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1
Content available Micromechanical models of ductile fracture of metals
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EN
In the present paper a few models of ductile fracture were presented. Alloys used in civil engineering most often crack due to void nucleation and growth. Voids are created on the border between matrix and inclusions (made of sulphur and manganese compounds). The majority of described models can be used for modelling of ductile fracture in micro scale. The Gurson Tvergaard Needleman (GTN) material model was found to be the most useful in modelling of plastic deformation of existing steel elements and structures in civil engineering. This paper was presented at seminar for Ph.D. candidates at Kielce University of Technology.
EN
The paper presents results of a numerical modelling of ductile fracture and failure of elements made of S235JR steel subjected to static tension. The analysis was performed using the Gurson-Tvergaard-Needleman (GTN) model, which takes into consideration the material structure. The GTN material parameters of S235JR steel were assumed basing on the results of its microstructural and strength properties. The aim of the research was to specify and test the procedure that enables one to perform engineering calculations of tensioned structural elements using the GTN material model. During numerical simulations, the mesh size-effect was analysed, basing on microstructurally-based length scales methods. The results show high sensivity of strength curves in the range from the maximum force to the failure depending on the method and mesh size applied.
PL
W artykule przedstawiono wyniki modelowania numerycznego pękania ciągliwego oraz zniszczenia elementów wykonanych ze stali S235JR poddanych statycznemu rozciąganiu. W analizie oparto się na modelu materiałowym Gursona-Tvergaarda-Needlemana (GTN), uwzględniającym strukturę materiałową. Parametry materiałowe modelu GTN stali S235JR przyjęto w oparciu o jej własności mikrostrukturalne i wytrzymałościowe. Celem badań było opracowanie i weryfikacja procedury umożliwiającej przeprowadzanie obliczeń inżynierskich rozciąganych elementów konstrukcyjnych przy zastosowaniu modelu GTN. Podczas symulacji numerycznych uwzględniono efekt wielkości siatki, stosując metody oparte na mikrostrukturalnych skalach długości. Uzyskane wyniki ujawniają wysoką wrażliwość krzywych wytrzymałościowych w zakresie od obciążenia maksymalnego do zniszczenia, w zależności od metody oraz wielkości siatki zastosowanej w obliczeniach.
EN
This work investigates rotational effects on propagation and reflection of waves at the free surface of a micropolar fibre-reinforced medium with voids under magnetic fields. When the P-wave is incident on the free surface, there exist four coupled reflected plane waves traveling in the medium; quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement (qTD) wave, quasi-transverse microrotational (qTM) wave and a wave due to voids. Normal mode analysis is adopted in concomitant with Snell’s laws, and appropriate boundary conditions in determination of the solution. Amplitude ratios which correspond to reflected waves in vertical and horizontal components are presented analytically and graphically.
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The evolution of the microstructure of hexanitrohexaazaisowurtzitane (CL-20) after a thermal stimulus plays a key role in the performance of CL-20. In the current work, microstructural variations of CL-20 caused by thermal treatment were investigated by X-ray diffraction, in situ variable-temperature optical microscopy, atom force microscopy, and small-angle X-ray scattering. A wave-like process, an abrupt volume expansion, movement, and fragmentation of CL-20 particles during phase transition were observed. After the phase transition (160 °C) the CL-20 sample acquired a very rough surface with numerous dimple depressions, and during the thermal decomposition stage (200 °C) a large number of voids were produced in both the bulk and the surface of the CL-20.
