The lifetime of plastic pipes for water supply and other applications is demanded to exceed at least 50 years. Such a long lifetime is difficult to prove by standard testing methods like the hydrostatic pres-sure test. However, it is possible to calculate an estimation of the lifetime, as the most frequently oc-curring mechanism of failure of plastic pipes is the creep crack propagation and subsequent failure. The method is based on describing the crack propagation by parameters of the linear-elastic fracture mechanics. An important part of this method is a finite element simulation of crack propagation in a pipe loaded by various types of loads. Residual stress, a side product of solidification after extrusion, is one of these loads. This thesis begins with an introductory part and literature review of the relevant topics – most of all the typical material properties of the pipe materials, mechanisms of failure, methods of residual stress determination suitable for plastic pipes and their results, methods of testing the materials and calculating lifetime. After the introduction, the problems to be solved are defined. The description of the residual stress state in the wall of various plastic pipes is the main topic. Both tangential (hoop) and axial residual stress in pipes of different dimensions and materials are determined using a combination of experiments and numerical simulations. Also, a simplified method of tangential residual stress is designed that can provide a sufficiently precise description of the tangential resid-ual stress state and is not difficult to carry out. A method to include the residual stress in the lifetime calculations and its influence on the lifetime is also dealt with. Apart from residual stress, the influence of soil loads in case of a buried pipe is studied. The residual stress can also influence the experimental determination of crack growth rate. If the CRB (cracked round bar) test is used to measure the crack growth rate, the crack can propagate asymmetrically due to the presence of residual stress in the specimens, which affects the results. Based on a finite element simulation of crack propagation in a CRB specimen, the severity of the influence is assessed.

The main goal of this work is the comparison of the size of the plastic zone at the crack tip for two analysis methods: an analytical linear method and an elastic-plastic analysis employing the Finite Element method (ANSYS software). All calculations were made for a crack loaded under pure shear modes. These types of loading are not sufficiently described in the literature. The first part of this work introduces the problem with the crack tip plastic zone using both linear and nonlinear fracture parameters. The second part is dedicated to the construction of the Finite Element model in the ANSYS software. The geometry of the samples and the loading levels were chosen to match an existing experimental test of the impact of shear modes on the crack behavior. In the third part of this thesis, the plastic zone radii for pure shear modes II and III are estimated using several methods and the results are compared. In the last part of this work, the same procedure as in the previous part is applied on a mixed-mode II+III loading. A result of this thesis is the assessment of the application limits of the linear analysis method used to estimate the size of the plastic zone at the crack tip for a specific geometry and material model.

This work is focused on the evaluation of the selected fracture parameters of quasi-brittle material, especially concrete, and an assessment of their dependence on the size and shape of the fracture process zone developing at the tip of the macroscopic crack during fracture. For this purpose, experimentally obtained loading diagrams published in the scientific literature have been utilized. These diagrams have been processed into a form enabling creation and calibration of numerical models of these tests in the ATENA FEM program. The results obtained from simulations of the three-point bending tests on beams of four sizes, with three notches lengths, using the created numerical models were used for determination of fracture parameters of concrete. Results of the work consist of the determined values of the specific energy dissipated for creation of new surfaces of the effective crack and an estimation of the specific energy dissipated in the volume of the fracture process zone, which exhibits specific parameters for each beam size and notch length.

The aim of this master thesis is to explore the influence of frictional forces to the stress and strain on the straight crack tip loaded in shear modes. The first section summarizes the most important things from the field of fracture mechanics. Especially theoretical knowledge about fracture parameters (stress intensity factor, J – integral) and their determination in computational environment ANSYS Workbench. The second part deals with computational modeling. At the beginning, is created the model of material, the model of geometry, the model of loads, etc. Then it is possible to solve the direct problem outlined in the introduction. A result of this thesis is the assessment of how the friction influences the fracture parameters in shear modes II and III.

