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Rheological-dynamical analysis of flexural fatigue on plain concrete beams

dc.contributor.advisorMilašinović, Dragan
dc.contributor.otherŠumarac, Dragoslav
dc.contributor.otherMilašinović, Dragan
dc.contributor.otherProkić, Aleksandar
dc.contributor.otherBešević, Miroslav
dc.contributor.otherGoleš, Danica
dc.creatorPančić, Aleksandar
dc.date.accessioned2022-04-12T18:21:44Z
dc.date.available2022-04-12T18:21:44Z
dc.date.issued2021-12-03
dc.identifier.urihttps://www.cris.uns.ac.rs/DownloadFileServlet/Disertacija162376348144283.pdf?controlNumber=(BISIS)117878&fileName=162376348144283.pdf&id=17912&source=NaRDuS&language=srsr
dc.identifier.urihttps://www.cris.uns.ac.rs/record.jsf?recordId=117878&source=NaRDuS&language=srsr
dc.identifier.urihttps://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisije162376366538949.pdf?controlNumber=(BISIS)117878&fileName=162376366538949.pdf&id=17913&source=NaRDuS&language=srsr
dc.identifier.urihttps://nardus.mpn.gov.rs/handle/123456789/18988
dc.description.abstractBetonske konstrukcije koje su izložene periodičnim opterećenjima mogu dobiti oštećenja koja nekad dovedu do loma. Ovaj fenomen pri kome se razvijaju oštećenja u materijalu pri naponima manjim od granice tečenja je poznat kao zamor materijala. Razvoj oštećenja u materijalu prilikom cikličnog djelovanja opterećenja se može posmatrati kroz tri faze: faza iniciranja prsline tj. stvaranje mikroprslina, zatim faza formiranja i stabilnog rasta prsline i treća faza koja predstavlja nestabilni razvoj prsline koji dovodi do loma materijala. Problem zamora je prvobitno ispitan na metalima, a problem se matematički opisuje kroz poznati Parizov zakon kojim se može dosta precizno opisati druga faza razvoja oštećenja. Parizov zakon povezuje gradijent širenja prsline sa faktorom intenziteta napona, koji je veoma bitan parametar mehanike loma. Danas su nastale razne modifikacije Parizovog zakona, kako na primjeni kod metala, tako i kod cementnih materijala. Kod betona se manifestuje dodatni problem veličine uzorka (size effect) kojim se otežava opisivanje zamora. Za matematičko opisivanje Parizovog zakona je neophodno imati eksperimentalne podatke na osnovu kojih se definišu parametri u jednačini. Razvoj efektivnijeg matematičkog aparata tj. metode pomoću koje se opisuje propagacija prsline kod betona je neophodna. U ovom radu se za rješavanje ovoga problema primjenjuje reološko-dinamička analogija. Reološko-dinamička analogija (RDA) je matematičko-fizička analogija koja je predložena u eksplicitnoj formi od strane Milašinovića D. D., a kojom se opisuje čitav niz neelastičnih i vremenski zavisnih problema vezanih 1D prizmatične elemente. Pomoću RDA se opisuje kritično mehaničko ponašanje viskoelastoplastičnih materijala pod dejstvom ciklične varijacije napona. U ovome radu se primjenjuje RDA teorija na problemu propagacije prslina betona koja se opisuje kroz primjere savijanja u tri tačke nearmiranih betonskih greda sa inicijalnom prslinom. Ovo omogućava da se razvoj prsline pri eksperimentalnom ispitivanju postiže na planiranom mjestu tj. sredini grede. S druge strane ovo onemogućava primjenu poznatih izraza iz otpornosti materijala kod proračuna ugiba ili napona, pa je time potrebna primjena linearno elastične mehanike loma ili metode konačnih elemenata. U ovome radu se prikazuje novi pristup koji kombinuje RDA teoriju, linearno elastičnu mehaniku loma (linear elastic fracture mechanics-LEFM) i metodu konačnih elemenata kako kod dinamičkog (zamor) tako i kod statičkog testa greda. Prema RDA se može opisati viskoelastično histerezisno ponašanje betona i odrediti brzina oslobađanja energije koja u vezi sa energijom loma određuje broj ciklusa opterećenja. Primjenom metode konačnih elemenata ili preko analitičkih izraza iz LEFM se određuje računski napon u vrhu prsline kod greda koji je potreban kod određivanja brzine oslobađanja energije, pa se time lokalizuje karakter problema. Savojna krutost grede ulazi u izraz za brzinu oslobađanja energije, a njena promjena sa dužinom prsline se određuje pomoću metode konačnih elemenata. Relativna frekvencija koja predstavlja odnos sopstvene frekvencije i frekvencije opterećenja takođe ulazi u izraz za brzinu oslobađanja energije prema RDA i mijenja se sa povećanjem dužine prsline. Određivanje relativne frekvencije se sprovodi primjenom metode konačnih elemenata. Koeficijent tečenja se pojavljuje kao veoma bitan parametar za analizu, koji se određuje iz linearne veze za naponom prema RDA teoriji. Nova metoda proračuna se pored analize dugih prslina može koristiti i kod opisa kratkih prslina modifikovanjem ranga napona u vrhu prsline primjenom linearne veze između ranga napona i dužine prsline prema Kitagawa-Takahashi dijagramu. Kritična dužina prsline koja predstavlja granicu između kratkih i dugih prslina je neophodan ulazni parametar za analizu ove oblasti. 