Jakub Kõo

Selle kollektsiooni püsiv URIhttp://hdl.handle.net/10492/7087

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Algparameetrite meetodi ühest esitusvariandist tugevusõpetuses
(Eesti Põllumajanduse Akadeemia, 1990) Kõo, Jakub
Tavaliselt esitatakse õppekirjanduses algparameetrite meetod staatika määratava tala sisejõudude ja siirete määramiseks eraldi. Allpool käsitletakse algparameetrite meetodi üldistatud varianti, mille puhul talale mõjuvad koormised esitatakse Diraci ja Heaviside´i funktsioonide abil lauskoormistena ning sisejõud ja siirded määratakse ühtse metoodika järgi sõltumata staatika määramatuse astmest.
Analysis of thermoelastic stresses in layered plates
(Tallinn University of Technology, 2008) Kõo, Jakub; Valgur, Jaak
This paper deals with thermoelastic effects in deformation of plates with arbitrarily changing elastic parameters and temperature through thickness. Using the semi-inverse method, a simple analytical solution is obtained for the thermoelastic problem of a nonhomogeneous plate with an arbitrary contour. Plates with free, sliding and fixed edges are considered. The results are applied to the layered plate. As an example of application, thermoelastic stresses and deformations are determined for a copper plate with a steel coating. The edge effects for this plate are examined by the finite element method.
The application of the method of holographic interferometry by modelling the bending of a straight strip substrate with the deposit : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1990) Kõo, Jakub; Lille, Harri; Smirnov, V.; Metšerjakov, M.
The results of modelling of the bending of a straight strip substrate with a deposit by bending a thermobimetallic strip in the case of a regular change of temperature are presented. The deposit was added or removed on the surface of the substrates with a relative thickness of less than 0.08 and a relative width of more than 0.16. The deformed surface of the substrate determined by the method of holographic interferometry is spherical.
Boundary effect in the case of deposition of the coating on a free edged thin-walled tube : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1974) Kõo, Jakub
The boundary effect at deposition of a coating on a thin-walled tubular substrate with free edges is examined. Using the equation of radial displacements of the long cylindrical shell with a uniform moment load on the edge, it is shown that with a precision of 5% the boundary effect can be considered attenuated at a length according to expression (7) where r₁ , h₁ and h₂ are given by Fig. 1, k = h₂/h₁ and µ is the Poisson´s ratio which is identical for substrate and coating materials.
Calculation of Eigenstresses in Electrodeposits by Deformation of a Thin Plate Cathode :[full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1959) Kõo, Jakub
Draw on the analogy between a libre thermal strain in a elastic body and a libre eigenstrain in a electrodeposit, for calculation of eigenstress (residual stress) in the superficial layer of a galvanic coating, formula (4) is obtained, where En, µ and β are the modulus of elasticity for coating, Poisson´s ratio (identical for coating and substrate) and free linear eigenstrain in the coating superficial layer. I addition eigenstrain β is calculated from the experimentally determined curvature of the substrate. The correspondind calculation formulae are presented for a plate substrate with free edges (Fig. 1a): formula (8), for slipping edges (Fig.1b): formula (36) and for fixed edges (Fig.1v): formula (38). Substitution these formulae in formula (4) yields the corresponding formulae of Stoney [2] an Brenner-Senderoff [3] complemented by factor 1/(1-µ) which modifies the formulae under consideration through taking account of the biaxial state of stress in a coated plate cathode.
Calculation of residual stresses in electrodeposited circular cylindres : [full text in Russian]
(Ленинградский сельскохозяйственный институт, 1961) Kõo, Jakub
The axially symmetric problem of thermoelasticity for a circular multilayer cylinder is solved. Using this solution and basing on the analogy between libre thermal strain in an elastic body and libre eigenstrain in a galvanic coating, the problem of determination of residual stresses (eigenstresses) in a circular cylinder with a galvanic coating is solved. The compatibility problems of the solution are considered. As an example, the residual stress distributions, calculated by using equations (30) for a hollow cylindrical substrate with a coating, are presented in Fig.3.
