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EN
Void initiation and growth serve as an important mechanism in ductile failures in metals. Particularly, on the micron-level, the extra hardening effect associated with strain gradient is accounted for by adopting strain gradient elasto-plasticity instead of the conventional plasticity. Effects of inertial, strain gradient hardening and thermal softening are formulated analytically for the case where a spherical void expands under external hydrostatic stress. As demonstrated by our results, the inertia effect firstly tends to hinder but then promotes the void growth. The threshold stress required for rapid void growth is lifted due to extra hardening of strain gradient so that the growth of a smaller void is delayed more remarkably. A considerable thermal softening phenomenon is observed here, which is caused by plastic work during the deformation process. The final void growth rate is mainly related to the maximum loading, which is consistent with the prediction based on the classical plastic theory.
EN
The paper presents results of numerical simulations of size effect phenomenon in concrete specimens. The behaviour of in-plane geometrically similar notched and unnotched beams under three-point bending is investigated. In total 18 beams are analysed. Concrete beams of four different sizes and five different notch to depth ratios are simulated. Two methods are applied to describe cracks. First, an elasto-plastic constitutive law with a Rankine criterion and an associated flow rule is defined. In order to obtain mesh independent results, an integral non-local theory is used as a regularisation method in the softening regime. Alternatively, cracks are described in a discrete way within Extended Finite Element Method (XFEM). Two softening relationships in the softening regime are studied: a bilinear and an exponential curve. Obtained numerical results are compared with experimental outcomes recently reported in literature. Calculated maximum forces (nominal strengths) are quantitatively verified against experimental values, but the force – displacement curves are also examined. It is shown that both approaches give results consistent with experiments. Moreover, both softening curves with different initial fracture energies can produce similar force-displacement curves.
EN
Nonproportional plastic deformations on the microscale are an emerging topic. A simplified theory of strain gradient elasto-plasticity is developed to study the evolution of yield strength in a copper wire sequentially experiencing tension and torsion. The pre-tension deformation and stress are inherited to the upcoming torsion process, resulting in a nonproportional loading condition. With consideration of the extra hardening effect due to strain gradient, pre-tension weakens the extra hardening effect of the strain gradient and the dependence on the wire radius. Cyclic torsion behavior is also investigated. Anomalous Bauschinger effect and plastic softening are found.
EN
In this study, an experimental research on the fracture parameters of self-compacting lightweight concrete (SCLC) using tap and magnetic water (MW) is presented. For all SCLC mixtures, common fracture parameters were specified by means of both work of fracture method (WFM) and the size effect method (SEM). Three-point bending tests were carried out on 90 notched beams with six mix compositions. The beams were made from mixes with three different water to cement (w/c) ratios of 0.37, 0.47 and 0.52; also, both tap and magnetic water were consumed in the concrete mixes, separately. The results of this research showed that by using MW in SCLC and decreasing w/c ratio from 0.52 to 0.37: (a) both initial fracture energy Gf and total fracture energy GF increased; (b) the fracture toughness and the mechanical properties of SCLC improved. Additionally, the achieved data exhibited that there was a reasonable relation between the total fracture energy obtained by WFM and the initial fracture energy achieved through SEM. The average of GF to Gf ratio in SCLC was 2.70. Furthermore, by using MW in SCLC mixtures, compressive strength, splitting tensile strength and modulus of elasticity increased up to 18%, 9% and 10%, respectively.
EN
Multiwalled carbon nanotubes (MWCNTs) have attracted huge attention due to their multifunctionality. Their unique properties allows for covalent and noncovalent modifi cations. The most simple method for functionalization of carbon nanotubes is their decoration with the oxygen containing moieties which can be further simultaneously functionalized for design of new class carriers for targeting and imaging. Here, we present methodology for chopping nanotubes, characterization of MWCNTs, the effect of size on the biocompatibility in culture of L929 mouse fi broblasts using WST-1, LDH and apoptosis assays. The analysis provides the optimal carbon nanotubes length and concentration which can be used for functionalization in order to minimize the effect of the secondary agglomeration when interacting with cells.
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.
