Modern methods of testing materials require the use of the latest technologies and combining measurement and calculation methods. It is important to find a quantitative way of describing, among other things, the failures so that it can help to design with high accuracy. This paper studies loading orientations on crack shape and fracture surface changes. The advantage of the entire fracture surface method is simplicity and applicability in studies on other materials, shapes and loadings. A higher values of fracture surface parameters (Sx, Vx) was observed in failure specimens with lower σ/τ (B/T) ratios. It has been observed that largest crack lengths with a small number of cycles occur for loading combinations different then B=T. As well as analyzed surface parameters Sx, Vx, are higher for larger number of cycles to crack initiation (Ni) values.
This article deals with determining of fatigue lifetime of aluminum alloy 6063-T66 during by multiaxial cyclic loading. The experiments deal with the testing of specimens for identification of the strain-life behavior of material, the modeling of combined loading and determining the number of cycles to fracture in the region of low-cycle fatigue. Fatigue tests under constant amplitude loading were performed in a standard electromechanical machine with a suitable gripping system. Based on the experimental results the fatigue design curves are compared to the fatigue data from the base material and the welded material and also multiaxial fatigue models, which are able to predict fatigue life at different loads.
The aim of this paper is to propose an algorithm for fatigue life determination with the use of widely-known criteria for the fatigue life considering proper determination of material characteristics, which are a function of the number of cycles to failure. The application of the modified algorithm has been presented within the criteria of Findley, Matake, Papadopoulos and Dang Van, and the results of calculations have been compared with test results for steels S355J2G3 and Ck45. For both materials analysed, the application of the modified algorithm in the fatigue criteria makes it possible to obtain much more precise results of the calculations for all types of the loading analysed.
Although in the scientific literature there are studies regarding optimization of structural members subject to static loads or even cyclic in-phase loads, the optimization of structures subject to cyclic, out-of-phase multiaxial loads is still an unexplored issue. In this paper, we present an approach to the problem of size optimization of rectangular cross-section members subject to multiaxial in-phase and out-of-phase cyclic loads. The objective of the optimization is to minimize the cross sectional area of such elements while retaining their fatigue endurance. Under the proposed methodology, optimum values of the area are achieved for six loading cases and for three values of the height to width ratio of the cross section, and these values are reported. The novelty of the approach lies in the inclusion of two multiaxial high cycle fatigue criteria, i.e., Dang Van and Vu-Halm-Nadot ones, as constraints for size optimization problems, fully integrated within an in-house developed tool, capable of handling non-proportional stresses. A plot of the feasible solution space for this optimization problem is also obtained.
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Many researches have shown that fatigue behaviour of a number of materials is significantly different in non-proportional loading conditions when compared to proportional ones. These differences concern stress–strain characteristics, fracture, the phenomena taking place in the material, and finally fatigue life. The aim of this study is to provide a survey on basic experimental results and methods of taking into account a material's sensitivity to non-proportionality of loading in multiaxial fatigue life estimation models for metals.
W pracy zaproponowano model szacowania trwałości zmęczeniowej wzmożonych stanach naprężeń, oparty na koncepcji płaszczyzny krytycznej, uwzględniający wpływ stycznych naprężeń średnich. Wyniki trwałości zmęczeniowej liczonej według zaproponowanego modelu porównano z wynikami badań zmęczeniowych próbek ze stopów aluminium 2017A-T4 oraz 6082-T6 oraz stali S355 w warunkach niesymetrycznego stałoamplitudowego zginania, skręcania oraz proporcjonalnych kombinacji zginania ze skręcaniem.
EN
This paper proposes a model for estimating fatigue life at multiaxial stress states, based on a critical pane concept, taking into consideration the effect of mean shear stress. The fatigue life test results calculated based on the proposed model were compared to results of fatigue tests of 2017A-T4 and 6082-T6 aluminium alloys and steel S355 samples in the conditions of constant-amplitude bending, torsion and proportional combinations of bending and torsion.
This paper proposes a model for estimating fatigue life under multiaxial stress states, based on critical plane concepts, taking into account the effect of mean shear stress. The fatigue life test results calculated on the basis of the proposed model are compared to the experimental ones related to 2017A-T4 and 6082-T6 aluminium alloy, S355J0 alloy steel under constant-amplitude bending, torsion and proportional combinations of bending and torsion; Ti-6Al-4V alloy under tension-compression, torsion and combination tension-compression – torsion. For the results obtained, statistical analysis is performed by comparing the calculation results proposed by Findley and Dang Van criteria with the experimental data.
