Centre of Excellence for Modern Composites Applied in Aerospace and Surface Transport Infrastructure

Final Report Summary - CEMCAST (Centre of Excellence for Modern Composites Applied in Aerospace and Surface Transport Infrastructure)

Executive Summary:

The project “Centre of Excellence for Modern Composites Applied in Aerospace and Surface Transport Infrastructure” - CEMCAST 245479 - aimed at continuation and advancement of activities initiated in FP6 ToK project MTKD – CT - 2004 – 014058 at the Centre for Modern Composite Materials (CMCM) created at the Lublin University of Technology (LUT), Poland. The main objectives were: a) to unlock and develop the full research potential and increase research capacities of the CMCM staff in the areas comprising modelling of composite and smart materials and their applications to aerospace and transport infrastructure (pavements and airfields), also modelling and control of dynamics of structures made of composites b) to establish new area of competence: innovative technologies for manufacturing of composites, c) to upgrade research equipment for testing of composite materials d) to increase contribution to regional economic and social development, e) to provide better integration and visibility of the CMCM in the ERA. The project objectives were accomplished by a coherent set of the following complementary actions: a) twinning collaboration with 11 universities from Bulgaria (Russe), Denmark (Aalborg), Germany (Magdeburg, Stuttgart), Greece (Athens), Italy (Ancona, Rome), Portugal (Porto), Romania (Timisoara), United Kingdom (Aberdeen, Glasgow), b) recruitment of: 5 researchers from Bulgaria, Greece, Romania, Russia, Ukraine, c) organisation of: 2 mini-symposia at international conferences (in Paris and Wien), course in International Centre for Mechanical Sciences (Udine, Italy), poster session at international conference (in Glasgow), 3 workshops (in Lublin), d) participation in 22 international conferences, which were held in 13 countries: Austria, Belgium, Czech Republic, France, Germany, Ireland, Israel, Italy, Poland, Romania, Russia, Turkey, United Kingdom and delivering 45 presentations, e) purchase of the following equipment: extension of the existing 3-D Image Correlation System, thermovision infrared camera, testing system for multi-axial loading of structural elements, stress screening system, corrosion chamber, temperature shock chamber, ageing chamber with fluorescence lamps, acoustic emission controller, system of acoustic emission signals together with cabling, sensors for acoustic emission, licence for LabVIEW programme, grip for stretching of composite plates, f) increased cooperation with regional enterprises (including SMEs): “WPRD” (local firm for road building), “Cree Yacht – yacht design and hitech-composites”, “WIT-COMPOSITES” (local SME), PZL Mielec S.A. Sikorsky Company, Technology Cluster “Aviation Valley".

The project implementation resulted in creating a leading research centre in the Middle-East part of Europe in the multidisciplinary area encompassing modelling and experimental testing of composite and smart materials and their application to aircrafts, pavements and airfields. Upgraded quality of research is clearly shown in the number of publications accomplished within CEMCAST: 2 books ( in Springer), 16 book chapters, 60 published articles (in 24 well recognised international journals - mainly: ICI Master Journal List), 4 articles in press, 7 articles in review. Implementation of CEMCAST strengthened co-operation with the regional industry by facilitating technology transfer and fostering innovations. In terms of socio-economic aspects the project helped to compensate disproportion (Lublin region is a less favoured one) and created good bases for diminishing the differences. CEMCAST increased capacity, visibility and competitiveness of the CMCM in the Middle – East part of Europe in the field of composite materials and their applications to engineering structures. As a result CMCM became an attractive partner for academic and industrial entities in Europe for participation in joint research projects within FP7 in the ERA.

Project Context and Objectives:

The CEMCAST project aimed at continuation and advancement of activities initiated in FP6 ToK project MTKD – CT - 2004 – 014058 at the Centre for Modern Composite Materials (CMCM) created at the Lublin University of Technology (LUT). The LUT – established in 1953 - is situated in Lublin (capital of the Lublin region). The LUT is the biggest technical university in the East-Middle part of Poland (employing 1150 staff members, among them 555 researchers - assistants, post doc, professors) and the biggest research centre in technical sciences – emerging excellence centre (in this part of Poland) in multidisciplinary areas of mechanics, material sciences, automation, means of transport design. Currently the scientific activity is focused on: application of modern composite materials in engineering design of transport infrastructure –pavements, bridges, airfields.

Within the project MTKD – CT - 2004 – 014058 (co-ordinated –like CEMCAST - by prof. T. Sadowski), new areas of competence - comprising modelling of composite materials and their applications to civil, mechanical and aircraft engineering - were developed.

CEMCAST project aimed at expanding of different aspects of composite technology and analyses curried out by the CMCM staff. in particular: introducing novel, innovative methodologies to modelling and testing of composites. The objective was to increase significantly overall capacity and research profile of the Centre in the following areas: modern technologies of composite materials, experimental testing of composite structural elements, multi-scale modelling of the different types of composites under various working conditions also nonlinear dynamics and vibrations of composite structures with active elements. Those scientific objectives were focused on new ideas and innovations in modelling of different types of composite materials and application of newly formulated concepts to solution of engineering problems in aerospace and surface transportation engineering. They can be presented as follows:

1. multidisciplinary (cross-disciplinary) approach to modelling of modern composite materials with application of multi-scale method, starting from atomistic microscope observations. It is new, fast emerging scientific field. The initial composite internal structure strongly influences the composite behaviour and degradation under different types of loading: static, cyclic, dynamic or impact ones. Additional influence of the water, aggressive environment and high temperature usually accelerate degradation process, which can be described at different scale levels (nano-, micro-, meso-, macro-) and requires inclusion of the physical aspects in the theoretical description.
2. modelling and control of dynamics of structures made of composites with embeded active elements taking into account geometrical and material nonlinearities, active and passive vibration suppression of chosen mechanical or/and civil engineering structures, study of possible transition from regular to irregular oscillations of design flexible composite structures, modeling of machining of composites.
3. experimental testing of newly created composite materials concerning estimation of the local stress concentration and resistance to defects propagation, composites properties during machining, testing of elements and structures under different type of excitations, modal analysis, experimental verification of vibrations control strategy.
4. industrial application of composite models in designing of engineering structures, e.g. smart composites in helicopters, active and passive dampers, thermal barrier coating of engine elements, joining technologies, pavements, bridges and airfields.

Moreover, by exchange of staff with leading European centres, the CMCM strived to keep abreast of any research and technological developments in the areas already represented by the Centre. The ultimate goal was to become the excellent centre, visible at EU level in modern composite materials and their application to solution of engineering problems on a research scale and in parallel on a small pre-industrial scale, through reinforcing of the RTD capacity and capability. On the local level the objective was to develop co-operation with the regional enterprises through sharing research expertise thereby allowing more extensive use of the Centre’s equipment and being involved in popularization of modern composites for novel and innovative technical applications in wide branches of engineering at SMEs. Development of long term cooperation with the regional industry dealing with aerospace and pavements responds to major socio-economic challenges in the region, by facilitating technology transfer and fostering innovations.

In order to participate in the improvement of the well-being of EU citizens and increase of the economic growth at the regional and European level one of the objectives in CEMCAST was to provide highly trained and qualified scientists and laboratories equipped with modern research infrastructures.

One of crucial objective was to improve an overall performance of the Centre by strengthening its capacity and visibility in the Middle – East part of Europe, to achieve the level comparable to that of the leading research centres in EU so as to become an attractive partner for academic and industrial entities in Europe and to participate in joint research projects within FP7 in the ERA.

Summarizing, in CEMCAST project the main objectives were:

• to unlock and develop the full research potential of the CMCM staff in the areas of competence advanced in the previous project (modelling of composite materials and their applications to civil, mechanical and aircraft engineering),
• to establish new area of competence: innovative technologies for manufacturing of composites,
• to broaden research on applications of composites to means of transport, also pavements and airfields,
• to upgrade research equipment for testing of composite materials,
• to improve research potential for increased contribution to regional economic and social development,
• to strengthen the capability of the CMCM researchers for successful participation in research activities at EU level and in FP7,
• to provide better integration and visibility of the CMCM in the ERA.

The project objectives were accomplished by a coherent set of the following complementary actions:

1. twinning collaboration with partners from the previous project - MTKD – CT - 2004 – 014058 - (long-term cooperation) and newly selected excellent research entities in the EU in order to strengthen or to set-up strategic partnership: collaboration was established with 11 universities from Bulgaria (Russe), Denmark (Aalborg), Germany (Magdeburg, Stuttgart), Greece (Athens), Italy (Ancona, Rome), Portugal (Porto), Romania (Timisoara), United Kingdom (Aberdeen, Glasgow),
2. recruitment of 5 experienced researchers from: Bulgaria, Greece, Romania, Russia, Ukraine were employed,
3. organisation of workshops and mini- symposia, to facilitate transfer of knowledge at national and international level: 2 mini-symposia at international conferences (in Paris and Wien), course in International Centre for Mechanical Sciences (Udine, Italy), poster session at international conference (in Glasgow), 3 workshops (in Lublin) were organised,
4. participation of the Centre’s staff in international events (conferences, scientific meetings): 45 presentations were given at 22 international conferences, which were held in 13 countries: Austria, Belgium, Czech Republic, France, Germany, Ireland, Israel, Italy, Poland, Romania, Russia, Turkey, United Kingdom,
5. substantial improvement of the existing research equipment: the following items were purchased - extension of the existing 3-D Image Correlation System, thermovision infrared camera, testing system for multi-axial loading of structural elements, stress screening system, corrosion chamber, temperature shock chamber, ageing chamber with fluorescence lamps, acoustic emission controller, system of acoustic emission signals together with cabling, sensors for acoustic emission, licence for LabVIEW programme, grip for stretching of composite plates,
6. increased cooperation with regional enterprises (including SMEs): “WPRD” (local firm for road building), “Cree Yacht – yacht design and hitech-composites”, “WIT-COMPOSITES” (local SME), PZL Mielec S.A. Sikorsky Company, Technology Cluster “Aviation Valley”,
7. dissemination and promotional activities: website and poster were created, brochures and flyers were widely distributed at workshops, seminars, conferences, meetings with the representatives of industry, articles were published in “Parliament Magazine”, on the DG Research Innovation website, website of National Contact Point, local newspaper and University Bulletin, presentations about CEMCAST were delivered at conferences and workshops.

Project Results:

Main S & T results in CEMCAST project were achieved by twinning cooperation with 11 European universities (comprising common research carried out mainly during incoming and outgoing visits) also recruitment of 5 foreign researchers at Lublin University of Technology (LUT). Topic of research was established for cooperation with each twinning university and each recruited researcher.

Main S & T results are presented in the following way:

A) S & T results obtained in twinning cooperation with each of 11 universities
B) S & T results obtained in common research with each of 5 recruited researchers

Ad A)

S & T results obtained in twinning cooperation with each of 11 universities:

1. Task 1.1. Twinning with Martin Luther University, next Otto-von-Guericke

University (Germany)

Topic: Modelling of thermomechanical behaviour of composites:

1. effective thermo-mechanical properties for polymeric and metallic foams
2. FGM materials – thermal barrier coating (TBC)
3. sandwich honeycomb plates

Ad 1. The new skills were obtained in the field of theoretical modeling and experimental testing of polymer foams. The following effects were investigated concerning assessment of the thermo-mechanical properties of the foam materials: significance of the density, loading rate, material orientation and temperature on dynamic compression behavior of rigid polyurethane foams.

The influence of impregnation on mechanical properties of polyurethane foams at room temperature was experimentally evaluated in both static and impact loading conditions.

For un-impregnated foam the energy absorbed to fracture was equal to the impact energy, while for the impregnated specimens the energy absorbed to fracture was approximately 80% of the impact energy, which indicated that the other part of the impact energy was consumed for internal damage. Different shapes of energy versus displacement curves were obtained for static and impact tess.

The other phenomenon investigated was estimation of the size effect on fracture toughness of polyurethane foams (3-point bending) under quasi-static and impact loading conditions with different values of load velocity (1-5 m/s). The fracture toughness was also strongly influenced by temperature, i.e. the significant decrease of the mechanical properties was observed.

