Papers by Author: Zdeněk Chlup

Abstract: The contribution deals with modelling and prediction of failure of mechanically loaded open cell ceramic foam structures by using 3D volume FE models constructed from CT scans of real foam specimens. The condition for crack initiation in particular struts comes from the coupled stress-energy criterion which combines two fracture-mechanics parameters of the investigated material – tensile strength and its fracture toughness. By combining of both stress and energy condition one obtains information about the crack initiation length which is later used (together with the tensile strength) for determination of the strut failure in the complex 3D FE model of the ceramic foam structure. The crack onset is considered in the critical location at the moment when the (tensile) principal stress under the strut surface (in a depth corresponding to the crack initiation length) exceeded the tensile strength of the strut. Such approach enables us to define failure also on relatively coarse meshes of the FE models where potential stress concentrations are not described precisely and therefore it is not possible to decide about the failure just based upon the value of tensile stress on the strut surface.

Abstract: The pyrolysis process of polysiloxane resin conducted in the temperature range 400 – 700 °C results in hybrid materials owning some polymeric (thermosetting) behaviour. A certain level of elastic recovery and/or viscoelastic flow showed at various steps of pyrolytic transformation was monitored using the instrumented Vickers hardness method. Determined indentation force-indentation depth curves reflect the mechanical response and the level of the transformation; however, the relaxation behaviour is not covered by this method fully. An extensive indentation relaxation was revealed in the material partially pyrolysed at 400 °C, about 16 % and 8 % when the HV 0.1 and the HV 0.2 loading were applied, respectively. Materials pyrolysed from 500 to 650 °C which exhibited the indentation relaxation below 1 % and the mostly elastic response on the loading were observed. Above the pyrolysis temperature of 600 °C a rapid onset of mechanical properties, namely indentation elastic modulus and hardness, was observed. The short-term indentation relaxation was evaluated via the indentation force relaxation method in the regime of constant indentation depth obtained at the moment of reaching an initial force of 0.981 N or 1.962 N. The obtained indentation force relaxation curves were analysed on the basis of a logarithmic function. The significant effect of the pyrolysis temperature as well as the influence of loaded volume was described.

Abstract: The work investigates an influence of the macroscopic stress concentrator inside the ceramic open cell foam structure on the fracture-mechanics response of the foam upon the tensile test. As the concentrator, the central crack/rectangular notch was taken into account. The influence of the crack/notch length and width on the stress concentration ahead the concentrator tip was assessed using the simplified FE beam element based model with irregular cells simulating the real ceramic foam structure. Average principal stresses calculated on set of struts ahead the crack/notch tip were compared with average stresses in the intact structure. It was found that the ratio of these stresses increases linearly with the crack length. The stress concentration ratio is slightly lower in case of thick rectangular notch than in case of a thin crack. Furthermore, the failure load leading to complete fracture of the studied specimens, subjected to the tensile loading, were calculated using the same model. It is shown that the difference factor between the critical fracture force in case of structure without concentrator and with concentrator is very close to the concentration factor calculated from the average stresses on particular struts in the region in front of the concentrator tip.

Abstract: Specific silicon nitride ceramics, the influence of the grain size and orientation on the bridging mechanisms was found. In ceramic matrix composites, crack-bridging mechanisms can provide substantial toughness enhancement coupled with the same and/or increased strength. The prediction of the crack propagation through interface elements based on the fracture mechanics approach and cohesive zone model is investigated. From a number of damage concepts the cohesive models seem to be especially attractive for the practical applications. Within the standard finite element package Abaqus a new finite element has been developed; it is written via the UEL (user’s element) procedure. Its shape can be modified according to the experimental data for the set of ceramics and composites. The element seems to be very stable from the numerical point a view. The shape of the traction separation law for four experimental materials is estimated via the iterative procedure based on the FEM modeling and experimentally determined displacement in indentation experiments, J–R curve is predicted and stability of the bridging law is tested.

Abstract: The aim of this work was preparation of alumina laminates and fibre reinforced alumina containing zirconia micro-fibres inside the inter-layer interface. Electrophoretic deposition was performed from concentrated isopropanolic suspensions stabilised by monochloracetic acid containing mixture of alumina powder and certain amount of zirconia micro-fibres. A method for in-situ monitoring of deposited amount of mixture of particles and fibres mass was applied to control deposition kinetics. Two different approaches for composite deposition were applied: pre-milling of powders mixture prior electrophoretic deposition and milling of suspension containing stabilization aid. Applying the optimised procedure the alumina laminates were prepared consisting of fibres in the interlayer boundary affected dramatically fracture response of these materials.

