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1

Size‑dependent constitutive model incorporating grain refinement and martensitic transformation

Liu Shengqiang, Li Wei, Shen Jinxia, Yang Xiaoming, Wang Baoyu, Liu Jinping

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e38, 2023

EN

The deformation behaviour of materials at the micro-scale level is different from that at the macro-scale level due to the effect of grain size (GS). The mechanism of the influence on martensitic transformation by GS is still unclear, and there are relatively few studies on the relationship between grain refinement and martensitic transformation, most of which focus on the relationship between the initial GS of the material and martensitic transformation. Therefore, in this study, the interaction between grain refinement and martensitic transformation was investigated using a dislocation density-based multiscale constitutive model that incorporated dislocation sliding, strain-induced martensitic transformation (SIMT) related to grain size, and grain refinement. The proposed model evaluated the GS-dependent deformation behaviour of 316L stainless steel (SS). Subsequently, a genetic algorithm was used to determine the parameters of the established model, and the calculated results were compared with that of the experimental data to verify the accuracy of the model. The developed multiscale constitutive model was implemented in Abaqus user subroutine to further investigate the deformation mechanism and validate its accuracy. The results demonstrated that the GS had a significant effect on the SIMT, with the volume fraction of martensite increasing with a rise in the initial austenite GS. In addition, grain refinement affected SIMT and the growth rate of martensite content decreased with the grain refinement caused by deformation. The formation of martensite led to grain refinement, with the refined grains producing negative feedback on the SIMT, thus inhibiting the occurrence of martensitic transformation. This study revealed the microscopic deformation mechanism of 316L SS and provided a constitutive model for micro-forming.

2

Measurement and analysis of pocket milling features in abrasive water jet machining of Ti-6Al-4V alloy

Natarajan Yuvaraj, Raj K. L. Naresh, Tandon Puneet

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e42, 2023

EN

The present work deals with the size effect of abrasive water jet milling parameters on the square pockets of Ti-6Al-4V alloy. In this study, the abrasive mesh size, water jet pressure and traverse rate were chosen as milling variables and their effect on pocket features such as depth of cut, undercut, material removal rate, and surface roughness were examined. This study also characterizes the milled pocket surfaces under different milling conditions. Most of the measurements and surface characterizations were done using the Dino-Lite Digital Microscope. For both #80 and #100 abrasives, the AWJ-milled pockets were formed with variations in depth milled and rugged surface by increasing the water jet pressure from 175 to 200 MPa under all the selected traverse rate conditions. Also, the variations of depth of cut in successive trajectories found to have a speed bump effect. At these settings, distribution of energy to the work material was more due to deceleration of jet in the boundary close by and changes made in the feed directions in raster path from 0° to 90° at a step-over distance of 0.2 mm. This yielded undercuts in the milled pocket corners. However, there was a significant reduction in the undercut with a water jet pressure of 125 MPa and a traverse rate of 3500 mm/min were employed. Besides, the abrasive mesh size #100 had a better surface topography, and also strong jet footprints were observed with mesh size of #80. Based on the experiments results, the size effect of different milling parameters was seen having influence on the pocket geometry and surface features.

3

Influence of shear depth on seismic performance of shear wall reinforced with BFRP bars: mesoscale modelings

Jin Liu, Miao Liyue, Du Xiuli

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e4, 2023

EN

The seismic performances of 28 geometrically similar concrete shear walls reinforced with basalt fiber-reinforced polymer (BFRP) bars were simulated using a mesoscale modeling approach. In the modeling, concrete heterogeneities were explicitly described, and the interaction between BFRP bars and surrounding concretes was also considered. The influences of shear depth, shear span ratio and vertical reinforcement ratio on the failure of shear walls were investigated. The simulation results indicated that with the increase of shear depth, the failure modes were basically the similar, while the nominal shear strength decreased significantly, namely, the presence of size effect was demonstrated. The shear wall would exhibit different failure modes as the shear span ratio varies. Moreover, it was found that the vertical BFRP bar presented an ignorable influence on the failure mode, while the increase of vertical reinforcement ratio would obviously improve the shear strength of BFRP-RC shear wall. Finally, the present simulated shear strengths were compared with some available size effect laws and some codes.

