Jakub Kõo

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

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Thermoelastic Stresses in Multilayered Plates Under Variable Heating in the Direction of Thickness :[full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1959) Kõo, Jakub
Thermoelastic equilibrium of multilayer isotropic plates (Fig. 1) Under variable heating in the thickness direction in considered. Proceedings from the well-known Kirchoff’s hypotheses, it is demonstrated that in the case of small deflections the solution of probleme is reduced to integration of differential equations (30) and to satisfy the boundary conditions for functions φ (stress function) and w (deflection function) where D’ designate reduced bending stiffness of a multilayered plate. Of the special cases for a plate with an arbitrary contour, the following fixing conditions are considered: 1) fixed edges (Fig. 3), 2) slipping edges (Fig. 4), 3) free edges. It is shown that for a plate with fixed or slipping edges w=0, but for a free plate w = 0,5K (x²+y²), i.e. a free plate is bent to spherical surface (K is a constant). Formulae (46), (47) and (57)-(60) may be readily adapted to calculate eigenstresses (residuals stresses) in galvanic coatings by the experimentally measured curvature at unilateral coating of a plate cathode.
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]).
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.
Eigenstresses in thin electrodeposits: [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1963) Kõo, Jakub
The eigenstress (residual stress) state of a thin superficial layer of an electrodeposit is considered. The analysis is based on Ilyushin´s theory of plasticity. It is established that the state of stress in the superficial layer is equal biaxial compression or tension defined for the elastic state according to formula (9), for initial stress, where E, µ and β are the modulus of elasticity, Poisson´s ratio and initial strain for the coating, respectively. At β>0 there occurs biaxial compression, at β<0 there occurs biaxial tension. It is shown that eigenstresses (residual stresses) in the thick deposit are expressed as the sum of initial stress and additional stress.
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 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 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.
On Calculation of Electrocrystallization Stresses by Deformation of a Band Cathode : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1969) Kõo, Jakub; Eesti Põllumajanduse Akadeemia
Revision of the method for calculation of electrocrystallization stresses by deformation of a band cathode proposed by M. J. Popereka [1-3] is suggested. Use of a during the coating process freely deforming rectangular plate cathode clamped in the limited region of the edge (see Fig.2) is proposed for rise precision.
Investigation of residual stresses in electrodeposits by strain measurement of a thin-walled tubular cathode : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1969) Kõo, Jakub
A method for experimental determination of residual stresses in electro-deposits is described. According to this method a deposit to be investigated is deposited on the external surface of a thin-walled tubular cathode (Fig. 4) placed in a tank with rotating anodes (Fig. 3). At the same time, by using electrical-resistance strain gauges on the internal surface of the cathode strains are measured as a function of variable deposit thickness. Initial stress and residual stresses are determined via approximation of experimental information, applying the method of averaged sum. Determination of elastic constants of the substrate and coating materials is described. Technological problems of strain measurement are considered. An example of the processing of measurement data is presented. Initial stresses are determined for a number of cathode materials and galvanic iron coatings (Table 3).
Once again about the force and deformation methods for determination of residual stresses in clamped bars and plates with coatings : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1971) Kõo, Jakub
Metrological equations for the indicated experimental methods are presented for rigidly clamped and slipping clamped substrates. It is pointed out that the equations derived remain valid when the layer adding or layer removal techno-logy is applied.
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.
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.
On determination of residual stresses in coatings : [full text in Russian]
(МГТУ им. Н. Э. Баумана, 1976) Kõo, Jakub
An integral approach is used for derivation of a metrological equation for experimental determination of residual stresses in coatings of bars and plates using strain measurement. Equation (1) is Volterra´s first kind integral equation where elastic constants of substrate and coating materials are assumed to be different. From this equation, by means of its reduction to the differential equation and integration, the metrological equation (2) is obtained. Problems of measurement data processing are adressed. As an example, the results of processing of experimental data for a data collection are presented (Fig. 1).
On the method for determining residual stresses in hollow spheres : [full text in French]
(VDI-Verlag, 1976) Kõo, Jakub
Known Peiter´s method [1; 2] for experimental determination of residual stresses in homogeneous hollow spheres from the circumferential strain measured on the internal surface at addition or removal of material on the external surface is extended for a radially inhomogeneous sphere.
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.
Thermal stresses in plates, cylinders and spheres with coatings : [full text in Russian]
(Eesti Põllumajanduse Akadeemia, 1977) Kõo, Jakub
Formulas for calculation of thermal stresses in plates, cylinders and spheres with coatings at uniform temperature variation are reduced.
Sur la détermination des contraintes résiduelles dans les cylindres creux non-homogénes
(Düsseldorf: VDI-Verlag, 1978) Kõo, Jakub
A theory is presented for determining residual stresses in non-homogeneous hollow cylinders by measuring deformations of the inside surface of the cylinders when material is added or removed from the outer surface. The solution of the problem is based upon regarding the non-homogeneous cylinder as a piece-wise homogeneous one and on the subsequent application of the Lamé formulas to those homogeneous layers. Three particular cases are examined: a cylinder with an unchangeable Poisson ratio, a homogeneous cylinder and a thin-walled two-layered cylinder. As an example the determination of residual stresses in a electrodeposit iron layer on a thin-walled copper cylinder is given.

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