Ad 2. Functionally Graded Materials (FGMs) are modern composites applied in different branches of engineering. They can be used in the form of structural elements like: beams, plates and shells. In the project, formulation of the new mathematical theory of rods made of FGM based on the deformable curve model with triad of rotating directors attached to each points, was done. The purely mathematical model was compared to numerical models elaborated within ABAQUS code – perfect coincidence of results was obtained. The new theory of the thermoelastic deformations of cylindrical multi-layered shells and plates using direct approach was formulated. Several engineering examples were calculated and compared to numerical ones.

The modeling of mechanical behavior of layered composites (FGM materials) applied for road structures was investigated with application of Finite Element Method and Artificial Neutral Networks. This allowed for determination of: stresses and displacements, cracks propagation in this complex layered systems creating road internal structure.

Thermal Barrier Coatings (TBCs) are modern composite layers applied for protection of critical parts in aero-engines and other structural elements subjected to sudden changes of the temperature. In the project the assessment of thermal shock resistance and mechanical properties at elevated temperature of ceramic composites and transparent ceramics (used for windows) were estimated. The results of these investigations were implemented in the numerical modeling of the turbine blades and vanes of the jet engines response to thermal shock problems. The multidisciplinary analysis of the operation of temperature increase in turbine blades in combustion engines by application of the TBC was successfully investigated.

Ad 3. The important contribution was done in the field of assessment of the mechanical response of sandwich plates with the core made of a polymer foam or a honeycomb, subjected to static or dynamic loading. In particular the new approaches were applied: 1) to assess the effective elastic properties of foam-filled honeycomb cores of sandwich panels, 2) to perform dynamic analysis of debonded sandwich plates with flexible core – numerical aspects and simulation, 3) to find dynamic behavior of sandwich plates containing single/multiple debonding, 4) in numerical study of the dynamic response of sandwich plates initially damaged by low-velocity impact, 5) to nonlinear dynamic analysis of harmonically excited debonded sandwich plates using finite element modeling, 6) to transient dynamic response of debonded sandwich plates predicted with the finite element.

2. Task 1.2 Twinning with the Aalborg University, Denmark

Topic: Structural characterisation of polymer matrix composites

The twinning cooperation between scientific groups from Aalborg University and Lublin University of Technology aimed at development of numerical and experimental methods of 3D structure characterization, especially microstructure of polymer matrix composites.

The first part of collaboration concerned the problems of the experimental and numerical analysis of failure of fibers reinforced polymers under static tension test. The carbon/epoxy and aramid/epoxy composites were made from the unidirectional prepregs consisting of thermosetting epoxy matrix. The FRP panels were manufactured by autoclave technique at the LUT. The quality of composite was carried out by NDT used supersonic flaw detector. Some samples was examined using microtomography method on Skyscan microtomograph. After static tension test the microstructure was analysed by SEM. Therefore the Abaqus/Standard programme with XFEM (eXtended Finite Element Method) and CZM (Cohesive Zone Method) was applied as a numerical analysis tool. The aim in leading calculations was defined as an optimal configuration in fiber/epoxy layer laminate. The laminate was performed to square plate and under tension and shearing load in aspect to guarantee the best strength parameters in composite structure. The numerical model of composite was prepared. Verification of numerical analysis was carried out by experimental studies (strength properties, microstructural analysis of failure). Microstructural analysis and numerical simulations indicated the fact that initiation of composite material damage took place at the interface as a result of cracking and loss of fibre/matrix connection. This resulted in weakening of the composite microstructure in this area through the initiation of a reinforcement cracking process, which lead to further structural degradation, consisting in propagation of matrix cracking and, as a result, complete damage of the composite structure.

The second aim of the research were composite structures particularly nanocomposite foams. Researchers in AU designed microcellular polymer nanocomposite foams as core materials with relatively low-cost and environmentally friendly for lightweight composite sandwich structures use in wide variety of sectors. The wind power, yachting and rail industries in particular expressed an interest in being able to use such novel materials.

The cooperation was focused on structural behaviour of the composite foams under compression load. The structural analysis of composite foams were studied using X-ray Computed Tomography (SkyScan). The static compression test was carried out using specially designed loading rig placed inside the X-Ray CT Skyscan 1174 chamber. This rig was designed and manufactured by AU researchers and handed over to LUT. The aim of research was microstructural analysis of composite foams, identification of geometrical parameters of foams and cells and interactions between compression loading and microstructural bevaviour of nanocomposite foams. Internal structure was reconstructed as a series of 2D cross sections which were then used to analyze the two and three dimensional morphological parameters of the object.

The international research experience gave the possibility to broaden the knowledge of complex structures – foams and nanofoams and improve knowledge and skills on carrying out novel experiments and techniques.

The new equipment for X-ray computer tomograph increased the possibility of study of deformation structures of polymer matrix composites in LUT laboratory. Moreover, the research team of LUT acquired the new competences in the field of the structure and mechanics characterization of composite foams.

3. Task 1.3 Twinning with the University of Glasgow, UK

Topic: Nonlinear dynamics and vibrations of composite structures with active elements

The research in this task was concentrated on:

1. Modelling and experimental testing of composite structures with embedded Shape Memory Alloys (SMA).
2. Modelling and experimental testing of composite structures with embedded PZT elements for vibration suppression.
3. Optimal control for design of intelligent composites.
4. Dynamics of autoparametric L-shaped beam structures.

A review of the fundamental science behind applications for shape memory alloys (SMAs) in mechanical engineering structures and machines was elaborated in a book chapter entitled "Applications for Shape Memory Alloys in Structural and Machine Dynamics" published by Springer in Solid Mechanics and Its Applications, Vol. 181,2012, ISBN 978-94-007-2472-3. Three models of SMA were considered in detail then a summary investigation of the effect of SMAs on the dynamics of beams and plates was given. Applications in rotor dynamics, for which SMA elements were shown to have considerable uses in the modification of resonant behaviour within the system, were demonstrated. The dynamics of composite beams and plates with integrated SMA elements, and the concept of antagonism as a means for the approximate equalisation of heating and cooling time constants, were presented.

The active elements play a very important role in aerospace and mechanical engineering applications. Therefore in the bilateral cooperation a special attention was paid to this topic. The results of application of Positive Position Feedback (PPF) and Nonlinear Saturation Controllers (NSC), applied for a composite beam model with geometrical nonlinearities were received. The study was performed for flexible composite beams, made of selected materials and excited by oscillations of the clamped end. The Macro Fibre Composite (MFC) was used as an active element, for nonlinear vibration suppression. Investigations of an influence of the particular control parameters allowed preparation of adequate optimization algorithms, selection of the control strategy and parameters optimization for operating system’s condition. The control algorithms were tested for external, parametric and self- excitation, and effectiveness of application of MFC actuators was shown. Elaborated methods were studied analytically by the Multiple Time Scale Method in Mathematica package, using symbolic manipulations. Numerical simulations were carried out in Dynamics and MatLab software by procedures for automatic calculations and data analysis. Some theoretical results were verified experimentally for beams and plates in a laboratory. The analysis was performed for finding relationships between the controller parameters and determination their optimal values. The objective function was defined as minimal transient response leading to minimal vibration amplitudes.

The cooperation on dynamics of autoparametric L-shaped beam structures was divided into two parts, (a) derivation of new equations of motion which took into account rotary inertia in the 3D space dynamics and (b) solving a linear eigenvalue problem of the structure. The differential equations of motion were derived on the basis of the Hamilton principle of least actions. The kinetic and potential energies were formulated on the basis of linear theory, considering inextensionality of the beams and the autoparametric couplings leading to autoparametric resonances. The vibration modes were determined analytically taking into account six coupled partial differential equations and associated boundary conditions. The approach allowed determining vibrations frequencies and modes versus selected parameters. The results were verified by the finite element method. The obtained solutions are essential for the further subject development. The linear modes formulated in 3D space can be used for modal reduction of a full nonlinear problem. It was shown that for lower vibration modes the results of analytical and finite element model are in a very good agreement, however for higher modes, the inextensionality condition was not well satisfied therefore the model in such a case should be corrected.

4. Task 1.4 Twinning with the University of Aberdeen, UK

Topic: Experimental and numerical analysis of structures with geometrical and material nonlinearities

Main results in this topic, based on the experimental test, numerical, and analytical analysis concerned the following research subjects:

a) Non-smooth dynamical systems
b) Dynamics of cutting process
c) Modelling of nonlinear phenomena activated by fluid flow - Vortex Induced Vibrations (VIV) and nonlinear dynamics of flexible structures

In the field of non-smooth dynamical systems the active suspension of structures was studied on the basis of modern elements, such as: magnetorheological dampers (MRD) and shape memory alloys (SMA) springs. Both suspension elements, SMA and MRD, were modelled and studied with hysteretic loops. The multinomial model was introduced to describe the hysteretic nonlinear relationship between strain, stress and temperature relationship of SMA. This suspension can be used in different mechanical systems in order to eliminate harmful effects of vibrations or earthquake.

Cutting process can be also treated as a kind of non-smooth dynamical system, where the tool loses contact with the workpiece or process is intermittent because of cutting tooth number in case of milling. Therefore, the new model of frictional chatter was developed in order to explain phenomena occurring in cutting processes and to gain a further insight into the mechanics of frictional chatter. The new idea based on the Rayleigh oscillator generating self-excited vibrations. The new approach which took into account also the forces acting on a tool flank was compared with the one developed by Wiercigroch and Krivtsov (Phil. Trans. The Royal Society of London A Mathematical Physical And Engineering Science, 2001). Next, the mathematical description of cutting process was formulated and numerical procedure to solve nonlinear and discontinuous differential equation of motion was proposed. For ease of numerical computations, the discontinuous sign function and the Heaviside function were replaced by their smooth approximations using the hyperbolic tangent and the exponential functions. The above replacement did not have any significant effects on the dynamics of the system, but simplified numerical calculations. In the future the results can be implemented to technological processes in order to active control and reduction of harmful chatter vibrations.

Additionally, ultrasonically assisted drilling (UAD) method is used for polymer composites reinforced with carbon fibres. UAD let us improve efficiency of cutting process.

Analysis of flexible structures e.g. risers used in an oil industry, subjected to fluid flow influence may lead, due to interactions of fluid and the structure, to so called, Vortex Induced Vibrations. This problem was discussed and investigated in the bilateral cooperation. A reduced, two-degree-of-freedom model was developed considering one mode response of the structure and one mode fluid flow represented by van der Pol model. The results of frequency locking zones and quasi-periodic zones were obtained by Multiple time Scale Method and verified by direct numerical simulation. The modulation equations were derived by Mathematica package and by hand in the first order approximation. The steady states were found in analytical form, which allowed immediate parametric study. The resonance curves and influence of van der Pol self-excitation, and also coupling parameters were determined.

5. Task 1.5 Twinning with the University Roma “Sapienza”, Italy

Topic: Modeling and nonlinear vibrations of flexible and composite structures

Research group in this topic have examined nonlinear dynamics and the behaviour of suspended cables with a sag. Particular attention has been paid to systems excited by support motion under multiple internal resonance conditions. Also impact of external excitation on the systems behaviour has been studied. Solutions have been obtained analytically by the multiple scale of time method and verified by numerical simulations. The results have shown a high sensitivity to excitation amplitude, support motion and to the prescribed initial conditions. The findings have led to formulation of the conditions for a possible cancellation phenomenon in the system.

Scientists involved in composite dynamics studies have concerned a modified general classical laminated plate theory exhibiting nonlinear curvatures. The formulated model included new features comparing to well established ones by von Karman. Within the research framework a discretized model suitable for the analysis of resonant finite-amplitude vibrations of the laminate plate with immovable or movable supports has been obtained via the Galerkin procedure. Periodic responses of single-mode and internally resonant two-mode models excited at primary resonance were obtained via the multiple scale method. The influence of plate thickness, aspect ratio, number of laminae, kind of material, mode number has been addressed. The comparison of nonlinear vibration results obtained with the new model and von Karman models for different boundary conditions confirmed the advantage of the new approach.

The researchers working on shape memory alloys elaborated a new, full thermo-mechanical numerical description of shape memory material. The model includes parameters to determine the shape of pseudo-elastic loop observed in SMA, thermal variables describing the heat production, absorption and exchange, and a parameter estimating the impact of the temperature changes on the pseudo-elastic loops. The proposed model has been thoroughly verified according to the available benchmark data. Finally, it has been used to study different methods of identification of regular and chaotic isothermal trajectories of a shape memory oscillator. The performed simulations showed the statistical tests based on the asymptotic properties of a Brownian motion chain to be a particularly useful criterion in quantitative evaluation of the regularity of the SMA dynamical solutions in isothermal conditions.

