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EN
A relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.
EN
The objective of this study is to present a numerical modeling of mixed-mode fracture in isotropic functionally graded materials (FGMs), under mechanical and thermal loading conditions. In this paper, a modified displacement extrapolation technique (DET) was proposed to calculate the stress intensity factor (SIFs) for isotropic FGMs. Using the Ansys Parametric Design Language APDL, the continuous variations of the material properties are incorporated by specified parameters at the centroid of each element. Three numerical examples are presented to evaluate the accuracy of SIFs calculated by the proposed method. Comparisons have been made between the SIFs predicted by the DET and the available reference solutions in the current literature. A good agreement is obtained between the results of the DET and the reference solutions.
EN
Purpose: The aim of the proposed research is to create a calculation model of surface fatigue crack growth at the axle of railway wheelset working under operational loads. Design/methodology/approach: The energy approach of the fracture mechanics was used to formulate the calculation model of fatigue crack propagation at the wheelset axle surface. The method of least squares was used to determine the investigated material mechanical constants that the kinetic equations of the calculation model contain. The system of differential equations of crack growth kinetics was solved numerically using the Runge-Kutta method. Findings: On the basis of the energy approach of the fracture mechanics the calculation model of fatigue macrocrack growth in three-dimensional elastic-plastic body in case of a mixed-mode I+II+III macromechanism of fracture has been built. On the basis of the created calculation model, the kinetics of the growth of fatigue cracks was investigated both in the middle part of the wheelset axle and in the axle journal. Research limitations/implications: The results obtained on laboratory specimens should be tested during a real railway wheelset axle investigation. Practical implications: The created calculation model can be used in practice to formulate method of residual lifetime estimation of railway wheelset axle. Originality/value: It was shown, that surface crack kinetics depends not only on the crack initial area but also significantly depends on the crack edge geometry and comparatively small crack-like defects at the wheelset axle surface can reach critical sizes in comparatively short run. It has been found that mechanical shear stresses caused by the weight of the loaded railway wagon in the cross section of the wheelset axle journal can significantly accelerate the growth of the transverse fatigue crack at the axle surface, reducing the period of crack subcritical growth by about 20%.
PL
W pracy przedstawiono wyniki badań betonów z łącznym dodatkiem krzemionkowych popiołów lotnych (Fly ash – FA) oraz mikrokrzemionki (Silica fume – SF). W celu potwierdzenia pozytywnego wpływu zastosowanych odpadów przemysłowych w betonie wykonano badania odporności na pękanie, według drugiego modelu pękania, a także wytrzymałości na ściskanie – fcm oraz rozciąganie pośrednie – fctm. Odporność na pękanie kompozytów oceniano na podstawie wyników krytycznego współczynnika intensywności naprężeń KIIc. Eksperymenty wykonano na betonie z różną kompozycją dodatków mineralnych – w młodym wieku, po 3 i 7 dniach dojrzewania betonu oraz po 28 dniach. Zastosowanie odpadów przemysłowych w postaci krzemionkowych popiołów lotnych i mikrokrzemionki zagęszczonej pozwala na ograniczenie zużycia cementu w betonie oraz zaoszczędzenie zasobów naturalnych do produkcji klinkieru, co spełnia koncepcje budownictwa zrównoważonego. Ponadto dzięki temu uzyskano korzystniejsze wartości parametrów: fcm, fctm oraz KIIc w porównaniu do wartości otrzymanych dla betonu odniesienia.
EN
Analysis of cracked cruciform specimens under biaxial loading conditions is very important and closer to reality in the study of behavior of marine, naval, aeronautical and railway structures. The aim of this work is to examine the evolution of fracture parameters in a combined mixed mode of an aluminum alloy A6082-T6 cruciform specimen as a function of the biaxial loading with different ratios. To this end, the effects of main parameters, such as load ratio, crack length, crack orientation and non-proportional loading coefficient have been analyzed and discussed in order to highlight fracture toughness of the studied material. The results show that the finite element method is a useful tool for calculation of crack characteristics in the mechanics of biaxial fracture. According to the obtained results, a non-proportional evolution of the fracture parameters, namely, the SIFs KI and KII , T-stress, and the biaxiality parameter was observed. Indeed, the latter depends considerably on the crack length, the angle of crack orientation and the applied biaxial loading. Detailed concluding remarks are presented at the end of this work.
