty SiC scaffolds is presented in [3]. The proposed finite element model of the AlSi12/SiC composite behavior describing gradual degradation under impact loading was tested for different scenarios of hitting. In all cases, the growth of damage in the composite is very realistic. These results lead to the conclusion the proposed finite element model is very effective. Acknowledgment: The results presented in this paper were obtained within the framework of research grant No. 2019/33/B/ST8/01263 financed by the National Science Centre, Poland. The numerical analyses were done in the ICM UW in Warsaw, CYFRONET AGH in Krakow and in CI TASK in Gdańsk, Poland.

Słowa kluczowe:
Impact, Interpenetrated Ceramic Composites, Fragmentation, Peridynamics

Streszczenie:
Multiphase Ceramic Composites (CCs) are used in several modern industries like aerospace, automotive, nuclear power, or defense. They are used in the situation of expected extreme loads like variable loads or impacts. The interpenetrating composites (IPCs) is a class of composites that are defined by the technological process. The IPCs consist of a crushable skeleton and a metallic phase introduced into the skeleton under pressure. The resulting material combines the features of the skeleton and the filling metal. Earlier analyses of the composite systems showed the significance of the interface between the particular phases [1, 2, 3] for the overall performance of the samples and its load-carrying capacity. An attempt to include the mechanical properties based on atomistic simulations is shown. An analysis of samples of IPC based on SiC ceramic skeleton and an aluminum alloy under impact conditions is performed. The 3D structure of the sample is obtained with CT scans. The numerical model takes into account the properties of the interfaces between the phases. It has been noted that the interface properties are a significant feature of the materials and the resulting numerical model.

Słowa kluczowe:
Metal-ceramic Interpenetrating Phase Composites, Impact Loading, Peridynamics,Finite Element Method, Atomistic Simulations

Streszczenie:
Ceramic two-phases composites are used in such industries as the armaments industry, aviation, automotive, nuclear power, and space exploration. In several areas, they stand as the source of technological progress. The material is often subjected to extreme loads, such as variable dynamic loads and high temperatures. The paper presents experimental investigations of ballistic impact on ceramic /metal composites. The internal structure of the novel material consists of ceramic foam made of SiC and filled with Al alloy. The experiment was performed using the ballistic stand and spherical impactor of diameter 5 mm and mass 0.5 g. The impactor hit the sample of diameter 30 mm and thickness 4 mm with a velocity of 600 m/s. Fig. 1 presents crater after impact and defragmented sample. The numerical analysis of the fragmentation process was performed using the finite element method. The internal structure of the composite was assessed using micro-CT selecting both phases, i.e., ceramic foam and AL alloy. The phases are joined by a continuous very small thickness interface. The numerical calculations allow for the description of the whole degradation process of the analysed interpenetrating composite up to the final failure by fragmentation and confirm the novel applicability of the material as a protective layer against the high-velocity impact. Acknowledgement The work has been performed under the research grants 2019/33/B/ST8/01263, National Science Centre, Poland. The analyses were done in the ICM UW in Warsaw and in CI TASK in Gdańsk, Poland. References [1] T. Ohji and M. Singh, Engineered Ceramics: Current Status and Future Prospects: Wiley, 2015.

Słowa kluczowe:
two-phase metal/ceramic composites, penetration experiments, numerical modelling

Streszczenie:
W pracy przedstawiono badania eksperymentalne kompozytów ceramicznych infiltrowanych poddanych działaniu obciążeń mechanicznych. Rozpatrywany typ kompozytów wytwarzany jest z pianki ceramicznej typu SiC, która wypełniona jest stopem AlSi. Ten typ zaawansowanego kompozytu jest stosowany w  przemyśłe kosmicznym, lotniczym i samochodowym.
Przeprowadzono obserwacje mikroskopowe struktury badanych kompozytów oraz pianki ceramicznej, wykonano skany micro-CT.
Odpowiedź na obciążenia dynamiczne zbadano prętem Hopkinsona używając próbek krępych.
Uzyskane wyniki pokazują postacie zniszczenia próbek cylindrycznych i beleczek. Wskazują one na istotny wpływ szkieletu ceramicznego na zachowanie kompozytu.