The scientific group working on dynamics of rotating structures derived a comprehensive, analytical model of a rotating composite beam. The model takes into account a number of non-classical effects that are often skipped in the literature. The considered phenomena include material anisotropy, transverse shear, rotatory inertia of a cross-section, both primary and secondary cross-section warpings as well as struc¬tural warping restraint. Also effects related to a nonconstant rotating speed and arbitrary beam preset angle have been analysed. Exemplary cases of an open and closed box-beam cross-section made of multi-layer laminate have been given. The conducted research has shown the lay-up stacking, variable rotating speed and nonzero pitch angle to have significant impact on observed bending, twisting and axial deformation modes and their spatial couplings.

Another area of activity has been related to multi-scale and multi-field description of composite materials. Research has been focused on deriving a multi-scale representation of continuum relevant to study fibre reinforced materials and granular ones. The proposed computational approach has been based on the definition of the constitutive relations with the related evolution laws at the microscopic level avoiding the macroscopic internal variables approaches. The derived method has been exploited to modelling cracked magnesium oxide composites and two-phase ceramic composites (Al2O3/ZrO2). The results showed that observed in these materials inter-granular crack propagation can be explained by taking into account in material deformation the porosity growth at metallic interfaces. Also the role of relative rotations in the occurrence of stress concentration and cracks has been proved to be of primary importance.

6. Task 1.6 Twinning with the Polytechnic University Marche (Ancona), Italy

Topic: Modeling of intelligent composite materials and mechanical systems with application of non-linear dynamics

The studies were focused on ”Nonlinear systems with multiple degrees of freedom and hysteresis”. In the frame of this activity interesting results were obtained on the methods and particular system responses in various condition of excitations.

1. In the first step, the nonlinear dynamics of a single-degree-of-freedom oscillator with an external excitation and complex non-viscous damping was examined. The complex nature of the damper introduces a hidden variable to the set of equations of motion. Nonlinear oscillations, bifurcations and the escape from the potential well in that system were examined. The shape of the resonance curve was obtained by the multiple time scales method and confirmed numerically. By treating the excitation and damping effects as perturbations we found the hetero-clinic orbits connecting the saddle points of the Hamiltonian and estimate the range of system parameters leading to a chaotic behaviour by means of the Melnikov method. This result was also confirmed by numerical simulations. The mechanism of escape from the potential well was analyzed by means of behaviour charts and basins of attraction. We also considered the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos was analyzed using the Melnikov's criterion for a transition to permanent or transient non-periodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincare sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. The attention was focused on the effects of the asymmetric potential term and the driven frequency. Finally, we applied the Melnikov theorem to the controlled system to explore the gain control. The model was latter extended to non-smooth potentials and a non-viscous damping term with a fractional derivative. Particularly, the influence of fractional degree of derivative on the system chaotic response appearance was studied.
2. By substituting the non-viscous damper by electrical degree of freedom, an energy harvesting system of two magnetopiezoelastic oscillators coupled by electric circuit and driven by harmonic excitation was examined. The research was focused on the effects of synchronization and escape from a single potential well. In the system with relative mistuning in the stiffness of the harvesting oscillators, the dependence of the voltage output for different excitation frequencies was shown. An alternative proposal of the inverted elastic beam was proposed as an energy harvester. The beam has a tip mass and piezoelectric layers which transduce the bending strains induced by the stochastic horizontal displacement into electrical charge. The efficiency of this nonlinear device was analyzed, focusing on the region of stochastic resonance where the beam motion has large amplitude. An increase of the noise level allowed the motion of the beam system to escape from single well oscillations and thus generate more power.
3. The phenomena of nonlinear vibration of a layered glass structure with nonlinear PVB adhesive layer in order to get the nonlinear resonance curves for different boundary conditions were studied. The work allowed determining analytical nonlinear model of the structure and the resonance curves for various characteristics of the interlayer. Moreover in order to validate results a finite element model of the structure was developed. The results were published in a joint journal paper. Furthermore, The problem related to pedestrian-inducted vibrations of footbridges was prepared by UM and published in a book chapter in: Solid Mechanics and Its Applications, Vol. 181, Springer, 2012, ISBN 978-94-007-2472-3.
7. Task 1.7 Twinning with the University of Stuttgart, Germany

Topic: Multiscale modelling and experimental analysis of ceramic matrix composites (CMC)

Elaboration of the new theory describing the 2 phase ceramic matrix composites Al2O3/ZrO2 subjected to mechanical loading – tension and compression was one of the main tasks in this twinning. Two-phase ceramic composite materials (e.g. Al2O3/ZrO2) had 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 acted as stress concentrators and locally changed the state of stress, leading to the development of mesocracks and finally macrocracks. Experimental results showed that defects developed mainly intergranular and caused inhomogeneity and induced anisotropy of the solid. Modelling of such material response was done applying multiscale approach describing different phenomena occurring at different scales: micro- meso- and macro-. In particular gradual degradation processes in tension and compression were described, taking into account so called R-curve effect.

A new numerical theory was proposed for modelling of the influence of porosity in the deformation of metal-ceramic composites. The composite consisted of brittle grains and metallic interfaces. In order to incorporated porosity growth inside the metallic interfaces due to mechanical loading the Gusron-Tvergaard model was applied. This model could be applied to description of different types of composites.

A novel description of continuous degradation process of interfaces inside the WC/Co composite microstructure was done by the finite element method. Particularly, micropores and microdefects evolution in the WC/Co composite under tension was investigated. The continuum damage process of the Co metallic interface material was described by: the XFEM (eXtended Finite Element Method) and Ductile Damage Criterion (Rice & Tracey theory). In both models, the effect of initial porosity of plastic interface material on mechanical properties of the composite using the Gurson-Tvergaard model was taken into consideration. The numerical analysis using the finite element method was conducted on the developed two-dimensional (2D) models, with generalized plane strain taken into consideration.

A new revisit of compact Mode II crack specimen: analysis and fracture interpretation was done and presented in 2 papers. The aim of the analysis was modelling of cracks propagation in compact shear (CS) specimens in brittle materials, like concrete. The experiments of cracks propagation in the Mode II were done to assess the fracture toughness of the material. Then 2 new approaches were applied. One was based on singular integral equations for the problem of the interaction of two parallel cracks under Mode II loading corresponding to the loading in the CS specimen. Approximate analytical formulas for the stress intensity factors at the crack tips were derived. The second approach was numerical calculation using Gauss-quadrature formulae for the corresponding integral equations. Other analysis was done with XFEM approach.

An experimental study on damage evolution of unfired dry earth under compression and determination of the fracture properties of unfired dry earth was estimated as an example of ceramic composite. The description of damage process was with application of “so called” deformation damage theory, where a damage parameter was associated with the total strain. Experimentally determined fracture toughness by 3-point bending allows for the full description. This research will be continued to create multiscale model for crack propagation in this type of brittle composite.

8. Task 1.8 Twinning with the National Technical University of Athens, Greece

Topic: Testing of polymer matrix composites. Multiscale modelling of damage and fracture processes

Polymer matrix materials are widely used in different parts of helicopters manufactured in “Agusta – Westland PZL Swidnik SA” (local enterprise). The most important from practical point of view is description of damage and fracture processes under different states of mechanical (quasistatic, dynamic, cyclic) and thermal loading. The proper selection of evolution equations for damage growth is of crucial importance for engineers designing of structural elements made of composites.

The research done within this task was continuation of the previous common research. The polymer matrix specimens were specially prepared at “Agusta – Westland PZL Swidnik SA” for testing. It was of crucial importance to perform estimation of water absorption by the composite and its further degradation by cyclic temperature changes. The temperature changes correspond to the real temperature fluctuation, which occur during airplane flights.

The experimental study was performed on glass-fiber 90o composites prepared at “Agusta – Westland PZL Swidnik SA”. The effects of the hydrothermal damage (hydrolysis) and the thermal shock damage due to liquid nitrogen damage on the moisture absorption/desorption behaviour in a glass-fiber composite system were investigated in this study. The second Fick model of moisture absorption/desorption was applied. An explanation of the inner micro-damage (micropores and microcracks) due to moisture migration and temperature changes, the micro-structure effects and the tensile/compressive stresses which were created due to liquid nitrogen, was given. In order to describe theoretically the analysed phenomena the Fick model was applied to estimate a longitudinal diffusivity and transversal one. To assess water damage (hydrolysis) and cracking processes the own numerical model for cracks initiation and propagation in the polymer matrix composite structure due to the gradient field of humidity or temperature was elaborated. Good agreement of experiments with numerical model was attained.

The second topic investigated within this task was experimental testing of layered beams made of 2 polymer matrix skins and polymeric foam core. Theoretical model was created using a direct approach which models slender bodies as deformable curves endowed with a certain microstructure. General formulas for the effective stiffness coefficients of composite elastic beams made of several non-homogeneous materials were derived. In case of small deformations, the theoretical predictions were compared with experimental measurements for the three-point bending of polymer matrix composite beams, showing a very good agreement. For functionally graded sandwich columns the analytical solutions of bending, torsion and extension problems were obtained and compared with numerical results computed by the finite element method.

The theoretical problem of an anisotropic, unbounded elastic polymer matrix composite containing three collinear equal cracks subjected to symmetrically tangential stresses was solved (case corresponding to Mode II of classical fracture). The elastic state created in the composite was determined using the formalism of Riemann-Hilbert problem and the representation of elastic stresses and displacements fields according to Lekhnitskii approach. Applying the asymptotical analysis, the asymptotic values of the stress and the displacement fields in a vicinity of the cracks tips were calculated.

9. Task 1.9 Twinning with the University of Porto, Portugal

Topic: Modelling and experimental testing of structures made of modern composite materials

The main activity in this twinning concentrated on the following research topics:

1. Modelling and experimental testing of modern composite material properties under static and dynamic loads.
2. Crack propagation and delamination problems.
3. Dynamics of composite structures with geometrical nonlinearities.

Applications of composites with variable stiffness to create and optimize mechanical properties of the structure were analysed. The reinforcing fibres, put inside the composite in a special curvilinear way allowed designing its special properties. The analysed periodic oscillations of Variable Stiffness Composite Laminates (VSCL) were considered. The present stage of the research based on the shooting method and alternatives, as the use of AUTO continuation software or a multiple scales based analytical approach were discussed. The intentions of this research was: (1) to find out how the linear natural frequencies and (mode) shapes evolve with the displacement amplitude in this new type of laminated composite material; (2) to describe modal interactions in VSCL due to the energy interchange under the coupling induced by non-linearity. The VSCL have curvilinear fibres and the carried out numerical analysis was based on a recently developed p-version finite element with hierarchic basis functions. The element followed the first order shear deformation theory and considered von Kármán’s type of non-linear terms. The time domain equations of motion were transformed to the frequency domain via the harmonic balance method. The ensuing frequency domain equations were solved by an arc-length continuation method. The FEM models of VSCL plates were built and a technique of discretization of curvilinear fibres’ orientation was elaborated. The natural frequencies and vibrational mode shapes of variable stiffness composite laminate (VSCL) plates with curvilinear fibers were studied. The received results were compared with already published results. In each ply of this rectangular VSCL, the fiber-orientation angle changed linearly with respect to the horizontal coordinate. To define the modes of vibration of the laminates, a new p-version finite element, which followed third-order shear deformation theory (TSDT), was employed. Proposed technique of discretization of curvilinear fibres’ orientation was used in case of buckling, as well as delamination modelling. Next, the problem of free vibration of VSCL plates was solved using the Koiter’s perturbations method. A plate model was adopted in the analysis.

Additionally a buckling of the VSCL plates was examined. The results obtained with the analytical-numerical method (ANM) were compared with finite element method. The FEM’ models delaminations in laminate composites using cohesive elements in ABAQUS code and tested changes in dynamical response of laminated beams depending on the damage were considered.

