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This paper investigates the collapse diagrams (energy-absorption and efficiency diagrams) under dynamic compression tests (drop tests) with an impact loading speed of 3.09m/s. Experimental tests were carried out at room temperature on seven different types of closed-cell rigid polyurethane foams with densities of 40, 80, 100, 120, 140, 145 and 300kg/m3respectively. Based on the measured load–displacement curves, authors plotted the variation of peak stress, energy-absorption and efficiency attributes with respect to density for each type of foam, highlighting the optimum foam density (100kg/m3). The influence of density and loading direction (in-plane and out-of-plane) on the main mechanical properties are also discussed. Following the investigations it was observed that both efficiency and energy absorption diagrams shows similar results, leading to the conclusion that both methods are reliable. Considering the test setup, a finite element analysis model was developed that aimed to replicate the experimental procedures. Simulations were performed in the commercial software Abaqus/Explicit using the implemented Elastic/Crushable foam constitutive model and using the static and dynamic test data for calibration. The energy-absorption and efficiency diagrams obtained from simulations were compared with the experimental data.

In this context, four specimens, i.e. (i) circumferentially notched cylindrical torsion (CNCT), (ii) circumferentially notched cylindrical direct tension (CNCDT), (iii) edge notch disc bend (ENDB) and (iv) three-point bend beam (3PBB), were utilized to measure the modes I and III fracture toughness values of gypsum. While the CNCT specimen provides pure mode III loading in a direct manner, this pure mode condition is indirectly produced by the ENDB specimen. The ENDB specimen provided lower KIIIcand a non-coplanar (i.e. twisted) fracture surface compared with the CNCT specimen, which showed a planar mode III fracture surface. The ENDB specimen is also employed for conducting pure mode I (with different crack depths) and mixed mode I/III tests. KIcvalue was independent of the notch depth, and it was consistent with the RILEM and ASTM standard methods. But the mode III fracture results were highly sensitive to the notch depth. While the fracture resistance against mode III was significantly lower than that of mode I, the greater work of fracture under mode III was noticeable. ©2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

This paper is focused on description of the mechanical response of the aluminum box-beams subjected to 3 point bending (3-PB). The main aim of this paper is to determine the effect of spacing between rivets on the equivalent stiffness and strength of the analised profile. The considered beams are composed of two sections: one of them is an aluminum omega profile and another is a composite flat sheet. Experimental tests were carried out for various spacing between rivets. Moreover, the corresponding numerical analyses by Finite Element Analysis (FEA) with application of the Abaqus software were done for estimate of the mechanical response of the box beams. The results show relationship between spacing of the rivets and values of carrying forces.

While the plane is maneuvering before start or landing, some solid particles (e.g. sand, dust, soil) can be sucked into an engine with the air. Their vast majority is stopped on the compressor blades, but the smaller ones are able to get into a hot part of the engine and cause erosion. Erosion is widely recognized as the second mechanism, after corrosion that reduces the TBC coating thickness. In many cases, erosion can completely remove it. Furthermore, TBC coatings are more susceptible to erosion due to their porous structure than full dense ceramic materials. In order to investigate the phenomenon of particles impact with diameter of 4mm, the pneumatic driven laboratory work station was built. The work station has an adjustable pressure, so that the foreign object may possess different kinetic energies. The pressure can be read on a digital pressure gauge and the shot release is done electrically. In addition, the work station has a universal cross table that provides precise positioning of the sample so as to be able to perform a dozen or so impacts in predetermined distance intervals. However, the most important component is the velocity measurement system which is used to determine the impact energy. The paper presents the results of 11 impacts made with different energies. The effect of complete destruction of the ceramic layer as well as indents without visible damage was achieved. Numerical simulations allowed to define the zones of stress influence of the individual indents. The brittle cracking model in Abaqus allowed the virtual representation of damage due to impact load.

This paper presents the results of Mode I fracture toughness tests of concrete with fly ash (FA) loaded in Mode I. Concrete composites with the addition of 0%, 20% and 30% siliceous FA were analysed. Fracture toughness tests were performed on a MTS 810 testing machine. The studies examined the effect of FA additive on the quasi-static fracture toughness KIcS. The analysis of the results revealed that a 20% FA additive causes an increase of KIcS value, while a 30% FA additive causes a decrease on fracture toughness. Additionally, the results demonstrate the possibilities of practical application of ARAMIS system for analysing the development of defects in the micro-structure of concretes containing FA additives. This system can be useful for macroscopic estimation of crack propagation.