The experimental testing of interpenetrating composite was presented for uniaxial compression or tension. The analysed composite was manufactured using SiC ceramic foaminfiltrated by an alloy of AlSi. This type of composites is used in cosmic, aerospace, or automotive idustries.
The response of the rested material waas investigated using stocky samples in the Hopkinson bar device.
The obtained results exhibit different modes of fracture of cylindrical and beam samples. They indicate the substantial influence of the ceramic skeleton on the behaviour of the composite under the dynamic loading.

Słowa kluczowe:
Kompozyty metalowo ceramiczne, kompozyty infiltrowane, skany CT, pręt Hopkinsona, dynamika, pękanie zniszczenie / Metal matrix composites, infiltrated composites, CT scanning, Hopkinson bar, dynamics, fracture, failure

Streszczenie:
Kompozyty ceramiczne infiltrowane (IPC) znajdują zastosowanie w kilku strategicznie ważnych gałęziach przemysłu. Przykładami są przemysł motoryzacyjny, energetyka jądrowa lub przemysł kosmiczny. Badany kompozyt składa się ze szkieletu SiC i wypełnienia stopem aluminium. Próbki poddawane są mechanicznemu obciążeniu udarowemu. Dla materiału kruchego zastosowany został konstytutywny model uszkodzeń zaś materiał wypełnienia jest modelowany jako sprężysto-plastyczny. Do obliczeń zastosowana została perydynamika. Ważnym parametrem jest uwzględniana w obliczeniach odporność na pękanie materiału szkieletu. Zbadane zostało zachowanie próbki dla małych i dużych prędkości uderzenia. Ostatnia uwaga dotycząca metody peridynamiki dotyczy jej praktycznego wykorzystania, a mianowicie wyniki badań numerycznych potwierdzają stosowalność metody do oceny materiałów IPC, mimo że metoda ta powinna być używana przy zastosowaniu masowo zrównoleglonego oprogramowania i nowoczesnych klastrów komputerowych by uzyskiwać wyniki w rozsądnym czasie.

Infiltrated ceramic composites (IPCs) are used in several strategically important
industries. Examples are the automotive industry, nuclear Energy, or the space industry. The
tested composite consists of a SiC skeleton and an aluminum alloy filling. The samples are
subjected to impact loading. For the brittle material, a constitutive model of damage has been
used, and the filling material is modeled as elastic-plastic. Peridynamics was used for the
calculations.
A final remark considering the peridynamics method concerns the practical use of
peridynarnics, namely, the results of the numerical studies confirm the feasibility of the method
for evaluation of the IPCs materials even though it should be used massively parallelized
software and up-to-date computer clusters to obtain results within a reasonable time.

Słowa kluczowe:
kompozyty metalowo-ceramiczne, kompozyty interpenetrowane, uderzenie, perydynamika / metal matrix composites, interpenetrated composites, impact, peridynamics

Streszczenie:
The silicon carbide (SiC) can be used for its foam production. It is used for infiltrated
composites fabrication. In this paper, a problem of an impact of a steel plate travelling
with high velocity hitting a silicon carbide sample (SCF) is considered. The presentation concerns
the modes of failure and degradation.

Słowa kluczowe:
SiC, silicon carbide foam, impact, compression, peridynamics

Streszczenie:
The paper presents the modelling of a ceramic foam that works as a skeleton of Interpenetrating Phase Composites (IPCs) before filling the preforms. The preforms are made of SiC or Al2O3. A dynamic analysis of the impact of such skeletons against the rigid surface is performed. The results of the quasi-static analysis will serve as a reference to the dynamic analyses. The analysis of the IPCs skeleton is performed due to evaluation of the role of the skeleton in a final product that is the filled IPCs.

