Modeling of fluid dynamics interacting with ductile fraction propagation in high pressure pipeline

This paper presents a computational model for the fluid dynamics in a fractured ductile pipe under high pressure. The pressure profile in front of the crack tip, which is the driving source of crack propagation, is computed using a nonlinear wave equation. The solution is coupled with a one dimensional choked flow analysis behind the crack. The simulation utilizes a high order optimized prefactored compact-finite volume method in space, and low dispersion and dissipation Runge-Kutta in time. As the pipe fractures the rapid depressurization take place inside the pipe and the propagation of the crack-induced waves strongly influences the outflow dynamics. Consistent with the experimental observation, the model predicts the expansion wave inside the pipe, and the reflection and outflow of the wave. The model also helps characterize the propagation of the crack dynamics and fluid flows around the tip of the crack.     

Dynamic measurements of initiation toughness at high loading rates

An experimental method is described for measuring the dynamic initiation toughness of a sharp stationary crack. A plane specimen is utilized which consists of a central region 50-mm wide and 200-mm long with integral dog-bone ends. The loading is accomplished by the detonation of four small explosive charges which produce two tensile stress waves upon reflection from the dog-bone ends. The stress waves meet at the midpoint of the specimen and reinforce to produce a relatively large, uniformly stressed region with a very high loading rate. The crack is positioned at the midpoint of the specimen at the location where the reinforcing tensile stress waves meet. A series of photoelastic experiments were conducted using Homalite 100 as the model material to observe, in a full-field view, the arrival of the dilatational waves, the subsequent development of the stress field at the tip of the stationary crack and the initiation of the crack. The isochromatic fringe pattern was also used to determine the instantaneous value of the stress-intensity factorK(t) after the characteristic fringe loops developed in the region near the crack tip. Finally,K(t) was measured using a single strain gage positioned and oriented so that its signal output was proportional toK(t) and independent of the next two higher order terms in the series representation of the strain field. A method was developed to determine the instant of initiation from the strain-time trace. Results obtained from the photoelastic and strain measurements of the dynamic-initiation toughnessK _ID were consistently higher than the static value ofK _IC . Paper was presented at the 1987 SEM Fall Conference on Experimental Mechanics held in Savannah, GA on October 25–28.     

The flow field near the triple point in steady shock reflection

This paper investigates the flow field near three intersecting shock waves appearing in steady Mach reflection. Results of numerical computations reveal a “von Neumann Paradox”—like feature for weak shock waves, in which the flow field between the reflected and the Mach stem is smooth with no distinct slip flow region and changes rather smoothly. An analytical solution of the Navier–Stokes equations constructed using a polar–coordinate system gives a flow field with the same properties as the numerical simulation.     

Optimization formulation of the evolutionary problem of crack propagation under quasibrittle fracture

For the evolutionary problem describing crack propagation in a solid with allowance for the irreversible work of plastic deformation due to the crack propagation, a general optimization formulation is proposed and investigated. For the optimum crack, data on the H²-smoothnesses of the displacement field in the solid and, hence, on the finiteness of the stress at the crack tip, are obtained. The solvability of the optimization problem (i.e., the existence of an optimum crack) is proved for a curvilinear crack propagation path specified a priori. For the particular case of a straight path, a generalized criterion of crack growth is proposed. The question of the choice of a crack propagation path is discussed and a comparison with existing fracture criteria is made. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 107–118, September–October, 2006.     

Mechanism of Fatigue-Crack Growth under Compressive External Stresses

A specimen with a crack shaped like a thin long defect with parallel edges and a rounded tip of finite radius is considered. When the specimen is subjected to compressive cyclic loads, the stresses in zones adjacent to the crack tip vary according to a sign-variable cycle because of plastic strains occurring at the crack tip. This can cause fatigue-crack growth. Results of numerical simulations and experimental data support the possibility of fatigue-crack growth in the field of compressive external stresses. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 108–115, November–December, 2005.     

Internal gravity waves in critical generation modes and in the vicinity of trajectories of motion of perturbation sources

The field of internal gravity waves in a layer of an arbitrary stratified fluid is studied for critical generation modes and in the vicinity of trajectories of motion of the perturbation sources. The exact solutions describing the structure of a separate mode of the wave field in the vicinity of the perturbation source in the critical generation modes are investigated, and expressions for the total field representing the sum of all wave modes are obtained. In the vicinity of the trajectories of the perturbation sources, asymptotic representations of the eigenfunctions and eigenvalues of the basic vertical spectral problem of internal waves are constructed in the approximation of large wave numbers and asymptotic expressions for a separate mode of the wave field are obtained that describe the spatial structure and features of the fields of internal gravity waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 70–79, September–October, 2008.     

Wave processes in solids with defects

The propagation of plane harmonic waves in viscoelastic and elastoviscoplastic materials are studied using the equations of the field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. Wave propagation velocities and refraction and absorption coefficients are determined. The structure of the waves and the correlation between the displacement waves and the defect-field waves determining plastic deformation are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 190–197, November–December, 2008.     

Influence of contact interaction between the sides of crack on characteristics of failure mechanics in action ofP- andSV-waves

The effect of contact between the sides of a rectilinear crack in the planeR ²={x: x₃=0} on the characteristics of the fallure mechanics is studied for the case in which the crack is affected by harmonic tensile-compression waves and shifts. The surfaces of the crack may assume any orientation relative to the direction of propagation of the waves. The presence of friction in the zone of contact of the sides of the crack is taken into account. The method of solving the problem stated is iterative in nature and is based on the solution of a sequence of boundary integral equations for the Fourier coefficients of the displacement discontinuity vector and the contact force vector. It is also corrected at each step of the solution so as to satisfy one-sided restrictions in the zone of contact. Kharkov Highway Technical Institute, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 70–75, February, 1999.     