3 Svi rezultati se prikazuju u obliku krive dužina prsline-broj ciklusa opterećenja, a pokazana su veoma dobra slaganja sa eksperimentalnim rezultatima od strane različitih autora. Eksperimentalna mjerenja su sprovedena i za jednu gredu bez inicijalne prsline pri čemu je mjerenje dužine prsline sprovedeno fotogrametrijom. Pored zamora sproveden je i proračun statičkog testa prema RDA u obliku krivih sila-ugib ili sila-otvaranje prsline (crack mouth opening displacement-CMOD) jer su veoma bitni za analizu zamora. Za ove krive se sprovodi proračun uzlazne grane kontrolisanim povećavanjem sile tj. napona u vrhu prsline, koji je povezan preko koeficijenta tečenja sa ugibom ili CMOD. Kod proračuna silazne grane se sprovodi iterativni postupak relaksacije napona analogno postupku na radnom dijagramu betona koji je izveden od strane Milašinovića D. D. Kroz primjere u ovome radu se pokazala i moguća primjena RDA teorije u kombinaciji sa drugim teorijama kojima se opisuje propagacija kratkih prslina kod betona kao i zamor metala kroz zamjenu modula elastičnosti sa RDA modulom. Na taj način se kod teorija koje se baziraju na Parizovom zakonu uvodi koeficijent tečenja i relativna frekvencija u razmatranje. Upoređivanjem svih eksperimentalnih rezultata prema RDA se dobija veoma dobro slaganje, te se može zaključiti da se ovaj pristup može koristi kod proračuna dužine prsline u betonu. Upravo zbog jednostavnog matematičkog proračuna i primjene metode konačnih elemenata ovo otvara mogućnosti za dalja ispitivanja na elementima sa složenijom geometrijom kao i kod drugih betonskih mješavina.sr
dc.description.abstractConcrete structures can be exposed to cyclic loads, which can damage the material and sometimes it leads to failure. This phenomenon in which damages develop in the material at stress less than yielding stress is known as fatigue. The development of damage in the material during the cyclic loads can be seen through three stages: crack initiation phase, stable crack growth and unstable crack growth which leads to failure. The problem of fatigue was at first researched on metals, and the problem is mathematically described through the Paris law, which can accurately describe the phase of stable crack growth. Paris law connects the crack growth with the stress intensity factor, which is a very important parameter of fracture mechanics. To date, many modifications of paris law have been made for its application on metals and cement materials. By concrete, an additional problem of the size effect manifests itself, which makes it difficult to describe fatigue. For the mathematical description of paris law is necessary to have the experimental data, which are used for defining the parameters in equation. The development of a more effective mathematical apparatus, i.e. methods for the concrete crack propagation is necessary. Rheological-dynamic analogy is applied to describe this problem. Rheological-dynamic analogy (RDA) is a mathematical-physical analogy proposed in explicit form by Milašinović D. D. and it describes a inelastic and time-dependent problems related to 1D prismatic elements. The RDA describes the critical mechanical behavior of viscoelastic materials under the cyclic stress variation. The application of RDA is used in this paper to analyze the crack growth of plain concrete and it is described through examples of the monotonic and cyclic three-point bending tensile tests on notched beams. The application of the initial crack enables the crack growth in the experimental study to be achieved at the planned site, i.e. in the middle of the beam. On the other hand, this prevents the application of known expressions from the continuum mechanics for stress or deflection calculation and thus requires the application of linear elastic fracture mechanics (LEFM) or finite element methods (FEM). This paper presents a new approach that combines RDA theory, linear elastic fracture mechanics (LEFM) and finite element method for dynamic (fatigue) and static beam loads. According to the RDA, viscoelastic hysteretic behavior of concrete can be described and the rate of energy release can be determined in connection with the fracture energy, which determines the number of load cycles. By applying the finite element method or through analytical expressions from LEFM, the stress at the crack tip is determined. It is required for determining the rate of energy release and thus the character of problem is localized. The bending stiffness enters in the expression for the rate of energy release and its change with crack propagation can be determined using the finite element