W pracy zaproponowano model szacowania trwałości zmęczeniowej w złożonych stanach naprężeń. Wyniki trwałości zmęczeniowej liczonej według zaproponowanego modelu porównano z wynikami badań zmęczeniowych próbek ze stopu aluminium 2017A-T4 oraz stali stopowej 5355JO w warunkach stałoamplitudowych proporcjonalnych kombinacji zginania ze skręcaniem z uwzględnieniem wartości średniej naprężeń. Wyniki badań eksperymentalnych porównano z wynikami obliczeń z wykorzystaniem modeli Goodmana, Gerbera, Morrowa, Findleya, Dang Vana, McDiarmida oraz Papadopoulosa. Dla otrzymanych wyników obliczeń przeprowadzono analizę statystyczną polegającą na obliczeniu pasma rozrzutu wyników porównania danych eksperymentalnych z obliczeniowymi.
EN
The paper proposes a model for estimating the fatigue life of the multiaxial stress states. The results of the fatigue life calculated according to the proposed model have been compared to the results of fatigue tests of specimens made of 2017(A)-T4 aluminum alloy and 8355JO alloy steel in conditions of constant amplitude proportionate combinations Of bending and torsion, while taking into account the mean stress. The experimental results have been compared to the results of calculations using models by Goodman, Gerber, Morrow, Findley, Dang Van, McDiarmid and Papadopoulos. Statistical analysis have been carried out for the results of calculations, involving the calculation of a scatter band for results of the comparison of experimental data with calculations.
The paper presents the comparison of experimental and calculated fatigue lives for EN AW-6082 T6 aluminium alloy. Hour-glass shaped specimens have been subjected to constant and variable amplitude uniaxial and multiaxial loadings, i.e. plane bending, torsion and their proportional combinations with zero mean values. Three multiaxial fatigue criteria based on the critical plane approach have been verified being the linear combination of shear and normal stresses on the critical plane. For the variable-amplitude loading, the rainflow cycle counting method and Palmgren-Miner hypothesis have been applied. The best fatigue criteria are pointed in the final conclusions.
W pracy przedstawiono propozycję nowego kryterium zmęczeniowego dla obciążeń nieproporcjonalnych, uwzględniającego wpływ wartości kąta przesunięcia fazowego δ i stosunku amplitud naprężenia stycznego i normalnego λ na trwałość zmęczeniową.
EN
In hereby work a proposal of new fatigue criterion for non-proportional loads, which includes influence of value of phase shift angle δ and shear to normal stress ratio λ, onto fatigue life.
Based on a literature review, the author provides a historical outline of the fatigue analysis and describes the current trends aiming at comprehension of the fatigue life of engineering structures under service loading. Next, an algorithm for multiaxial fatigue life prediction is identified, describing steps of calculation. Classification criteria of fatigue failure and components of the stress state in multiaxial loading conditions are also presented, recognising the importance of the so-called Standarised Load Histories (SLH) used in the comparative analysis of fatigue life of finished products.
Przy formułowaniu modeli służących do szacowania trwałości zmęczeniowej lub granicy zmęczenia dla materiałów poddanych obciążeniom wieloosiowym bardzo istotne jest wyznaczanie zakresów, amplitud, wartości średnich itp. wielkości fizycznych związanych z obciążeniem. Jedną z tych wielkości jest drugi niezmiennik dewiatora stanu naprężenia. Praca dotyczy analizy wpływu kąta przesunięcia fazowego oraz stosunku amplitud okresowo zmiennych składowych złożonego obciążenia zmęczeniowego na cechy ścieżek obciążenia w przestrzeni dewiatorowej, na podstawie których wyznacza się zakres zmienności drugiego niezmiennika dewiatora.
EN
During the formulation of models for estimation fatigue life, strength and limit of materials subjected to multiaxial loads, determination of ranges, amplitudes, mean values etc. of quantities related to load is of very high importance. One of these quantities is second invariant of deviatoric stress. Hereby work concerns analysis of influence of phase shift angle and periodic components of fatigue load ratio on features of load paths in deviatoric stress space, on basis of which, range of second invariant of deviatoric stress is being determined.