PL
W technologii bezołowiowego lutowania obserwuje się nasilenie zjawiska powstawania pustych przestrzeni w połączeniach lutowanych. Liczba, wielkość i umiejscowienie pustych przestrzeni może w istotny sposób wpływać na jakość połączeń lutowanych, zwłaszcza połączeń podzespołów BGA i CSP. Powstawanie pustych przestrzeni w połączeniu lutowanym jest zwykle przypisywane pułapkowaniu części lotnych z pasty lutowniczej lub z innych materiałów, takich jak płytka drukowana(powłoka lutowna, maska przeciwlutowa) lub metalizacji wyprowadzeń podzespołów. W przypadku bezołowiowych past mogą to być pary rozpuszcza­ników, pary wodnej lub gazy powstające z rozkładu produktów reakcji chemicznych aktywatora topnika podczas procesu lutowania. Ilość i rozmiar pustych przestrzeni w dużej mierze zależy od właściwości reologicznych pasty, proszku lutowniczego i rodzaju topnika w paście, ale też od rodzaju lutownej powłoki zabezpieczającej na płytce drukowanej, jaki i od charakterystyki temperaturowo-czasowej procesu lutowania. Artykuł prezentuje wyniki badań powstawania pustych przestrzeni w odniesieniu do warunków procesu lutowania i rodzaju lutownej powłoki zabezpieczającej płytki. Jakość połączeń lutowanych określano na podstawie kontroli rentgenowskiej, oceny zgładów metalograficznych oraz pomiarów siły ścinania podzespołów.
EN
Implementation of lead-free reflow soldering aggravates some problems with quality and reliability of solder joints. One of the issues is formation of voids that are usually generated by trapped gas within solder joints when solder is at molten state. The outgassing substance is generally produced by the evaporation of the solvent in the solder paste and the rheological additives in the solder paste that may evaporate in the heating process during reflow. The outgassing substance may also be generated by the metallization of the substrate, component or the solder powder surface during the fluxing reaction in the reflow process. The effect of voids on the reliability of solder joint may depend not only on the size, but also on frequency and location. This paper presents results from a study of formation of voids with regards to reflow process and PCB surface finishes. Detection of voids was done by cross-sectional analysis. Shear strength measurements of chip capacitor were also carried out.
EN
A phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in the context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x-z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions on the free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of the impedance parameter and the angle of incidence.
EN
In the present investigation, axi-symmetric deformation due to a mechanical and thermal source in a homogeneous, isotropic, thermoelastic half-space with voids has been investigated. An integral transform technique has been used to solve the problem. As an application of the problem (i) continuous normal force (ii) normal force over the circular region (iii) thermal point source (iv) thermal source over the circular region have been considered. The components of displacement, stress, temperature distribution and change in volume fraction field are obtained in the transformed domain and inverted numerically using numerical inversion technique. For a specific model, the effect of voids on these quantities has been depicted graphically.
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Content available remote Deformations due to mechanical sources in elastic solid with voids
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EN
Void effects of a load applied normal to the boundary and moving at a constant velocity along one of the coordinate axis in an elastic half space is studied. The analytic expressions for displacement, force stress and volume fraction field for concentrated normal point force, uniformly distributed force, linearly distributed force and moving concentrated normal force are obtained by employing the eigen value approach after applying the integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically. Some particular cases have been deduced.
EN
The dynamic response of a homogeneous, isotropic, generalized thermoelastic half-space with voids subjected to normal, tangential force and thermal source is investigated. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict voids effect in the Lord-Shulman (L-S) theory and Green-Lindsay (G-L) theory for an insulated boundary and temperature gradient boundary.
10
Content available remote Surface waves in a micropolar elastic solid containing voids
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EN
The present paper investigates the effect of voids on the propagation of surface waves in a homogeneous micropolar elastic solid medium which contains a distribution of vacuous pores (voids). The general theory for surface wave propaga-tion in micropolar elastic media containing voids has been presented. Particular cases of surface waves (Rayleigh’s, Love’s and Stoneley’s) in micropolar media which contain vacuous pores have been deduced from the above general theory. Discussions have been made in each case to highlight the effect of voids and micropolar character of the material medium separately. Their joint effect has also been studied in details. Modulation of Rayleigh wave velocity has been studied numerically. It is observed that Love waves are not affected by the presence of voids.
EN
The paper analyses the load-bearing capacity of S235JR steel elements subjected to complex stress states, taking into account the effect of microstructural damage. Assessing the material required conducting a microstructural analysis and standardized tensile strength tests. A modified Gurson-Tvergaard- Needelman (GTN) model was used to numerically analyse S235JR steel elements under the action of complex stresses. The results of the numerical analysis were reported to be consistent with those obtained during the strength tests. The method for the numerical calculations was described along with the admissible results and the criteria of failure for S235JR steel basing on the modified GTN model and the development of microdamage. As S235JR steel is a common structural material in Poland, the investigation results will be of use to a number of engineers and other specialists responsible for determining the load-carrying capacity and structural safety of elements or whole systems.