Calculation of residual stresses in electrodeposited spheres : [full text in Russian]
(Сельхозиздат, 1962) Kõo, Jakub
The polar-symmetric problem of thermoelasticity for a multilayer sphere is solved. Using this solution and based on the analogy between a libre thermal strain in an elastic body and a libre eigenstrain in a galvanic coating, the problem of determination of residual stresses (eigenstresses) in a multilayer galvanically grown sphere is solved. The compatibility problem of the solution is considered. As an example, residual stresses are determined for a coating on a thin-walled spherical substrate (application of equations (38) and (51) which modify the Mills method [7]).
Consideration of Thermal Stresses in Experimental Residual Stress Analysis for Coatings
([Warsaw University of Technology], 2004) Kõo, Jakub; Ryabchikov, Alexander; Estonian Agricultural University
Usually, the coefficients of thermal expansion of the coating and substrate are different and the temperature of coating process differs from room temperature (20ºC). Therefore thermal stresses are generated in coated parts. In experimental analysis of residual stresses it may turn out that caoting temperature differs from the temperature at which the deformation parameters of the substrate are measured. In Susch cases the measurement results have to be corrected taking into account the thermal stresses. In this study, the equations for correction of the residual stresses in coatings, determined from the measured longitudinal deformations of the wire, and from the tubular and strip substrates [1-3], are presented. Three examples of application are given.
Determination of eigenstresses in electrodeposits by deformation of a thin-walled tube cathode: [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1963) Kõo, Jakub
A new technique for experimental determination of initial stress was developed. According to this, a coating to be investigated will be applied on the external surface of a thin-walled tubular cathode (see Figs. 2, 3). In addition, by using of electrical-resistance strain gauges on the internal surface of the cathode, strains are measured as a function of variable coating thickness. Initial stress is determined via approximation of experimental information. As an example in Fig.4 the distributions of measured deformations and initial and eigen- stresses (residual stresses) for a galvanic steel coating of a thin-walled tubular cathode are presented.
Determination of Eigenstresses in Machine Elements Restored by Galvanic Coatings : [Autoreferat for the degree of Candidate of Engineering Sciences : full text in Russian]
(Leningrad Agricultural Institute, 1965) Kõo, Jakub
Extended summary of thesis for the degree of Candidate of Engineering Sciences): [full text in Russian]. This thesis of J. P. Kõo (Supervisor: Professor, Doctor of Engineering Sciences S. G. Gutman) for the degree of Candidate of Engineering Sciences is completed at Leningrad Agricultural Institute and at Estonian Agricultural Academy in 1957- 1965. The following research results are obtained: 1. A survey of the studies focusing on experimental techniques for determination of eigenstresses (henceforth residual stresses) in galvanic coatings is provided. 2. An algorithm for determination of residual stresses in machine elements restored by addition of galvanic coatings is proposed. 3. Presence of an equibiaxial state of residual stress in the superficial layer of a galvanic coating is established [8]. 4. A classification of galvanic coatings onto thin and thick coatings is offered. 5. Algorithms for calculation of residual stresses in plates coated at fixed, slipping or free edges are developed [5] (extension of the work of Stoney [2] and of Brenner and Senderoff [3). In particular, for a free plate substrate with unilateral coating for the deformation and the curvature measuring methods Stoney´s differential formulas are extended (see(Egs.(15)) and their integration is considered. 6. Problems related to determination of residual stresses in cylinders [6] and spheres [7] at application of galvanic coatings are solved. 7. Formulas for calculation of thermal stresses in galvanically covered plates, cylinders and spheres are established. 8. Techniques for determination of the initial stress (stress in the superficial layer) of a coating from deformation parameters measured at application of the coating are critically examied. 9. A new technique for experimental determination of initial stress is developed [9]. According to this, a coating to be investigated will be applied on the external surface of a thin-walled tubular cathode (see Fig.5). In addition, by using of electrical-resistance strain gauges on the internal surface of the cathode, strains are measured as a function of variable coating thickness (see Fig.6). Initial stress is determined (see Table 2) via approximation of experimental information by Eq.(19). 10. Examples of investigation of residual stresses for some details restored with the help of an iron galvanic coating are presented.