EN
In this paper, size dependent axisymmetric shell element formulation is developed by using the modified couple stress theory in place of classical continuum theory. Since the study of nanoshells is conducted in nanodimensions, the mechanical properties of nanoshells are size dependent; therefore, taking into consideration the size effect, nonclassical continuum theories are used. In the present work the mass–stiffness matrix for axisymmetric shell element is developed, and by means of size-dependent finite element, the formulation is extended to more precisely account for nanotube vibration. It is shown that the classical axisymmetric shell element can also be defined by setting length scale parameter to zero in the equations. The results show that the rigidity of the nanoshell in the modified couple stress theory is greater than that in classical continuum theory, which leads to the increase in natural frequencies. The findings also indicate that the developed size dependent axisymmetric shell element is able to cover both cylindrical and conical shell elements and is reliable for simulating micro/nanoshells. Using size dependent axisymmetric shell element increases convergence speed and accuracy in addition to reducing the number of the required elements.
8
Content available remote Efekt skali w próbach zginania obrotowego
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.
9
Content available Ubiquitiformal fracture energy
EN
The ubiquitiformal fracture energy is proposed in the paper and its explicit expression is obtained. Moreover, the numerical results for concrete are found to be in good agreement with those for the critical strain energy release rate. The discrepancy between the numerical results of the traditional fracture energy and the critical strain energy release rate can be explained reasonably, which implies that the ubiquitiformal fracture energy should be taken as an available fracture parameter of materials. Finally, it is numerically found for some concrete that there is not size effect for the ubiquitiformal fracture energy.
EN
The study presents a method to determine the σa − N curve (high cycle fatigue) for profiles made of AW-6063 T6 aluminium alloy. Experimental material data for a mini specimen taken directly from the tested item and selected empirical correlations allowing for a size effect have been used. A model yielding the lowest relative error of estimating the fatigue life is presented.
11
EN
The objective of this paper is to investigate the effects of scale of an auxetic cellular material sample on the evaluation of elastic properties. Size and boundary effects are studied in detail. This is achieved by conducting computer simulations of the auxetic structure under the typical loading exerted by the compression and simple shearing test performed by means of ABAQUS FEA. The material microstructure is discretized by the plane network of Timoshenko beam elements. The results of the studies give insight to the scale effects. Structures with designed properties can be potentially used for engineering applications.
EN
The purpose of the current study is to address the nonlinear buckling and postbuckling response of nanoscaled cylindrical shells made of functionally graded material (FGM) under hydrostatic pressure aiming to investigate the sensitivity to the initial geometric imperfection in the presence of surface effects and thermal environments. According to a power law distribution, the material properties of the FGM nanoshell are considered change through the shell thickness. Also, the change in the position of physical neutral plane corresponding to different volume fractions is taken into account to eliminate the stretching-bending coupling terms. In order to acquire the size effect qualitatively, the well-known Gurtin-Murdoch elasticity theory is incorporated within the framework of the classical shell theory. Using the variational approach, the non-classical governing equations are displayed and deduced to boundary layer type ones. Afterwards, explicit expressions for the size-dependent radial postbuckling equilibrium paths of imperfect FGM nanoshells are proposed with the aid of a perturbation-based solution methodology. It is displayed that by moving from the ceramic phase to the metal one, the critical buckling pressure decreases, but the postbuckling stiffness increases, because in contrast to the ceramic phase, the surface modulus and residual surface stress associated with the metal phase have the same sign.
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.
EN
A simple gradient-enhancement of the classical continuum theory of plasticity of single crystals deformed by multislip is proposed for incorporating size effects in a manner consistent with phenomenological laws established in materials science. Despite considerable efforts in developing gradient theories, there is no consensus regarding the minimal set of physically based assumptions needed to capture the slip-gradient effects in metal single crystals and to provide a benchmark for more refined approaches. In order to make a step towards such a reference model, the concept of the tensorial density of geometrically necessary dislocations generated by slip-rate gradients is combined with a generalized form of the classical Taylor formula for the flow stress. In the governing equations in the rate form, the derived internal length scale is expressed through the current flow stress and standard parameters so that no further assumption is needed to define a characteristic length. It is shown that this internal length scale is directly related to the mean free path of dislocations and possesses physical interpretation which is frequently missing in other gradient-plasticity models.
15
Content available remote Wpływ efektu skali na proces mikrotoczenia
PL
W artykule opisano jeden z głównych problemów występujących w procesie mikroskrawania, tzw. efekt skali. Przejawia się on nieliniową zależnością pomiędzy grubością usuwanego naddatku a siłami występującymi w procesie mikroskrawania. Opisano również wyniki badań wstępnych procesu toczenia mikroelementów.
EN
In the article, one of the main problems occurring during microcutting, which is called the size effect, has been described. It means that with the decrease of depth-of-cut, the nonlinear relation between uncut chip thickness and cutting forces is observed. The results of the preliminary tests of the turning process of microelements have been also presented.