PL
W artykule przedstawiono wyniki analizy nośności elementów wykonanych ze stali S235JR pracujących w złożonych stanach naprężenia z uwzględnieniem wpływu uszkodzeń mikrostrukturalnych. Opracowano zmodyfikowany model Gursona-Tvergaarda-Needelmana (GTN) dla stali S235JR poprzez wykonanie badań mikrostrukturalnych, przeprowadzenie normowych prób rozciągania oraz ich modelowane numeryczne. Zmodyfikowany model GTN zastosowano w analizie numerycznej elementów pracujących w złożonych stanach naprężeń. Stwierdzono zgodność uzyskanych wyników w stosunku do rezultatów badań wytrzymałościowych. Opisano sposób prowadzenia obliczeń numerycznych wraz z analizą możliwych do uzyskania wyników oraz określono kryteria zniszczenia stali S235JR w oparciu o zmodyfikowany model GTN i rozwój mikrouszkodzeń.
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Content available remote Generalized thermoelastic plane harmonic waves in materials with voids
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EN
The aim of the present paper is to give a detailed account of the plane harmonic generalized thermoelastic waves in solids containing vacuous voids based on the modified fourier law of heat conduction. The general characteristic equation being quartic suggests that there are four longitudinal waves, namely: quasi-elastic [...], quasi-thermal [...], volume fraction [...] and micro-thermal [...], in addition to transverse waves, which can propagate in such solids. The transverse waves get decoupled from the rest of the field quantities and hence remain unaffected due to temperature variation and porosity effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. The general complex characteristic equation has been solved by using descartes algorithm along with irreducible case of cardano's method with the help of demoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation. The propagation of waves in non-heat conducting solids has also been discussed. Finally, the numerical solution of the secular equation is carried out to compute phase velocities, attenuation coefficients and specific loss factors of thermoelastic waves which are presented graphically.
EN
The problem considered is that of an isotropic, micropolar thermoelastic medium with voids subjected to the Thomson effect. The solution to the problem is presented in the context of the refined multiphase-lags theory of thermoelasticity. The normal mode analysis was used to obtain the analytical expressions of the considered variables. The nondimensional displacement, temperature, microrotation, the change in the volume fraction field and stress of the material are obtained and illustrated graphically. The variations of these quantities have been depicted graphically in the refined-phase-lag theory, Green and Naghdi theory of type II, Lord and Shulman theory and a coupled theory. The effects of the Thomson parameter and phase lag parameters on a homogeneous, isotropic, micropolar thermoelastic material with voids are revealed and discussed. Some particular cases of interest are deduced from the present investigation.
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Content available remote Response of thermoelastic half-space with voids due to inclined load
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EN
A two-dimensional deformation of a homogeneous, isotropic, thermoelastic half-space with voids as a result of an inclined line load is investigated by applying the Laplace and Fourier transforms. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The displacements, stresses, temperature distribution and change in the volume fraction field so obtained in the physical domain are computed numerically. The variations of these quantities have been depicted graphically in the coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) for an insulated boundary.
EN
In recent years, composite structures have become very popular for different applications, predominantly in the aerospace industry. Their mechanical properties provide very useful materials in aviation as a primary structure. It is well known that glass/epoxy polymer composite is characterised by its lightweight and corrosion resistance in comparison to traditional materials. The main aim is to guarantee durability and safety during the manufacturing process in the case of the possible appearance of structural defects. Porosity and delamination detection is a very important factor in solving the problem of quality. One of the basic non-destructive testing methods of detecting discontinuities in structures used in aviation is ultrasonic inspection with C-scan images. Their objective is to analyse the composite structures particularly for quality inspection in aviation. This paper presents research about the relationship between the attenuation level of an NDT technique (C-scan) and void content in glass/epoxy composites. An analysis of the microstructure and characteristics of discontinuities are presented and discussed. The observations have given the results of three distinguished types of microstructures depending on the attenuation level in ultrasonic testing. The level of void content for this specific type of composite was determined from 2% to 5% and this can be classified as a medium quality composite structure. A linear dependence was found between the attenuation level in ultrasonic inspection and the percentage of voids content in a glass fiber reinforced polymer composite. The correlation between ultrasonic inspection and the analysis of microstructure is a useful method in composite structures engineering.
