Mathematical simulation of the strength of a pipe with three-dimensional defect

We develop a mathematical model of plastic fracture of a thin-walled pipe with three-dimensional part-through “smooth” defect and compute the degree of weakening caused by this defect. The defect is simulated by an elliptic (in plan) slot appearing in the pipe. It is necessary to find the level of internal pressure under which the material in the zone of the defect passes into the limiting state. or sufficiently deep defects whose sizes are much smaller than the radius of the pipe, the problem of determination of the stress-strain state in the zone of the defect under given internal pressure is reduced to the solution of a nonlinear system of two one-dimensional integral equations. This system is solved by using an original algorithm and the limiting pressure is found within the framework of the proposed mathematical model. Under certain assumptions concerning the distribution of stresses in the zone of the defect, we deduce a formula which expresses the limiting pressure via the sizes of the defect and the strength characteristics of the material. The results of theoretical analysis are compared with numerical data obtained by the method of finite elements. PNVP “Integrator”. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 1, pp. 65–70, January–February, 1998.     

Pipe-defect assessment based on the limit analysis, failure-assessment diagram, and subcritical crack growth

We analyze the serviceability of a pipe containing a defect by the following three methods: limit analysis, failure-assessment diagram, and subcritical crack growth. The use of the proposed complex approach is explained by the fact that, despite the plasticity of pipe steels, they can suffer quasibrittle fracture (under the conditions of plane deformation) or fail as a result of plastic collapse. Moreover, the final fracture of a pipe with defect is preceded by the stage of stable crack growth. Therefore, in analyzing the serviceability of the pipe, one should also take into account the “leak-before-break” criterion. To take into account all these circumstances, it is necessary to use the indicated three methods, as in the case of evaluation of the serviceability of a pipe of API X52 steel containing a surface semielliptic notch. Defects of this sort reflect the influence of the surface gouges and dents responsible for the failures of pipes under the action of internal pressure. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 1, pp. 119–127, January–February, 2006.     

Prediction of the service life of pipeline elements subjected to the action of hydrogen-containing media

We study the process of crack propagation in a preliminarily hydrogenated pipe placed in a hydrogen-containing medium. The crack growth rate is mainly controlled by the mass transport of hydrogen into the prefracture zone. We obtain an approximate solution of the problem of diffusion of hydrogen in the vicinity of the crack tip and establish the dependence of the crack growth rate on the crack tip opening displacement. This dependence is used for the determination of the residual service life of damaged elements of the pipe. The pipe is made of 4147 steel and the defect is modeled by a semielliptic longitudinal crack on the internal surface of the pipe. We show that the initial concentration of hydrogen may significantly accelerate the fracture process. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 4, pp. 43–48, July–August, 1999.     

Compressor-adsorber with a heat pipe

A design and mathematical model of a compressor-adsorber employing a heat pipe are described. Based on numerical solution, the effect of the finning parameters on adsorber efficiency is analyzed. Academic Scientific Complex “A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus,” Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 4, pp. 531–539, July–August, 1996.     

Lorentz Force Eddy Current Testing: a Prototype Model

We report an investigation of the motion of a free-falling permanent magnet in an electrically conducting pipe containing an idealized defect. This problem represents a highly simplified yet enlightening version of a method called Lorentz force eddy current testing which is a modification of the traditional eddy current testing technique. Our investigation is a combination of analytical theory, numerical simulation and experimental validation. The analytical theory allows a rigorous prediction about the relation between the size of the defect and the change in falling time which represents the central result of the present work. The numerical simulation allows to overcome limitations inherent in the analytical theory. We test our predictions by performing a series of experiments. We conclude that our theory properly captures the essence of Lorentz force eddy current testing although a refinement of the experiment is necessary to reduce the discrepancy to the predictions. In spite of its apparent simplicity the present system can serve as a prototype and benchmark for future research on Lorentz force eddy current testing.     

Classical Approach to Analyzing the Influence of Edge Boundary Conditions on Stresses and Flexibility of Pipe Elastic Bend

A new analytical method is proposed for the analysis of boundary effect in a pipe bend portion loaded by bending moment combined with internal pressure. The proposed method is based on the simplifying hypotheses, which make possible to represent all deformation- and force-related parameters in terms of the tangential displacement assumed in the form of the Fourier series expansion by the circumferential coordinate. A set of quadric differential equations by axial coordinate containing unknown displacement expansion coefficients is derived. We obtained an analytical approximate solution for a pipe bend portion and precise solution for a straight pipe, which are expressed via Krylov functions. We formulate the application procedure for the method of initial parameter, where the values of tangential and longitudinal displacements, axial and tangential forces are used as boundary conditions. We present the equations relating the above-mentioned parameters in the initial and end sections of the pipe bend portion. The results obtained are compared with the available published data. __________ Translated from Problemy Prochnosti, No. 4, pp. 64 – 94, July – August, 2005.     