EN
A numerical method for 2D LEFM crack propagation simulation in a cement mantle of the total hip replacement (THR) is presented. This work is based on the implementation of the displacement correlation technique (DCT) and the maximum circumferential stress (MCS) theory in a finite element code, using the Ansys Parametric Design Language (APDL). At each crack increment length, the crack direction angle is evaluated as a function of stress intensity factors (SIFs). The crack box technique is investigated for crack propagation simulation. The advantage of this technique is facilitation of the automatic remeshing of the structure during crack extension. In this paper, we analyzed the mechanical behavior of cracks initiated in the cement mantle by evaluating the SIFs. The effect of the cavities and the initial crack directions on the crack growth path has been highlighted.
PL
Podjęto próbę przedstawienia zarysu mechaniki pękania. Omówiono zagadnienia struktury betonu, jego porowatości, strefy przejściowej, kruszywa oraz toku badawczego stosowanego w mechanice pękania.
EN
The article attempts to present the outline of fracture mechanics. Issues of the structure of concrete, its porosity, transition zone, aggregate and the research process used in fracture mechanics are discussed.
EN
Aluminum alloys are widely used for fabrication of aircraft, civil structures, and space vehicles. Fatigue life consideration of a material is the most important design criteria in many such critical applications. In this research work, a widely used Aluminum alloy AA2219-T87 was TIG welded using AA2319 as a filler material. The effect of natural aging on Fatigue Crack Propagation Rate (FCPR) of welded and non-welded compact tension (CT) specimens (AA2219˗T87) is studied. The relationship between stress intensity factor (ΔK) and crack ratio (a/W) for different value of the crack length in base metal and the welded zone is presented. Paris curves for both welded and non-welded specimens and compared to study the effect of natural aging (NA) on FCGR and compared with non-aged specimens. The results obtained provide a base for the development of Structural Health Monitoring systems for the propagation of crack growth in such components.
EN
This article presents numerical finite element method (FEM) analysis of the stress concentration at toes and crack-like faults in load-carrying fillet welded cruciform joints with transversal slits resulting from non-fused root faces. Potential fatigue damage of such joints subjected to cyclic tensile and bending loads appears in the form of fatigue cracks starting from the weld roots or toes. The aim of this article is to find qualitative and quantitative relationships between geometrical parameters of the load-carrying fillet welded cruciform joint subjected to tensile and bending loads and the stress concentration at weld toes and roots. The results of the analysis represented by the stress concentration factors (SCFs) and the stress intensity factors KI and KII are shown in the form of tables, graphs and mathematical formulas, which may be applied for fatigue assessment of such joints.
EN
Two-dimensional stationary problem of heat conduction and thermoelasticity for infinite elastic body containing periodic system of inclusions and cracks is considered. Solution of the problem is constructed using the method of singular integral equations (SIEs). The numerical solution of the system integral equations are obtained by the method of mechanical quadrature for a plate heated by a heat flow, containing periodic system elliptic inclusions and thermally insulated cracks. There are obtained graphic dependences of stress intensity factors (SIFs), which characterise the distribution of intensity of stresses at the tops of a crack, depending on the length of crack, elastic and thermoelastic characteristics inclusion, relative position of crack and inclusion.