In the jet engine the temperature of exhaust gases should be as high as possible, from the point of view of its efficiency. The value of this temperature is limited by toughness of the turbine blades material. Superalloy Inconel 625, which is commonly used in aerospace industry, indicates 13% less yield point in 800OC than in 25OC. The temperature of exhaust gases can reach 1500OC. The blade material has to be protected due to this fact. The one possibility of turbine blade protection is using of thermal barriers coatings (TBC). The coating has a very low thermal conductivity and therefore it protects against the thermal shock failure of the substrate material. The TBC can be manufactured as: 1) monocrystalline, 2) layered structures (e.g. [1-3]) or 3) as a functionally graded material (e.g. [4-7]). The differences between the properties of blade material and TBC can lead to significant increase of the high shear stresses in the substrate-TBC interface.In this paper numerical analyses of cooled turbine blade with various kinds of functionally graded thermal coatings were performed. The main aim was to find the optimal material properties distribution of the functionally graded TBC to avoid damage initiation and growth between TBC and substrate. In the calculations the effect of temperature on material properties both mechanical and thermal was taken into consideration.

A description of processes of formation and propagation of cracks in material requires the knowledge of all fracture mechanics parameters, i.e.: KIc, KIIc and KIIIc. In this study a new testing method and estimation of the fracture toughness in Mode III (antiplane shear) of concretes containing: 0, 20 and 30% volume content of the class F fly ash (FA) was proposed. Fracture toughness tests were performed on axial torsion machine MTS 809 Axial/Torsional Test System. The studies examined effect of FA additive on the parameter KIIIc. In order to determine the fracture toughness KIIIc a special device was made. Experimental investigation under third mode fracture was carried out both in young and mature concrete composites (after: 3, 7, 28, 90, 180 and 365 days). 20% addition of FA as well as a 30% addition of FA causes a reduction in fracture toughness of young concrete. After 28 days of couring a significant increase of the KIIIc was noticed in composites with a 20% additive of FA while concrete mixtures with a higher additive of FA still had lower analyzed fracture mechanics parameter.

Indentation in brittle solids involves many complex phenomena related to cleavage and contact, as well as intrinsic stress singularities, which are almost impossible to capture with traditional continuum approach and FEA at mesoscale. In case of a two-phase ceramic composite [1–3] the number of unknown material and interfacial constants, that have to be calibrated experimentally, increases rapidly [4, 5]. In this paper, nanoindentation in zirconia-toughened alumina (ZTA) is modelled using discrete (peridynamical) approach

Different types of techniques are used in joining of aircraft structures. The classical solutions are mechanical or bonding joining. A prospective alternative to the currently used connections (e.g. mechanical, adhesive and hybrid ones) is a socket - pin connection type. Generally, they are purely mechanical joints. Depending on the shape, they have different commercial names such as: Interlock, Snaplock, Snapfit Gridlock. The idea of these connections relies on the fact, that between the socket and the pin we need a suitable interference fit or specially formed clip to carry the load. The advantages of this type of connection of different structural parts is very fast assembly after pressing joined parts together. The use of socket - pin connection eliminates the presence of the human error and reduces production costs as an individual connection is made by CNC machine tools.The paper presents an analysis of the influence of a several technological problems concerning the socket and the pin manufacturing, on the value of force required for the joint connection and disconnection. A number of numerical simulations was made in ABAQUS program to examine the effect of such parameters as: the presence of interference fit, the use of spherical latches, the use of different rigidity in the shaft by making cuts with variable width and length, the use of different angles of inclination of the working part of the slot.

The heat transfer problem in the 2-phase composite material containing metallic and elastic phases, subjected to quick temperature variations, is the aim of theoretical analysis. The full description of the composite behaviour starts from the formulation of governing equations at 2-scale levels: micro-and macro-, passes through specification of the internal structure of the composite and finishes by numerical solution of the heat transfer problem through the considered material sample. The most important in the analysis are thermo-mechanical properties of the composite components creating the material. The big difference of the both phases properties (mismatch) can create additional difficulty in the exact thermal description of the composite. It is necessary also to specify by scanning electron microscopy (SEM) observations a real material internal structure, which includes: grain shapes and matrix, to create of the proper size of the Representative Volume Element (RVE) for numerical calculations.In the numerical example we analyse cermet, i.e. the composite build up of metallic matrix (cobalt) and tungsten carbide elastic grains, which exhibits high brittleness. Heat transfer across this very complex material causes heat flux concentrations in the metallic phase and further stress concentrations. These concentrations act as sources of damage initiators at the binder/carbide grains interfaces. The obtained results lead to the conclusion that the spatial distribution and content of the metallic phase first of all influence the heat transfer across the 2-phase composites.