Above ground steel storage tanks are used worldwide for the storage of various liquids. EN 14015:2005, which has traditionally been used to design the tanks, does not necessarily fulfil the requirements of the Swedish Building Code. This has been underlined by hand calculation models in EN 1993-1-6:2007, EN 1993-4-2:2007 and numerical analysis using Finite Element Method (FEM). Therefore, this thesis investigates the differences between these design models and, preliminarily, the use of high-strength steel in tank shells. A 10600 m3 cylindrical steel tank of diameter 26 m and height of 21 m located in Gothenburg, Sweden is studied. The study is limited to the assessment of the stress in the shell courses due to the hydrostatic pressure from the fluid action of a filled tank, and the buckling behaviour of the shell courses of an empty tank subjected to self-weight, snow and wind loads. Particularly, models of the tank shell with a yield strength of 355 MPa are investigated in detail, while the results of the 700 MPa model are considered as preliminary study, since the material is currently not used for tank shells. An analysis of the fluid action on the tank shell courses in each of the three hand calculation models, showed that the EN 14015 model utilizes thicker courses than both Eurocodes. One benefit of the Eurocode models is that they do not limit the thickness of the shell courses, but it is still necessary to have thicker courses in the upper part of the tank in order to achieve sufficient resistance against buckling. EN 14015:2005, on the other hand, limits the minimum thickness to 6 mm for the investigated tank. Furthermore, only EN 1993-1-6 is applicable to the models with a yield strength of 700 MPa as per EN 1993-1-12 and this resulted in a uniform shell thickness of 6 mm. However, an increase in yield strength has no buckling benefits whatsoever.  Buckling is the most critical aspect as observed in this study. EN 14015 has no specific buckling calculations but uses the approach of determining the number of stiffening rings which are deemed adequate against buckling. In this study, 3 secondary stiffening rings were found to be adequate. In comparison, the results of EN 1993-4-2 are very conservative and lead to a very high and uneconomical number of stiffening rings, ranging from 30 to 52 stiffening rings depending on the reliability class. EN 1993-1-6 resulted in 6-17 stiffening rings, for reliability classes 1-3 and fabrication classes A-C. Therefore, the so-called analytical models in the Eurocodes result in a much denser spacing of stiffening rings than 14015:2005.  The buckling stresses due to the design loads were found to be lower than the yield strength of the tank shells for both hand calculation and FEM models. This means that the tank shells failed in buckling before the yield strength of the material was reached. Based on the parametric study of the EN 1993-1-6 (355 MPa) model regarding reliability class 1 and fabrication class A using FEM, the spacing of the stiffening rings can be increased up to 60 % (from 3825 mm to 6120 mm) with the variable loads also increased simultaneously up to 3.8 times before the shell buckles. Therefore, the design of future tanks using numerical analysis guarantee’s more reliability than all the aforementioned standards.  The design for buckling according to EN 14015 is only valid for a design snow load and under-pressure ≤ 1.2 KN/m2. However, according to the standard itis possible to agree to use it for larger actions or use another design model for buckling.