4

Efekt skali w ocenie odporności ogniowej aluminiowo-szklanych ścian działowych. Cz. 1

Sędłak Bartłomiej

Świat Szkła

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2022

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R. 27, nr 3

20--25

5

Efekt skali w ocenie odporności ogniowej aluminiowo-szklanych ścian działowych. Cz. 2

Sędłak Bartłomiej

Świat Szkła

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2022

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R. 27, nr 5

24--29

6

Efekt skali w ocenie odporności ogniowej aluminiowo-szklanych ścian działowych. Cz. 3

Sędłak Bartłomiej

Świat Szkła

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2022

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R. 27, nr 6

30--33

7

Diagrams of statistical strength criterion for reinforced composite materials

Kvit Roman, Salo Tetyana

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 2

43--51

EN

The model of a plate brittle material reinforced with randomly sized and placed rigid rectilinear inclusions that do not interact with each other is considered. The geometric parameters of inclusions (length and orientation) are statistically independent random variables, with certain given laws of probability distribution. Diagrams of statistical strength criterion for such plates are constructed under conditions of comprehensive tension-compression. The diagrams are constructed for plates using a material of a different structural inhomogeneity and Poisson’s ratio of an elastic homogeneous matrix. The statistical nature of the scale effect is studied, the intensity of which depends on the type of stress state.

8

Scale effect of cement mortar specimens subjected to high temperatures using uniaxial compressive and splitting tensile tests

Xiong L. X., Zhang X. J., Xu Z. Y., Geng D. X.

Archives of Civil Engineering

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2020

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Vol. 66, nr 3

139--155

EN

In this study, cubic and cylindrical cement mortar specimens were first subjected to high temperatures, then the cubic and cylindrical specimens were taken out and conducted with uniaxial compressive test and splitting tensile test, respectively. The effect of the length to side ratio on the uniaxial compressive properties and the effect of thickness-to-diameter ratio on the splitting tensile properties of cement mortar specimens after high temperature were studied. Test results show that: (1) With temperature increasing from 25 ºC (room temperature) to 400 ºC, the compressive strength and elastic modulus of cubic specimens with three kinds of side lengths decrease; the decreasing rates of compressive strength and elastic modulus of cubic specimen with side length of 70.7 mm is higher than those of cubic specimens with side length of 100 mm and 150 mm, and the strain at the peak stress of cubic specimens with three kinds of side lengths increase. (2) After the same temperature, the tensile strength of cylindrical specimen decreases with the thickness-to-diameter ratio increasing from 0.5 to 1.0. The decreasing rate of tensile strength of cylindrical specimen with thickness-to-diameter ratio is highest when the temperature is 25 ºC (room temperature), followed by that after the temperature of 200 ºC, and that after the temperature of 400 ºC is the lowest.

9

On the combined asymptotic-tolerance modelling of dynamic problems for thin biperiodic cylindrical shells

Tomczyk B., Litawska A.

Vibrations in Physical Systems

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2018

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Vol. 29

art. no. 2018020

EN

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss a new averaged general asymptotic-tolerance model for the analysis of selected dynamic problems for the shells under consideration. This model is derived by applying the combined modelling which includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. The differences between the general combined model proposed here and the corresponding known standard combined model derived by means of the more restrictive concept of slowly-varying functions are discussed.

10

Badanie efektu skali poprzez modyfikację odcinka pomiarowego próbki przy zginaniu obrotowym oraz ocena wpływu chropowatości

Niesłony A., Agrest D.

Modelowanie Inżynierskie

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2018

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T. 36, nr 67

44--48

PL

W artykule przedstawiono zarys historyczny badań nad zjawiskiem efektu skali. Opisane zostały warunki przeprowadzenia prób zmęczeniowych oraz uzyskane wyniki. Otrzymano zauważalny efekt skali podczas próby zginania obrotowego. W pracy przedstawiono także spostrzeżenia dotyczące wpływu wybranych czynników na wyniki badań. Zauważono, że jednym z istotnych czynników jest jakość powierzchni próbek. Przedstawiono wykresy wskazujące na zależność chropowatości powierzchni próbek na ich wytrzymałość podczas próby zginania obrotowego.

EN

The article presents a historical outline of research on the phenomenon of scale effect. The conditions for conducting fatigue tests and the results obtained have been described. A noticeable scale effect was obtained during a rotational bending test. The paper also presents observations regarding the influence of selected factors on test results. It was noted that one of the important factors is the surface quality of the specimen. The graphs show the dependence of the surface roughness of the specimen on their strength during a rotational bending test.

11

Micro-vibrations and wave propagation in biperiodic cylindrical shells

Tomczyk B., Litawska A.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 3

789--807

EN

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to study a certain long wave propagation problem related to micro-fluctuations of displacement field caused by a periodic structure of the shells. This micro-dynamic problem will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling applied here includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Both these procedures are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. It will be shown that the micro-periodic heterogeneity of the shells leads to exponential micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

12

Influence of scale effect and time on strength properties of polymer composite made by vacuum method

Chatys R., Piernik K.