Słowa kluczowe:
interpenetrating phase composites, metal-matrix composites, ceramic skeleton, peridynamics, high-performance computing

Streszczenie:
The paper presents modelling and experimental testing of non-linear degradation processes developing in the two-phase ceramic matrix (CMCs) and metal matrix composites (MMCs) subjected to quasi-static and dynamic compressive loading. Modelling was performed by a multiscale approach using both: (1) analytical and (2) numerical methods and selected Representative Volume Elements (RVE) based on SEM observations of composites. Both quasi-static and dynamic experimental tests were done applying standard MTS (100 kN) servo-hydraulic machine and Split Hopkinson Pressure Bar (SHPB) stand for impact tests with loading velocities 20 – 30 m/s. As a result, we observed for CMCs in quasi-static loading failure mode by splitting of cylindrical samples, whereas for impact loading dynamic crushing process took place.

Słowa kluczowe:
metal-matrix composites, dynamic testing, Split Hopkinson Pressure Bar, peridynamics

Streszczenie:
Quasi-static degradation of brittle composites exhibits different mechanical responses under uniaxial tension and uniaxial compression. In this paper, we analysed cracking processes and failure under quasi-static loading of 2 phase ceramic material made of alumina and zirconia mixture, subjected to tension and compression. Constitutive modelling of two-phase ceramic composites obeys description of (1) elastic deformations of initially porous material, (2) limited plasticity and (3) cracks initiation and propagation. Modelling of polycrystalline ceramics at the mesoscopic level under mechanical loading is related to the analysis of a set of grains, which create a so-called Representative Volume Element (RVE). The basic elements of the defect structure inside polycrystal are: micro- and meso-cracks, kinked and wing cracks. To get the macroscopic response of the material one can calculate averaged values of stress and strain over the RSE with the application of an analytical approach. The dynamic degradation process was illustrated for 2 phase ceramic matrix composite and cermet, which was subjected to short compressive impulse. The pulse duration was 10-7s and the applied pressure level - 480 MPa. In the proposed, more advanced finite element formulation of the cermet behaviour is was necessary to take into account the following data and phenomena revealing inside of the RVE: (1) spatial distribution of the cermet constituents, (2) system of grain boundaries/binder interfaces modelled by interface elements, (3) rotation of brittle grains. The cermet response due to pulse loading is significantly different in comparison to the quasi-static behaviour, i.e. the stress distributions and microcracking processes are quite different.

Słowa kluczowe:
cermets, dynamic behaviour, brittle cracking

Streszczenie:
Gradual degradation of brittle composites exhibits different mechanical response under uniaxial tension and uniaxial compression. In this paper, we analysed cracking processes and failure under quasi-static loading of 2 phase ceramic material made of Al2O3 and ZrO2 mixture, subjected to tension and compression. Constitutive modelling of two-phase ceramic composites obeys description of (1) elastic deformations of initially porous material, (2) limited plasticity and (3) cracks initiation and propagation. Modelling of polycrystalline ceramics at the mesoscopic level under mechanical loading is related to the analysis of a set of grains, i.e. Representative Volume Element (RVE). The basic elements of the defect structure inside polycrystal are micro-cracks and meso-cracks, kinked and wing cracks. To get a macroscopic response of the material one can calculate averaged values of stress and strain over the RSE with an application of the analytical approach. High strain rate degradation process was illustrated for Al2O3/ZrO2 composite, which was subjected to short compressive impulse. The pulse duration was 10-7s. In the proposed more advanced finite elements formulation it was necessary to take into account the following data and phenomena appearing inside of the RVE: (1) spatial distribution of the composite constituents, (2) system of grain boundaries/binder interfaces modelled by interface elements, (3) rotation of brittle grains. The numerical model of gradual degradation of the Al2O3//ZrO2 composite response due to pulse compressive loading presents correctness and capability of the proposed FEM approach.