[pt] A avaliação da propagação de trincas de fadiga inclui a identificação da direção da trinca, o conhecimento do Fator de Intensidade de Tensões (SIF) equivalente, a determinação de uma taxa de crescimento de comprimento de trinca por número de ciclos da/dN e o estabelecimento de uma regra de propagação de trinca conectando SIF e da/dN, como uma regra de tipo Paris. Quando ocorrem cargas mistas e não proporcionais, esses parâmetros ainda não são totalmente compreendidos. Esta tese trata de algumas das variáveis que influenciam a propagação de trincas sob carregamento no modo misto não proporcional. A técnica de Correlação de Imagens Digitais (DIC) foi utilizada para a aquisição de imagens de corpos de prova submetidos a carregamento proporcional e não proporcional cíclico. Dois tipos de corpos de prova foram utilizados. Primeiramente, dois corpos de prova planos foram testados; um disk compact tension (DCT, em inglês) e um compact tension modificado (C (T) em inglês). Eles foram submetidos a carregamento cíclico induzindo o modo I de abertura de trinca ou modos I e II de abertura de trinca proporcionais. Em segundo lugar, os dados DIC adquiridos anteriormente, e em outro lugar, para cinco tubos finos sujeitos a carregamento cíclico foram analisados. Os tubos finos tiveram entalhes usinados a partir dos quais as trincas por fadiga iniciaram e se propagaram. Esses cinco tubos finos foram submetidos a diferentes casos de carga proporcional e não proporcional. Um corpo de prova tipo tubo fino foi exposto a carga axial e apresentou modo de abertura de trinca tipo I. Os outros quatro foram submetidos a carregamento de torção ou carga axial-torcional mista e exibiram todos os três modos de abertura de trinca I, II e III. Os campos de deslocamento adquiridos experimentalmente com a técnica DIC foram processados para calcular independentemente o SIF para cada modo de abertura existente usando formulações de mecânica de fratura elástica linear (MFLE). Uma formulação delas utilizou dados de deslocamento de campo completos adquiridos em pequenas áreas que circundavam a ponta da trinca. Outra formulação usou dados adquiridos de um par de pontos localizados ao longo dos flancos opostos das faces da trinca. Os SIFs determinados foram usados para encontrar os SIFs equivalentes e faixas de SIF equivalentes usando o critério da tensão máxima de tração (para ambas as versões 2D e 3D de combinações dos modos I-II e modos I-II-III respectivamente) que implicitamente incluíram o ângulo de propagação de trinca. Verificou-se que a inclusão do SIF no modo III experimentalmente determinado efetivamente faz diferença nas faixas do SIF e dos SIF equivalentes estimados. A curva da/dN versus faixa do SIF equivalente foi elaborado com as taxas de crescimento de trinca medidas experimentalmente e as faixas de SIF que foram encontradas usando a suposição amplamente aceita de que as trincas cresceram na direção que maximiza a tensão de tração. Para isso, extensões do modelo de Schollmann et. al. e bem como o modelo de Erdogan-Sih, que são geralmente aplicados ao carregamento proporcional, foram usados para determinar os SIFs equivalentes e faixas de SIF equivalentes para os casos de carregamento proporcional e não proporcional. Finalmente, a segunda zona da regra de Paris (da/dN versus faixa do SIF equivalente) foi plotada para os cinco casos de carregamento nos tubos finos mostrando que eles caíram dentro de uma faixa razoavelmente fina e dispersa. / [en] Fatigue crack propagation assessment includes identifying the crack direction, knowing the equivalent Stress Intensity Factor (SIF) range, determining a crack length growth rate per number of cycles (da/dN), and establishing a crack propagation rule connecting the equivalent SIF and da/dN rate, such as a Paris type of rule. When mixed and non-proportional loading occur, those parameters are not fully understood yet. This thesis deals with some of the variables that influence crack propagation under non-proportional mixed mode loading. The Digital Image Correlation (DIC) technique was used to acquire images of test specimens subjected to cyclic proportional and non-proportional loading. Two types of specimen samples were used. Firstly, two different plate test specimens were tested; a disk compact tension (DCT), and a modified compact tension, C(T). They were subjected cyclic loading inducing crack opening mode I or proportional crack opening modes I and II. Secondly, the previously and elsewhere acquired DIC data for five thin tubes subject to cyclic loading were analyzed. The thin tubes had pre-fabricated slit-notches from which fatigue cracks initiated and propagated. Those five thin tubes were subjected to different cases of proportional and non- proportional loading. One tube specimen was exposed to axial loading and presented mode I crack opening. The other four were subjected to torsion loading or mixed axial-torsional loading and exhibited all three I, II and III crack-opening modes. The experimentally acquired DIC displacement fields were processed to independently calculate SIF for each existing opening mode using linear elastic fracture mechanics (LEFM) formulations. One formulation used full field displacement data acquired in small areas that surrounded the crack tip. Another formulation used data acquired from a pair of points located along the opposite crack flanks. The determined SIFs were used to find equivalent SIFs and equivalent SIF ranges using the maximum tensile stress criterion (for both 2D and 3D versions of combinations of modes I-II and modes I-II-III respectively) which implicitly included the crack propagation angle. It was found that the inclusion of the experimentally determined mode III SIF indeed makes a difference in the determined equivalent SIF and equivalent SIF ranges. A da/dN versus equivalent SIF ranges plot was drafted with the experimentally measured crack growth rates and the SIF ranges that were found by using the widely accepted assumption that the cracks grew in the direction that maximizes the tensile stress. For this, extensions of the Schollmann et. al. model as well as of the Erdogan-Sih model, which are generally applied to proportional loading, were used to determine equivalent SIFs and equivalent SIF ranges for the cases of proportional and non-proportional loading. Finally, the second stage of the Paris rule (da/dN versus SIF range) was plotted for the five thin tubes loading cases showing that they fell inside a reasonably thin scattered band.