11
Content available remote Analiza parametrów mechaniki pękania w warunkach I modelu obciążenia betonu
PL
Według najnowszych prognoz, fibrobetony jako jeden z kompozytów betonowych będą stale rozwijane. Kluczowa dla budownictwa idea zrównoważonego rozwoju zakłada bowiem tworzenie trwałych konstrukcji. Dodatek zbrojenia rozproszonego do betonu poprawia jego odporność na pękanie, a tym samym wydłuża okres eksploatacji. Znajomość parametrów mechaniki pękania jest więc tu kluczowa. Celem niniejszej pracy było określenie wpływu dodatku włókien bazaltowych do betonu na wartości współczynnika intensywności naprężeń oraz wielkość rozwarcia szczeliny (tzw. COD). Badania przeprowadzone zostały przy użyciu betonowych dysków o średnicy 150 mm i grubości 50 mm ze wstępnie uformowanymi szczelinami o długości 15, 45 lub 75 mm. Próby były prowadzone w warunkach I modelu obciążenia z wykorzystaniem maszyny wytrzymałościowej Zwick/Roell Z250. Otrzymane wyniki wskazują na zmianę charakteru pracy badanych elementów. Próbki bez włókien wykazywały typowo quasi-kruche cechy betonu, natomiast wraz ze wzrostem ilości dodawanego zbrojenia rozproszonego nabierały one cech quasi-plastycznych. Zależność ta nie była jednak jednoznaczna dla wszystkich próbek, co wynikało z heterogenicznej struktury betonu oraz tendencji do zbrylania się włókien.
EN
Nowadays fibre concrete, as one of the concrete`s composites, is still developing. The major idea of sustainable development deals with durability of constructions. Fibres in concrete improve resistant to cracks and by that increase durability. Taking this phenomenon into consideration, the knowledge of fracture mechanics parameters is really important. The aim of this paper was to determine the influence of basalt fibres addition to stress intensity factor and crack opening displacement (COD). Concrete discs 150 mm width and 50 mm thick with crack length’s 15, 45 or 75 mm were studied. Load was applied according to opening mode. Zwick/Roell Z250 machine was used in the experiment. Samples without fibres behave as quasi-brittle but these ones with fibres worked more like quasi–plastic material. Results were very diversified, because of heterogenic structure of concrete and the fibres tendency to fuse.
12
Content available Diagnostics of concrete elements after the fire
EN
The paper presents selected methods for determining the influence of fire on the load capacity of concrete elements - diagnostics and damages arising after application of fire temperatures. The subject may not seem new in terms of the well-known drop in the strength of concrete in fire conditions, but an important aspect discussed in the paper is the fracture toughness of concrete depending on high temperatures. Destructions, caused by fire temperatures, affects the physical and mechanical properties of concrete, and their size can be assessed using the stress intensity factor. According to our own research, the critical stress intensity factor KIC of concrete decreases faster than the dynamic modulus of elasticity, and also faster than compressive and tensile strength. The paper describes selected methods of diagnostics of construction elements from concrete damaged by fire.
PL
W referacie przedstawiono wybrane metody określania wpływu pożaru na nośność elementów betonowych - diagnostykę oraz uszkodzenia powstające po aplikacji temperatur pożarowych. Temat może nie wydaje się nowy w aspekcie, powszechnie znanego spadku wytrzymałości betonu w warunkach pożarowych, jednak istotnym zagadnieniem poruszonym w referacie jest odporność betonu na pękanie w zależności od wysokich temperatur. Destrukcje powstałe pod wpływem temperatur pożarowych wpływają na właściwości fizykomechaniczne betonu, a ich wielkość może być oceniana za pomocą współczynnika intensywności naprężeń. Z badań własnych wynika, że krytyczny współczynnik intensywności naprężeń KIC betonu zmniejsza się szybciej niż dynamiczny moduł sprężystości Edyn, a także szybciej niż wytrzymałość na ściskanie i rozciąganie. W referacie opisano wybrane metody diagnostyki elementów konstrukcyjnych z betonu, uszkodzonych przez pożar.
13
Content available remote Evolution of tenacity in mixed mode fracture - volumetric approach
EN
In fracture mechanics most interest is focused on stress intensity factors, which describe the singular stress field ahead of a crack tip and govern fracture of a specimen when a critical stress intensity factor is reached. In this paper, stress intensity factors which represents fracture toughness of material, caused by a notch in a volumetric approach has been examined, taking into account the specific conditions of loading by examining various U-notched circular ring specimens, with various geometries and boundary conditions, under a mixed mode I+II. The bend specimens are computed by finite element method (FEM) and the local stress distribution was calculated by the Abaqus/CAE. The results are assessed to determine the evolution of the stress intensity factor of different notches and loading distances from the root of notch. This study shows that the tenacity is not intrinsic to the material for all different geometries notches.
