Papers by Author: Tomáš Profant

Abstract: The aim of the paper is quantify the material length scale parameter of the simplified form of the strain gradient elasticity theory (SGET) using first principles density-functional theory (DFT). The single material length scale parameter l is extracted from phonon-dispersions generated by DFT calculations and, for comparison, by adjusting the analytical SGET solution for the displacement field near the screw dislocation with the DFT calculations of this field. The obtained results are further used in the SGET modeling of cracked nanopanel formed by the single tungsten crystal where due to size effects and nonlocal material point interactions the classical fracture mechanics breaks down.

Abstract: A stress distribution in vicinity of a tip of polygon-like inclusion exhibits a singular stress behaviour. Singular stresses at the tip can be a reason for a crack initiation in composite materials. Knowledge of stress field is necessary condition for reliable assessment of such composites. A stress field near the general singular stress concentrator can be analytically described by means of Muskhelishvili plane elasticity based on complex variable functions. Parameters necessary for the description are the exponents of singularity and Generalized Stress Intensity Factors (GSIFs). The stress field in the closest vicinity of the SMI tip is thus characterized by 1 or 2 singular exponents (1 - λ) where, 0<Re (λ)<1, and corresponding GSIFs that follow from numerical solution. In order to describe stress filed further away from the SMI tip, the non-singular exponents for which 1<Re (λ), and factors corresponding to these non-singular exponents have to be taken into account. Analytical-numerical procedure of determination of stress distribution around a tip of sharp material inclusion is presented. Parameters entering to the procedure are varied and tuned. Thus recommendations are stated in order to gain reliable values of stresses and displacements.

Abstract: The goal of the contribution is to develop an asymptotic interface crack-tip solution under conditions of plane strain for a bi-material that obeys a special form of linear isotropic gradient elasticity. Several fracture mechanics problems have been solved in the past within the framework of strain gradient elasticity which is capable to capture additional length/size parameters. However to our best knowledge no solution concerning an interface crack is available in the literature.

Abstract: 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.

Abstract: The domain of the generalized stress intensity factors dominance ahead of the notch tip can be rather small with respect to the length of the perturbing cracks initiated from the tip of the notch. Thus the non-singular terms of the stress asymptotic expansion at the notch tip would play an important role in the notch tip stability. Following the procedures dealing with complex potential theory and path-independent two-state integrals developed for the singular stress analysis of the stress concentrators one can evaluate their magnitude and include them to the energy release rate of the preexisting crack initiated from the notch tip applying the matched asymptotic procedure. The presented analysis should lead to better understanding of the notch stability process and precising of the notch stability criteria.

Abstract: 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.

Abstract: The paper deals with a creation of computational model of a high porous ceramic material. This type of material has a large-scale industrial utilization. The computational model was created based on micro-CT data in the ANSYS 14.0 software using Finite Element Method. A creation of a porous ceramic struts model which respect a micro architecture is quite difficult (computer demanding and micro-CT data). The micro-CT slices are converted into a 3D model using image processing (used software STL Model Creator). The local first principle stress was analyzed because, ceramic is the brittle material. Furthermore, the influence of the thick layer around the individual struts was analyzed.

Abstract: In the range of linear elastic fracture mechanics, the critical loading assessment of structures made of two dissimilar materials is usually based on the assumptions of the prevailing normal mode of loading. However, in engineering practice there are cases of loading and failure close to the shear mode of loading. The aim of the work is to study the stress distribution in the vicinity of a bi-material notch subjected to a combination of normal and shear modes of loading. Then the stability criteria use knowledge of common fracture mechanics properties for normal I and shear II modes of loading. The assessment of crack initiation conditions is shown on a specimen with two different bi-material notches under loading of a varying direction.

Abstract: 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.

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.