PL
Struktury kompozytowe w ostatnich latach stanowią bardzo popularne rozwiązania w odniesieniu do różnych zastosowań, w szczególności w lotnictwie. Dobre właściwości mechaniczne predysponują te materiały na odpowiedzialne części struktur. Kompozyty polimerowe wzmacniane włóknem szklanym charakteryzują się niską gęstością i odpornością korozyjną w porównaniu do tradycyjnych materiałów. Głównym zadaniem podczas ich wytwarzania jest zagwarantowanie trwałości i bezpieczeństwa w procesie produkcji ze względu na możliwość wystąpienia defektów w strukturze. Wykrywanie porowatości i delaminacji stanowi istotny czynnik w rozwiązywaniu problemu jakości. Defektoskopia ultradźwiękowa jest jedną z podstawowych metod nieniszczących do wykrywania nieciągłości, szczególnie w strukturach stosowanych w lotnictwie. W artykule przedstawiono badania wpływu poziomu nieciągłości na poziom tłumienia metodą obrazowania C-scan w kompozytach polimerowych wzmacnianych włóknem szklanym. Zaprezentowano analizę mikrostruktury oraz charakterystykę nieciągłości. Wyróżnione zostały trzy typy mikrostruktury w zależności od poziomu tłumienia. Poziom porowatości dla badanej struktury kompozytowej został określony w zakresie od 2% do 5%, klasyfikując tę strukturę jako średniej jakości. Wykazano liniową zależność pomiędzy poziomem porowatości a procentowym udziałem porowatości w kompozycie polimerowym wzmacnianym włóknem szklanym. Korelacja pomiędzy badaniami ultradźwiękowymi i analizą mikrostruktury stanowi pomocną metodę w inżynierii struktur kompozytowych.
EN
The present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.
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The present investigation deals with the deformation of a micropolar thermoelastic medium with voids due to distributed mechanical thermal sources acting on the plane surface. The analytic expressions of displacement components, force stress, couple stress, change in volume fraction field and temperature distribution are obtained in the physical domain for Green-Lindsay (G-L) theory of thermoelasticity after applying the integrai transforms. These expressions are then inverted by using a numerical inversion method. The numerical results are presented graphically for a mechanical/ thermal uniformly distributed source. Some particular cases have also been deduced.
PL
W Instytucie Tele- i Radiotechnicznym od wielu lat prowadzone są prace badawcze, pozwalające ocenić jakość uzyskanych połączeń lutowanych po montażu elektronicznym. Obecnie szerokim zainteresowaniem naszych klientów cieszą się badania rentgenowskie, ze względu na szybką wykrywalność różnego rodzaju wad w badanych połączeniach, bez konieczności trwałego niszczenia zmontowanych płytek.
EN
In Tele and Radio Research Institute research works have been conducted for many years which allows to assess the quality of formed solder joints after electronic assembly. Currently, our customers are widely interested in X-ray inspection, due to the fast detection of various types of defects in the tested connections, without permanently destroying the assembled board.
20
Content available remote Analysis of stresses in Al-5%Si alloy under loading conditions
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EN
Purpose: This paper analyses the structure and tensile strength of AlSi5Cu2 silumin produced in accordance with PN-EN 1706:2001, categorized as C355 in the US. The study was supplemented with a numerical failure analysis conducted with Abaqus 6.12. Design/methodology/approach: The alloy selected for this study was an Al base alloy containing 5% Si and 2% Cu. Tensile tests on notched round bars with three sizes of the notch radius were performed. Findings: A micromechanical model for the ductility of plastically deforming material was applied to the alloy using the finite-element program ABAQUS. The model is validated by comparing the predictions to experimental results. Research limitations/implications: Average stress triaxiality and ductility for the three types of tensile test specimens were obtained. Originality/value: This paper presented computer simulation of the stress state in notched specimens.
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