The numerical aspects of modelling of the damaged zone were discussed. There were prepared several models of beams with different finite elements and a layer of cohesive elements in order to model delaminated region behaviour. Comparison of such results found an application in developing a dynamic method of damage assessment. The laminated composite beams with embedded inserts of material with known friction coefficient were tested experimentally and numerically Analytical models based on the Timoshenko beam allowing for temperature effects were elaborated. In numerics, the Finite Element Method, as well as the Finite Differences Method were exploited. The commercial software codes were used - Abaqus, Nastran and Matlab. The results were positively verified experimentally with a shaker enforcing vibrations of the beam samples and with high speed camera registering the dynamical answer of the beam. The modal analysis of composite beams was performed numerically and experimentally. The laboratory tests in laminated composites – DCB, ENF, 3PB and 4PB in order to get experimentally material data for numerical models of delaminated beams were conducted. The beams were of three kinds: carbon-epoxy, glass epoxy and Kevlar-epoxy; the last one was reinforced by fabric.

The nonlinear model of the compressed columns, under dynamical load, close to the critical buckling point was developed, and then, reduced to a set of two coupled nonlinear ordinary differential equation. The analytical solutions was sought by Multiple Scales of time and numerical methods. The dynamic response of thin-walled composite columns subjected to in–plane pulse loading was described for three chosen stability criteria. Additionally, the attention was paid to the influence of the time of tracking of dynamic response on critical values of the dynamic load factors.

10. Task 1.10 Twinning with the Politehnica University of Timisoara, Romania

Topic: Numerical and mathematical modelling of cracks propagation in composite materials, including pavements (layered composites). Experimental verification.

The main areas of the scientific activities performed in this task were as follows:

1. Modelling of cracks propagation in composite materials (polymer matrix materials, foams, ceramics composite materials, pavements)
2. Experimental verifications

The fracture toughness of the polyurethane foams is very important material feature necessary for modeling of the composite degradation process. The estimation of this material properties was done for quasi-static and dynamic loading. The performed experimental program allowed for making a comparison between dynamic and static fracture toughness of polyurethane rigid foams. Static three point bending tests and instrumented impact tests were performed using single edge notch specimens. The obtained results showed that for all foam densities the dynamic fracture toughness was higher than the static toughness. Density appeared to have the main influence on both static and dynamic fracture toughness. A quasi brittle fracture without plastic formations and cushioning was observed for all foam densities.

The presence of cracks had a major impact on the reliability of advanced materials, like fiber or particle reinforced composites, layered composites, laminated composites. The new methodology for investigation of crack propagation paths in four point bending aluminium–PMMA specimens was elaborated and investigated experimentally and numerically. For engineering application, it is very important to estimate the crack path, and the influence of the interface on the fracture parameters. The crack propagation paths of a sub-interface crack in a four point bending bi-material specimen made half of Aluminium half of PMMA was presented. Experimental crack paths were obtained using fatigue tests and were compared with the simulated ones by finite element analysis code FRANC2D/L. A good correlation between curvilinear trajectories of experimentally observed and numerically simulated cracks was observed. An estimation of crack growth rates of a sub-interface crack was also presented.

Mode II fracture analysis is especially important for many engineering composites. 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 civil engineering industry. The experiments were 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 enabled observation of defect initiation and development, there was no need to input the original conditions. Most numerical calculations coincided with results of experimental research. There was a convergence of: cracks shapes, maximum critical force values, force - displacement graphs.

The next topic related to behavior of polymer matrix composites deal with mathematical modelling and experimental study of parallel cracks propagation in an orthotropic elastic composite. Such a case takes place in many engineering problems, particularly in operation of aircrafts, where local parallel cracks in structural parts of airplane can appear. The most important is to investigate if the cracks are stable or become suddenly unstable under certain level of loading. The novel analytical model, numerical simulations and experimental studies of the parallel cracks propagation and interaction were presented. Two cases of cracks configuration were considered: two equal cracks and two un-equal cracks. The mathematical model was elaborated for two parallel cracks with different lengths in Mode I of fracture. Following Muskhelishvili formalism the stress and displacement fields were determined in the vicinity of the crack tips and using Griffith–Irwin theory the interaction between cracks was studied. The numerical calculations done within Finite Element Analysis (FEA) allowed for estimations of the GI and GII for different directions of cracks propagation. The important for kinks initiation was the value of GII, but the growth of the cracks depended mainly on GI in considered two cases of cracks arrangement. The tests were performed for the orthotropic polymer matrix composite material used for production of helicopter parts. The two cases of cracks configuration were experimentally examined, i.e. the equal and un-equal cracks. In order to assess the displacement and strain fields in the tested materials, the 3-D digital image correlation system ARAMIS was used. The system allowed for displacement and strain measurement in all three directions, on the whole measured area of a specimen, particularly near edges of cracks. Comparison to analytical analysis and numerical calculations confirmed correctness of the proposed models.

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 and 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. A cracked sandwich plate loaded by 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 stress and displacement distributions were investigated. The Stress Intensity Factors were determined based on numerical results using displacement extrapolation method. The results for the non-dimensional stress intensity factors showed that at lower crack lengths the influence of material mismatch was lower but this influence increased with increasing the crack length.

11. Task 1.11 Twinning with the University of Rousse, Bulgaria

Topic: Impact loading response of modern composite materials applied in aerospace and surface transportation.

The main areas of the scientific activities performed in this task concerned investigation of laminated glass progressive failure under low velocity impact by experimental and computational tests, as it is really necessary for better understanding of the failure and for proper optimization of laminated glasses applied in aerospace ( windows in airplanes). The second topic was consideration of dynamic cracks propagation problem in FGM materials under thermal shock.

Within this topic, to assess the mechanical response of laminated glass subjected to low-velocity impact the following activities were performed:

• experimental testing of laminated glass behaviour applied for windows in airplanes under static and impact loading (at different impact velocities of 1, 2, 3, 4, and 4.8 m/s with Instron Dynatup machine and high speed camera recording the impact) for different types of specimens including special devices for compressive shear tests and uniaxial tensile tests
• numerical modelling of laminated glass behaviour applied for windows in airplanes under static and impact loading. The new shell finite element for multi-layered laminated glass was developed. The results of finite element simulations of laminated glass fracturing under low velocity impact concerned a quarter of circle laminated glass plate. The numerical analysis was done in ABAQUS in order to investigate the capability of finite elements to model the fracturing of laminated glass.

The investigation showed circumferential pattern of cracks on the impact side of the glass layers and radial pattern of cracks on the other side of the glass layers.

In order to improve the finite element model of laminated glass that was previously used, a new model of full circle of laminated glass plate was prepared.

The second topic was consideration of dynamic cracks propagation problem in FGM materials under thermal shock. The analysis was done with application of ABAQUS numerical code. To solve this problem, 2 new subroutines were elaborated to describe the thermal and mechanical response of elements made of Functionally Graded Material (FGM) in elastic range, with temperature dependent properties, such as the module of elasticity and the Poisson ratio, expansion coefficient, specific heat and conductivity. Orthotropic functionally gradient material has been considered. The newly created subroutines UMATHT, and UEXPAN are very general and allow to find the temperature distribution during the thermal shock in the material of the TBC (Thermal Barrier Coating). Moreover, the crack propagation problem in FGM strip was solved with application of newly elaborated subroutines and application of XFEM approach. The elaborated method allowed for investigation of the cracks propagation in FGM with continuous changes of thermo-mechanical properties, or in the layered composites.

Ad B)

S & T results obtained in common research with each of 5 recruited researchers:

1. Researcher: Prof. Vera E. Petrova from Voronezh State University (Russia), employment period: 5.04.2011 – 31.03.2013

Topic: Thermal shock modelling in modern composite materials, damage and fracture process in functionally graded materials

In this topic, the following 2 research problems were considered:

1. “Theoretical analysis and modeling of Mode II cracks in Compact Shear Specimen”
2. “Interaction of edge cracks in a semi-infinite functionally graded material under residual stresses caused by cooling”.

Ad. 1. For experimental investigation of Mode II fracture and determination of the stress intensity factors the Compact Shear Specimen (CSS) was used. The real problem can be modeled by different ways transferring from simplest cases to more complicated ones. The simplest case is the problem for two parallel cracks under shear loading in an infinite plate. The analysis (analytical and semi- analytical) of this problem was done. The following results were obtained:

• The problem for two parallel cracks under shear loading corresponding to the loading in the CS specimen was considered with the presence of an additional loading which varied with a coordinate along the crack lines. This load could be residual stresses in a non-homogeneous material with properties varied with the coordinate. The problem was formulated by means of singular integral equations.
• An approximate analytical solution was obtained for far distances between the cracks. Asymptotic analytical formulas for the stress intensity factors (SIFs) were obtained as series in a small parameter λ=2a/d, the ratio of the crack sizes to the distance between cracks.
• Numerical solution of the problem was performed for more common cases. The influence of the crack inclination angle to the remote shear loading and of the distance between cracks on the SIFs was analyzed.
• Theoretical analysis and fracture interpretation of Compact Shear (CS) specimen for Mode II fracture testing of materials was done by means of two fracture criteria: the maximum circumferential stress criterion and the criterion of minimum strain energy density (SED) Smin.

Ad 2. Interaction of edge cracks in a semi-infinite functionally graded material under residual stresses caused by cooling

The investigation was devoted to a problem of the interaction of two edge cracks inclined arbitrary to the boundary of a non-homogeneous half-plane. A functionally graded (FG) material was located in the region with width h. The half-plane was subjected to one thermal shock. It should be noted that the problem for two interacting cracks can get more results for further modeling of crack propagation in materials than the problem for parallel cracks of equal length and equally spaced. The following results were obtained:

• The problem for two arbitrary inclined edge cracks in a non-homogeneous half-plane under tension and residual stresses was formulated by means of singular integral equations. The Young’s modulus and the coefficient of thermal expansion of the FGM were functions of coordinate y, E(y) and αt(y) and presented in exponential form. The FGM was cooled from sintering temperature.
• Solution was done numerically. Using Gauss’s quadrature formulae for the regular and singular integrals the integral equations were reduced to the system of NxM (N=2 – number of cracks, M – number of nodes) algebraic equations. The computer program was written for MatLab software.
• Stress intensity factors were calculated and, then, using maximum circumferential stress criterion, the fracture angles were derived (the angles of deviations of initial crack propagation).
• The results were verified by comparing the obtained stress intensity factors with existing in the literature solutions for periodic edge cracks in a homogeneous half-plane and for a single oblique edge crack. Good agreement was observed. The comparison of this semi-analytical results for the case of FGM half-plane with edge cracks with FE results in ABACUS is in progress now and will be continued.

Journal papers:

1. V.E. Petrova, L. Marsavina, T. Sadowski, “Revisit of compact mode II crack specimen: Analysis and fracture interpretation”, Theor. Appl. Fract. Mech. 59 (2012), 41-48
2. V. Petrova, T. Sadowski, “Theoretical analysis of Mode II cracks in a Compact Shear Specimen”, Comp. Mater. Sci. 64 (2012), 248-252

Journal papers in preparation:

3. V. Petrova, T. Sadowski, “Edge cracks in a non-homogeneous material under thermal loading”, Meccanica (2013)

Proceeding of the conference (cited in Scopus)

3. V. Petrova, T. Sadowski, “Theoretical modeling and analysis of mode II cracks in compact shear specimens”, ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers, 2601-2611

Proceeding of other conference

4. V. Petrova, T. Sadowski, “Compact Shear Specimen for Mode II Fracture Tests: Analysis and Fracture Interpretation”, CD-ROM Proc. 19th European Conference on Fracture Mechanics for Durability, Reliability and Safety, 26-31August, 2012, Kazan, Russia, 7 pages, ISBN: 978-5-905576-18-8

2. Researcher: Assoc. prof. Mircea Birsan from University “A.I. Cuza” of Iasi (Romania), employment period: 5.01 – 4.10.2011

Topic: Layered composite plates and shells subjected to thermal and mechanical loading

In this topic, 2 main research problems were investigated:

1. Deformation of composite multi-layered cylindrical shells under thermo-mechanical loading

Deformation of multi-layered cylindrical shells made of orthotropic materials was investigated. These kind of structures are widely used in aerospace industry, so that the study of such problems is of great interest. To model the multi-layered thin structures, a direct approach to shell theory was employed, in which the shell-like bodies were described as deformable surfaces with a triad of rigidly rotating directors attached to each point.

The deformation of cylindrical shells with arbitrary shape of cross-section (not necessarily circular), and made of orthotropic materials were investigated. A quite general set of constitutive equations which can describe various types of composite shells, such as multi-layered shells or reinforced shells was considered. In this framework it was necessary to consider the following mechanical problem: ﬁnd the equilibrium of cylindrical shells under the action of resultant forces and moments applied to the end edges of the cylindrical shell, and the action of given body loads (body forces and couples).