EN
Research in the field of fracture mechanics and determination of material characteristics are used for practical purposes, such as the assessment of static and dynamic strength of structural components, analysis of their fatigue life or extending the life span of their operation. A structural component, considered to be safe from fatigue cracking point of view, was investigated and results were presented in this article. In particular, an analysis was made to determine the stress intensity factor for the cracked wing flap construction, based on static and fatigue tests, using the Irwin-Kies theory. The flap with a service crack was subjected to fatigue tests with a load similar to the one registered during flight measurements. The flap without a service crack was subjected to static tests, after cutting the cracks of specified lengths and shapes (similar to the service crack) in the skin of the flap. The article presents changing the length of the flap crack in subsequent load cycles, change in the maximum values of force and the crack opening displacement in subsequent load cycles, dependence of P-COD in the first and second stage of fatigue testing of the wing flap, dependence of the wing flap compliance on the length of the crack and experimentally determined dependence for wing flap. The occurrence of a flap crack up to approximately 230 mm does not cause a significant growth of the stress intensity factor.
EN
Purpose: Carefully investigate the stress-strain state of the side grooved I-beam specimen with edge crack and determine the effect of crack length and crack faces friction on stress intensity factor at transverse shear. Design/methodology/approach: The finite element method was used to estimate the stress-strain state of I-beam specimen at transverse shear. For this purpose, a fullscale, three-dimensional model of the specimen was created, which precisely reproduces its geometry and fatigue crack faces contact. For the correct reproduction of the stress singularity at the crack tip, a special sub-model was used, which has been tested earlier in solving similar problems of fracture mechanics. In order to improve the accuracy of the calculations, for crack plane and cross-section of the specimen on the crack extension modeling, an algorithm for changing the crack length without changing the total number of elements in the model was developed and applied. Young's modulus and Poisson's ratio of structural steels were specified for the model material. The static loading of the model was realized assuming small scale yielding condition. The stress intensity factor was found through the displacement of nodes in the prismatic elements adjacent to the plane and the front of the crack. Findings: Mathematical dependences, which show an increase of stress intensity factor in the I-beam specimen with an increase in the crack length, and its decrease with an increase of crack faces friction factor at transverse shear, were established. The results are compared with the partial cases known from the literature and their good convergence was shown. Research limitations/implications: By analyzing the obtained graphical dependences, it is established that for relative crack lengths less than 0.4 there is a significant influence of the initial notch on the stress-strain state of the specimen, and for the lengths greater than 0.9 an influence of constrained gripping part took place. For this reason, all subsequent calculations were carried out in the range of relative crack length from 0.4 to 0.9, which represents the applicability range of the final calculation formula. Increasing of the crack faces friction factor from 0 to 1 monotonically reduces the stress at the crack tip. For a short crack, this effect is 1.5 times greater than for a long one, which is reflected by the calculation formula. Practical implications: Using the proposed calculation formula, one can calculate the stress intensity factor in the I-beam specimen, and to determine the crack growth resistance characteristics of structural steels at transverse shear. Originality/value: A new, easy-to-use in engineering calculations formula is proposed for stress intensity factor determination in the I-beam specimen at transverse shear. The formula takes into account crack faces friction for various crack lengths.
EN
To ensure reliability of pressure vessels during service it is necessary to (1) know properties of materials used in their design and (2) evaluate vessels’ behaviour under different working conditions with satisfying accuracy. Due to various technical and/or technological requirements, nozzles are usually welded on vessel’s shell producing geometrical discontinuities that reduce the safety factor. To evaluate their influence, vessels with two different nozzles were experimentally studied and critical areas for crack initiation have been identified by 3D Digital Image Correlation (DIC) method. After that, the numerical analysis of equivalent 3D finite element model was performed and obtained results were compared with experimental values. In the most critical area, next to the one of the nozzles, crack was initiated and then growth of the damage was simulated using extended finite element method (XFEM). In this paper evaluation of stress intensity factors (SIFs) along crack path is presented, as well as the most probable direction of the crack propagation on the shell. Based on SIFs values, critical length of the crack and number of pressure cycles to the final failure were estimated.
