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1

Fatigue process of steel in building structures - assessment criteria and methods of analysis

Rowiński Sławomir

Materiały Budowlane

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2025

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nr 5

40--49

EN

The aim of this study was to analyze the mechanism of fatigue crack propagation in steel and to assess the fatigue strength of structures based on the stress intensity factor. The article presents the stages of crack initiation and propagation in steel elements subjected to cyclic loading. The static load-bearing capacity condition in the presence of material defects is discussed. A key part of the study is the analysis of the Paris curve. The application of Wöhler fatigue curves in the assessment of steel fatigue durability is also presented.

PL

Celem pracy była analiza mechanizmu propagacji pęknięć zmęczeniowych w stali oraz ocena wytrzymałości zmęczeniowej konstrukcji na podstawie współczynnika intensywności naprężenia. W artykule przedstawiono etapy inicjacji i propagacji pęknięć w elementach stalowych poddanych obciążeniom cyklicznym. Omówiono warunek nośności statycznej w obecności defektów materiałowych. Kluczową częścią pracy jest analiza krzywej Parisa. Przedstawiono również zastosowanie krzywych zmęczeniowych Wöhlera w ocenie trwałości zmęczeniowej stali.

2

Evaluating the stress intensity factor for R350HT rail steel in relation to microstructure parameters

Żak Sylwester, Junak Grzegorz, Woźniak Dariusz, Żak Artur, Chmiela Bartosz, Jabłońska Magdalena Barbara

Advances in Science and Technology. Research Journal

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2025

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Vol. 19, no. 4

349–364

EN

The study highlights the advancement of rail transport, focusing on the distinct requirements of high-speed passenger transit and robust freight operations. Passenger rails emphasize geometric precision, such as straightness and minimal dimensional deviation, to reduce vibrations and improve safety and comfort. Freight rails, in contrast, require exceptional durability to withstand high axial loads, plastic deformation, and abrasive wear due to heavy tonnage. A key parameter for all rail types is the stress intensity factor (KIc), which ensures rail integrity by preventing crack propagation. The study confirmed that tested rail types (60E2, 54E4, and 49E1) meet the EN 13674-1 standard for mechanical properties, indicating effective heat treatment. Residual stress levels were found to be low, particularly in lighter rails, enhancing resistance to brittle fracture. All rails exhibited a fine, fully pearlitic microstructure with cementite lamellae spacing between 92 and 106 nm, contributing to mechanical strength and durability. The low residual stress and high KIc support extended rail life and safety, as larger critical crack sizes minimize fracture risk. These findings underline the reliability and safety of rail materials under operational conditions, with consistent pearlitic structures and optimized stress properties ensuring robust performance.

3

Analysis and calculation of stress intensity factors for type I cracks on the edge of elliptical holes under internal pressure

Chen Shiwei, Xing Minglu, Liu Yaxin, Yin Yanchun, Li Yurong, Li Longfei

Journal of Theoretical and Applied Mechanics

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2024

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Vol. 62 nr 1

157--169

EN

The stress intensity factor and stress field expression for long cracks near an infinite-length plate bore are calculated using the Muskhelishvili Complex Function Approach. It applies to engineered bore edge cracks, especially under the condition in which the elliptical bore is subjected to internal pressure or only the surface of the crack is subjected to internal pressure. The formula is validated by numerical simulation and applies both to elliptical and circular holes. The variation of stress intensity factor with crack length is analyzed when the special round hole is only subjected to internal pressure. It has practical application value in fracture engineering.

4

Study on the stress intensity factor of a compact specimen under the pre-compressed load condition

Wu Dongquan, Liu Zixiang, Li Dinghe, Zhang Zhiqiang, Chen Jianguo

Journal of Theoretical and Applied Mechanics

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2023

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Vol. 61 nr 1

37--47

EN

Structural components are often operated under combined stress conditions (primary and secondary stresses), but the stress levels generated by residual stress (or secondary stress) is hardly ever evaluated. Hence, stress intensity factors at the crack tips of a compact tension (CT) specimen under a pre-compressed load condition are analyzed using the finite element method. Then, the average residual stress intensity factor is calculated and analyzed. As the crack length α0/W increases, the average residual stresses σave/σ0 grows under the same pre-compression load. σave/σ0 increases rapidly at a low range of the pre-compression load but tends to a constant in a high range of the load. The distribution of the average residual stress intensity factors Kave and Κave/σ0 of the CT specimen with same crack length under different pre-compression loads have the same tendency. Additionally, the distribution of Κave and KFEM under different pre-compression loads are also similar. Nevertheless, Kave estimated by the average residual stress is too conservative and not accurate, and the method is complex, which depends on the analysis of simulation. Therefore, a simple method for calculating Mode I stress intensity factor K for this model is presented. A group of examples is presented to verify the accuracy of the method.

