Papers by Author: Oldřich Ševeček

Abstract: The assessment of conditions of crack initiation in a tip of a bi-material notch composed of two orthotropic materials is dealt. The assessment of the bi-material orthotropic notch stability criteria based on standard linear elastic fracture mechanics can lead to incorrect results due to a change of fracture mechanics properties. The change of the fracture mechanics properties are taken into account in the discussed stability criterion. It is shown that the criterion of this kind can qualitatively and quantitatively influence the results, and it contributes to more reliable assessment of components with geometrical and/or material discontinuity.

Abstract: Ceramic laminates designed with strong interfaces have shown crack growth resistance (R-curve) behaviour through microstructural design (e.g. grain size, layer composition) and/or due to the presence of compressive residual stresses, acting as a barrier to crack propagation. The goal of the contribution is to model the mechanism of crack bifurcation in laminar ceramics with large compressive stress which still have not been satisfactory explained. Experimental observations of the crack path in the multilayered ceramics tested under several kinds of loading showed crack penetration (i.e. crack propagating normal to the layers followed by crack bifurcation when the crack propagated from the tensile to the compressive layer. Numerical results [1] show that the initiation of crack bifurcation can be explained by the near-tip J-integral, provided that micro-cracks exist near the crack tip. We revisit the problem using the concept of Finite fracture mechanics and the matched asymptotic expansion method in order to evaluate the energy release rate criteria describing the competition of the crack bifurcation and straight crack propagation near behind the bimaterial interface.

Abstract: 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.

Abstract: The evaluation of the generalized stress intensity factor (GSIF) and T-stress for the case of the surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The combination of the discretization, numerical and analytic methods is used. The discretization method, such as common finite element method (FEM), is served to include the boundary condition to the GSIF solution and to describe the remote stress and displacement field region with the low influence of the singularity of the crack tip. The Lekhnickii-Eshelby-Stroh (LES) formalism is used to derive the approach solution for the near stress field of the crack tip and the singularity problem in an orthotropic 'trimaterial' using the Schwartz-Neumann's alternating technique. The problem of the stress singularity is treated as a non-linear eigenvalue problem, which leads to the characteristic equation for the stress singularities of the form rδ −1 , 0 <δ <1. Two ways of the evaluation of the GSIF are presented, using the reciprocal theorem ψ -integral) and the crack model by means of continuous distribution of dislocations. Both results are compared for a specific material. The continuous distribution of dislocations technique is also used for determination of the T-stress.

Abstract: Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimilar elastic anisotropic materials. The link to the configurational forces approach is suggested.

Abstract: 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.

Abstract: 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.