Elastoplastic state of a thin-walled pipe under pressure in the process of bending with tension (Compression)

We analyze the elastoplastic state of a rectilinear element of a thin-walled pipeline under pressure in the process of bending with tension (compression) and determine the characteristics of its stiffness. To solve this problem, we use a numerical method based on the deformation theory of plasticity and the momentless theory of shells. The problem is reduced to a one-dimensional problem and the proposed approach enables us to substantially simplify the procedure of numerical calculations. The idea of this approach can be described as follows: the longitudinal stresses and the components of strains are decomposed into two parts, one of which depends only on internal pressure and the second of which reflects the work of the pipe as a rod. By using this computational procedure and also the Mathcad PLUS-6.0 mathematical package, we analyzed the influence of internal pressure and longitudinal forces on the bending strength of the rectilinear elements of main pipelines. A numerical example is presented. The results of numerical calculations are displayed in the form of plots. “L’vivs’ka Politekhnika” State University, Lvov, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 99–105, November–December, 1998.     

Plastic limit load of Grade 91 steel pipe containing local wall thinning defect at high temperature

This paper aims to predict the plastic limit load of Grade 91 pipe at high temperature by experimental and numerical analysis methods. The elastic–plastic constitutive relation of P91 considering creep damage at high temperature is proposed and the effectiveness is verified by high-temperature instantaneous tensile test after creep of P91 sample. Then, using the elastic–plastic constitutive relation considering creep damage, the plastic limit loads of P91 pipe containing local wall thinning (LWT) defect at high temperature have been calculated by finite element (FE) method and the accuracy is checked by high-temperature burst experiment after creep of T91 pipe containing LWT. Finally, the fracture analysis and metallographic analysis of Grade 91 sample and pipe containing LWT defect are performed. The results show that the elastic–plastic constitutive relation of P91 considering creep damage proposed by this paper can well describe the elastic–plastic behavior of P91 under creep condition and is useful to calculate the plastic limit load of P91 pipe containing LWT. The failures of P91 tensile samples and T91 pipes containing LWT defect are both plastic fracture. This research would provide an optional method for structure integrity analysis of the pipe containing LWT defect at high temperature.     

Ultrafiltration in a pipe filter with gelation

We investigate the process of unsteady-state ultrafiltration with gelation under laminar flow conditions in a pipe filter with nonideal selectivity of its membrane. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 3, pp. 503–508, May–June, 1998.     

Modeling of ion-implanted arsenic diffusion in a polysilicon-silicon system

A model of transfer processes of impurity atoms in a poly silicon-silicon system which describes the segregation of the impurity at the phase boundary is constructed. An algorithm is developed and numerical calculations are made for arsenic diffusion with allowance for a nonuniform defect distribution at the phase boundary. Translated from Inzhenerno-Fisicheskii Zhurnal, Vol. 70, No. 6, pp. 1025–1032, November–December, 1997.     

Analysis of the stressed state in equal-diameter T-joints of pipelines. Part 1. Action of internal pressure and bending moments in the plane of a T-joint

We analyze the stressed state of two types of T-joints in which the union makes angles of 45° and 90° with the main pipe. The character of the distribution of stresses in a T-joint illustrates the distinctive features of its operation under the action of internal pressure and bending moments applied in the plane of the T-joint. On the basis of the theory of strength for specific distortion strain energy, we determine the stress concentration factors for all considered loading modes. The numerical values of the stress concentration factors are compared with the experimental data obtained by other authors. Translated from Problemy Prochnosti, No. 6, pp. 116–123, November–December, 1998.     

Flow of a gas out of the vessel to a medium with counterpressure under the conditions of intense heat supply

The basic regularities of the influence of heat supply on the parameters of the flow have been elucidated with the use of analytical and numerical solutions of the quasi-one-dimensional problem on flow, through a pipe, of the gas out of a vessel with prescribed pressure and stagnation temperature to a medium with a prescribed counterpressure. It has been shown that changeover from the stationary outflow to an unsteady self-oscillatory regime of outflow is possible with increase in the thermal action on the flow. The asymptotic dependences of the flow parameter in the case of an infinitely large supplied heat have been obtained; these dependences are used in finding the scale quantities and unified generalized dependences for the period-averaged parameters of nonstationary self-oscillatory flows. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 530–537, May–June, 2008.     

Residual strength of cylindrical elements with cracks healed by using the injection technology

We obtain an approximate analytic solution of the problem of filled cracklike defect in a cylinder and determine the degree of hardening of a cylindrical structural element containing a crack filled with injection material. The parameters specifying the efficiency of injection strengthening are established. The results of experimental verification confirm the theoretical predictions concerning the possibility of strengthening of structural elements by the injection technologies of healing the defects. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 1, pp. 99–103, January–February, 2007.     

