Oldřich Ševeček

Validity of the Finite Fracture Mechanics Based Asymptotic Analysis for Predictions of Crack Deflection in Thin Layers of Ceramic Laminates

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection occurs is only one order higher than the crack extension lengths considered within the solution. A purely FEM based calculation of the energy and stress conditions, necessary for the crack propagation, serves as the reference solution to the problem. The asymptotic analysis is used after for calculations of the same quantities (especially of energy release rate – ERR). This concept enables semi-analytical calculations of ERR or changes in potential energy induced by the crack extensions of different lengths and directions. Such approach can save a large amount of simulations and time compared with the pure FEM based calculations. It was found that the asymptotic analysis provides a good agreement for investigations of the crack increments enough far from the adjacent interfaces but for longer extensions (of length above 1/5-1/10 of the distance from the interface) starts more significantly to deviate from the correct solution. Involvement of the higher order terms in the asymptotic solution or other improvement of the model is thus advisable.

Crack Propagation from Bi-Material Notches – Matched Asymptotic Procedure

The methods based on the properties of the two-state integrals allow one to calculate the amplitude of singular and the other terms of the Williams’ asymptotic expansion. The paper is focused on the use of the Y-integral, whose application is conditioned by the knowledge of the so-called auxiliary solution of the solved problem. On the other hand, the Y-integral can be applied to the analysis of the problems with various geometries, e.g. the analysis of the bi-material notches. The application of the Y-integral can be also extended to the matched asymptotic procedure, which allows one to predict the behavior of the cracked notches or following crack growth near the bi-material interfaces.

Solution Methods for General Stress Concentrators in Anisotropic Heterogeneous Media

The increasing use of fibre-reinforced composites in high performance structures has brought a renewed interest in the analysis of cracks, wedges, and multi-material wedges in anisotropic materials. This paper will address three crucial stages of the general stress concentrator analysis: i) numerical procedures for the determination of eigenvalues and eigenvectors in Williams-like asymptotic expansion for multi-material wedge; ii) approaches to an accurate calculation of the near crack tip fields – the application of so-called two-state (or mutual) conservation integrals; iii) application of fracture criteria for the assessment of fracture inception at the general stress concentrators - concept of the so called finite fracture mechanics.

Analysis of Edge Bridged Crack in Bimaterial Anisotropic Half-Space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half- space is analyzed for a general case of elastic anisotropy bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (ψ - integral) is discussed as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM.

Computational Analysis of Crack-Like Defects Influence on the Open Cell Ceramic Foam Tensile Strength

This work deals with a computational analysis and quantification of the influence of processing (primarily crack-like) defects of various amount on the (tensile) strength of open cell ceramic foam structures. This information is essential e.g. for application of these materials in the mechanically loaded application, where a design with certain reliability to operating conditions is required. The analysed ceramic foam structures are composed of both regular and irregular cells and crack-like defects (pre-cracked struts) are simulated inside them. The foam structure is modelled using a 3D FE beam element based model created by utilization of the Voronoi tessellation technique. The tensile strength upon presence of various amount of pre-cracked struts is analysed based upon an iterative FE simulation on whose base the critical failure force leading to specimen fracture is determined. The performed parametric study relates the tensile strength of the foam structure to the amount of initial defects. With increasing amount of these defects, the foam strength decreases by approximately 30% with every 10% of broken struts. This information can be directly used for a fast estimation of the foam tensile strength if the fraction of broken struts to the intact ones is known (e.g. from a microscopic analysis).

Optimization of Design Parameters of Fracture Resistant Piezoelectric Vibration Energy Harvester

This paper is focused on an analysis of a multilayer ceramic-based piezoelectric vibration energy harvester, which could be excited by ambient vibrations or external forces and thus provide a useful source of electricity for modern electronics. The proposed multilayer concept of the energy harvester enables introduction of tensile / compressive residual stresses inside particular layers. These stresses are intended to be used for enhancement of the harvester ́s fracture resistance and simultaneously for the improvement of the energy gain upon its operation. A crack arrest, by means of compressive residual stresses (in the outer “non-piezo” layer), will be utilized to this end. Primarily, the extended classical laminate theory (taking into account the piezoelectric characteristics of selected layers) will be used to define various designs of particular layers with various levels of residual stresses inside them. The weight function method is subsequently employed to select a design, which is most resistant to propagation of preexisting cracks. Selected laminate configurations are verified by means of FE simulations. Such analysis is essential for development of new energy harvesting systems formed of new smart materials and structures, which could be integrated in future development processes.

Fracture-Mechanics Behaviour of Ceramic Foam with Macroscopic Stress Concentrator upon the Tensile Test

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.

Influence of the Ceramic Foam Structure Irregularity on the Tensile Response

To better understand response or fracture conditions of the ceramic foam materials to the mechanical loading, a finite element (FE) analysis of these structures has to be employed. The cellular structure of foams can be modelled either using a detailed realistic FE model based on the computer tomography scans or by using of simplified, beam element based, models. Nevertheless a main drawback of the realistic foam modelling consists in its high demandingness on computational resources. Therefore, simplified models are welcome substitutions (at least for analysis of the global mechanical foam response). The regular foam structure, based e.g. on Kelvin cells, is simple from the modelling point of view, but it doesn´t exactly capture the fully random character of the real foam structures and corresponding response to the external load. Definition of the random beam foam structure (respecting the real cell shapes and their distribution within volume), can thus improve this deficiency. The main aim of this work is thus to compare these different modelling approaches and quantify the influence of the foam irregularity on the response of ceramic foams to external (tensile) loading for various model sizes.

Criterion for Crack Kinking out of the Interface of Two Orthotropic Layers Subjected to Thermal and Mechanical Loading

The problem of crack path stability along the interface between two orthotropic elastically dissimilar materials under the presence of in-plane residual stresses is analyzed using the concept of Finite Fracture Mechanics and matched asymptotic procedure. An energy based fracture criterion is introduced for this problem and it is investigated whether and how is the criterion for the prediction of crack kinking from the interface affected by residual stresses. The complex stress intensity factor and the T-stress characterizing the stress state at the crack tip are calculated both for the thermal (residual stresses) and mechanical loading using the two-state integral. The matched asymptotic procedure together with FEM is used to derive the change of the potential energy induced by the crack growth by crack increment of finite length.

Crack Deflection from the Interface between Two Orthotropic Materials-Effect of Higher Order Terms in Asymptotic Analysis

The problem of crack deflection from the interface between two orthotropic materials is analyzed using the concept of Finite fracture mechanics and matched asymptotic procedure. A fracture criterion based on the energy approach is introduced for this problem. The main input for such criterion is the complex stress intensity factor calculated e.g. using the two-state integral. However for more precise predictions of the crack propagation also higher order terms of the asymptotic expansion are advisable to involve in the fracture criterion. To this end a T-stress term will be calculated and considered as the second input parameter. The matched asymptotic procedure together with FEM is used to derive the change of the potential energy induced by the incremental crack growth.