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Determination of T stress for arbitrary oriented crack terminating at interface between two dissimilar materials
Gröger, Roman
The most important factors describing the fracture-mechanics behavior of layered structures are the generalized stress intensity factor and also T stress describing the amplitude of the stress field independent on the radial distance from the crack tip.. Direct methods of the calculation of such parameters are well known and their accuracy is critically assessed by the experimental measurements. The present work proposes an alternative method of determining of the elastic T stress based on the validity of the reciprocal work theorem using the integration of the strain energy along a circular path surrounding the crack tip. The results obtained from a model of a crack terminating at interface between two dissimilar elastic materials are compared with the usually used direct approach. It is shown that such this term is not negligible and generally need to be taken into account in the considerations on the stability of layered materials.
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Theoretical background for determining the fracture-mechanics parameters using the Boundary Element Method
Gröger, Roman
Boundary Element Method is a powerful tool for certain class of Solid Mechanics problems, where the fundamental solution of the governing differential equation is known. This article briefly outlines the theoretical background of BEM for plane problems as well as integral identities for calculation of internal stresses and displacements. Chapter 2 introduces the most useful contour integrals for calculation of fracture parameters in two-parameter linear elastic fracture mechanics. These coefficients are solved using the stress and strain tensor field calculated using BEM. All the proposed and discussed approaches are compared and the differences between FEM and BEM are discussed.
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Application of contour integrals to assessment of notch stability in linear elasticity
Gröger, Roman ; Knésl, Zdeněk
The article yields a teoretical background of a well- sophisticated numerical method for calculation of GSIF and T stress, especially for case when the integration across the nonhomogeneous material interface is unavoidable. The main advantage of the integral approach over the well-known direct methods is its accuracy induced by monotonous convergence of the solution. This work contributes to more accurate description of the instability state of V-notches in composite structures.
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Integral methods for the determination of fracture characteristics of general stress concentrators
Gröger, Roman
The integral appoaches for calculation of generalized stress intensity factors (GSIF) are presented. Integral identities are derived using the Betti reciprocal theorem as a superposition of two independent solutions satisfying the sam boundary conditions. The complementary solution for computation of GSIF is assembled using the negative eigenvalues lambda. This algorithm yields a set of integral identities that allow to estimate GSIF separately for mode I and II. A quantitative comparsion of the integral approach with recently used extrapolation method is proposed in conclusion.
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Calculation of fracture parameters for the cracked bodies strengthened by circular patches
Gröger, Roman
The present article yields a quantitative characterization of the influence of geometry and material properties on the values of fracture parameters. Both the cracked sheets with single and double circular patches are used for the analysis. The desired value of elastic T stress is obtained using the conservation M integral resulting from the Eshelby integral concept. For the SIF calculation, the indirect method of J integral is used and the general concept for the SIF separation in case of a mixed mode of loading is discussed here. The reduction effect is specified by the ratios of SIF and T stress. The method of stiffening the region surrounding the crack tip can be used as an alternative method of the lifetime prolongation, but cannot be used in all cases. Sometimes the usual method of the crack tip singularity cancellation is the only one to repair the structure.
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Analýza algoritmů výpočtu T napětí s ohledem na vliv vyšších členů Williamsova rozvoje
Gröger, Roman
A comparison between a couple of difference methods for quantification of T stress is presented. The stress distribution around a crack tip is expressed using the first four terms of Williams eigenfunction expansion for specimens corresponding to low constraint (SECT) as well as three-point bending specimens with high constraint. The dominant regions are quantified by accounting the different number of stress terms. An alternative method for calculation of T stress using the conservation integrals is used to compare the obtained results with the products of more accurate integral method. The appropriate ratios of r/a, on which the difference methods give the reasonable results, are outlined in conclusion.
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Two-parameter characterisation of a crack growing in the vicinity of the material interface
Gröger, Roman ; Knésl, Zdeněk
A crack propagating in the vicinity of the material interface is analyzed. The problem is solved in the range of two-parameter linear elastic fracture mechanics. The aim of the contribution is to assess the influence of T stress on the direction of a crack growing to the interface. The interface is modelled for different material properties characterised by the Dundur's composite parameters. First the effect of the interface on T stress value is studied and values of KI, KII and T stress are estimated. Consequently the two-parameter modification of MTS criterion and Sih's SED criterion is used for prediction of a crack propagation direction. Both these approaches are compared. It is concluded that the negative values of T stress stabilize the crack propagation perpendicularly to the interface.
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Calculation of the fracture parameters for a crack growing from the tip of a V-notch
Gröger, Roman ; Hutař, Pavel
This article yields a comparison of two principles for caculation of the fracture parameters - the direct finite element method and hybrid element method. The stress intensity factor and the T stress for a crack growing from the tip of a nonsingular stress concentrator for a large variety of notch angles is obtained. It is discussed the sensitivity of each parameter on the ratio of crack length to the width of the specimen. The obtained results can contribute to more precise characterisation of the crack instability state in a case of the combination V-notch + crack.
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