5

Study on tensile fracture failure of a steel plate with a surface crack

Chong Zhewen, Tao Jing, Xie Yuehui, Wu Dongrong, Li Tao

Journal of Theoretical and Applied Mechanics

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2023

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Vol. 61 nr 2

343--354

EN

In order to study the effect of different surface crack parameters on the fracture failure of steel plate, the model was established by FEM. The results showed that the edge surface crack has the greatest influence on the fracture failure of the steel plate, and for non-edge surface cracks, the central surface crack has the greatest influence on the fracture failure of the steel plate. The larger the a/t and the smaller the a/c, the easier the steel plate fracture failure occurs. The a/c has a certain influence on the variation law of K and the position where Kmax appears.

6

Numerical analysis of fracture behavior of functionally graded materials using 3D-XFEM

Benhamena Ali, Fatima Benaoum, Foudil Khelil, Baltach Abdelghani, Chaouch Mohamed Ikhlef

Advances in Materials Science

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2023

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Vol. 23, nr 3(77)

33--46

EN

This paper presents the numerical evaluation of mixed stress intensity factors (SIFs) and non-singular terms of William's series (T-stress) of functionally graded materials (FGMs) using three-dimensional extended finite element method (3D-XFEM). Four-point bending specimen with crack perpendicular to material gradation have been used in this investigation in order to study the effect of some parameters (crack position, crack size, specimen thickness) on the failure of FGMs materials. The fracture parameters (KI KII, phase angle ψ and T-stress) obtained by the present simulation are compared with available experimental and numerical results. An excellent correlation was found of the 3D-XFEM simulations with those available in the literature. From the numerical results, a fitting procedure is performed in order to propose an analytical formulation and subsequently are validated against the 3D-XFEM results.

7

Influence of form defect on the mechanical behavior and stress intensity factor of shrink-fitted thick-walled cylinders

Boutoutaou Hamid, Chebbab Brahim, Belmessous Abdelmounaime

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 4

40--51

EN

In this research work, the finite element software, ABAQUS is used to study by simulations the influence of form defect on mechanical behavior of a shrink-fitted assembly presenting internal radial cracks. Under the action of contact pressure induced by the tightening between two cylinders, these cracks resulting from incorrect assembly operations or materials elaboration defect, can be harmful to the assembly. Various simulations were carried out in two modeling cases, taking into account the geometric parameters of defect (amplitude Df), of cylinders (thickness t) and of cracks (length a, ratio a/t). Another important parameter such as the tightening was also considered in the modeling. The first modeling relates to the case with defect, external cylinder presents an oval (elliptical) form defect and internal radial cracks. The other concerns the perfect equivalent case (without form defect). The comparison of results obtained by two models shows that form defect modifies the uniformity of equivalent stresses distribution in cylinders and increases the value of stress intensity factor (SIF) KI in cracks. Defect amplitude and tightening significantly influence the value of equivalent stress and that of stress intensity factor (SIF) KI.

8

Study of load bearing capacity of an infinite sheet weakened by multiple collinear straight cracks with coalesced yield zones

Shekhar S., Akhtar Naved, Hasan S.

Materials Science Poland

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2021

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Vol. 39, No. 2

265--284

EN

This paper is concerned with the analytical solution of a multi-side damage problem. The objective is to investigate the load-bearing capacity of an infinite elastic-plastic plate weakened by three pairs of collinear straight cracks with coalesced yield zones. Stress intensity factors (SIFs) are obtained when yield zones are subjected to three different patterns of yield stress distribution, i. e., constant, linearly, and quadratically varying. Muskhelisvili's complex variable approach is applied for uncovering the solution to this problem. The problem is solved and analyzed rigorously based on Dugdale's hypothesis. The numerical results are deduced for the load-bearing capacity of the plate and yield zone lengths. These results are analyzed and demonstrated graphically for various mechanical loading conditions and different crack lengths.