Słowa kluczowe:
brittle composites, representative volume element, degradation, damage, peridynamics

Streszczenie:
Assessment of impact techniques is given in [1]. A basic model of a two-phase material is presented in [2]. Two-phase composites are of vital applications in modern technology, for example cutting tools, implants, jet engines. Examples of such materials are WC/Co and Al2O3/ZrO2. Highly innovative technologies need applications of modern polycrystalline materials. The manufactured polycrystalline materials are planned to have controlled internal structure. However, even though the process is controlled the internal structure can be still complex due to engineering requirements. The novel multiphase materials possess different internal geometries, for example (i) with regular of disordered internal structures with introduced fibers, particles or nanoparticles (ii) with a functional gradation of mechanical or physical properties (iii) fabricated as regular of irregular layered materials structures. The analyses of modern composites require efficient computational methods and codes. The new method that has been developed mostly in the last ten years is peridynamics [3,4]. The developments resulted in a highly parallelised code [5] that we use in our analysis. We further investigate the model of cermet that has been developed with the finite element method [6, 7, 8]. The primary goal of the paper is to investigate the previously formulated models of the twophase composite under impacts. We have taken into account the spatial distribution of cermet phases, grain/binder interfaces modelled by interface elements and movement of brittle grains. We analyse a sample of the material that can be considered as Representative Volume Element RVE and do verification of the material properties of the RVE by multiplication of the elementary sample with complex geometry [9]. In Fig. 1, we illustrate an outline of the analysis. It is an Al2O3/ZrO2 polycrystal that hits a rigid obstacle with a velocity V. In this case, the velocity of the impactor is 100 m/s. We observe the damage development in the interfaces calculated with finite element and PD methods at time 10 ns. Further on, we consider damage models [10], elastic-plastic [11] and elastic-viscous-plastic models [12].

Słowa kluczowe:
two phase composites, damage, elasoplasticity, impact, peridynamics

Streszczenie:
Quasi-static degradation of brittle composites exhibits different mechanical response under uniaxial tension and uniaxial compression. In this paper we analysed cracking processes and failure under quasi-static loading of 2 phase ceramic material made of alumina and zirconia mixture, subjected to tension and compression. Constitutive modelling of two phase ceramic composites obeys description of: (1) elastic deformations of initially porous material, (2) limited plasticity and (3) cracks initiation and propagation. Modelling of polycrystalline ceramics at mesoscopic level under mechanical loading is related to analysis of a set of grains, which create so called Representative Volume Element (RVE). The basic elements of the defect structure inside polycrystal are: micro- and meso-cracks, kinked and wing cracks. To get macroscopic response of the material one can calculate averaged values of stress and strain over the RSE with application of analytical approach. Dynamic degradation process was illustrated for 2 phase ceramic matix composite and cermet, which was subjected to short compressive impulse.
The pulse duration was 10-7s and the applied pressure level - 480 MPa. In the proposed more advanced nite elements formulation of the cermet behaviour is was necessary to take into account the following data and phenomena revealing inside of the RVE: (1) spatial distribution of the cermet constituents, (2) system of grain boundaries/binder interfaces modelled by interface elemnets, (3) rotation of brittle grains. The cermet response due to pulse loading is signifcantly different in comparison to the quasistatic behaviour, i.e. the stress distributions and microcracking processes are quite different.

Słowa kluczowe:
brittle composites, damage, quasi-static behaviour, dynamics, RVE

Streszczenie:
The ceramic composites Al2O3/ZrO2 are used for different kind of implants since they are nontoxic and nonallergic [1]. The composites of different composition of both compounds are obtained by sintering at the temperature 1600◦C. The amount of zirconia in the composite is normally up to 30% volume. The investigation of such properties like Youngs modulus, toughness and flexural strength is presented in [2]. The properties of ZrO2 compound with stabilization of Y2O3 are described in [3].