The authors present results of a fatigue test for specimens made of the aluminium Allom 2017A-T4 and alloy steels S355J2WP and S355J2G3 subjected to constant-amplitude proportional combined bending with torsion including mean stress values and for the S355J2WP alloy steel under uniaxial constant-amplitude and random loading with both zero and non zero mean stress values. The test results were compared with the results of calculations according to the models proposed by Goodman, Gerber and Morrow as well as the stressstrain parameter. In the case of calculations based on the stresses, the multiaxial stress state was reduced to a uniaxial one using the Huber-Mises relationship. As for the method based on strain energy density, the multiaxial stress state was reduced to the uniaxial one with use of the stress-strain parameter. The plane in which the stress-strain parameter of shear loadings reaches its maximum value is assumed to be the critical plane.
This paper deals with fatigue behavior of pure copper in different load conditions, including complex proportional and non-proportional loads. The material has been chosen due to its potential high sensitivity for nonproportional loads. The aim of this paper is search for relationship between the fatigue life of pure copper and shear stress vector paths in non-proportional load conditions.
The paper presents a review and verification of integral fatigue criteria. The review signals the key assumptions and criteria structure elements. The verification has been developed drawing on the experimental data reported in literature containing fatigue life for uniaxial, combined proportional and non-proportional loads. The verification involves a comparison of computational fatigue life with the experimental one. To determine the quality of the results generated, statistical parameters were used. As a result of the analysis the best and the worst criteria were pointed to.
PL
Celem niniejszej pracy jest ocena możliwości szacowania trwałości zmęczeniowej za pomocą całkowych kryteriów zmęczeniowych. Podejście całkowe bazuje na założeniu, że dla prawidłowej oceny zachowań zmęczeniowych konieczne jest zsumowanie (scałkowanie) wartości parametru zniszczenia na wszystkich płaszczyznach przechodzących przez rozpatrywany punkt materiału. Analizę przeprowadzono dla trzech najczęściej spotykanych kryteriów całkowych: kryterium Zennera i dwóch kryteriów Papadopoulosa. Uzyskane wyniki porównano z kryterium zmęczeniowym McDiarmida, bazującym na konkurencyjnym w stosunku do całkowego podejściu płaszczyzny krytycznej, oraz powszechnie stosowanym w wielu obszarach wytrzymałości materiałów kryterium Hubera-Misesa-Hencky’ego.
The purpose of this paper is to provide a simple approach for indication of those places of machine parts, where the fatigue crack initiation begins. This method uses FEM and the cyclic stress-strain curve for calculating the stress state on specimens. The multiaxial fatigue failure criterion based on the critical plane approach was used for reduction of the random spatial stress state into the equivalent uniaxial one. The critical plane position was established with the use of the variance method, and fatigue life was determined with assumption of linear damage accumulation. Experimental verification of the proposed method was performed with the use of results of fatigue tests for St52.3 structural steel subjected to biaxial random tension-compression. Cruciform specimens with four holes were tested. During the tests, the place and time of crack initiation were observed. It was shown, that the proposed method for determination of the places of fatigue crack initiation gave results well correlated with the data obtained from experiments. The proposed method could be applied by engineers in order to identify the places and time of fatigue cracks initiation.
PL
Celem niniejszej pracy jest przedstawienie prostego podejścia w wyznaczaniu tych miejsc w elementach maszyn, gdzie nastąpi inicjacja pęknięć. Niniejsza metoda wykorzystuje metodę elementów skończonych (MES) i krzywą cyklicznego odkształcenia w celu obliczenia stanu naprężenia w próbkach. Wieloosiowe kryterium zmęczenia oparte na założeniach płaszczyzny krytycznej zostało zastosowane w celu redukcji przestrzennego losowego stanu naprężenia na ekwiwalentny jednoosiowy. Położenie płaszczyzny krytycznej zostało zdefiniowane przy pomocy metody wariancji, natomiast trwałość zmęczeniowa została wyznaczona zgodnie z założeniami liniowej hipotezy sumowania uszkodzeń. Weryfikacja eksperymentalna zaproponowanej metody została przeprowadzona na podstawie wyników badań zmęczeniowych stali konstrukcyjnej St52.3 poddanej dwuosiowym losowemu obciążeniu rozciąganiem-ściskaniem. W niniejszych badaniach zostały zastosowane próbki krzyżowe z czterema otworami. W trakcie badań były rejestrowane miejsca oraz czas inicjacji pęknięcia. Wykazano, że proponowana metoda wyznaczania miejsc inicjacji pęknięć dała wyniki pokrywające się z otrzymanymi w trakcie eksperymentu. Proponowana metoda może zostać zastosowana przez inżynierów w celu identyfikacji miejsc oraz czasu, w którym nastąpi inicjacja pęknięć zmęczeniowych.