Composites Theory and Practice

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2018

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R. 18, nr 2

103--109

EN

This paper discusses and attempts to analyze the impact of the method of forming fibrous composite materials on the quality of the laminates. The model assumes that the composite consists of components having individual physico-mechanical properties with a symmetrical structure [0/90/0/90]s. This article uses experimental data of a contact-formed composite (Composite I) and a vacuum bag composite (Composite II) with a polyester matrix (Firestop 8175-w-1) reinforced with E glass matte fabric. Before the samples were cut, the parameters and technological criteria of the formed composite were determined such as the amount of resin and soaking time of the composite reinforcement with the polymer resin. The influence of matrix plastification and a more packed structure in the produced composites on the scale effect (for samples with larger and smaller measuring bases), the dispersion and mean value of strength from the time of aging were determined.

PL

Omówiono i podjęto próbę analizy wpływu metody formowania włóknistych materiałów kompozytowych na jakość laminatów. W modelu założono, ze kompozyt składa się z komponentów, mających indywidualne fizykomechaniczne właściwości o symetrycznej strukturze [0/90/0/90]s. W tym artykule wykorzystano eksperymentalne dane kompozytu formowanego metodą kontaktową (kompozyt I) i worka próżniowego (kompozyt II) o osnowie poliestrowej (Firestop 8175-w-1) wzmocnionej mato-tkaniną szklaną typu E. Przed wycięciem próbek określono parametry i kryteria technologiczne formowanego kompozytu: jak ilość i czas nasączania wzmocnienia kompozytu żywicą polimerową. Określono wpływ plastyfikacji osnowy i bardziej upakowanej struktury w wytworzonych kompozytach na efekt skali (dla próbek z większą i mniejszą bazą pomiarową), rozrzut i wartość średniej wytrzymałości od czasu starzenia.

13

Efekt skali w próbach zginania obrotowego

Agrest D.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2017

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z. 108

7--10

EN

At work describes the size effect. Tests were carried out for specimens of varying length of the load segment. That is not standard approach because the size effect mainly is observed when the size of the cross section is modifying. The study was carried out on a series of cylindrical specimens. Received results were compared with the theoretical assumptions. It also discusses factors affecting the test results and announced further work in the area of size effect.

14

Size effect in high-cycle fatigue

Tomaszewski T., Sempruch J.

Journal of Machine Construction and Maintenance - Problemy Eksploatacji

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2017

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no. 1

29--35

EN

The paper describes size effect in reference to available empirical and analytical models. The size effect of an object on strength properties was classified from 3 perspectives: statistical, geometrical, and technological. The following part of the paper identifies a verification method that has been supplemented by proprietary experimental test results obtained for a minispecimen made of aluminium alloy EN AW-6063.

PL

Artykuł przedstawia efekt skali w odniesieniu do dostępnych modeli empirycznych i analitycznych. Wpływ efektu skali na wytrzymałość zmęczeniową obiektu został sklasyfikowany z trzech różnych perspektyw: statystycznej, geometrycznej oraz technologicznej. W artykule zidentyfikowano metodę weryfikacji, która została uzupełniona przez wyniki badań eksperymentalnych dla minipróbki stopu aluminium EN AW-6063.

15

A new tolerance model of vibrations of thin microperiodic cylindrical shells

Tomczyk B., Litawska A.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2017

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z. 64, nr 2/I

203--216

EN

The objects of consideration are thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a micro-periodic structure in circumferential direction (uniperiodic shells). At the same time the shells have constant structure in axial direction. The aim of this contribution is to formulate and discuss a new nonasymptotic averaged model for the analysis of selected dynamic problems for these shells. This, so-called, general tolerance model is derived by means of a certain extended version of the known tolerance modelling of micro-heterogeneous media. This version is based on a new notion of weakly slowly-varying functions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the tolerance model have constant coefficients depending also on a period of inhomogeneity. Hence, the model makes it possible to investigate the effect of a cell size on the global shell dynamics (the length-scale effect). The differences between the general tolerance model proposed here and the corresponding known standard tolerance model derived by means of the more restrictive concept of slowly-varying functions are discussed.

PL

Przedmiotem rozważań są cienkie liniowo-sprężyste powłoki walcowe typu Kirchhoffa- Love’a mające periodycznie mikro-niejednorodną strukturę w kierunku obwodowym. Powłoki takie nazywamy uniperiodycznymi. Celem pracy jest sformułowanie nowego, nieasymptotycznego, uśrednionego modelu służącego do analizy wybranych zagadnień dynamiki takich powłok. Przedstawiony ogólny model tolerancyjny wyprowadzony jest w oparciu o pewną zmodyfikowaną wersję znanej techniki tolerancyjnego modelowania struktur mikro-niejednorodnych. Wersja ta bazuje na nowym pojęciu funkcji słabo wolno-zmiennej. W przeciwieństwie do równań wyjściowych dla analizowanych powłok niejednorodnych mających współczynniki periodyczne, silnie oscylujące i nieciągłe, równania modelu tolerancyjnego mają stałe współczynniki. Ponadto, współczynniki te zależą od parametru długości mikrostruktury. Tym samym umożliwiają badanie efektu skali.

