Fatigue properties of notched specimens made of FeP04 steel

Fatigue properties of the specimens with different notches made of FeP04 steel are presented. The specimens ware characterized by double symmetric lateral notches with a notch root radius ranging from ρ = 0.2 to 10 mm. The MTS 809 servo-hydraulic device was used for tests. All fatigue tests were performed under force control, by imposing a constant value of the nominal load ratio (R = 0) and a load amplitude Pa = 6 kN for the notch root ρ = 0.2 mm and 7 kN for the notch root ρ = 1.25; 2.5 and 10 mm. The test frequency varied from 13 and 15 Hz. During the tests under constant load fatigue weakening of the material and an increase in strain were observed.Подані втомні властивості зразків з подвійними симетричними боковими вирізами (радіуси концентратора від ρ = 0,2 до 10 mm) з сталі FeP04. Для випробувань використовували сервогідравлічний пристрій МТС 809. Втомні випроби виконані за постійного номінального коефіцієнта навантаження (R = 0), амплітуди навантаження 6 kN для радіуса концентратора ρ = 0,2 mm і 7 kN для радіусів ρ = 1,25; 2,5 і 10 mm. Частота навантаження 13...15 Hz. Під час випробувань з постійним втомним навантаженням спостерігали знеміцнювання матеріалу зі збільшенням деформованості.Представлены усталостные свойства образцов с двойными симметричными боковыми вырезами (радиусы концентратора от ρ = 0,2 до 10 mm) из стали FeP04. Для испытаний использовали сервогидравлическое устройство МТС 809. Усталостные испытания выполнены при постоянном значении номинального коэффициента нагружения (R = 0), амплитуде нагружения 6 kN для радиуса концентратора ρ = 0,2 mm и 7 kN для радиусов ρ = 1,25; 2,5 и 10 mm. Частота нагружения изменялась в пределах от 13 до 15 Hz. Во время испытаний с постоянным усталостным нагружением наблюдалось разупрочнение материала и увеличения деформируемости

Random and free observables saturate the Tsirelson bound for CHSH inequality

Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation

Comparison of the calculated and experimental fatigue lives under non-proportional bending with torsion of 10hnap steel

The paper contains the results of fatigue tests of 10HNAP steel under nonproportional bending with torsion. The circular smooth specimens were tested. The tests were carried out at the fatigue test stands MZGS-200PL and MZGS-200L. The best results of experimental and calculation lives consistence for the considered materials was obtained using the criterion of maximum shear stresses in the critical plane and the Palmgren-Miner hypothesis of damage accumulation

Descriptions of reversed yielding in bending

Existence of Bauschinger effect in bending-unbending of copper beams has been shown from experiment. In modelling of the Bauschinger effect, it is shown that a significant second plastic penetration can occur with the release of the moment required for an elasticplastic bending of a beam. The theory is given for both linear and parabolic hardening material models. The elastic and plastic strains are developed from each hardening model to express the beam curvature of the unstressed neutral axis. Conditions are expressed, using the normalized stress—strain response of a rectangular beam section, for which the release is purely elastic and elastic—plastic. Under the latter the depth to which a second zone of plasticity penetrates is given. Two stress distributions: one for applying the moment and the other for its release, are sufficient to derive the residual stress. Residuals found for parabolic hardening are believed to be more realistic than those from simpler linear or perfectly plastic models, particularly, where a second penetration is evident

Asymptotic behaviour of a structured population model on a space of measures

In this paper we consider a physiologically structured population model with distributed states at birth, formulated on the space of non-negative Radon measures. Using a characterisation of the pre-dual space of bounded Lipschitz functions, we show how to apply the theory of strongly continuous positive semigroups to such a model. In particular, we establish the exponential convergence of solutions to a one-dimensional global attractor

Crack growth of explosive welding zirconium-steel bimetal subjected to cyclic bending

The paper presents the fatigue test results including the cracks growth in the composite zirconium-steel subjected to oscillatory bending. Specimens of square cross-section without melted layer and with a melted layer were tested. In the specimens the net ratio of thickness of steel to zirconium layers was h1 : h2 = 2.5 : 1. It was observed that a higher fraction of the intermetallic inclusions near the interface increase the fatigue life. Two different interaction mechanisms between a crack and interface were observed