PL
Szerokie zastosowanie profili kształtowych niesie ze sobą konieczność określenia własności zmęczeniowych materiału, z którego są produkowane. W wyniku procesu produkcyjnego takich profili, materiał wejściowy poddawany jest znacznym odkształceniom plastycznym i wpływowi ciepła. Skutkuje to koniecznością prowadzenia badań na gotowych elementach, z których niemożliwe jest pobranie próbki normatywnej. W pracy opisano metodykę badań zmęczeniowych (geometria próbki, obciążenia, stanowiska badawcze, analiza wyników) z wykorzystaniem minipróbek możliwych do pobrania z profili kształtowych.
EN
A vast application of shape profiles brings the need to determine the fatigue properties of the materiał they are produced from. As a result of the production processes of such profiles, the initial materiał was exposed to considerable plastic deformations and the effect of heat. It results in the need of performing tests with finished components from which it is impossible to sample a normative specimen. The paper describes the fatigue testing methodology (specimen geometry, loads, testing stand, analysis of the results) in the use of mini specimens which can be taken from shape profiles.
PL
Podczas zmniejszania wymiarów geometrycznych części metalowych odkształcanych za pomocą obróbki plastycznej do rozmiarów odpowiadających mikroskali, zrozumienie i przewidywanie zjawisk kształtowania plastycznego staje się trudne. Tradycyjne modele deformacji materiału są nieodpowiednie dla mikroskali ze względu na występujący tzw. efekt skali, który odpowiada za odmienne zachowanie się materiału podczas mikroformowania plastycznego. W pracy zbadano, jaki jest wpływ efektu skali dotyczącego zarówno wielkości ziarna materiału jak i geometrycznego skalowania wielkości próbki na naprężenia uplastyczniające materiału. Wykorzystując model konstytutywny uwzględniający dwa analizowane efekty skali, przeprowadzono symulacje MES dla procesu ściskania walcowych próbek wykonanych z różnymi współczynnikami skali.
EN
When the geometry of deformed metal part is scaled down to micro-scale, the understanding and prediction of micro deformation behavior becomes difficult. This is because the conventional material deformation models are no longer valid in micro-scale due to the size effect, which affects the deformation behavior in micro plastic deformation. In this research the grain and geometry size effect on the flow stress of workpiece is thus investigated. Using constitutive model considered size effects, the micro-bulk upsetting with different scale parameters are numerically simulated by Finite Element Method.
PL
Przeprowadzono badania przyczepności elementów zespolonych złożonych z dwóch betonów o różnym czasie dojrzewania, ocenianej metodą rozłupywania. Stwierdzono, że wytrzymałość przyczepności zależy od wielkości elementów zespolonych, a więc podlega efektowi skali. Natomiast nie stwierdzono różnic przyczepności w przypadku gdy elementy te były wykonano z dwóch betonów tej samej klasy, lub różnych klas.
EN
The adhesion of two concrete placed at different time, being the members of composite element, was tested applying splitting method. It was establish that the adhesion strength is different for the variable dimensions of these composite elements, thus is depending of the size effect. However, no differences of adhesion strength were found when comparing two elements, which members were produced of concretes having the same or different strength.
PL
W pracy przedstawiono próbę analizy nośności na przebicie płyt krępych za pomocą metody kratownicowej (strut-and-tie, S-T). Procedura obliczeniowa została porównana z wynikami własnych badań eksperymentalnych. Zakres analizy obejmuje wyłącznie elementy bez zbrojenia poprzecznego obciążone osiowo symetrycznie.
EN
The punching shear behavior of thick reinforced concrete slabs was analyzed in this paper by using strut-and-tie model (S-T). Calculating procedures were compared to our own experimental test results. The analyzed elements were subjected to symmetric loading and without shear reinforcement.
20
Content available remote Multifractal scaling law for high-cycle fatigue strength applied to aluminum alloy
EN
Fatigue strength of the material decreases with an increase in the cross sectional area of the specimen. Such phenomenon can be described phenomenologically applying the fractal approach, describing a change in the strength properties by applying the fractal dimension. With that approach involves modelling the damage of a material ligament. The damage size depends on the defects and microfractures in the object analysed. The effect of the disordered material microstructure on the mechanical properties is decreasing with an increase in the cross sectional area of the object. Bearing that in mind, the description of the size effect should use nonlinear scaling (multifractal scaling law). That approach was used for the results of high-cycle fatigue studies, for various aluminum alloys. Determining the model parameters facilitates the evaluation of fatigue life and strength for the plants with a different geometry than the specimens studied in the lab.
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