Abstract: Recently it was possible to prepare tailored laminates with perfect and strong interface of layers with precise thickness management. Tailoring of ceramic laminates to obtain optimal mechanical properties with enhanced fracture resistance is possible when predictions based on numerical calculations are employed. Extraordinary mechanical properties were achieved via high internal stresses development during material processing. The aim of this investigation can be seen in two directions. The enhanced crack free green bodies through incorporating small volume fraction of micro-fibres to the powders were prepared. Additionally, control of the crack propagation by incorporated directionally oriented micro-fibres both in the volume and in individual layers. In this contribution both alumina and zirconia micro-fibres were used to help eliminate drying defects in the green body stage before sintering. The co-deposition of ceramic micro-fibres and powder led to the preparation of microstructures having unique orthogonal fracture properties. Developed laminate with thin layers created by zirconia micro-fibres in the alumina matrix seems to be the most promising. This type of material exhibited potential of the crack trapping and deflection even when very small amount of micro-fibres was used.

Abstract: Silicon nitride based ceramics have received considerable attention during the last decades due to their very good room and high-temperature properties. Ceramics such as silicon nitride (Si₃N₄) are acknowledged as first choice for modern bearing applications. The influence of grain bridging on the strength and toughness was found. The prediction of crack propagation through interface elements based on the fracture mechanics approach and cohesive zone model is investigated from amount damage models. Using cohesive models the behaviour of materials is realized by two types of elements. The former is the element for classical continuum and the latter is the connecting cohesive element. Within the standard finite element package Abaqus the new finite element has been developed; it is written via the UEL procedure. The shape of the traction separation law for experimental materials is estimated from macroscopic tests, J–R curve is predicted and stability of the bridging law is tested. The shape of the bridging law is verified using the microindentation test, where the maximum crack length not exceeded 150 μm. The scope of the bridging effect is verified using the standard XFEM elements implemented in Abaqus.

Abstract: Specific silicon nitride based materials are considered according to certain practical requirements of process, the influence of the grain size and orientation on the bridging mechanisms was found. Crack-bridging mechanisms can provide substantial increases in toughness coupled with the strength in ceramics. The prediction of the crack propagation through interface elements based on the fracture mechanics approach and cohesive zone model is investigated and from the amount of damage models the cohesive models seem to be especially attractive for the practical applications. Using cohesive models the behaviour of materials is realized by two types of elements. The former is the element for classical continuum and the latter is the connecting cohesive element. Within the standard finite element package Abaqus a new finite element has been developed; it is written via the UEL (users element) procedure. Its shape can be very easily modified according to the experimental data for the set of ceramics and composites. The new element seems to be very stable from the numerical point a view. The shape of the traction separation law for three experimental materials is estimated from the macroscopic tests, JR curve is predicted and stability of the bridging law is tested.

Abstract: The fracture behaviour of long fibre reinforced composites is predetermined mainly by properties of fibre-matrix interface. The matrix prepared by pyrolysis of polysiloxane resin possesses ability to resist high temperatures without significant damage under oxidising atmosphere. The application is therefore limited by fibres and possible changes in the fibre matrix interface. The study of development of interface during high temperature exposition is the main aim of this contribution. Application of various techniques as FIB, GIS, TEM, XRD allowed to monitor microstructural changes in the interface of selected places without additional damage caused by preparation. Additionally, it was possible to obtain information about damage, the crack formation, caused by the heat treatment from the fracture mechanics point of view.

Abstract: The laminated ceramics can provide a flaw tolerant behaviour compare to the monolithic ceramics. Two ways how to ensure flaw tolerant behaviour of layered materials are known. The first is based on production of weak interfaces between layers allowing delamination without catastrophic failure. The second way, on the contrary, uses strong bond between layers ensuring high strength and stiffness. The presence of internal stresses developed due to differences in shrinkage of individual layers can effectively change the crack path or even more to stop the crack propagation. Laminated structures with strong bond between layers can be prepared by various methods including tape casting, slip casting and last but not least by electrophoretic deposition. The electrophoretic deposition is probably the most suitable method which is able to create sharp and therefore strong interface in wide range of preciously set layer thicknesses. This contribution demonstrates a way how to determine level of internal stresses based on combined numerical simulation and dilatometric measurements. For this purposes alumina and zirconia monoliths and laminates were prepared. The numerical model of laminated structure using measured data was created for FEM simulation to obtain a stress distribution.