Fatigue crack growth in AlCu4Mg1 under nonproportional bending with torsion loading

The paper presents the experimental results of fatigue crack growth on AlCu4Mg1 aluminium alloy under proportional and non-proportional bending with torsion obtained at Opole University of Technology. Specimens with square sections and stress concentrations in the form of external one-sided sharp notches were used. The tests were performed in the high cycle fatigue regime for the stress ratio R = –1 and phase shift between bending and torsion loading equal to φ = 0; 45° and 90°. Three paths of loading were used: line, ellipse and circle. The fatigue crack growth was cyclically measured with use of the optical microscope (magnification of 25 times), strain gauges and computer allow to register signals of loading. In the tested specimens, it was possible to observe growth of cracks conforming with mixed mode I + III. The crack growths were non-uniform at both sides of the specimen surface, however the difference between crack lengths was rather small. In the biaxial tests, influence of bending was six times greater because of the notches in the bending plane. The test results were described by the stress intensity factor range, ∆K.Подано експериментальні результати втомного росту тріщин в алюмінієвому сплаві AlCu4Mg1 в умовах пропорційного і непропорційного згину з розтягом. Досліджено прямокутні зразки з концентратором на згин. Випроби виконано в умовах високочастотної втоми при R = –1 і торсійного навантаження φ = 0; 45° і 90°. Використано лінійне, еліптичне і колове навантаження. Втомний ріст тріщини виміряно за допомогою мікроскопа з 25-кратним збільшенням. Реалізовано I + III моди навантаження. Ріст тріщин на двох бокових поверхнях зразків неоднаковий, проте різниця в довжинах тріщини від концентратора несуттєва. Побудовані діаграми втомного росту тріщини для складного наватаження і показано, що вплив навантаження згином на розмах ∆K у п’ять разів сильніший порівняно з навантаженням закрутом.Представлены экспериментальные результаты усталостного роста трещин в алюминиевом сплаве AlCu4Mg1 в условиях пропорционального и непропорционального изгиба с растяжением. Использованы прямоугольные образцы с концентратором на изгиб. Исследовали в условиях высокочастотной усталости при R = –1 и торсионного нагружения φ=0; 45° и 90°. Использовали линейное, эллиптическое и круговое нагружение. Усталостный рост трещины измеряли с помощью микроскопа с 25-кратным увеличением. Реализованы I + III моды нагружения. Рост трещины на двух боковых поверхностях образцов неодинаков, но разница в длине трещины от концентратора несущественна. Построены диаграммы усталостного роста трещины для сложного нагружения и показано, что влияние нагружения изгибом на растяжение ∆K в пять раз сильнее, чем нагружения кручением

Fatigue tests of materials with the controlled energy parameter amplitude

Abstract The paper presents a procedure of the determination of the fatigue energy characteristic diagram by using a controlled strain energy parameter which can be an alternative to the well-known stress and strain fatigue curves description of structural materials. The work contains the results of fatigue tests carried out in accordance with the procedure shown in the paper. Obtained test results were presented on diagrams and critically discussed

Models of initiation fatigue crack paths proposed by Macha

Professor E. Macha devoted his academic life to solving the problems connected with randommultiaxial fatigue in components of machines and structures. In his studies he formulated stress, strain andenergy criteria related to critical plane concept. He also proposed several methods to determine critical planeposition. In particular, he formulated and verified weight functions applied in order to determine critical planeposition. The variance method constituted another significant contribution to the development of methods fordetermining critical plane position. Apart from these criteria, Macha was exploring energy approach in fatigue ofmaterials and the development of fatigue cracks.He has also observed that strain characteristics multiplied by stress amplitude determined at specimen half-lifeare applied to estimate fatigue life using energy criteria. However, for cyclically instable materials, stressamplitude value may differ a lot; therefore he proposed the method to determine energy fatigue characteristicsdirectly from experimental research