Compression fracture specimens are ideally suited for miniaturization down to tens of microns. Fracture testing of thermal barrier coatings, ceramics and glasses are also best accomplished under compression or indentation. Compression fracture specimen of finite size with constant form factor was not available in the literature. The finite-sized specimen of edge cracked semicircular disk (ECSD) is designed which has the property of constant form factor. The novel ECSD specimen is explored further using weight function concept. This thesis, therefore, is mainly concerned with the design, development and geometric optimization of compression fracture specimen vis a vis their characterization of form factors, weight functions and isotropic points in the uncracked geometry. Inspired by the Brazilian disk geometry, a novel compression fracture specimen is designed in the form of a semicircular disk with an edge crack which opens up due to the bending moment caused by the compressive load applied along its straight edge. This new design evolved from a set of photoelastic experiments conducted on the Brazilian disk and its two extreme cases. Surprisingly, normalized mode-I stress intensity factor of the semicircular specimen loaded under a particular Hertzian way, is found constant for a wide range of relative crack lengths. This property of constant form factor leads to the development of weight function for ECSD for deeper analysis of the specimen. The weight function of a cracked geometry does not depend on loading configuration and it relates stress intensity factor to the stress distribution in the corresponding uncracked geometry through a weighted integral. The weight function for the disk specimen is synthesized in two different ways: using the conventional approach which requires crack opening displacement and the dual form factor method which is newly developed. Since stress distribution in the uncracked specimen is required in order to use weight function concept, analytical solution is attempted using linear elasticity theory. Since closed form solution for stresses in the uncracked semicircular disk is seldom possible with the available techniques, a new semi-analytical method called partial boundary collocation (PBC), is developed which may be used for solving any 2-D elasticity problem involving a semi-geometry. In the new method, part of the boundary conditions are identically satisfied and remaining conditions are satisfied at discrete boundary points. The classical stress concentration factor for a semi-in finite plate with a semicircular edge notch re-derived using PBC is found to be accurate to the eighth decimal. To enhance the form factor in order to test high-toughness materials, edge cracked semicircular ring (ECSR) specimen is designed in which bending moment at the crack-tip is increased significantly due to the ring geometry. ECSR is analyzed using nite element method and the corresponding uncracked problem is analyzed by PBC. Constant form factor is found possible for the ring specimen with tiny notch. In order to avoid varying semi-Hertzian angle during practice and thereby ensure consistent loading conditions, the designs are further modified by chopping at the loading zones and analyzed. Photoelastic isotropic points (IPs) which are a special case of zeroth order fringe (ZOF) are often found in uncracked and cracked specimens. An analytical technique based on Flamant solution is developed for solving any problem involving circular domain loaded at its boundary. Formation of IPs in a circular disk is studied. The coefficients of static friction between the surfaces of disk and loading fixtures, in photoelastic experiments of three-point and four-point loadings, are explored analytically to confirm with experimental results. The disk under multiple radial loads uniformly spaced on its periphery is found to give rise to one isolated IP at the center. Splitting of this IP into a number of IPs can be observed when the symmetry of normal loading is perturbed. Tangential loading is introduced along with normal loading to capture the effect of the composition on formation of IPs. Bernoulli's lemniscate is found to fit fringe order topology local to multiple IPs. Isotropic points along with other low fringe order zones including ZOF are ideal locations for material removal for weight reduction. Making a small hole in the prospective crack path at the IP location in the uncracked geometry might provide dual benefits: 1. Form factor enhancement; 2. Crack arrestor. Thus, this thesis describes experimental, theoretical and computational investigations for the design, development and calibration of novel compact compression fracture specimens.

The diploma thesis is focused on the evaluation of mechanical fracture parameters of concrete after exposure to high temperatures. In the introductory theoretical part general principles of fracture mechanics with the concentration on a linear elastic fracture mechanics and non-linear fracture models for the concrete are summarized. The meaning of the three-point bending fracture test used for determination of fracture parameters is also explained. Further the influence of high temperatures on the partial components of concrete and general modeling of temperature loading is described. The practical part is concerned with the evaluation of fire experiments on the concrete panels including numerical simulations using GiD and ATENA software. The evaluation of data obtained from the three-point bending test carried out on specimens with initial stress concentrator taken from concrete panels is a main part of the diploma thesis. The values of modulus of elasticity, effective fracture toughness, work of fracture and fracture energy are determined from the measured F–d and F–CMOD diagrams after their proper corrections in the GTDiPS application. The evaluation of the selected mechanical fracture parameters was performed by StiCrack software using effective crack model and work of fracture method and DKFM_BUT software using the double-K fracture model. Finally, the attention is paid to the analysis of the obtained data.

This Ph.D. thesis was written under the supervision of Assoc. Prof. Luboš Náhlík, Ph.D. and Assoc. Prof. Pavel Hutař, Ph.D. Thesis is focused mainly on application of generalized linear elastic fracture mechanics, which allows description of crack behaviour propagating from general singular stress concentrators, such as material interfaces or sharp V-notches, and verification of validity of used fracture criteria. The obtained results were used in the next part of the thesis, which deals with the issue of crack propagating in ceramic composites, where the stress distribution field is strongly influenced by the existence of material interface and presence of residual stresses, that arise during manufacturing process of composite.

Presented diploma thesis is concerned with problems of a stress singularity exponent and a generalized stress intensity factor determination, by dint the stress field in the vicinity of the stress concentrator can be consecutively determined. This task is possible to sectionalize into three parts. The first part summarizes basic information about linear anisotropic materials, deals with fundamentals of the linear elastic fracture mechanics and introduces its generalization to the case of the generalized stress intensity factors. The second part is dedicated to a special theory of anisotropic elasticity - Lekhnitskii-Eshelby-Stroh formalism (LES). Furthermore, a theory of the psi-integral is introduced, by dint the stress intensity factor is determined. The final part applies the LES theory and the psi-integral to the concrete material configuration of a crack on the bimaterial interface, a special example of a sharp bimaterial notch. By means of analytical-numerical algorithm in ANSYS and Silverforst FNT95 software the stress singularity exponents and generalised stress intensity factors are consecutively computed.