method. The relative frequency, which represents the ratio of eigenfrequency and load frequency, enters in the expression for the rate of energy release according to the RDA and it is also changed with the crack propagation. The determination of relative frequency is carried out using the finite element method. Creep coefficient is also shown as very important parameter for the analysis and it can be determined using linear law according RDA theory. In addition to describing the long crack growth, the new method of calculation can also be used by the short crack growth analysis. It is necessary to modify the stress range at the crack tip and it is used a linear law between the stress range and the crack length according to the Kitagawa and Takahashi diagram. Critical crack length presents the border between short and long cracks and it is necessary for short crack analysis according RDA. 5 All results are shown in the form of the crack length-number of load cycles and they have a very good match with experimental results by different authors. Experimental measurements were also conducted for one beam without an initial crack, where the measurement of the crack length was carried out by photogrammetry. In addition fatigue tests, the results of RDA and experimental curves force-deflection or force-crack mouth opening displacement (CMOD) have been compared. These tests are necessary for fatigue calculation according RDA. For these curves, the calculation of the ascending branch is carried out, controlled by increasing the force, i.e. by increasing the stress in the crack tip, which is connected with creep coefficient and deflection or CMOD. During the calculation of the descending branch, an iterative stress relaxation procedure is carried out, analogous to the procedure on the working diagram of concrete performed by Milašinović D. D. Through examples, the possible application of RDA theory has been shown in combination with other theories describing the propagation of short cracks by concrete as well as metal fatigue through the replacement of elasticity modulus with the RDA modulus. In this way, the paris law based theories introduce a creep coefficient and relative frequency into consideration. By comparing all experimental results with RDA is obtained very good match and it can be concluded that this approach can be used by the calculation of the crack growth in concrete. Precisely because of the simple mathematical calculation and application of the finite element method, this opens up possibilities for further testing on elements with more complex geometry and other concrete mixtures.en
dc.description.abstractConcrete structures can be exposed to cyclic loads, which can damage the material and sometimes it leads to failure. This phenomenon in which damage develop in the material at stress less than yielding stress is known as fatigue. The development of damage in the material during the cyclic loads can be seen through three stages: crack initiation phase, stable crack growth and unstable crack growth which leads to failure. The problem of fatigue was at first researched on metals, and the problem is mathematically described through the Paris law, which can accurately describe the phase of stable crack growth. Paris law connects the crack growth with the stress intensity factor, which is a very important parameter of fracture mechanics. To date, many modifications of Paris law have been made for its application on metals and cement materials. An additional problem of the size effect occurs in concrete members, which makes it difficult to describe fatigue. For the mathematical description of Paris law it is necessary to have the experimental data, which are used for defining the parameters in equation. The development of a more effective mathematical apparatus, i.e. methods for the concrete crack propagation is necessary. Rheological-dynamical analogy is applied to describe this problem. Rheological- dynamical analogy (RDA) is a mathematical-physical analogy proposed in explicit form by Milašinović D. D. and it describes inelastic and time-dependent problems related to 1D prismatic elements. The RDA describes the critical mechanical behavior of viscoelastic materials under the cyclic stress variation. The application of RDA is used in this paper to analyze the crack growth of plain concrete and it is described through examples of the monotonic and cyclic three-point bending tensile tests on notched beams. The application of the initial crack enables the crack growth in the experimental study to be achieved at the planned position, i.e. in the middle of the beam. On the other hand, this prevents the application of known expressions from the continuum mechanics for stress or deflection