Słowa kluczowe:
Al2O3/Zr02, composite compositions, impact, peridynamics

Streszczenie:
Materiały metaloceramiczne są często stosowane w elementach, które mogą być poddane uderzeniom. Jednak większość prac dotyczących obciążeń dynamicznych dotyczy kompozytów warstwowych. Techniki oceny obciążeń uderzeniowych dla kompozytów dobrze przedstawione są w pracy [1]. Przykładem kompozytu dwufazowego jest WC/Co. Ten rodzaj kompozytu jest często modelowany jako posiadający sprężysto plastyczne wypełnienie oraz sprężyste ziarna. Powodem tego jest wysoka odporność na zniszczenie materiału WC. Przedstawiamy rozszerzenie wcześniej opracowanych modeli [2], w których zakładana była idealna sprężystość ziaren. W nowym modelu zakładamy możliwość zniszczenia ziaren. Badamy układ, w którym próbka uderza o sztywną ścianę z różnymi prędkościami.

Słowa kluczowe:
Obciążenia uderzeniowe, węglik wolframu, kompozyt dwufazowy, metoda elementów skończonych

Streszczenie:
Cermet Materials (CM) are often used for manufacturing of different cutting tools. They have very good mechanical, wear and thermal properties. In our opinion, the dynamic load is still not enough thoroughly analysed, and the impact load as well. The tools are subjected to different dynamic effects.We have taken into account complex spatial distribution of cermet phases, grain/binder interfaces modeled by interface elements, possibility of cracks appearance within binders using interface elements as well, and rotation of brittle grains.
The main goal of the presentation is to develop further previously formulated models of two-phase composite [1-4] to capture effects of temperature due to impact. The source of the thermal loading is the conversion of plastic work into heat [5, 6]. The increase of temperature takes place in the Co interfaces. We investigate adiabatic and fully coupled solutions.
We note differences in the behaviour of the samples when the thermal loading is not considered. We have found that the thermal softening effect in the interface material is important as well. We enhance the description of the damage mechanism in the presence of temperature increase.
Acknowledgements
This work was financially supported by Ministry of Science and Higher Education (Poland) within the statutory research (IPPT PAN) and National Science Centre (Poland) project No 2016/21/B/ST8/01027 (Lublin University of Technology). The calculations were done at the Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Poland. The licenses for the MSC Patran and Abaqus programs were provided by Academic Computer Centre in Gdańsk, Poland.
References:
[1] Sadowski T, Hardy S, Postek E. Prediction of the mechanical response of polycrystalline ceramics containing metallic intergranular layers under uniaxial tension. Comput Mat Sci 2005;34:46-63.
[2] Sadowski T, Hardy S, Postek E. A new model for the time-dependent of polycrystalline ceramic materials with metallic inter-granular layers under tension. Mat. Sci. Eng. A 2006;424:230-238.
[3] Sadowski T, Postek E, Denis C. Stress distribution due to discontinuities in polycrystalline ceramics containing metallic inter-granular layers. Comput Mat Sci 2007;39: 230-236.
[4] Postek E, Sadowski T. Dynamic pulse sensitivity of WC/Co composite, (accepted in Composite Structures).
[5] Wriggers P, Miehe C, Kleiber M, Simo JC. On the coupled thermomechanical treatment of necking problems via finite element methods. Int. J. Num. Meth. Eng. 1992; 33:869–883.
[6] Rojek J, Onate E, Postek E. Application of explicit FE codes to simulation of sheet and bulk metal forming processes. J. Mat. Proc. Tech. 1998; 80–81: 620–627.

Słowa kluczowe:
cermet composites, coupled solutions, thermomechanics

Streszczenie:
Generally, the papers on dynamic loading of composites more focus on the layered composites, for example [1]. High attention is paid to blast load. However, in our opinion, the process of impact a gap for analysis of WC/Co composite during impact conditions. During impact of WC/Co composite objects and the other composites with metallic binder heat of plastic work is generated. If the process is fast enough the problem can be treated as adiabatic. However, more common situation is slower process when the heat is generated in metallic interfaces and the neighbouring grains are heated due to conduction. The process should be rather considered as coupled [2]. We developed our model of WC/Co composite towards impact load, [3].

Słowa kluczowe:
thermomechanics, coupled problems, composites

Słowa kluczowe:
Metal-Ceramic Composite, Interface Elements, Crack Propagation at Composite Junctions