A new general analytical solution procedure for this problem was established. Thus, the solution for the displacement and rotation field was expressed in terms of the exact solutions to auxiliary boundary-value problems for ordinary differential equations. In order to verify obtained results, it was shown that obtained solutions were in agreement with classical results concerning the deformation of cylindrical elastic shells, for isotropic materials. This general method was applied to the case of a three-layered circular cylindrical shell to determine the closed-form solution for the displacement and rotation fields. These analytical solutions were in very good agreement with some numerical results obtained by a finite element analysis with ABAQUS.

The thermal effects in this direct approach to shell theory were described by means of two temperature fields, which represented the temperature of the two faces of the shell. The deformation of cylindrical multi-layered orthotropic shells due to a given temperature distribution in the body was investigated.

2. Mechanical behavior of thermoelastic rods and composite beams made of porous materials like metal foams and functionally graded materials

To model the mechanical behavior of composite rods, the approach of directed curves was employed. In the theory of directed curves, the rod-like body was represented as a deformable curve endowed with a triad of rigidly rotating vectors (also called directors) attached to each point. The triads of directors accounted for rotations of the cross-sections about the middle axis of the rod. The main difficulty in the direct approach was the determination of the effective stiffness coefficients appearing in the one-dimensional constitutive equations in terms of the three-dimensional elasticity constants. The determination of effective stiffness coeffcients was important because it allowed to reduce the treatment of three-dimensional problems to much simpler one-dimensional problems. To identify these mechanical properties for general non-homogeneous rods, a comparison was done of the solutions of extension, bending and torsion problems in the direct approach with the corresponding results from the three-dimensional elasticity theory. Thus, we obtained the effective bending stiffness, extensional stiffness, torsional rigidity and other coupling coefficients. Also, to determine the effective shear stiffness, the shear vibrations of rectangular beams in the two approaches (direct and three-dimensional) was compared. For examples, general formulas for the effctive stiffness coefficients of beams composed of several different non-homogeneous materials, either orthotropic or isotropic, were elaborated. These formulas were expressed in terms of the solutions to some auxiliary plane strain boundary-value problems deﬁned on the cross-section domain. In general, the solutions of these auxiliary boundary-value problems are not easy to ﬁnd in a closed form, but in some special cases for the geometry/material parameters one can obtain the results in closed form. As an application, the analytical modeling was employed to analyze the deformation of FGM beams made of metal foams. The mass density distribution of the cellular material in the beam was given by a power law function of the cross-section coordinate, while the Young’s mod¬ulus was expressed by the Gibson-Ashby (1997) formula for closed-cell aluminum foams. Finally, verification of analytical solutions was done by comparison of the results obtained in the direct approach of FGM beams with the numerical solution of various bending problems (can¬tilever beams, three-point bending) modelled by a ﬁnite element analysis using ABAQUS.

The usefulness of the formulas is illustrated by considering different types of sandwich beams. Sandwich structures are widely used because of their ability to provide high bending moment stiffeness coupled with light weight. Because of this, sandwich panels are often used in applications where weight saving is critical: in aviation, ship building and construction. That’s why attention was focused to sandwich beams with foam core and determined the analytical expressions for effective bending stiffness, shear stiffness, and torsional rigidity. A comparison of the proposed theory was done with the classical expressions taken from the classical books of Allen (1969), Zenkert (1997), and Gibson and Ashby (1997), as well as experimental measurements obtained for the three-point bending of sandwich beams.

Journal papers:

1. M. Birsan, H. Altenbach, T. Sadowski, V. Eremeyev, D. Pietras, “Deforma¬tion analysis of functionally graded beams by the direct approach”, Composites Part B: Engineering, 43 (2012), 1315-1328.
2. M. Birsan, T. Sadowski, L. Marsavina, E. Linul, D. Pietras, “Mechanical be¬havior of sandwich composite beams made of foams and functionally graded materials”, International Journal of Solids and Structures, 50 (2013), 519-530.
3. M. Birsan, T. Sadowski, D. Pietras, “Thermoelastic deformations of cylindrical multi-layered shells using a direct approach”, Journal of Thermal Stress (in print).
4. M. Birsan, “On a problem of Truesdell for anisotropic elastic shells”, Anale Stiin¬tiﬁce Univ. ‘A.I. Cuza’ Iasi, Serie Matematica, 57 (1),91-110, 2011

Contribution to books:

M. Birsan, T. Sadowski, D. Pietras, “Cylindrical Orthotropic Thermoelastic Shells Modeled by Direct Approach”, Encyclopedia of Thermal Stress, Springer –Verlag (Ed: R.Hetnarski) 2013

3. Researcher: Assoc. prof. Vyacheslav Burlayenko from National Technical University Kharkov (Ukraine),

- employment period: 24.06.2010 – 24.06.2012

Topic: Modeling and experimental investigations of damage and fracture process in the sandwich structures under mechanical loading

- employment period: 25.06.2012 – 31.03.2013

Topic: Layered composite plates and shells subjected to thermal and mechanical loading

The following 3 problems were considered:

1. Dynamics of sandwich plates initially damaged by partial skin/core debonding

Debonding (or delamination) at the interface between the face sheets (skins) and the core was found to be one of the main pre-failure modes in the sandwich constructions that determines their integrity and safety. This defect can be caused by both improper manufacture operations and high level loading or unfavorable environment conditions. Because, sandwich plates are widely exploited in high performance structures, their reliability and endurance is a problem of high interest among engineers. Therefore, to provide the efficient application of sandwich plate-like structural elements, their strength calculations at the stage of their design are needed. An important issue within the strength analysis is dynamic loading. The purpose of this research was to appreciate the influence of the partial skin-to-core debonding on dynamics of sandwich plates.

The finite element method (FEM) was utilized as a research tool for solution of the debonded sandwiches. In this respect, static linear and nonlinear analyses, modal frequency analysis, steady state forced vibration analysis, based on the both linear and nonlinear approaches and transient dynamic analysis of beams and plates containing debonding was carried out with the commercially available ABAQUS code. Both the explicit and implicit solvers were exploited in those investigations. In particular the following analyses were performed: a) modal analysis, b) transient dynamic analysis, c) steady state forced vibration analysis, d) dynamics of post-impacted sandwich plates.

2. Vibration-based damage detection of sandwich plates with debonding

The results obtained in investigations regarding the dynamics of debonded sandwich plates can be useful in the development of damage detection (debonding identification) techniques using vibration based data. Thus, finite element numerical experiments could be used instead of complex and expensive experiments for data acquisition. In this direction, the using of free, transient and steady state dynamic responses of sandwich plates in the context of the health monitoring and damage detection of sandwich constructions weakened by debonding was performed. Natural frequencies and mode shapes of debonded sandwich plates as well as dynamic responses of plates subjected to transient and harmonic loadings were analyzed from the standpoint of damage detection. Parametric studies over a wide range of debonding zone sizes, numbers and locations, with different driving frequencies and spatial positions of the applied loading were carried out to study effects of these parameters on dynamic behaviors of the damaged sandwich plates and to give recommendations for non-destruction monitoring techniques.

3. Debonding propagation analysis of sandwich plates subjected to dynamic loading

Analyzing the transient dynamics of debonded sandwich plates was seen that plates’ dynamic behavior involving contact-impact phenomenon in the detached surfaces clearly demonstrated complex dynamic stress state at the imperfect face sheet-to-core interface. Thereby, it is reasonably to suggest that a debonding propagation will be one of more possible failure modes caused by the interlaminar stresses So, the aim of the study was to estimate conditions for debonding propagation (stress state at points of the debonded zone boundary) and to model the debonding growth under dynamic loading.

The debonding of sandwich plates subjected to dynamic loading were simulated with ABAQUS/Explicit calculating at every time increment for: stress analysis, failure analysis and contact analysis which were interrelated between them. The influence of the loading rate on the debonding growth by modeling the separation of the face sheet from the core under different speeds and simulating the behavior of sandwich plates excited with a concentrated sinusoidal force taking into account the debonding growth were finally studied.

Journal papers:

1. V. Burlayenko, T. Sadowski, “Finite element nonlinear dynamic analysis of sandwich plates with partially detached facesheet and core”, Finite Elements in Analysis and Design 62 (2012), 49-64
2. V. Burlayenko, T. Sadowski, “A numerical study of the dynamic response of sandwich plates initially damaged by low-welocity impact”, Comput. Mat. Sci. 52 (2012), 212-216
3. V. Burlayenko, T. Sadowski, “Dynamic behavior of sandwich plates containing single/multiple debonding”, Comput. Mat. Sci. 50 (2011), 1263-1268
4. V. Burlayenko, T. Sadowski, “Influence of skin/core debonding on free vibration behaviour of foam and honeycomb cored sandwich plates”, Int. J. Non-Linear Mechanics 45 (2010), 959-968
5. V. Burlayenko, T. Sadowski, “Effective elastic properties of foam-filled honeycomb cores of sandwich panels”, Composite Structures 92, (2010), 2890-2900.

Journal papers in review:

1. V. Burlayenko, T. Sadowski, “Nonlinear dynamic analysis of harmonically excited debonded sandwich plates using finite element modeling”, Int. J. of Non-linear Mechanics (in review)
2. V. Burlayenko, T. Sadowski, “Transient dynamic response of debonded sandwich plates predicted with the finite element” Int. J Mechanical Sciences (in review)

Proceedings in the conferences

1. V. Burlayenko, T. Sadowski, “Numerical Modal Analysis of Sandwich Plates Partially Damaged Due to Impacts”, Proceedings of the 3rd International Conference Nonlinear Dynamics ND-KhPI 2010, September 21-24, 2010, Kharkov, Ukraine, pp. 284-289. (September 2010)
2. V. Burlayenko, T. Sadowski,” FE Modeling of Dynamics of Impact-Damaged Sandwich Plates with Intermittent Contact in Detached Fragments”, Chapter 6: Monograph – “ Aspects of fracture and cutting mechanics of materials”. Edited by J. Jonak, Lubelskie Towarzystwo Naukowe, Lublin 2010, pp. 71-79. (December 2010)
3. V. Burlayenko, T. Sadowski,” Numerical Modeling of Sandwich Plates with Partially Dedonded Skin-to-Core Interface for Damage Detection”, Proceedings of the 8th International Conference on Structural Dynamics EURODYN 2011, 4 – 6 July 2011, Leuven, Belgium, G. De Roeck, G. Degrande, G. Lombaert, G. Muller (Eds.) ISBN-978-90-760-1931-4, p. 2242-2249. (July 2011)
4. V. Burlayenko, T. Sadowski, “Post-impact dynamic response of sandwich plates with foam and non-metallic honeycomb cores”, Proceedings of the 7th European Nonlinear Dynamics Conference ENOC 2011, 24 – 29 July 2011, Rome, Italy, D. Bernardini, G. Rega and F. Romeo (Eds.) ISBN: 978-88-906234-2-4, 6 pages. (July 2011)
5. V. Burlayenko, T. Sadowski, “Dynamic Analysis of Debonded Sandwich Plates with Flexible Core - Numerical Aspects and Simulation”, Advanced Structured Materials, Volume 15, Shell-like Structures, H. Altenbach and V.A. Eremeyev (eds.) Springer-Verlag 2011. Part V, p. 415-440. (August 2011)
6. V. Burlayenko, T. Sadowski, S.A. Nazarenko, “ Numerical modeling of dynamics of sandwich plates with partially damaged facesheet-to-core interface”, Proceedings of the Contemporary problems of mathematics, mechanics and computing sciences. N.N. Kizilova and G.N. Zholtkevych (eds.) Publishing house PPB Virovec’ A.P. Kharkov, 2011, pp. 13-25. (December 2011)
4. Researcher: Dr. Fotios Georgiades from National Technical University of Athens –PhD thesis (Greece), employment period: 01.11.2010 – 31.10.2012

Topic: Nonlinear dynamics and control of flexible structures with active elements

The research concerned (a) dynamics and control of beams with application to helicopter blades, (b) modeling of active elements embedded in beam structures (c) nonlinear normal modes (NNMs) of cables, (d) L-shaped beam dynamics, (e) non-smooth system identification.