Gas-dynamic flow structure of a system of plane supersonic intersecting jets in a hypersonic flow

Turbulent motion is described by a system of parabolized Novier-Stokes equations which is closed by the (k-ε) model of turbulence. In the numerical calculations performed by the method of decomposing the flow vectors, the complex pattern of the interaction between perturbation waves is shown. In addition, it is shown that the system of shock waves on a gas-dynamic site causes the production of the pulsation-motion energy and the appearance of dissipative cellular structures in the field of kinetic turbulence energy. Al-Farabi Kazakh National State University, Almaty 480121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 108–114, January–February, 1999.     

Uniform far field asymptotics of internal gravity waves from a source moving in a stratified fluid layer with smoothly varying bottom

The far field asymptotics of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern of the ocean shelf eract analytic expressions are obtained for the rays, and the properties of the phase structure of the wave field are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 111–120, May–June, 1998. This work was financially supported by the Russian Foundation for Basic Research (project No. 96-01-01120).     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System

We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.     

Magnetovibrational flows in a magnetic fluid

A new type of flow in a magnetic fluid has been experimentally detected and investigated. The interaction between an alternating nonuniform magnetic field and a magnetic fluid leads to the parametric excitation of traveling capillary-gravitational waves which are the direct cause of the average flow. A necessary condition of formation of hydrodynamic flows in an alternating field is also the presence of time-dependent harmonics with multiple frequencies synchronized with the first harmonic, so that the time dependence of the ponderomotive force is generally pulsed. It is shown that for plane vibrational flows the classical theory cannot explain the high intensity of the average flows observed. It is suggested that the high intensity of magnetovibrational flows is related to the violation of the cylindrical symmetry of the traveling capillary-gravitational waves and the transition to a three-dimensional motion. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–133, January–February, 1998.     

Effect of viscosity on the propagation of nonlinear Alfvén waves along a tangential magnetohydrodynamic discontinuity in an incompressible fluid

It is proposed to consider the propagation of surface waves along a tangential magnetohydrodynamic discontinuity in the particular case where the fluid velocities on both sides of the interface are equal to zero. In [1] it was shown that waves called surface Alfvén waves may be propagated along the surface separating a semi-infinite region without a field from a region with a uniform magnetic field. The linear theory of surface Alfvén waves in a compressible medium was considered in [2]. In [3] the damping of surface Alfvén waves as a result of viscosity and heat conduction was investigated. The propagation of low-amplitude nonlinear surface Alfvén waves in an incompressible fluid in the absence of dissipative processes is described by the integrodifferential equation obtained in [4]. By means of a numerical solution of this equation it was shown that a perturbation initially in the form of a sinusoidal wave will break. The breaking time was determined. In this paper the equation derived in [4] is extended to the case of a viscous fluid. It is shown that the equation obtained does not have steady-state solutions. The propagation of periodic disturbances is investigated numerically. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–104, November–December, 1986. The author wishes to thank L. S. Fedorov for assisting with the calculations.     

The equilibrium of a piezoceramic cylindrical body with a parabolic crack

A conjugate electroelastic field in a piezoceramic cylinder with a parabolic crack under static loading is investigated. Uniformly tensile stresses and an electric potential are applied to the end faces of the cylinder. The following two types of electric conditions are considered at the crack boundary: the electric potential is continuous across the crack and the normal component of the electric-displacement vector on the crack surface is equal to zero. For each of these cases, expressions for some quantities characterizing the disturbed field in the crack plane and formulas to calculate the stress intensity factors are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 72–80, March, 2000.     

Improved model of the griffith crack

The plane-stress state of a cracked continuous medium in tension is determined using relaxation elements. The stress state is analyzed at the tip of a crack surrounded by a plastically deformed material as a band of localized plastic deformation (LPD) shaped like an elongated ellipse. The plastic deformation considerably decreases the stress concentration at the crack tip. As the localization of the plastic deformation increases, the stresses at the crack sides decrease to zero. The decrease in stresses at the tip is accompanied by an increase in the concentration and gradients of the stresses at the end of theLPD band. Here the region of perturbation of the stress field is comparable with the width of the band. Institute of Physics of Strength and Materials Science, Tomsk 634055. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 132–141, November–December, 1998.     

Universal regularities of hydraulic fracturing within the framework of the Perkins-Kern-Nordgren model

An algorithm that permits one to find a solution of the Perkins-Kern-Nordgren problem for standard regimes of hydraulic fracturing is suggested. The universal qualitative specifics, of the behavior of a crack is shown; in particular, the asymptotics of crack opening at the tip is found, and it is shown that the character of the crack is determined by the rate of increase or decrease in the crack size. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 149–157, May–June, 1998.     

Analysis of the derivative of the energy functional with respect to the length of a curvilinear crack in an elastic body with a possible crack-edge contact

A homogeneous two-dimensional body with a crack of variable length is considered. At the crack edges, conditions are formulated in the form of inequalities that describe mutual nonpenetration of the edges. The derivative of the elastic-energy functional with respect to the length of the curvilinear crack is analyzed. It is shown that the derivative is independent of the crack path, provided that the curve along which the crack propagates is reasonably smooth. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 138–145, September–October, 2007.     

Griffith crack moving in a piezoelectric strip

Summary  The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack in a piezoelectric strip. Received 14 August 2001; accepted for publication 24 September 2002 The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported by the National Natural Science Foundation of China under Grant 70272043.