9

2D and 3D numerical simulation of fatigue crack growth path and life predictions of a linear elastic

Bashiri Abdullateef H.

Materials Science Poland

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2021

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Vol. 39, No. 2

285--297

EN

This paper describes implementation of the finite element method (FEM) to investigate crack growth problems in linear elastic fracture mechanics and the correlation of results with experimental and numerical data. The approach involved using two different software to compute stress intensity factors (SIFs), the crack propagation trajectory, and fatigue life estimation in two and three dimensions. According to the software, crack modeling might be run in various ways. The first is a developed source code program written in the Visual Fortran language, while the second is the widely used ANSYS Mechanical APDL 19.2 software. The fatigue crack propagation trajectory and the corresponding SIFs were predicted using these two software programs. The crack direction was investigated using the maximum circumferential stress theory, and the finite element (FE) analysis for fatigue crack growth was done for both software based on Paris's law. The predicted results in both software demonstrated the influence of holes on the crack growth trajectory and all associated stresses and strains. The study's findings agree with other experimental and numerical crack propagation studies presented in the literature that reveal similar crack propagation trajectory observations.

10

Diagnostyka konstrukcji betonowych po działaniu wysokich temperatur pożarowych (cz. 1)

Plechawski Stanisław

Budownictwo i Prawo

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2021

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R. 25, nr 3

7--10

PL

W artykule zaprezentowano wybrane metody określania wpływu wysokich temperatur pożarowych na nośność konstrukcji betonowych – diagnostykę oraz uszkodzenia powstające po działaniu tych temperatur. Istotną kwestią poruszoną w artykule jest wpływ pożaru na odporność betonu na pękanie i jej zależność od wysokich temperatur. Destrukcje powstające pod wpływem wysokich temperatur pożarowych definitywnie wpływają na mechanikę pękania betonu, a ich wielkość może być oceniana za pomocą współczynnika intensywności naprężeń. W artykule opisano wybrane metody diagnostyki elementów konstrukcyjnych z betonu uszkodzonych przez pożar.

EN

The article presents selected methods of determining the effect of high fire temperatures on the load-bearing capacity of concrete structures – diagnostics and damage occurring after the application of these temperatures. An important issue discussed in the article is the influence of fire on the cracking resistance of concrete and its dependence on high temperatures. Failures occurring under the influence of high fire temperatures definitely affect the fracture mechanics of concrete, and their magnitude can be assessed by means of the stress intensity factor. This paper describes selected methods for diagnosing structural elements made of concrete damaged by fire.

11

Diagnostyka konstrukcji betonowych po działaniu wysokich temperatur pożarowych (cz. 2)

Plechawski Stanisław

Budownictwo i Prawo

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2021

|

R. 24, nr 4

32--36

PL

W artykule zaprezentowano wybrane metody określania wpływu wysokich temperatur pożarowych na nośność konstrukcji betonowych – diagnostykę oraz uszkodzenia powstające po działaniu tych temperatur. Istotną kwestią poruszoną w artykule jest wpływ pożaru na odporność betonu na pękanie i jej zależność od wysokich temperatur. Destrukcje powstające pod wpływem wysokich temperatur pożarowych definitywnie wpływają na mechanikę pękania betonu, a ich wielkość może być oceniana za pomocą współczynnika intensywności naprężeń. W artykule opisano wybrane metody diagnostyki elementów konstrukcyjnych z betonu uszkodzonych przez pożar.

EN

The article presents selected methods of determining the effect of high fire temperatures on the load-bearing capacity of concrete structures – diagnostics and damage occurring after the application of these temperatures. An important issue discussed in the article is the influence of fire on the cracking resistance of concrete and its dependence on high temperatures. Failures occurring under the influence of high fire temperatures definitely affect the fracture mechanics of concrete, and their magnitude can be assessed by means of the stress intensity factor. This paper describes selected methods for diagnosing structural elements made of concrete damaged by fire.