One of the essential goals was to derive the equations of motion of beams and blades with active elements and examine their dynamics taking into account rotation of the structure. The equations of motion for transverse vibration of isotropic beams, symmetric composite beams, isotropic beams with embedded two different patches from each side of the beam were derived. Nonsmooth dynamics of a beam with PZT patches with different behaviour in tension and compression and symmetric composite beam with PZT patches having symmetric behaviour were studied as well. The equations of beams’ dynamics with PZTs considered an open circuit of active element and also warping of a composite beam was analysed. The equations of dynamics and the normal modes of cantilever beam for several cases grouped in differential equations were examined. The solution was certified by Finite Element Method (FEM) and the numerical code in a commercial FEM system was prepared. In order to obtain real physical data of the considered structures experimental tests and experimental modal analysis of composite cantilever beam was performed. The equations of asymmetric composite beam were discretized with finite element formulation and then the results crosschecked with Abaqus models and also with theoretical values. The dynamic characteristics of a composite beam with the attachment of PZT patches were examined and it was shown that if just one PZT was attached then the beam was no longer symmetric, which resulted in linear normal modes with coupled motions. Next, dynamics of a rotating beam with PZT patches for several cases were studied and the existence of coupled motions was shown on a Campbell’s diagrams. Numerical modal analysis of rotating composite beam using voltage in active element and also rational placement of PZT was performed.

A particular attention was paid for a derivation of equations of motion of a rotating composite Timoshenko beam. The structure was considered in a very general configuration, with an open and closed cross-section, non-constant angular velocity, nonzero pitch angle, an arbitrary composite configuration, and various external forces. The equations of motion were derived for a case of an active element, considering poling direction in the longitudinal direction of the beam.

A nonlinear lump mass model of helicopter bladed disk assembly was also taken into the research. It was shown that during normal operation the localized nonlinear normal modes of the bladed disk might be excited.

Nonlinear normal modes of vibrating cables were determined. The code implementing the Adaptive Newmark Algorithm for numerical integration of high DOFs dynamical systems in time domain was written the codes for numerical computation of Nonlinear Normal Modes developed earlier at University of Liege was modified significantly to meet new research requirements. The codes were developed for a numerical continuation of solutions of algebraic equations which determines the Nonlinear Normal Modes. The developed codes were applied in examination of cable dynamics for several excitations. Some results were compared with other software, with a very good agreement.

The coupled L-shaped beam structures, which are common in aerospace and mechanical engineering, may perform autoparametric vibrations and then in resonance zones an increase of vibrations can be observed. The linear and nonlinear equations of motion for L-shaped beams were derived. The linear problem of six coupled Partial Differential Equations was solved analytically. It was shown that in a case of L-shaped beam structure in deriving the equations of motion the rotary inertia terms had to be considered. The analysis of the structure allowed for determining of linear modes for in-plane and out-of-plane motions. A parametric study was performed to determine the first natural frequency for in-plane and out-of-plane motions. The nonlinear equations of motion up to third order were derived too.

The preliminary studies for the development of non-smooth system identification methods of piecewise linear dynamical systems were also discussed.

Journal papers:

1. Georgiades F., Warminski, J., 2011, ‘Excitation of a Localized Nonlinear Normal Mode of a Bladed Disk Assembly Lump Mass Nonlinear Model,’ Transactions of the Institute of Aviation (Warsaw-Poland)- ISSN 0509-6669.
2. Latalski, J., Georgiades, F, Warminski, J., 2011, ‘Mode Shape Variation of a Composite Beam with Piezoelectric Patches,’ Transactions of the Institute of Aviation (Warsaw-Poland)- ISSN 0509-6669
3. Georgiades F., Warminski, J., Cartmell, M. P., ‘Towards Linear Modal Analysis for an L-Shaped Beam: Equations of Motion,’ Mechanics Research Communications, Volume: 47 Pages: 50-60 Published: JAN 2013
4. Georgiades F., Warminski, J., Cartmell, M. P., ‘Linear Modal Analysis of L-Shaped Beam Structures,’ Mechanical Systems and Signal Processing, in press, 2013 http://dx.doi.org/10.1016/j.ymssp.2012.12.006
5. Georgiades, F., Latalski, J., Warminski, J., ‘Equations of Motion of Rotating Composite Beams with a Nonconstant Rotation Speed and an Arbitrary Preset Angle,’ submitted to International Journal of Solids and Structures, IJSS-D-13-00254, 2013.

Participation in conferences

6. Latalski, J., Georgiades, F., Warminski, J.,2011, “Dynamic Analysis of a Composite Beam with an Embedded Active Element”, 2nd Polish Congress in Mechanics-Poznan
7. Georgiades, F., Warminski, J.,2011, “Excitation of a Localized Nonlinear Normal Mode of a Bladed Disk Assembly Lump Mass Nonlinear Model”, VIII Polish Forum in Rotorcraft 2011, 17.06.2011 Warsaw, Poland
8. Latalski, J., Georgiades, F., Warminski, J., “Mode Shape Variation of a Composite Beam with Piezoelectric Patches”, VIII Polish Forum in Rotorcraft 2011, 17.06.2011 Warsaw, Poland
9. Georgiades F., Warminski, J., Cartmell, M. P., ‘Nonlinear Modal Analysis of L-shape Beam Structure,’ NNMS2012, 1-5.07.2012 Haifa, Israel
10. Georgiades F., Warminski, J., Cartmell, M. P., ‘Linear modal analysis of L-shaped beam structures - parametric studies,’ Modern Practice in Stress and Vibration Analysis (MPSVA 2012), 29 – 31.08.2012 Glasgow, UK
11. Latalski, J., Georgiades F., Warminski, J., ‘Rational Placement of a Macro Fibre Composite Actuator in Composite Rotating Beams,’ Modern Practice in Stress and Vibration Analysis (MPSVA 2012), 29 – 31.08.2012 Glasgow, UK
12. Latalski, J., Georgiades F., Warminski, J., ‘Modeling and Dynamics of Composite Rotating beams with Active Elements ’, Modern Practice in Stress and Vibration Analysis (MPSVA 2012), 29 – 31.08.2012 Glasgow, UK
13. Latalski, J., Georgiades F., Warminski, J.,’ Analysis of coupled vibrations of a nonlinear composite rotating beam’, Euromech Colloquium n. 541, New Advances in the Nonlinear Dynamics and Control of Composites for Smart Engineering Design, Senigallia, Italy, 3-6 June 2013

5. Researcher: Dr. Emil Manoach from Bulgarian Academy of Sciences (Bulgaria), employment period: 05.11.2010 – 04.11.2012

Topic: Numerical modelling, optimisation and experimental investigations of flexible structures taking into account delamination and temperature influence

The main research activities were connected with theoretical, numerical and experimental modeling of nonlinear dynamic behaviour of composite beams having delamination (faults). The goals were to develop a model for thermoelastic, large amplitude vibrations of laminated beams with defect, to adopt and to check theoretically and experimentally the Poincaré based damage detection criterion for composite beams; to study the influence of the temperature on the damage detection process; to develop a new model for dynamic behaviour of composite beam with delamination which takes into account the complex phenomena arising during the damage detection process, to study experimentally the influence of delaminations and inclusions on the dynamic behaviour of composite beams.

In order to model the delamination, the reduced rigidity was considered in a certain area of the structure. This approach was simple and it did not complicate processes arising during the dynamic behaviour of a beam with delamination (the friction between layers, change in the stress field and in the damping properties, etc.). Such approach is accepted in many damaged detection studies. The so called pseudo-load mode superposition method was used to solve the problem numerically. Then the damage index developed previously the employed researcher was adopted for the case of a beam with reduced rigidity and temperature loading and was tested for the considered structures. The damage index was based on the analysis of Poincaré maps of the system response. This approach was new for the field of the structural health monitoring. In this work the influence of the elevated temperature on the damage detection process for the first time was shown. It was demonstrated that the temperature could either strengthen the influence of the defect or mask it. It was shown that in some cases of loading, the level of the damage index increased with the temperature elevation, i.e. the elevated temperature strengthened the influence of damage, when in other cases, the relation between damage index and temperature was opposite – the increased temperature decreased the damage index in the delaminated area. It was shown that neglecting the influence of the operating temperature might lead to wrong results in the damage detection process.

One of the main goals for the study was to test and to validate experimentally the applicability of the new method for detection of delamination in composite structures.

The tests were performed in LUT Laboratory of Department of Applied Mechanics by a use of the high speed camera, shaker and a data acquisition system. Series of test were performed for laminated beams without delamination and with delamination effects. All tests were performed on healthy and damaged beam samples with the same geometry produced in LUT Laboratory of Material Engineering Department. Delamination (damage) was artificially introduced in the mid-plane of the laminate by a PTFE foil on the whole width of the beams. Special markers were plotted at the beam cross section in order to form nodes for computations. The performed tests convincingly showed that the proposed Damage Index was sensitive to delamination and predicted well the presence of delamination as well as its location.

A new model of dynamic behaviour of composite beams having delamination was developed as well. The model was based on the Timoshenko beam theory and considered contact/separation of the sublaminates during forced response. The contact interaction was modelled by two parametric elastic foundations thus it considered the normal and shear forces arising during the contact between the sublaminates. Additional damping due to the friction between delaminated parts of the beam was also introduced in the model. A numerical approach based on the finite difference method and the Gear’s method was applied and a computer programme was created in order to solve the nonlinear equations describing the dynamic behaviour of the beam. The same algorithm was tested the Runge-Kutta method but it turned out that this method was not efficient in that case. The obtained numerical results for forced response of the beam with delamination confirmed the applicability of the model and the applied numerical method to describe the arising phenomena due to delamination. It was shown that additional damping, due to the contact interaction between the sublaminates, leaded to increasing damping of the total response of the beam. It was shown that the influence of shear forces arising during the contact between sublaminates increased with the increase of the thickness of the beam. The influence of the location of the delamination on the beam response was also demonstrated.

Series of experimental studies were performed for samples with various inclusions between composite layers. Small parts of the beams were replaced by steel or aluminium layers. The goal was to study the effect of the delamination and inclusion on the beam responses. The samples allowed studying experimentally the influence of the additional friction between the sublaminates on the beam response and the influence of the shear forces arising during the contact interaction of the sublaminates. Special devices were constructed by the team of LUT in order to ensure the clamped-clamped boundary conditions. The beam were subjected to dynamic loading by a modal hammer and to a harmonic loading by shaker. The experimental results allowed verification the developed numerical code and to determine real physical data introduced into the model.

A preliminary study of large thermoelastic vibrations of Timoshenko beam were carried out. Equations in time and frequency domain were derived in order to clarify the influence of different kinds of nonlinearities and the influence of mechanical and thermal loading on arising phenomena such as non-periodic and chaotic behaviours, buckling, instability, etc. This part of work is in progress and will be continued.

Journal papers:

1. Manoach, E., Samborski, S., Mitura, A., Warminski, J., “Vibration based damage detection in composite beams under temperature variations using Poincare´ maps”, Int.J. Mechanical Sciences, 62 (2012) 120–132
2. Manoach, E., Warminski, J., Mitura, A., Samborski, S., “Dynamics of a composite Timoshenko beam with delamination”, Mechanics Research Communications, 46 (2012), pp. 47-53
3. Manoach, E., Samborski, S., Warminski, J., “Delamination detection of laminated, nonlinear vibrating and thermally loaded beams”. In “Vibration Problems ICOVP 2011”, Springer Proceedings in Physics 139, (2011). pp. 67-74.
4. Manoach, E., Samborski, S., Mitura, A., Warminski, J., “Vibration and damage detections of composite beams with defects”, Transactions of the Institute of Aviation (Poland), No 218, 44-53, (2011) ISSN 0509-6669 ;
5. Manoach, E., Warminski, J, Mitura, A., Samborski, S., “Dynamics of a laminated composite beam with delamination and inclusions”, a special issue "Dynamics of Composite Nonlinear Systems and Materials for Engineering Applications and Energy Harvesting" of the European Physical Journal (EPJ), paper accepted, 2013.