This paper presents preliminary results of fatigue tests of selected construction materials, which have been exposed to the simultaneous operation of the bending and torsional loads at different mix of these loads. This kind of load generally applies to much responsible construction, especially of machinery for transport. For example, rail transport is one of the most popular measures, which uses different types of locomotives. However, it is no matter what sort of the type of railway vehicle it is, because in each there we can notice a multi-axis load driving axle wheel assemblies. During the technical inspection of these items, ultrasonic flaw detectors are used to detect damage in the material that arose during the exploitation, but are not visible during the external inspection. For this reason, there are many problems, that arise during the diagnostic process using ultrasonic flaw detectors, because it is not always possible to accurately detect the resulting or arising defect in the material axes, especially in some of the built-axes, which can be studied only from the front (on both sides of the mounting of bearings). Taking into account the safety and technical problems in rail transport, it is important to carry out fatigue tests of low- and high-cycles on samples subjected to multiaxial stress state. Initially, there were taken into account the lightweight aluminum (AlMg2Mn0.47Fe0.5) that have been repeatedly multiaxial charged at different percentage of bending and twisting. The results will be referenced to the occurrence of the bending and twisting, as well as to the results obtained with the simultaneous influence of corrosive conditions due to the attempt to make the best possible mapping of the prevailing conditions in which different structural elements must actually work. The load on the low cycle fatigue and high cycle fatigue were chosen after corrosion- stress testing on the same aluminum alloy. In addition, cases of multiaxial fatigue are not as described and explained in detail as the cases of uniaxial fatigue. In spite of this fact, it is necessary to create detailed criterions for multiaxial with low- and high-cycles load.
This article deals with determining of fatigue lifetime of structural materials during by multiaxial cyclic loading. The theoretical part deals with the fatigue and with the criterions for evaluation of multiaxial fatigue lifetime. The experimental part deals with modeling of combined bending - torsion loading and determining the number of cycles to fracture in region low-cycle and high-cycle fatigue and also during of loading with the sinusoidal wave form under in phase Φ = 0° and out phase Φ = 90°.
We can distinguish a group of multiaxial fatigue criteria based on the approach to the critical plane position. It has been proved that these criteria perform their role in the case of materials which could be classified as intermediate between brittle and elastic-plastic materials. The author analyzed the test results obtained by Kueppers and Sonsino for tube-flange aluminium welded joints under combined cyclic proportional and non-proportional bending with torsion.
The paper presents the procedure of estimation of fatigue life in the high- cycle fatigue regime under a multiaxial random loading using the spectral method. The procedure consists of application of the power spectral density function of the equivalent stress in the fatigue life assessment together with the known spectral method developed for the uniaxial stress state. The model proposed by Miles and Dirlik was presented as an example. Two groups of multiaxial fatigue failure criteria have been distinguished: the criteria based on the critical plane approach and the criteria using invariants of the stress state. Two sets of experimental data were used in order to compare the calculated and experimental fatigue lives. It has been shown that under the multiaxial random loading the results of fatigue life calculated according to the considered method are well correlated with the results of experiments if the multiaxial fatigue failure criterion is properly selected for mechanical parameters of the tested material.
PL
Wpracy przedstawiono metodologię wyznaczania trwałości zmęczeniowej w zakresie dużej liczby cykli przy obciążeniu losowym z wykorzystaniem metody spektralnej. Metodologia ta wykorzystuje funkcję gęstości widmowej mocy naprężenia ekwiwalentnego przy wyznaczaniu trwałości zmęczeniowej wraz ze znanymi jednoosiowymi modelami spektralnymi. Jako przykład przedstawiono modele proponowane przez Milesa i Dirlika. Wyróżniono dwie grupy kryteriów wieloosiowego zmęczenia: kryteria opierające się na pojęciu płaszczyzny krytycznej i kryteria wykorzystujące niezmienniki stanu naprężenia. W celu porównania obliczeniowej i eksperymentalnej trwałości zmęczeniowej wykorzystano dwa zestawy danych otrzymanych przy kombinacji zginania ze skręcaniem. Wykazano, że przy wieloosiowym obciążeniu losowym trwałości obliczeniowe korelują dobrze z otrzymanymi podczas eksperymentu, jeżeli zostanie zastosowane odpowiednie do właściwości mechanicznych materiału kryterium wieloosiowego zniszczenia zmęczeniowego.
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