12

The calculation of stress intensity factor steel of railway wheels

Vakulenko Igor, Proydak Svetlana, Askerov Hangardas

Zeszyty Naukowe. Transport / Politechnika Śląska

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2020

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z. 109

187--193

EN

From an analysis of the dependence complex of carbon steel properties on structural parameters, it was found that for an isostructural state, the influence of austenite grain size on impact strength exceeds the dependence on carbon content. As a result of explaining correlation relationships between individual mechanical characteristics, to evaluate critical stress intensity factor, a relationship is proposed based on the use of impact strength. The proportionality coefficient in proposed dependence is determined by ratio of elongation to narrowing at tensile test.

13

Stress intensity factor in the assessment of frost degradation of high-strength fibre-reinforced concretes

Borowska Sylwia Anna

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

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2020

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Z. 26 (176)

12-17

EN

The paper presents an assessment of the degradation of cyclic freeze/thaw on high-strength concretes, based on changes in the stress intensity factor KIC cycles and the total mass of surface scaling after 28 and 70 cycles. The degree of degradation was compared with the modification of stress intensity factor values. Three types of high-strength concretes (compressive strength about 90 MPa) were tested: concrete without fibres, concrete with steel fibres in the amount of 0.5% by volume (39 kg/m3) and concrete with a mixture of steel fibres (19.5 kg/m3) and basalt (6.8 kg/m3). The testing methodology is based on RILEM recommendations [1] and ASTM C666 [2] and PKN – CEN/TS 12390 Slab Test [3].

PL

W pracy przedstawiono ocenę degradacji betonów wysokowytrzymałych poddanych cyklicznemu zamrażaniu/rozmrażaniu, w oparciu o zmiany współczynnika intensywności naprężeń KIC. Stopień zniszczenia na skutek cyklicznego zamrażania/rozmrażania BWW określono za pomocą modułu sprężystości podłużnej E, ubytku masy, redukcji wytrzymałości na ściskanie, wyznaczanych po 150, 250, 300 oraz 350 cyklach oraz sumarycznej masy złuszczeń powierzchniowych po 28 i 70 cyklach. Stopień degradacji porównano z modyfikacją wartości współczynnika intensywności naprężeń. Badaniom poddano trzy rodzaje betonów wysokiej wytrzymałości (wytrzymałość na ściskanie około 90 MPa): beton bez dodatku włókien, beton z włóknami stalowymi w ilości 0,5% objętości (39 kg/m3) oraz beton z mieszanką włókien stalowych (19,5 kg/m3) oraz bazaltowych (6,8 kg/m3). Metodologię badań oparto na zaleceniach RILEM [1] oraz normach ASTM C666 [2] i PKN – CEN/TS 12390 Slab Test [3].

14

Stress and displacement intensity factors of cracks in anisotropic media

Kuznetsov S., Karakozova A.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

212--218

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.

15

Computation of SIFs for cracked FGMs under mechanical and thermal loadings

Ait Ferhat Yazid, Boulenouar Abdelkader

Archives of Mechanical Technology and Materials

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2020

|

Vol. 40

12--19

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.

16

Assessing surface fatigue crack growth in railway wheelset axle

Rudavskyi D. V., Kaniuk Yu. I., Duriagina Z. A., Kulyk V. V., Shefer M. S., Dolinska I. Ya.

Archives of Materials Science and Engineering

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2020

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Vol. 106, nr 2

59--67

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%.

17

Ocena zastosowania popiołów lotnych i mikrokrzemionki w betonie

Gil Damian Marek, Golewski Grzegorz Ludwik

Przegląd Budowlany

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2019

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R. 90, nr 10

142--145

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.

18

Numerical investigation of mechanical behavior of cracked cruciform specimens in aluminum alloy 6082-T6 subjected to different biaxial loading conditions

Khelil Foudil, Aour Benaoumeur, Talha Abderrahim, Benseddiq Noureddine

Journal of Theoretical and Applied Mechanics

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2019

|

Vol. 57 nr 4

1021--1037

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.

19

Crack growth path simulation in a cement mantle of THR using crack box technique

Boulenouar Abdelkader, Bendida Nadjet

Journal of Theoretical and Applied Mechanics

|

2019

|

Vol. 57 nr 2

317--329

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.

20

Wybrane kompozyty cementowe w warunkach pożaru

Plechawski Stanisław

Inżynieria i Budownictwo

|

2019

|

R. 75, nr 10

472--477

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.