Determination of Eigenstresses in Machine Elements Restored by Galvanic Coatings : [Dissertation for the degree of Candidate of Engineering Sciences : full text in Russian]
(Ленинградский сельскохозяйственный институт, 1965) Kõo, Jakub; Gutman, S. (juhendaja)
Autoreferat of the thesis is available http://hdl.handle.net/10492/8534
Determination of residual stresses in bars and plates using the strain measurement method : [full text in Russian]
(МГТУ им. Н. Э. Баумана, 1969) Kõo, Jakub
An integral approach is used for derivation of a metrological equation for the indicated measurement method . The equation (1) is Volterra´s first kind integral equation from which, by means of its reduction to the differential equation and integration, metrological equation (4) is obtained. Problems of measurement data processing are addressed. As an example, determination of residual stresses in the galvanic iron coating of a plate-like cathode is presented.
Determination of Residual Stresses in Brush-Plated Coatings by Mechanical and X-ray Techniques
(Linköping University, 1997) Lille, Harri; Kõo, Jakub; Haav, Aksel
The determination of residual stresses is studied in brush-plated nickel coatings of different thickness, deposited on brass strip substrates with two different dimensions. Residual stresses in the surface layer were found by the deformation method, displacement of the free end of the coated region of the cantilevered strip substrate or the axial strain of the free surface serving as experimental information. The x-ray diffraction technique was employed to determine residual stresses in specimens (8x10 mm) cut from the middle of the coated strip substrate by using lattice parameters measured for two different ψ values. Comparable values of residual stresses, 350-450 MPa and 280-480 MPa, were obtained in coating with a thickness of 45-110 μm by using the mechanical method and the x-ray diffraction technique respectively.
Determination of residual stresses in coated plates using layer growing/removing methods: 100th anniversary of Stoney’s equations
(Tallinn University of Technology, 2010) Kõo, Jakub; Valgur, Jaak
In connection with the 100th anniversary of Stoney’s equations, some historical remarks are made with respect to the development of these equations. In the capacity of an example of the extension of Stoney’s equations, a unique algorithm of the layer growing/removing methods for determination of residual stresses in isotropic inhomogeneous coated plates is presented. Using a computer program based on this algorithm, residual stresses are computed in a detonation gun sprayed WC-Co coating.
Determination of Residual Stresses in Coatings and Coated Parts
(Tallinn Technical University, 1994) Kõo, Jakub
The methods of experimental residual stress analysis in coatings available at present are indirect. A distinct deformation parameter of a substrate or a coating should always be measured, from which the values of residual stresses can be calculated. At the same time, distinction should be made between layer-growing (nondestructive) and layer-removing (destructive) measurement methods. In the case of growing methods, a deformation parameter is measured by applying a coating a coating to the substrate, while in the case of layer-removing methods, by removing it from the substrate. G. Stoney was the first to use a layer-growing method for determination of residual stress in galvanic coatings. By using his method (proposed in 1909), residual stress in a coating is calculated by the curvature measured during the unilateral coating of a free straight strip substrate assuming a one-dimensional state of stress. In the course of time various layer-growing methods have been developed for determination of residual stresses in coatings. Still, layer-removing methods are also applied for determination of residual stresses in coatings. It has been established that layer-growing and layer-removing methods can be described by a single algorithm. Algorithms of this kind have been developed by the author of this thesis for a free plate with a unilateral coating, for a hollow cylinder and for a hollow sphere with an outer coating. This thesis summarizes the research conducted by the author and the coauthors in the field of experimental mechanics of residual stresses in coatings and coated parts between 1965 and 1994. The thesis contains the following sections: 1. Determination of residual stresses in coated parts: general algorithm; 2. Determination of residual stresses in bars, plates, cylinders and spheres with a thick coating; 3. Methods for determination of initial stress; 4. Thermal stresses in coated parts; 5. Some results of the experiments; Conclusions; Bibliography (Main publication on the subject of the thesis; Abstracts of main reports on the subject of the thesis; References); Appendix: Examples of application.