Life assessment for a gas turbine blade under creep conditions based on continuum fracture mechanics

Based on the semi-analytic finite element method and relationships of the continuum fracture mechanics, a numerical investigation on the creep and extension of the continuum fracture zone in a gas turbine blade is performed. The value of life prior to the formation of a crack-like defect and applicability limits of the relationships of continuum fracture mechanics are determined. __________ Translated from Problemy Prochnosti, No. 4, pp. 87–93, July–August, 2006.     

Defect propagation at a circular interface

In this paper a nonlinear, nonuniform cohesive zone is employed to study the detailed features of quasi-static defect evolution in a simple, planar elastic system consisting of a circular inclusion embedded in an unbounded matrix subject to different remote loading configurations. The inclusion–matrix interface is assumed to be described by Needleman-type force-separation relations characterized by an interface strength, a characteristic force length and a shear stiffness parameter. Interface defects are modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body inclusion displacement, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. For equibiaxial tension, quasi-static defect initiation and propagation occur under increasing remote load. For decreasing characteristic force length, a transition occurs from more or less uniform decohesion along the bond line to propagation of a crack-like defect. In the later case a critical failure load is well defined and interface failure is shown to be defect dominated (brittle decohesion). For interfaces with large characteristic force length, the matrix “lifts off” the inclusion accompanied by a delay in defect propagation (ductile decohesion). The decohesion modes ultimately give rise to a cavity with the inclusion situated within it on the side opposite to the original defect. Results for small characteristic force length show consistency with England’s results for the sharp arc crack on a circular interface (England AH (1966) ASME J Appl Mech 33:637–640) Stress oscillation and contact at the tip of the defect are observed primarily for small characteristic force lengths under extremely small loading. Results for remote tension, compression and pure shear loading are discussed as well. In the final section of the paper the results obtained in the first part are utilized to estimate the plane effective bulk response of a composite containing a dilute distribution of inclusions with randomly oriented interface defects.     

On the critical size of microcracks initiated in materials

We obtain an explicit expression for the potential energy of an elastic body containing a crack with prefracture zones at its tips. This expression is used to construct an analytic dependence of the critical size of a microcrack required for its transformation into a macroscopic defect by using the theory of catastrophes. The reliability of the obtained theoretical values of the critical size of a microcrack is corroborated by comparing these results with the available experimental data. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 34, No. 3, pp. 79–83, May–June, 1998.     

Prediction of residual pipeline resource taking into account the operation loading conditions

An effective energy approach to the evaluation of the residual service life of a pipe of oil pipeline containing a crack on its inner surface for the two-frequency loading mode of biaxial tension-compression has been proposed. The two-frequency variations of pressure in the pipe are caused by the turbulence of the oil flow (high frequency), opening and closing of the gate valves, and the shutdowns of the pumps (low frequency). __________ Translated from Problemy Prochnosti, No. 1, pp. 44–52, January–February, 2009.     

Analysis of the limiting plastic state of a thick-walled bent pipe

We propose an engineering approach to the determination of the limiting state of a bent pipe. In the first stage, the influence of some groups of external loads is analyzed separately. Then it is necessary to determine the coefficient of reduction of internal moments under the combined action of external bending moments and internal pressure. In the final stage, we use a specially developed general approach to the analysis of the limiting state at a given point of the cross-section of a bent pipe for the obtained system of internal forces, namely, for the bending moment, the tensile force acting in the circumferential direction, and longitudinal and tangential forces. We also demonstrate the possibility of application of the obtained results to the approximate analysis of cracks and three-dimensional defects appearing in a bent pipe. Scientific and Engineering Center of Materials-Science Support of the Production and Certification of Equipment of Nuclear Power Plants at the Institute for Problems of Strength of the National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 131 – 150, March – April, 1998.     

Inverse problem of thermoelasticity for the isotropic medium containing a cavity in the case of triaxial tension with constant temperature on the surface

We consider the inverse problem of thermoelasticity for an isotropic medium containing a cavity of unknown shape and subjected to the action of mechanical and thermal loads. Nonlinear equations are deduced for the geometric parameters of an ellipsoidal equistressed cavity. Similar relations for mechanical loads obtained by the other authors follow from the constructed equations as special cases. The numerical analysis is performed and the relationship between the values of the loads and the parameters of the cavity is investigated. The stresses on the equistressed surface of the cavity are found and the influence of temperature on the relationship between the parameters of loads and the geometric characteristics of the equistressed cavity is analyzed. __________ Translated from Problemy Prochnosti, No. 1, pp. 121–131, January–February, 2007.     

Dynamic instability of a pipe with internal mobile liquid blocks

We consider the problem of parametric vibrations of a rectilinear pipeline with internal mobile liquid blocks. As a result of its solution, we determine the influence of the size of the liquid blocks and their velocity on the character of the loss of stability of the pipe. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 114–121, May–June, 1999.