PL
Aby zapewnić niezawodność zbiorników ciśnieniowych podczas pracy, konieczna jest (1) znajomość właściwości materiałów zastosowanych do ich konstrukcji oraz (2) wystarczająco dokładna ocena zachowania zbiornika w różnych warunkach pracy. Ze względu na różne wymagania techniczne i/lub technologiczne, króćce zwykle spawa się do płaszcza zbiornika, w wyniku czego powstają geometryczne nieciągłości, które zmniejszają współczynnik bezpieczeństwa. Aby ocenić ich wpływ, przeprowadzono eksperymentalne badania zbiorników z dwoma różnymi króćcami i określono obszary krytyczne dla inicjacji pęknięć wykorzystując metodę trójwymiarowej cyfrowej korelacji obrazu (DIC). Następnie przeprowadzono analizę numeryczną równoważnego modelu elementów skończonych 3D, a uzyskane wyniki porównano z wartościami eksperymentalnymi. W najbardziej krytycznym obszarze, w pobliżu jednego z króćców, inicjowano pęknięcie, a następnie symulowano rozwój uszkodzenia przy użyciu rozszerzonej metody elementów skończonych (XFEM). W artykule przedstawiono ocenę współczynników intensyfikacji naprężeń (SIF) wzdłuż ścieżki pękania oraz najbardziej prawdopodobnego kierunku propagacji pęknięć na płaszczu zbiornika. Na podstawie wartości SIF, oszacowano krytyczną długość pęknięcia i liczbę cykli ciśnieniowych do ostatecznego uszkodzenia.
EN
In this study, the plane receding contact problem for a functionally graded (FG) layer resting on two quarter-planes is considered by using the theory of linear elasticity. The layer is indented by a rigid cylindrical punch that applies a concentrated force in the normal direction. While the Poisson’s ratio is kept constant, the shear modulus is assumed to vary exponentially through-the-thickness of the layer. It is assumed that the contact at the layer-punch interface and the layer-substrate interface is frictionless, and only the normal tractions can be transmitted along the contact regions. Applying the Fourier integral transform, the plane elasticity equations are converted to a system of two singular integral equations, in which the contact stresses and the contact widths are unknowns. The singular integral equations are solved numerically by Gauss–Jacobi integration formula. Effects of the material inhomogeneity, the distance between quarter-planes and the punch radius on the contact stresses, the contact widths, and the stress intensity factors at the sharp edges are shown. Although the theoretical analysis is formulated with respect to elastic quarter planes, the numerical studies are carried out only for rigid ones.
EN
The paper presents the solution linear elasticity problem for an isotropic plate weakened by a hole and two co-axial cracks. The plate is exerted by uniform traction at infinity. The corresponding 2D problem is solved by the method of Kolosova-Muskhelishvili complex potentials. The method implies reduction of the problem to simultaneous singular integral equations (SIE) for the functions defined the region of the cracks and hole. For particular case the solution the SIE is obtained analytically in a closed form. A thorough analysis of the stress intensity factors (SIF) is carried out for various cases of the hole shape: penny-shaped, elliptical and rectangular.
EN
The problem of longitudinal shear of bimaterial with thin nonlinear elastic inclusion at the interface of matrix materials is considered. Solution of the problem is constructed using the boundary value problem of combining analytical functions and jump functions method. The model of the thin inclusion with nonlinear resilient parameters is built. Solution of the problem is reduced to a system of singular integral equations with variable coefficients. The convergent iterative method for solving such a system is offered for various nonlinear strain models, including Ramberg-Osgood law. Numerical calculations are carried out for different values of non-linearity characteristic parameters for the inclusion material. Their parameters are analysed for the tensely-deformed matrix under loading a uniformly distributed shear stresses and for a balanced system of the concentrated forces.
20
Content available remote Prediction of crack propagation direction in the cemented total hip prosthesis
EN
The major inconvenient of the Poly methyl methacrylate (PMMA) is the crack formation; this phenomenon takes place during the polymerization process which is the result of an exothermic chemical reaction. In this context, this study aims to predict the behavior of macros cracks situated in the most heavily loaded sites in newly used bone cement. In fact, the prediction of crack propagation directions in bone cement during exercising the most practiced activity by patients allows determination of the most favorable cracking directions and subsequently provides orientations for the studies aiming to fight against this phenomenon.
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