Waste tires create big problem in the world as for their utilization. One domain in which this material is able to found promising application is civil engineering. The waste tires additive in the concrete manufacturing leads to change of mechanical properties such as: Young modulus, compressive strength, fracture toughness, energy absorption, brittleness, water absorption etc. It was partly reported in the literature only for the plain concrete. There is no investigations for a lean concrete - the material which has potential applications as a subgrade of roads. The aim of this paper is to investigate the importance of the rubber particles addition in the lean concrete production as for modification of the basic mechanical properties and further degradation of the material due to mechanical loading. The new technology of compaction of the concrete was elaborated to perform basic test: cyclic uniaxial compression and cyclic bending. In order to describe gradual degradation of the rubberized lean concrete a scalar damage parameter D related to loading history was proposed. The current value of the elastic modulus was expressed as E=Eo(1-D), where Eo denotes the initial value of the Young’s modulus. The paper includes also a numerical model of the beam made of the rubberized lean concrete, which is subjected to 3-point bending deformation. The stress distribution in this beam is highly non-homogeneous with visible stress concentrations around the rubber particles.

Thermal Barrier Coatings (TBCs) have been extensively used in aircraft engines to improve durability and performance. They protect critical engine parts such as blades and combustion chambers, which are exposed to high temperatures and corrosive environment.Testing of coated metallic alloys, subjected to ageing process, allows determination of the TBCs properties. In this paper we performed 2 tests: uniaxial tension and bending. The aging of samples was carried out in 1000°C for times: 48h, 89h, 185h and 353h. Thermally Grown Oxide (TGO) layer thickness (SEM observations) and the strain level corresponding to damage of the TBCs were determined experimentally.The experimental results were used to build numerical model in Abaqus program. Brittle cracking damage model was applied to describe of the TBC layer degradation. Surface based cohesive behavior was used to model delamination of the interface between a bond coat (BC) and a top coat (TC).The proposed numerical model describes with high accuracy experimental results.

Cellular materials represent a new class of materials; main parameters that characterize the cellular structure are relative density, shape of the cell (open or closed), wall thickness and cell diameter. The purpose of this paper is to investigate the microstructure of foams materials and also to determine the flexural properties of this rigid PUR foams using Digital Image Correlation (DIC). The rigid PUR foams cells morphology and pore distribution for three densities (100, 145 and 300 kg/m3) were studied before testing through scanning electron microscopy. Determination of flexural properties was carried out on rectangular beam samples using ARAMIS 2D system. This method provides a substantial increase in accuracy for measuring strain and is based on the calculation of surface deformation using a set of digital images from undeformed stage to different deformed stages. The specimens were subjected to static three points bending tests with loading rate of 2 mm/min, at room temperature and loading was applied in rise direction of the foam. Experimental results show that main mechanical properties such as flexural modulus and flexural strength values increases with increasing of density.

The study focused mainly on one of the parameters of mount technology - tolerance for fitting the rivet in the hole in riveted and hybrid (riveted adhesive) joints. The research included numerical simulations of double lap joints with four rivets arranged in two rows and subjected to uniaxial tension. Simulations were carried out in Abaqus both for the purely mechanical and the hybrid joints. The connections without clearance (neat-fit) and with clearance of 0.2 mm, as well as with interference of-0.2 mm. The presence of clearance in one of the holes in the hybrid joint causes a decrease in the capacity of the hybrid connection by about 15% in configuration 1 (Fig. 2). This decrease can be even higher (21%) in the worse clearance placement, i.e. in configuration 2 (Fig. 2). The study shows that the occurrence of clearance in the holes can lead to dangerous consequences, so it is recommended to use holes calibration or develop a special type of rivet.

Polyurethane (PUR) foam materials represent a class of materials widely used for impact protection and energy absorption. This paper presents a characterization of different rigid PUR foams under compressive impact loading by means of energy absorption and efficiency diagrams. Compressive properties were investigated on cubic specimens on the foams’ rise direction at room temperature with a loading rate of 3.09 m/s for three different closed-cell foams with densities of 100 kg/m3, 160 kg/m3 and 300 kg/m3 respectively. Experimental results show that the compression modulus, yield stress and plateau stress increase with density. Most of the energy is absorbed in the plateau region because of the cell deformation associated with this phenomenon, allowing greater absorption of impact energy at nearly constant load. Authors have found that both the energy absorption and efficiency diagrams are consistent and present similar results for studied foams.

