Determination of residual stresses in glass shells by a computational-experimental method

A method is proposed for determining the technological residual stresses in glass shells of revolution based on the solution of inverse problems of shell theory with proper stresses and the use of experimental data obtained by the photoelastic method. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 100–105.     

Determination of residual stresses in plastics

A method is proposed for calculating the residual stresses in hot-molded plastics parts. Data are presented for a polyester glass-reinforced plastic.Mekhanika Polimerov, Vol. 3, No. 5, pp. 827–832, 1967     

Numerical investigation of residual thermal stresses in welded joints of heterogeneous steels with account of technological features of multi-pass welding

The paper describes a two-dimensional mathematical model to evaluate stresses in welded joints formed in multi-pass welding of multi-layered steels. The model is based on a system of equations that includes the Lagrange's variational equation of the incremental theory of plasticity and the Biot's variational principle for heat transfer simulation. In the constitutive equations, the changes in the volume which occur as a result of phase transitions can be taken into account. Therefore, the prehistory and impact of thermal processing of materials on macroscopic properties of the medium can be considered.The variational-difference method is used to solve both the heat transfer equation for calculation of the non stationary temperature field and the quasi-static problem of thermoplasticity at each time-step. The two-dimensional problems were solved to estimate the residual thermal stresses (for the case of plane stress or plane strain) during cooling of welds and assessing their impact on strain localization in the heat-affected zone under tensile and compressive loading considering differences in mechanical properties of welded materials.It is shown that at initial stages of the plastic flow, the residual stresses significantly affect the processes of stress concentration and localization of strains in welded joints. To estimate the model parameters and to verify the modeling results, the available experimental data from scientific literature obtained on the basis of the Satoh test for different welding alloys was used.     

A nondestructive numerical-experimental method of determining the residual stresses in welded shells of revolution

We propose a numerical-experimental method of determining the residual stresses in welded shells of revolution. We solve the inverse conditionally correct problem of recovering the complete picture of the residual stress state from part of the experimental values obtained by the method of photoelasticity. We apply the numerical spline-collocation method. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 149–151.     

Determination of the residual stresses in wound glass-reinforced plastic rings

The stresses that develop during winding in wound glass-reinforced plastic rings change during polymerization, when the modulus of elasticity in the radial direction is reduced by heating. Further changes occur in connection with cooling and removal from the mandrel. The theoretical relations obtained for determining these stresses are found to be confirmed by experiment.Bauman Moscow Higher Technical College. Translated from Mekhanika Polimerov, No. 5, pp. 892–898, September–October, 1969.     

A Green's function method of determining the residual stresses in cylindrical glass shells

We propose a way of modifying the mathematical model of the nondestructive theoretical-experimental method of determining the residual stresses for a specific collection of technological conditions for welding two cylindrical glass shells. The method is based on the general theory of boundary-value problems for ordinary differential equations.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 69–73.     

Diagnostics of residual stresses and estimation of their influence on the static strength of welded joints of pipes with different thicknesses with crack-type defects

Within the framework of the calculation-experimental method suggested by Pidstryhach and his followers, a athematical model for definition of residual stresses in the zone of circular welded joints of pipes with different thicknesses is developed. We constructed a functional to determine the residual thermoplastic strains on the basis of theoretical relations and experimental data obtained by a nondestructive (semidestructive) methods. Using the two-parametric criterion R6 of fracture mechanics and a failure assessment diagram constructed on its basis, the strength reserve coefficients of a welded joint of the main pipeline with different thicknesses under internal pressure and the presence of a surface crack in the thinner pipe wall are determined. The influence of residual stresses on the strength reserve coefficients is estimated.     

The inverse conditionally correct problem of determining the residual stresses in compound welded shells of revoltuion

We solve the inverse conditionally correct problem of recovering the complete picture of the residual stressed state for a compound shell welded from two parts, one cylindrical and the othe conical. We apply the partial values of the stresses obtained experimentally by the method of photoelasticity. We also apply the numerical method of spline-collocations. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 130–134.     

Determination of residual stresses in a layered system during two-sided high-temperature spray-coating

In order to describe the process of high-temperature spray-coating of covering layers, we prescribe boundary conditions determining the effect of the covering layers on the heat-exchange of the sublayer with the medium, and generalize to the case in which the quantity of heat introduced by the jet of plasma-forming gas is taken into account. Analytic expressions for the thermal stress state in a sheet with covering layers on each side are obtained. Computations of residual stresses in a steel sheet and the forces in the spray-coating on its surface are conducted for the cases of nichrome and aluminum alloys.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie, Polya, No. 29, pp. 8–12, 1989.     