16

Most podwieszony - kreowanie przestrzeni i konsekwencje konstrukcyjne

Żółtowski K.

Builder

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2017

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R.21, nr 8

76--79

EN

Design and construction – challenges for bridge designers and builders. Cable stayed and suspended bridges, Aesthetics and structural consequences. The paper deals with aesthetic and structural aspects of designed pylons for cable stayed or suspension bridges. Author pays attention to fact, that extraordinary structural solution implemented to footbridge or small viaduct can work properly thanks to phenomena of scale effect. Extraordinary structure solution implemented as aesthetic elements to the large bridge can create serious problems with general carrying capacity of structure or at least makes it extremely expensive. Several examples are presented and discussed.

17

Wyniki doświadczeń nad efektem skali w belkach betonowych ze zbrojeniem bazaltowym

Korol E., Ostaszewska M., Suchorzewski J., Tejchman J.

Inżynieria i Budownictwo

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2016

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R. 72, nr 1

44--47

PL

Przedstawiono wyniki doświadczeń dotyczących efektu skali podczas trzypunktowego zginania belek geometrycznie podobnych. Wyniki porównano z wynikami normowymi. Podkreślono wady i zalety zbrojenia bazaltowego.

EN

The results from experimental investigation of size effect in geometrically similar concrete beams reinforced with BFRP (Basalts Fiber Reinforced Polymer) bars subjected to 3-point bending are presented. Experimental results are compared with theoretical results evaluated based on design codes. Advantages and disadvantages of BFRP bars are emphasized.

18

Wpływ ładowności pojazdów w transporcie samochodowym na efektywność przewozów

Milewski D.

Zeszyty Naukowe. Problemy Transportu i Logistyki / Uniwersytet Szczeciński

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2015

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Nr 29

417--427

PL

W artykule omówiono problem tzw. efektu skali w transporcie, zwłaszcza w transporcie drogowym. W praktyce jest wiele czynników, wpływających na efektywność tej gałęzi gospodarki. W większości są to czynniki zewnętrzne, niezależne od przedsiębiorstw transportowych. Ich udział jest szczególnie wysoki w sektorze drogowym. Co więcej, bardzo trudno uzyskać korzyści skali z powodu ograniczonej ładowności pojazdów. Celem artykułu jest przedstawienie praktycznych determinant efektywności ekonomicznej transportu drogowego oraz czynników umożliwiających osiąganie korzyści skali.

EN

The paper discusses the problem of the so called “scale effect” in transport, especially in the road transport. In practice the are many factors, which influence the effectiveness in this branch of the economy. Mostly these are external factors independent of transport enterprises. The share of such factors is especially high in the road sector. What’s more it is very difficult here to obtain the benefits of scale due to the limited load capacity. The goal of the paper is to present practical determinants of the economical effectiveness of the road transport and factors enabling the obtaining scale effects.

19

Opis niezawodnościowy efektu skali w zmęczeniu elementów maszyn

Agrest D.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2015

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z. 106

28

PL

W artykule przedstawiona została koncepcja opisu efektu skali obserwowanego w zmęczeniu materiałów elementów maszyn przy wykorzystaniu teorii niezawodności szeregowego układu obiektów. Zakłada się, że efekt skali spowodowany jest logicznym połączeniem objętości lub powierzchni referencyjnych, dla których jest znana pełna statystyka parametrów zmęczeniowych. Połączenie to ma strukturę szeregową, dla której niezawodność maleje wykładniczo wraz ze zwiększeniem liczby elementów. W celu weryfikacji założeń teoretycznych opisu efektu skali przeprowadzone zostaną próby zmęczeniowe na próbkach w dwóch wariantach wymiarowych przy obrotowym zginaniu z wykorzystaniem stali C45. Koncepcja badań została opisana w artykule.

20

Modelowe ujęcie efektu skali na użytek obliczeń wytrzymałości zmęczeniowej

Sempruch J., Strzelecki P., Tomaszewski T.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2015

|

z. 106

85

PL

Efekt skali opisuje zależność wytrzymałości zmęczeniowej materiału lub elementu konstrukcyjnego od rozmiaru obiektu. Koniecznym jest jego szersze uwzględnienie w praktyce inżynierskiej. W zakresie analizy własności zmęczeniowych prezentowanych w niniejszej pracy ma miejsce ,,przeliczenie” charakterystyki σ-N z warunków właściwych dla próbek normatywnych (badania materiałowe) na warunki rzeczywiste. W ogólności problem dotyczy obiektów wymiarowo mniejszych, jak i większych od próbek normatywnych. Ponadto w pracy analizowano wybrane modele analityczne opisujące wpływ efektu skali. Prezentowane analizy zweryfikowane dla stopu aluminium AW-6063 T6 i stali nierdzewnej 1.4301.