A numerical procedure of assessment of Thermal Stress Intensity Factors (TSIFs) of an edge crack in a strip made of Functionally Graded Material (FGM) subjected to thermal cooling process was elaborated. In order to perform it own subroutines in ABAQUS code were created. The analyzed ZrO2+Ti6AlV material in the form of the FGM is applied as cylinder liners (Thermal Barrier Coatings TBC) of aircrafts engines and is subjected to extremely quick temperature changes during the engine work. Therefore estimation of the TSIF to determine fracture process in the ZrO2+Ti6AlV material is important for designing of the structural element thermal protection and further safety of aircrafts passengers.

In this paper we study the interaction of two unequal collinear cracks in a pre-stressed fiber reinforced wood composite material in anti-plane mode of fracture. A mathematical model is associated to the mechanical problem. Starting from the boundary, constitutive and far field conditions we obtain the representation of the incremental displacement, stress and strain fields using two complex potentials. Using Sih s generalized fracture criterion we determine the critical incremental shear stress which produce crack propagation and the crack tips propagation direction in a particular case of a Pine wood composite.

This paper presents theoretical modeling of two-phase ceramic composites subjected to compression. The meso-mechanical model allows for inclusion of all microdefects in the polycrystalline structure that exists at the grain boundary interfaces and inside the grains. The constitutive relations for the Al2O3/ZrO2 composite with the gradual degradation of the material properties due to different defects development were formulated.

Hybrid joining of structural parts (e.g. [3-1) is relatively new approach to create more safe and reliable connection of the critical part of engineering structures. In this paper we consider hybrid joint consisting of 2 aluminum stripes and an angle bar (e.g. [7]) joined by 2 simple techniques: hot spot welding (HSW) and adhesive bonding (AB). The samples were subjected to fatigue tests in order to find fatigue response at different level of load amplitude. New method of plastic deformation measurement during fatigue was proposed with application of Digital Image Correlation (DIC) method. Numerical analysis of the hybrid joint fatigue response was proposed in the paper taking into account both: gradual degradation of the bonding layer and plastic damage in the aluminium strips due to cyclic loading.

Adhesive bonding of two different materials appears in many modern engineering applications, e.g.: airplanes, boats, cars etc. In many practical problems the adhesive bonding is subjected to shear loading. Therefore this is important to investigate the whole deformation process of the considered type of joints under monotonic loading, to get information about the shear strength and strain concentrations. Such concentrations lead to microdefects initiation and their further coalescence to create a main crack. The unstable crack propagation leads to final failure of the adhesive joint. The Digital Image Correlation (DIC) System - ARAMIS allows for constant monitoring of the deformation state up to the final failure. The tests were performed for bi-material specimens made of adhesively bonded PMMA and aluminum strips (Fig.1) and for pure PMMA and pure aluminum specimens. Additionally, two strain gauges on each homogeneous specimen and four on the bimaterial ones are used for strains estimations. The four point bending Iosipescu tests were performed using MTS machine with constant speed. In the first method (DIC) the ARAMIS system recorded a displacement distribution in samples with frequency 1Hz. In the second method the strains were recorded by the strain gauges - using analog output channels of the HOTTINGER data Acquisition System - MGCPlus, the current value of the load using analog output channel of the MTS machine was recorded too. The load-displacement curves were obtained for the whole deformation process and the shear strength of the joints was estimated. The energy absorption of the joints was calculated.

This paper presents the size effect on fracture toughness of polyurethane foams (PUR 40), with nominal density 40 kg/m3, closed-cell rigid foams widely used for sandwich cores. Determination of the fracture toughness was carried out by three-point bending tests (TPB), on notched specimens, at room temperature (20±2ºC). To determine the size effect in Mode I fracture toughness, specimens geometrically similar in two dimensions with length-to-width ratio 5:2 were selected. The specimens were subjected to a quasi-static loading with a speed of 2 mm/min, which was applied exactly on the notch direction. A strong size effect in the closed-cell PUR foam is experimentally demonstrated, by considering a smooth transition between strength of materials approach (with no size effect) and asymptotic case of linear elastic fracture mechanics.