Participation in confereces:

1. E. Manoach, S. Samborski and J. Warminski, “Delamination detection of laminated, nonlinear vibrating and thermally loaded beams”, The 10th biennial International Conference on Vibration Problems (ICOVP 2011), 5-8.09.2011 Prague, Czech Republic
2. E. Manoach, A. Mitura, J. Warmiński, S. Samborski, “Dynamics and Fault Localization of Composite Beams with Delamination, The 8th European Solid Mechanics Conference” 9-13.07. 2012, Graz, Austria

Conclusions:

In CEMCAST project the main S & T results were achieved in the following areas:

a) novel modelling of FGM composites, foam materials and sandwich panels subjected to mechanical and thermal loading,
b) new experimental methods for monitoring cracks propagation process in brittle matrix composites and foam materials under quasi-static, cyclic and impact loadings,
c) elaboration of new technologies of composites production (applied in aerospace, mechanical and pavements engineering),
d) theory of elasticity and nonlinear oscillations,
e) modelling of delamination of ply composites,
f) analysis of rotating composite beam with embedded active elements,
g) new method of defects detection based on nonlinear dynamic phenomena,
h) modelling of materials with memories,
i) bifurcation theory and numerical continuation methods,
j) dynamics of autoparametric composite beam structures,
k) modelling and experimental tests of composite materials machining,
l) methods of active control based on nonlinear phenomena.

Potential Impact:

The potential impact of the CEMCAST project has a long-term sustainable effect and was obtained in the following areas:

1. Upgrading the quality of research carried out at the Centre of Modern Composite Materials (CMCM)
2. Modernisation of research equipment
3. Strengthened international position of the CMCM by increased research capacity
4. Better integration of the CMCM in the ERA
5. Deeper involvement of the CMCM in EU projects (FP7)
6. Closer co-operation with the regional and European industry
7. Improved research capacity for increased contribution to regional economic and social development
8. Encourage young staff to do research in the attractive area – modern composite materials
9. Improvement of research management and organisational skills

Here is detailed description:

Ad.1. Upgrading the quality of research carried out at the CENTRE of Modern Composite Materials (CMCM)

High level modern research is increasingly complex, interdisciplinary and costly. It demands also an increase in the mobility of persons and ideas. Within CEMCAST project, the CMCM became active and started to play a leading role in modelling and testing of modern composite materials, their applications to engineering structures – aircrafts, airfields, pavements and analysis of dynamics structures made of composites. It resulted in exploring new and emerging scientific and technological areas to anticipate future science and technology needs.

The CMCM developed research capacities and capabilities, also applied innovative and multidisciplinary approach in mechanics of composite materials and non-linear mechanics by twinning with the 11 leading EU centres and recruitment of 5 foreign researchers. This twinning and recruitment resulted in unlocking and developing full research potential comprising:

• multiscale modelling of materials with internal structure including anisotropy, reinforcement and incipient damage growth
• testing of influence of water, an aggressive environment and high temperature on a composite behaviour
• modelling of delamination in layered composites
• numerical and mathematical models of crack propagation in composites
• modelling of thermo-mechanical behaviour of composites
• impact loading response of composites
• modelling and control of dynamics of smart composites
• analysis of flexible composite structures
• modelling of machining of composites
• modelling of dynamic phenomena in mechanical and structural systems
• dynamics of non-linear systems with discontinuities
• application of Finite Element Analysis to designing of structural elements
• Finite Element Analysis to static and dynamic analysis of composites
• numerical analysis of non-linear, ideal and non-ideal parametric and auto-parametric systems with applications to smart materials
• modelling of the composite response under fatigue loading
• analysis of parametric and auto-parametric vibrations of coupled non-linear systems
• non-linear vibrations, chaos and control of systems in mechanical and road engineering
• static and dynamic analysis of pavements
• acquirement of the experimental techniques: determination of R-curve, characterising of the adhesive and shear strength interfaces, testing methods at high temperatures
• detecting damage from measuring changes in the dynamic response
• experimental analysis of non-linear dynamic systems including data signal analysis
• signal analysis of experimental results in cutting process of modern composite materials

Twinning with 11 universities from Bulgaria (Russe), Denmark (Aalborg), Germany (Magdeburg, Stuttgart), Greece (Athens), Italy (Ancona, Rome), Portugal (Porto), Romania (Timisoara), United Kingdom (Aberdeen, Glasgow), significantly increased research capacity and overall RTD capability of the Centre. New knowledge absorbed by the CMCM’s staff from incoming researchers as well as new testing methods and experimental techniques acquired by secondments of the Centre’s staff at twinning institutions increased the scientific level and research quality of each individual participant in the project and the Centre as the whole (WP1).

Recruited 5 researchers (from Bulgaria, Greece, Romania, Russia, Ukraine) synergistically bridged existing research groups, introduced new areas of research, trained the CMCM’s staff and carried out joint research. It resulted in establishing of ground for a new complex approach covering multi-disciplinary approach of composite modelling, giving the wider insight into modern materials – from their properties till application in engineering structures (WP2).

Upgraded quality of research was clearly shown in the number of publications and participation in conferences. Publication activity in CEMCAST was as follows: 2 books ( in Springer), 16 book chapters, 60 published articles (in 24 well recognised international journals - mainly: ICI Master Journal List), 2 articles in press, 8 articles in review. Research results obtained within CEMCAST were shown in 45 presentations delivered at 22 international conferences which were held in 13 countries: Austria, Belgium, Czech Republic, France, Germany, Ireland, Israel, Italy, Poland, Romania, Russia, Turkey and United Kingdom.

Ad.2 Modernisation of research equipment

The equipment purchased within CEMCAST- comprising devices for testing damage and crack propagation in composites under mechanical (quasi-static, dynamic, cyclic, impact) and thermal loading, also for testing composites behaviour in an aggressive environment and at different humidity - significantly enlarged experimental capacity by introducing new testing methods and experimental techniques. As a result, the CMCM became more attractive for the regional industry and potential scientists looking for possibility of doing high level experiments in modern discipline (composite materials and their applications) (WP5). The purchased equipment is as follows:

1. Extension of the existing 3-D Image Correlation System ARAMIS for high speed measurements of shape and displacements due to different types of loading, including dynamic loading ((cyclic or impact) with very quick changes of deformation due to variation of mechanical or thermal loading. Together with the extension of the System ARAMIS, additional software and small equipment: ATOS, PONTOS, TRITOP was purchased. These items incredibly increase testing possibilities of ARAMIS system.. Purchased equipment is of crucial importance because it significantly increases possibility of carrying out modern tests on composites used in aerospace industry and for road surfaces. It also increases competitiveness in application for next project.
2. Thermovision infrared camera – is a complete solution for inspection of components for cracks and other defects for a great variety of materials (metal, ceramics, composites) and structural elements like turbine blades (surface cracks and micro-cracks in the depth of the blade). It allows for non-destructive testing of aircrafts structures for defects like delamination, loose rivets, cracks or water inclusions.
3. Testing system for multi-axial loading of structural elements - dynamic loading with temperature chamber and furnace. Multi-axial testing of modern composite materials applied for aerospace and pavement industry are of crucial importance, particularly with the possibility of estimation of temperature from – 700 to + 3000C. The parts of the aircrafts engines, e.g. turbine blades are subjected to high temperature and their testing as for fracture toughness should be performed with furnace (up to 14000C).
4. Stress screening system for monitoring of the behaviour of composite materials subjected to thermal loading with variation of the temperature up to 15 degrees/min. The system will be used for testing of structural elements applied in the aerospace and pavement industry. The system will be used together with the extended ARAMIS system in order to monitor defects growth under quick temperature changes.
5. Corrosion chamber which allows for: salt spray test, corrosion climate alternating test and walk-in salt spray test, will be used for testing of layered materials for pavements. and aircraft parts which are also influenced to different corrosive environments. (e.g. condensed water test with SO2), what could be investigated as for life time prediction of the structural parts or advanced materials.
6. Temperature shock chamber allows to determine the influence of the sudden temperature changes on the composite specimen or structural parts behaviour (e.g. degradation process). Other important result of this test is to estimate the safe operation of the specimen or structural element after sudden temperature changes. The aircraft parts and pavements are subjected to quick temperature variations and therefore tests under temperature shock are necessary to check all composite materials response.
7. Ageing chamber with fluorescence lamps – it is a device which considerably increases possibility of testing of composites in different environmental conditions. This equipment allows for testing of the modern hybrid joints applied in aeroplane structural elements to verify the influence of ageing process on the mechanical response, reliability and durability of these elements. Such tests are of crucial importance for safety of passengers. Together with corrosion and temperature shock chambers it creates good platform for great variety of tests which can be carried out on composites.
8. Acoustic emission controller – it is very modern device for non-destructive method (using acoustic signals appearing during degradation growth) and it considerably enlarges possibility of monitoring of damage growth and cracks propagation in structural parts of aeroplanes and modern composites applied in transport surface infrastructure. This device is essential supplement to the equipment planned in Annex I because – together with purchased items - allows for complex testing of degradation processes in composites (very important for safety reasons in aeroplanes).
9. System of acoustic emission signals together with cabling for monitoring of crack propagation in the structural composite elements applied in aerospace and surface transport infrastructure. They allow for damage assessment under mechanical and thermal loading in order to estimate damage tolerance of the critical structural elements of aircrafts which is necessary to know during maintenance of the aircrafts and helicopters in order to increase safety of flights.
10. Sensors for acoustic emission it is a part of system of acoustic emission signals which is fasten to the surface of the structural element in order to register an acoustic emission signal.
11. Licence for LabVIEW programme. LabVIEW software is very useful for measurement or control system integrating all the tools that engineers and scientists need to build a wide range of applications in dramatically less time, LabVIEW is a development environment for problem solving, accelerated productivity, and continual innovation
12. Grip for stretching of composite plates – it is an unique experimental stand to perform crack propagation process in composite samples of big dimensions (natural size). It allows to perform tests in polymer matrix composite materials used for manufacturing of the airplane structural parts (elements of the fuselage and wings) subjected to monotonic or fatigue uni-axial tension.

Ad.3 Strengthened international position of the CMCM by increased research capacity

Organisation of workshops, mini-symposia at international conferences and international courses created a platform to present increased research capacity (in co-operation with the twinning partners and recruited researchers) and strengthened international position of the CMCM (WP3).. The following events were organised:

1. Mini-symposium on “Multiscale and Multiphysics Computational Methodologies for Complex Materials” at IVth European Conference on Computational Mechanics, 16-21 May 2010, Paris (France). Organizers: Prof. P. Trovalusci (from twinning institution: University of Rome “La Sapienza”), Prof. T. Sadowski (coordinator of CEMCAST), V.Sansalone (France), B.Schrefler (Italy).
2. Mini-Symposium (No: MS 622) on: “MULTISCALE AND MULTIPHYSICS MODELLING FOR COMPLEX MATERIALS” organised within 6th European Congress on Computational Methods in Applied Sciences and Engineering, 10-14 September 2012, Wien (Austria). Organisers: Prof. T. Sadowski (coordinator of CEMCAST), Prof. P.Trovalusci (from twinning institution – University of Rome “La Sapienza”, Prof. R. de Borst (expert in CEMCAST), Prof. B. Schrefler (Italy).
3. Course: “MULTISCALE MODELLING OF COMPLEX MATERIALS” was organized by Prof. T. Sadowski (coordinator of CEMCAST) and Prof. P.Trovalusci (from twinning institution – University of Rome “La Sapienza”) in the International Centre for Mechanical Sciences (CISM), Udine (Italy), 21-25 May 2012.
4. Poster session – devoted to research achievements obtained in CEMCAST – was organized by prof. J. Warminski at the conference: “Modern Practice in Stress and Vibration Analysis”, MPSVA 2012, 29-31 August, Glasgow (UK).
5. Workshop: “Nonlinear Dynamical Phenomena in Mechanical, Aerospace and Civil Engineering” was organised by prof. J. Warminski at Lublin University of Technology on 22-23 October 2012. At the event 25 regular presentations and 7 short presentations were delivered by researchers from Poland, Germany, Italy, Portugal, Slovenia, Ukraine, Bulgaria and United Kingdom.
6. Workshop: “Dynamics of Functionally Graded Materials and Systems with Hysteresis” was organized by prof. G. Litak and prof. E. Manoach at Lublin University of Technology on 19 March 2012. At the event 14 presentations were delivered by researchers from Poland, Germany, France, Italy and United Kingdom.
7. Euromech Colloquium no 541 – “NEW ADVANCES IN THE NONLINEAR DYNAMICS AND CONTROL OF COMPOSITES FOR SMART ENGINEERING DESIGN” 3-6 June, 2013, Senigallia - Ancona (Italy). Organisers: Chair – Prof. S. Lenci (from twinning institution – Polytechnic University of Marche, Italy), Co-Chair: Prof. J. Warminski (from coordinating institution – Lublin University of Technology, Poland). This event will be a very good platform for presentation of increased research capacity and strengthened international position obtained.within CEMCAST project.