Calculation of the residual stresses in wound glass-reinforced plastics

The effect of the winding and polymerization conditions on the residual stress distribution in wound glass-reinforced plastic cylinders is subjected to a numerical analysis. The calculations are based on the method proposed in [1]. The computer data are examined and the theoretical and experimental results compared.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1026–1030, November–December, 1970.     

Determination of the reliability of glass structures with steady and alternating loads

A method is developed for determining the reliability (nonfailure probability) of glass structures for a prescribed loading duration by alternating loads; an equation is obtained for calculating the reliability of glass structures from material (glass) strength parameters. It is shown that reliability with steady loads is a particular case of reliability with alternating loads. The method developed is based on a correlation established between long-term strength of the material and glass structure, and use of a new criterion of equal reliabilities for alternating loads.Lvov. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 90–97, 1990.     

Structural residual stresses in oriented glass-reinforced plastics

A previously proposed method is used to obtain expressions for calculating the residual stresses as a function of the physicomechanical properties of the polymer matrix and the reinforcement ratio. The calculation results are presented and the corresponding state of stress and strain analyzed. There are considerable deviations (in the magnitude and distribution of the stresses) from models that neglect or only take partly into account the interaction of the fibers.Moscow Ordzhonikidze Aviation Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1051–1058, November–December, 1968.     

Thermal stresses in viscoelastic structures

Zusammenfassung Das thermo-mechanische Verhalten eines statisch unbestimmten Fachwerks wird untersucht unter der Annahme, dass die Fachwerkstäbe der Maxwellschen Spannungs-Formänderungsbeziehung gehorchen. Insbesondere wird der Einfluss typischer Last- und Temperaturänderungen besprochen. Obwohl der genaue Zusammenhang zwischen Spannung und Kriechgeschwindigkeit in Baumetallen weniger einfach ist als der für das Maxwellsche Material vorausgesetzte lineare Zusammenhang, kann man erwarten, dass das hier besprochene Modell den Einfluss von Kriechvorgängen auf die Spannungen in statisch unbestimmten Konstruktionen qualitativ wiedergibt.

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The results presented in this paper were obtained in the course of research sponsored by the Ballistic Research Laboratories of Aberdeen Proving Ground under contract DA-19-020-ORD-798.     

Computation of thermal residual stresses in optic fibers

We propose an analytic method of determining all the components of the residual stress tensor in optic fibers. The method is based on solving a plane problem for a cylindrical structure with singular stresses. We obtain closed-form solutions of the problem in the case of a piecewise-constant distribution of free deformations that model the presence of inclusions in the fiber with different values of the thermal coefficient of expansion. We also consider inclusions with cross sections in the shape of a circle, a central ellipse and a central annular sector. We describe the results obtained on this basis in the computation of residual thermal stresses.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 79–83.     

Investigation of the residual stresses in the carbamide polymer-glass boundary layer

The residual stresses at the carbamide polymer-glass interface have been investigated for the first time. It has been established that a high residual stress level exists in the polymer-glass boundary layer. Methods of reducing the residual microstress level are indicated.     

Invariant operators and separation of residual stresses

We consider the equations of linear theory of elasticity in stresses for the threedimensional space. Solutions are decomposed into sums of stationary solutions not satisfying the compatibility condition (residual stresses) and nonstationary solutions satisfying the compatibility condition and hence represented through the displacements. The construction of this decomposition is reduced to solving a series of Poisson equations.     

Shrinkage stresses in bonded plexiglas structures

It is shown by means of photoelasticity that the shrinkage stresses associated with cold polymerization of the adhesive layer in bonded plexiglas structural elements seriously reduce the reliability of the structure. By suitable heat treatment it is possible to reduce the shrinkage stresses by a factor of approximately four without distorting the shape of the element and increase the permissible stresses by a factor of almost three.S. M. Kirov Ural Polytechnical Institute, Sverdlovsk. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 734–736, July–August, 1968.     

Calculation of the residual stresses and strains in wound reinforced-plastic products

A method is proposed for determining the residual stresses and strains in wound glass-reinforced plastic products. The fabrication process is divided into five stages: winding, heating polymerization, cooling, and removal from the mandrel. The initial stresses that develop during winding and the subsequent stress increment associated with heating are taken into account. Polymerization is treated as a process during which the mechanical and thermophysical properties of the material change. Chemical shrinkage of the resin and its filtration through the fiberglass are disregarded. Equations are derived for the residual radial and peripheral stresses in the finished product, for the residual change in inside diameter, and for the temperature at which the product is released from the mandrel during the cooling process. The experimental data relating to two types of wound products are discussed. The results of a computation of the residual stresses and the residual changes in inside diameter are compared with the experimental data.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 134–139, January–February, 1969.