Mode II fracture analysis is especially important. This mode is vital in relation to concrete, due to its relatively low shearing strength and high sensitivity to such type of stress. Nowadays, the structural concretes containing an additives of fly-ash are quite commonly used in the construction industry. Initial cracks origin and development research was carried out using samples for three concrete mixtures: concrete without silica fly-ash (FA), concrete with 20% and concrete with 30% FA additive. 150x150x150 concrete cube with two initial cracks was used as a test sample. Experimental investigation under Mode II fracture was carried out in concrete composites at early age (after 3, 7, 14 and 21 days). X-FEM method enables observation of defect initiation and development, there is no need to input the original conditions. Calculations used peak principal stress criterion. Most calculations coincide with results of experimental research. There was a convergence of: cracks shapes, FQ critical force values, force - displacement graphs.

Effectiveness of internal combustion turbines in aero-engines is limited by comparatively low temperature of exhaust gas at the entry to turbine of the engine. A thermal efficiency and other capacities of turbine strongly depend on the ratio of the highest to the lowest temperature of a working medium. Continuous endeavour to increase the thermal resistance of engine elements requires, apart from laboratory investigations, also numerical studies in 3D of different aero-engine parts. In the present work, the effectiveness of the protection of turbine blades by thermal barrier coating and internal cooling under thermal shock cooling was analysed numerically using the ABAQUS code. The phenomenon of heating the blade from temperature of combustion gases was studied. This investigation was preceded by the CFD analysis in the ANSYS Fluent program which allows for calculation of the temperature of combustion gases. The analysis was conducted for different levels of the shock temperature, different thickness of applied TBC, produced from different kinds of materials.

Abstract: Ceramic-metal interfaces are often present in composite materials. The presence of cracks has a major impact on the reliability of advanced materials, such as fiber or particle reinforced ceramic composites, ceramic interfaces and laminated ceramics. The understanding of the failure mechanisms is very important, as is as the estimation of fracture parameters at the tip of the crack approaching an interface and crack propagation path. A cracked sandwich plate loaded with axial uniform normal stress was numerically investigated using plane strain Finite Element Analysis. The numerical results for the singularity orders were compared with the analytical solution. The influences of the material combination and crack length on the radial and circumferential stresses and displacement distributions were investigated. The Stress Intensity Factors were determined based on numerical results using a displacement extrapolation method. The results for the non-dimensional stress intensity factors show that at lower crack lengths the influence of material mismatch is lower, but this influence increases with increasing crack length.

Two-phase ceramic composite materials, (CMC, e.g. Al2O3/ZrO2), have a non-linear and complex overall response to applied loads due to: different phases, existence of an inital porosity, development of limited plasticity and internal microdefects. All microdefects act as stress concentrators and locally change the state of stress, leading to the development of mesocracks and finally macrocracks. Experimental results show that defects develop mainly inter-granular and cause inhomogeneity and induced anisotropy of the solid. Modelling of such material response is possible by multiscale approach describing different phenomena occuring at different scales: micro- meso- and macro- ones. The paper presents uniaxial tension process of the Al2O3/ZrO2 composite with the gradual degradation of the material properties due to different defects development.

Ceramic – metal interfaces are often present in composite materials. The presence of cracks has a major impact on the reliability of advanced materials, like fiber or particle reinforced ceramic composites, ceramic interfaces, laminated ceramics. The understanding of the failure mechanisms is very important, as much as the estimation of fracture parameters at a tip of the crack approaching an interface and crack propagation path. The asymptotic solution of the stress field at the tip of a crack normal to a bi-material interface is presented. A cracked sandwich plate loaded by uniform normal stress was numerically investigated using Finite Element Analysis. The numerical results of the circumferential stress distribution were compared with the analytical solutions. The results for the non-dimensional stress intensity factors show that at lower crack lengths the influence of material mismatch is lower but this influence increases with increasing the crack length.

In this paper we study the behaviour of a Mode I crack in a pre-stressed wood composite material. A mathematical model is associated to the mechanical problem. Starting from the boundary, constitutive and far field conditions we obtain the representation of the incremental displacement, stress and strain fields using two complex potentials. Using numerical analysis we determine the critical value, which causes crack propagation and the direction of crack propagation in a particular case of a Pine wood composite.