Determination of Residual Stresses in Coatings and Coated Parts: Extended variant with additional information
(Estonian Agricultural University, 1993) Kõo, Jakub
The methods of experimental residual stress analysis in coatings available at present are indirect. A distinct deformation parameter of a substrate or a coating should always be measured, from which the values of residual stresses can be calculated. At the same time, distinction should be made between layer-growing (nondestructive) and layer-removing (destructive) measurement methods. In the case of growing methods, a deformation parameter is measured by applying a coating a coating to the substrate, while in the case of layer-removing methods, by removing it from the substrate. G. Stoney was the first to use a layer-growing method for determination of residual stress in galvanic coatings. By using his method (proposed in 1909), residual stress in a coating is calculated by the curvature measured during the unilateral coating of a free straight strip substrate assuming a one-dimensional state of stress. In the course of time various layer-growing methods have been developed for determination of residual stresses in coatings. Still, layer-removing methods are also applied for determination of residual stresses in coatings. It has been established that layer-growing and layer-removing methods can be described by a single algorithm. Algorithms of this kind have been developed by the author of this thesis for a free plate with a unilateral coating, for a hollow cylinder and for a hollow sphere with an outer coating. This thesis summarizes the research conducted by the author and the coauthors in the field of experimental mechanics of residual stresses in coatings and coated parts between 1965 and 1994. The thesis contains the following sections: 1. Determination of residual stresses in coated parts: general algorithm; 2. Determination of residual stresses in bars, plates, cylinders and spheres with a thick coating; 3. Methods for determination of initial stress; 4. Thermal stresses in coated parts; 5. Some results of the experiments; Conclusions; Bibliography (Main publications on the subject of the thesis; Abstracts of main reports on the subject of the thesis; References); Appendix: Examples of application. In the form of an additional information list of titles and copies of the main publications on the subject of the thesis, as well as information about the defence of the thesis and a copy of the issued doctoral diploma are submitted.
Determination of residual stresses in coatings of bars, plates and cylindrical shells (Estonian Agricultural Academy. Scientific investigations report for 1971-1975) : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1975) Kõo, Jakub
This report was completed by supervisor of the topic, Candidate of Technical Sciences (PhD) J. P. Kõo. The folloving research results are obtained: The theory of layer growing/removing experimental methods for determination of residual stresses in coatings of bars/plates and cyndrical shells is developed on supposition that elastic parameters of the substrate and coating change arbitrarily in the direction of thickness. In this connection methods of measuring of curvature or deformation of bars/plates with free edges (Stoney´s method) and with fixed edges (Soderberg-Graham´s method) and measuring of deformation of a free cylindrical shell ( a recent method) are considered. For the reliability of the calculations approximation of the measured parameters with an analytical expression is recommended. An example of application for a galvanic steel coating on a thin-walled tubular substrate by the layer growing method is given. Here the computation of the approximation parameters on a computer is considered.
Determination of residual stresses in coatings of rigidly clamped rods and plates by measuring strain: [full text in Russian]
(Институт проблем прочности НАН Украины, 1975) Kõo, Jakub
Residual stresses in clamped rod and plate coatings can be determined by using a known method of deflection measurement, developed further in papers [2-7]. However, the wide application of strain gauges in modern measurement technology justifies in many cases the use of the proposed method. It is based on measurement of the strain arising on the free side of the substrate when the clamped edges becom free after building up the coatings up to required thicknesses. Metrological equations are derived and an example of determination of residual stress for a coating is presented.
Determination of residual stresses in cylinders with coatings : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1977) Kõo, Jakub
Experimental determination of residual stresses in coated long hollow circular cylinders by measuring circumferential and longitudinal strains at material adding or removal is considered. Metrological equations for radial and circumferential residual stresses (6) and (7) are derived by using Lame´s formulas. Equation (10) for calculation of axial stress is obtained from the integral expression of the longitudinal force. Metrological equations (11) for a thin-shelled cylinder are presented.
Determination of residual stresses in deposits by measuring the deformation of a thin-walled ring-shaped substrate: [full text in Russian]
(Technische Hochschule Zwickau, 1989) Kõo, Jakub; Lille, Harri
A metrological equation is proposed for the indicated experimental method. In this case the substrate is considered to be a short cylindrical shell ( Fig.). The proposed equation permits calculation of surface stress (initial stress) from circumferential strain measured on the internal surface of the substrate by using of electrical-resistance strain gauges.

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