Ad 4. Better integration of the CMCM in the ERA

Participation of the CMCM staff in international conferences created possibility for dissemination of research results obtained through absorbed knowledge and joint research. It increased visibility of CMCM research groups at international level and exposed especially young staff to an international environment. Presentation of research achievements at international events created new international contacts thus providing better integration to ERA (WP 4).

Research results obtained within CEMCAST were presented at the following conferences:.

1. IV European Conference on Computational Mechanics – ECCM 2010, Paris (France), 16–21 May 2010
2. Conference: Aspects of fracture and cutting mechanics of materials, Kazimierz Dolny (Poland), 21–23 October 2010
3. IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design, NDATED, Aberdeen, (UK), 27-30 July 2010
4. International Workshop on Computational Mechanics of Materials – IWCMM 20, Loughborough (UK), 8-10 September 2010
5. Computer Methods in Mechanics, CMM 2011, Warsaw (Poland), 9-12 May 2011
6. 8th National Rotorcraft Forum 2011, Warsaw (Poland), 17 June 2011
7. 8th International Conference on Structural Dynamics, EURODYN 2011, Leuven, (Belgium), 4-6 July 2011
8. 7th European Nonlinear Dynamics Conference, ENOC 2011, Rome (Italy), 24-29 July 2011
9. 21st International Workshop on Computational Mechanics of Materials, IWCMM 21, Limerick (Ireland), 21-24 August 2011
10. EUROMECH Colloquium 527-Shell-like Structure-Nonclassical Theories and Applications, Leucorea, Wittenberg (Germany), 22-26 August 2011
11. 2nd Congress of Polish Mechanics, Poznań (Poland), 28–31 August 2011
12. 2nd International Conference on Material Modelling, ICMM 2011, Paris (France), 31 August -2 September 2011
13. International Conference on Vibration Problems, ICOVP 2011, Prague (Czech Republic), 5-8 September 2011
14. 4th International Conference on Structural Analysis of Advanced Materials, ICSAAM 2011, Sinaia (Romania), 7-11 September 2011
15. “4th International Conference on Localization, Energy Transfer and Nonlinear Normal Modes in Mechanics and Physics” NNM2012, Haifa (Israel), 1- 5 July 2012,
16. “6th International Conference on Advanced Computational Engineering and Experimenting” ACE-X2012, Istanbul (Turkey), 1-4 July 2012
17. “8th European Solid Mechanics Conference”, Graz (Austria), 9-13. July 2012
18. “19th European Conference on Fracture”, Kazań (Russia), 26-31 August 2012
19. “1st EUROMECH Colloquium on Time-periodic Systems – Current Trends in Theory and Applications”, Frankfurt (Germany), 27-30 August 2012
20. “Modern Practice in Stress and Vibration Analysis”, MPSVA 2012, Glasgow (UK), 29 – 31 August 2012
21. „European Congress on Computational Methods in Applied Sciences and Engineering” ECCOMAS 2012, Wien (Austria), 10 – 14 September 2012
22. „4th International Conference on Crath Paths”, CP 2012, Gaeta (Italy), 19 – 21.09.2012

Conferences were held in 13 countries:

Austria, Belgium, Czech Republic, France, Germany, Ireland, Israel, Italy, Poland, Romania, Russia, Turkey, United Kingdom. 45 presentations were given at mentioned conferences.

Ad 5. Deeper involvement of the CMCM in EU projects (FP7)

Dissemination activities in CEMCAST were very effective. Project became so visible at the international level and capability for participation in FP7 increased so much that coordinator received the following propositions for next proposals preparation:

• Prof. Alessandro Pirondi (from University of Parma, Italy) proposed coordinator of CEMCAST – prof. T. Sadowski - to prepare common proposal (with 7 other international partners) titled: “Virtual Assessment of low-velocity impact damage in composite airframes”- VIVID - Call identifier: AAT-2012-RTD-1. Coordinator of CEMCAST was planned to be coordinator of WP2 – “Experimental testing”. Tests were planned in the project to be carried out on the equipment purchased within the previous EU project coordinated by T. Sadowski (ToK) and recent CEMCAST project. Project was prepared and submitted, but was not approved by EC.
• Prof. Eann Patterson (from University of Liverpool, United Kingdom) proposed coordinator of CEMCAST – prof. T. Sadowski - to prepare common proposal (with 8 other international partners) titled: “Joint Assessment in Composite Bonded Interfaces with Augmentation by Nanoparticles”- JACOBIAN - Call identifier:7FP-NMP-2012-SMALL-6. Proposal was prepared and submitted, but was not approved by EC.

Ad.6 Closer co-operation with the regional and European industry

The CEMCAST implementation strengthened co-operation with the regional industry by facilitating transfer of technology and fostering innovations (WP 6).

In “industry-academia” collaboration, the following activities were performed:

1. Cooperation was developed with the local enterprise for road building - “WPRD”. Researchers involved in CEMCAST created new technology for manufacturing of composites which will be applied by the mentioned enterprise for road foundations. In this new technology rubber fines were added (4%) as one of the components. This material (rubber fines) was possessed from another local SME – “Orzel S.A.”
2. Cooperation was developed with the SME “Cree Yacht – yacht design and hitech - composites”. It was elaborated programme of carrying out strength tests (uni-axial tension) on polymer composite samples (supplied by “Cree Yacht”) using DIC method in the laboratory at LUT. These samples will be tested on the equipment purchased within CEMCAST.
3. Meeting with directors of the Executive Boards of the Local Roads in Krasnystaw District and Leczna District was organized at Lublin University of Technology. It was devoted to discussion on application of newly developed composites within CEMCAST for modernization of local roads.
4. Meeting with representatives of the leading aviation companies, so called “Aviation Valley Day” was organized at Lublin University of Technology. In this event participated representatives of the following companies: WSK “PZL-Rzeszów” S.A. PZL Mielec S.A. Sikorsky Company, Hamilton Sundstrand, Pratt&Whitney Kalisz, Goodrich, Hispano Suiza and PZL Swidnik S. A. That meeting initiated cooperation with the PZL Mielec A Sikorsky Company: The samples of hybrid joints of the structural elements applied in “Bryza” airplane produced in PZL Mielec were tested on the equipment purchased within CEMCAST. Tests on monotonic and fatigue loading with the influence of temperature effects were carried out.
5. Cooperation was developed with the regional SME “WIT-COMPOSITES” - concerning the technological aspects of production of innovative composites which can be applied in aerospace. WIT-Composites company – in cooperation with CMCM staff - elaborated methodology of manufacturing of sandwich plates made of polymer foams of different densities with gradation of the mechanical properties (FGM materials) and two glass fibers polymer matrix skins. The problems of highly innovative structural elements joints, so called “grid-lock”, were discussed in order to create Polish improved version much better in comparison to solution elaborated by USA aerospace industry.

Additionally, it was discussed common participation in the future projects. Currently common proposal – together with WIT-Composite company and PZL Mielec S.A. Sikorsky Company - is under preparation. The aim is to participate in the biggest Polish project dealing with aerospace called “InnoLot” which will be financed by National Centre for Research and Development.

6. Co-operation with the Centre of Advanced Technologies “AERONET – Aviation Valley” (Rzeszów). That Centre aims at implementing of different innovative technologies worked out at universities placed in the east-middle and east-south regions of Poland to Polish aeronautical industry sector joint in the Technology Cluster “Aviation Valley” (http://aeronet.pl http://www.dolinalotnicza.pl). Researchers involved in CEMCAST participate in the project, which is accomplished within “AERONET – Aviation Valley”. It is national strategic research project entitled: “Modern Material Technologies for Aerospace Industry” (total funds: 27 mln €). This project is financed from Structural Funds and done within “Innovative Economy Operational Programme” – priority 1: Research and development of new technologies, co-ordinated by the Ministry of Science and Higher Education. There was synergy between this project and CEMCAST.

Ad. 7. Improved research capacity for increased contribution to regional economic and social development

Implementation of CEMCAST project established a leading research centre in the Lublin region of Poland (and in the Middle- East part of Europe) in the multidisciplinary area encompassing modelling and experimental testing of composite materials and their application to means of transport (aircrafts), pavements and airfields. Such significant position surely increases international competitiveness of the CMCM in the mentioned field. As a result – long term research and collaborative capacity of the CMCM with the EU institutions (universities) was developed. This centre became attractive for scientists from different countries. It is of crucial importance for Lublin region, because the Middle - East part of Poland – where Lublin is situated – is a less favoured region compared to middle and western parts of Poland. Implementation of that project created good bases for diminishing the differences. Strengthening of the research potential at Lublin region and providing well-trained staff for the regional industry (by implementing this project) increases competitiveness of the region in applying for the structural funds. Is is in accordance with EC regional policy consisting in levelling differences between regions. Implementation of CEMCAST project increased competitiveness in proposals preparation within EU FP, created regional well equipped experimental centre for testing of composites and regional stimulator for regional industry.

Experience of working with people from several countries (which took place in CEMCAST) resulted in additional learning effect towards cultural understanding and bringing people closer together.

Ad 8. Encourage young staff to do research in the attractive area – modern composite materials

CEMCAST project prepared young scientists who can meet EC expectations, namely scientists, who can induce progress in mechanics of composite materials with application to structural elements, who can develop visions on a solid understanding of the different aspects. Young researchers were trained by twinning partners and recruited researchers to make them to be able to become leading figures in mechanics of composite materials and analysis of non-linear dynamical systems. Cooperation with foreign researchers and participation in international conferences caused that the young staff gained a broad view, global understanding and the ability to collaborate, to make and realise suggestions coming from other domains. Training of such highly qualified staff is very important outcome of the project.

Ad.9. Improvement of research management and organisational skills

Except scientific expertise obtained from the twinning partners, which was crucial for achieving of the project objectives, also managerial skills of foreign researchers involved in the project were fully utilised in efficient management of the project. Twinning partners and members of the International Advisory Board were effective managers, deans, directors, heads of successful teams and leaders or participants of international projects. All of them were involved in projects employing similar management procedures to those which were used in CEMCAST. Regular contacts with all partners through: exchange visits, organisation of common events (workshops, seminars) created a natural platform for direct discussions on managerial and organisational aspects in the project and also for implementation of the best practice.

Implementation of CEMCAST increased visibility of particular research groups existing in the Centre and fostered co-operation among them in organisational aspects. The CMCM staff (especially young researchers) gained broader skills including: ability to communicate and organisational skills. Managerial skills were considerably developed. (WP8).

The potential impact can be estimated on two levels:

– at national level the CMCM became:

1. leading research centre working in the field of modern composite materials technology and non-linear sciences with application to the civil and mechanical engineering
2. regional well equipped experimental centre for testing properties of composite materials and engineering structures
3. wanted partner for the regional industry and SMEs
4. regional stimulator for the local industry and SMEs by:

• introduction of scientific innovations to the local enterprises
• designing of new engineering materials
• promotion of new technologies of composites and structural elements production

5. more competitive in applying for structural funds
6. strengthen in terms of socio-economical aspects. The Middle - East part of Poland (where the Centre is situated), is less favoured region in comparison to western part of the country, so it needs stronger support. It is consistent with the government policy. The project compensated disproportion at the national level. The CMCM staff gained knowledge concerning management of European projects. Young staff at the Centre was encouraged and involved to actively participate in the implementation of CEMCAST

– at international level the CMCM became:

1. important research centre in the Middle-East part of Europe; mentioned new areas of competence are consistent with EC priorities, so implementation of the project contributed to structuring the ERA
2. important place for establishing international scientific co-operation with universities and enterprises from different European countries by joint research within FP7 and other bi-lateral projects
3. more competitive in proposals preparation within FP7
4. important place for promotion of regional scientific and technological achievements of the Middle – East part of Poland
5. organiser of the important international meetings, like conferences and workshops
6. the bridge between EU and East Europe universities and industry from Ukraine, Belarus and Russia

List of Websites:

www.cemcast.pollub.pl

Project coordinator:

Prof. Tomasz Sadowski
e-mail: t.sadowski@pollub.pl sadowski.t@gmail.com
phone: +48 81 5384386

final1-final-disseminational-materials.pdf

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Final Report Summary - CEMCAST (Centre of Excellence for Modern Composites Applied in Aerospace and Surface Transport Infrastructure)

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