The plywood material is widely used in civil engineering and furniture industry as cheap, strong, and lightweight material. The progressive failure of the plywood is difficult to be modeled and predicted because of the complexity of its structure and the interaction between different modes of orthogonal damages and interlayer failure. The microstructure of the wood determines the failure of the plies. A micromechanical material model of wooden veneers is developed, which is based on a representative volume cell (RVC) taken from the tubular microstructure of the wood and represented as a truss structure with longitudinal, transverse, and diagonal bar finite elements. The damage variables prescribed for each type of the bars determine the progressive degradation of the material stiffness. The 2-D damage material model of wooden veneers is utilized as user-defined material in continuum shell elements of ABAQUS™ finite element code. The parameters of the model are determined to simulate the behavior of single veneers in tension tests in different directions of loading. Together with cohesive elements representing the interface between the plies, the suggested model can be used to simulate and analyze the progressive failure and damage interaction in the plywood. The simulations could give us better understanding of the complex failure of the plywood, the succession of the damage development and reveal the weakest link in the material. The analysis can be used for optimization of the plywood layup.

. Polyurethane foam materials are widely used as cores in sandwich composites, for packing and cushioning. The main characteristics of foams are light weight, high porosity, high crushability and good energy absorption capacity. The paper presents the experimental results obtained for the mechanical properties of polyurethane foams in different loading conditions and the influence of impregnation on the mechanical properties. A 200 kg/m3 density polyurethane foam was investigated in the experimental program in three different Strength of Materials laboratories from Lublin, Bucharest and Timisoara. The paper assesses the possibility to describe the polyurethane foam behaviour trough compression tests, micromechanical models and Finite Element Analysis (FEA). The micromechanical models and Finite Element Analysis could be used successfully for representing the engineering stress – strain behaviour if the compression tests provide reliable material parameters.

Modelling of polycrystalline ceramics built up of different phases has been done within mesomechanical approach. Porous ceramics consists of matrix material and second phase – pores. Such material has non-linear and complex overall response to applied load. Modelling of porous polycrystalline material was performed by multiscale approach describing different phenomena occuring at different scales: micro- meso- and macro- with application of averaging procedure over the Representative Surface Element (RSE).

Polyurethane foam materials are widely used as cores in sandwich composites, for packing and cushioning. This paper presents the experimental results obtained for the mechanical properties of polyurethane foams in different loading conditions and the influence of impregnation on the mechanical properties. A 200 kg/m3 density polyurethane foam was tested in tension, compression and three point bending. The experimental results show that the impregnation layer has no effect on the strength of the foam, but has considerable influence on the tensile and flexure modulus.

The aim of the paper is theoretical modelling and experimental verification of the nonsymmetric thermal shock crack propagation in compound ceramic Al2O3 and ZrO2. The theoretical problem formulation concerns the thermal shock problem in a strip or bar made of nonhomogeneous material, which can exhibit local fluctuation of its mechanical and thermal properties. Such approach allows for: analysis of the real non-homogeneous ceramic materials and solution of the composition optimisation problem for composite material with respect to thermal shock sensitivity. In particular the presented approach enables estimation of the stress intensity factors during thermal shock for any continuous composition of the ceramic material.

The aim of the paper is theoretical modelling and experimental verification of the nonsymmetric thermal shock crack propagation in compound ceramic Al2O3 and ZrO2. The theoretical problem formulation concerns the thermal shock problem in a strip or bar made of nonhomogeneous material, which can exhibit local fluctuation of its mechanical and thermal properties. Such approach allows for: analysis of the real non-homogeneous ceramic materials and solution of the composition optimisation problem for composite material with respect to thermal shock sensitivity. In particular the presented approach enables estimation of the stress intensity factors during thermal shock for any continuous composition of the ceramic material.

The paper deals with the experimental method of the mechanical properties estimation at the beginning of deformation process (elastic behaviour) of the material as well as during the whole deformation stages. The idea of the method results from the observation of the loading and unloading process of the material and analysis of the strain stage.

Some numerical examples were presented to describe deformation process of semi-brittle polycrystalline ceramic materials, following paper [4]. The damage growth can be modelled as quasi-linear function of the stress state, what is easily applicable to solutions to many practical engineering problems.

This article discusses the construction of constitutive equations for the quasi-static deformation process of semi-brittle materials from the onset to the state pre ceding final failure. The simple connection between mesomechanical and phenomenologi cal modelling of damage is possible. The generalization of the damage measurement idea by unloading modulus [31] allows one to follow the whole non-linear unloading process in the multi-axial state of stress, specifying all mechanisms contained in it.