calculation and thus requires the application of linear elastic fracture mechanics (LEFM) or finite element methods (FEM). This paper presents a new approach that combines RDA theory, linear elastic fracture mechanics (LEFM) and finite element method for dynamic (fatigue) and static beam loads. According to the RDA, viscoelastic hysteretic behavior of concrete can be described and the rate of energy release can be determined in connection with the fracture energy, which determines the number of load cycles. By applying the finite element method or through analytical expressions from LEFM, the stress at the crack tip is determined. It is required for determining the rate of energy release and thus the character of problem is localized. The bending stiffness enters in the expression for the rate of energy release and its change with crack propagation can be determined using the finite element method. The relative frequency, which represents the ratio of eigenfrequency and load frequency, enters in the expression for the rate of energy release according to the RDA and it is also changed with the crack propagation. The determination of relative frequency is carried out using the finite element method. Creep coefficient is also shown as very important parameter for the analysis and it can be determined using linear law according to RDA theory. In addition to describing the long crack growth, the new method of calculation can also be used for the short crack growth analysis. It is necessary to modify the stress range at the crack tip and use a linear law between the stress range and the crack length according to the Kitagawa and Takahashi diagram. Critical crack length presents the border between short and long cracks and it is necessary for short crack analysis according to RDA. All results are shown in the form of the crack length-number of load cycles and they have a very good compliance with experimental results by different authors. Experimental measurements were also conducted for one beam without an initial crack, where the measurement of the crack length was carried out by photogrammetry. In addition to fatigue tests, the results of RDA and experimental curves of force-deflection or force-crack mouth opening displacement (CMOD) have been compared. These tests are necessary for fatigue calculation according to RDA. For these curves, the calculation of the ascending branch is carried out, controlled by increasing the force, i.e. by increasing the stress in the crack tip, which is connected with creep coefficient and deflection or CMOD. During the calculation of the descending branch, an iterative stress relaxation procedure is carried out, analogous to the procedure on the working diagram of concrete performed by Milašinović D. D. Through examples, the possible application of RDA theory has been shown in combination with other theories which describe the propagation of short cracks in concrete as well as metal fatigue through the replacement of elasticity modulus with the RDA modulus. In this way, the Paris law based theories introduce a creep coefficient and relative frequency into consideration. By comparing all experimental results with RDA very good compliance is obtained and it can be concluded that this approach can be used for the calculation of the crack growth in concrete. Precisely because of the simple mathematical calculation and application of the finite element method, this opens up possibilities for further testing on elements with more complex geometry and other concrete mixtures.  en
dc.languagesr (latin script)
dc.publisherУниверзитет у Новом Саду, Грађевински факултетsr
dc.rightsopenAccessen
dc.sourceУниверзитет у Новом Садуsr
dc.subjectPropagacija prsline, Zamor betona, Reološko dinamička analiza zamorasr
dc.subjectcrack propagation, fatigue of concrete, rheological-dynamical analysis of fatigueen
dc.titleReološko dinamička analiza zamora nearmiranih betonskih greda opterećenih na savijanjesr
dc.title.alternativeRheological-dynamical analysis of flexural fatigue on plain concrete beamsen
dc.typedoctoralThesissr
dc.rights.licenseAttribution-NonCommercial-ShareAlike
dcterms.abstractМилашиновић, Драган; Прокић, Aлександар; Бешевић, Мирослав; Голеш, Даница; Шумарац, Драгослав; Милашиновић, Драган; Панчић, Aлександар; Реолошко динамичка анализа замора неармираних бетонских греда оптерећених на савијање; Реолошко динамичка анализа замора неармираних бетонских греда оптерећених на савијање;
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/142536/Izvestaj_komisije_12160.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/142535/Disertacija_12160.pdf
dc.identifier.rcubhttps://hdl.handle.net/21.15107/rcub_nardus_18988


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