Strain rate intensity factors for a plastic mass flow between two conical surfaces

The concept of strain rate intensity factor was introduced in [1], where the asymptotic expansion of the velocity field in a perfectly rigid-plastic material was obtained near the maximum friction surface, which is determined by the condition that the specific friction forces on this surface are equal to the simple shear yield strength. In particular, it was shown in this paper that near the maximum friction surface the equivalent strain rate (the second invariant of the strain rate tensor) tends to infinity inversely proportional to the square root of the distance to this surface. We note that the same result was obtained in the case of plane flow in [2]. The strain rate intensity factor is defined to be the coefficient of the leading singular number in the series expansion of the equivalent strain rate near the maximum friction surface. It was shown in [3] that there is a sufficiently complete formal analogy between the strain rate intensity factor and the stress intensity factor in mechanics of cracks [4]. In [5], it was suggested to use the concept of strain rate intensity factor to estimate the thickness of the layer near the friction surface where one should take into account viscosity effects. (Thus, this is an intensive strain layer formed as a result of a very large equivalent strain rate.) Therefore, the problem of calculating the strain rate intensity factor in specific processes is topical in the development of the general concept based on the use of the strain rate intensity factor and its applications in the theory of metal forming processes. These factors have already been calculated for several processes such as plane upsetting and drawing [3]. In the present paper, we calculate the distribution of the strain rate intensity factor in a plastic mass flow through an infinite converging channel formed by two conical surfaces on which the law of maximum friction acts (Fig. 1). A specific characteristic of this problem is the existence of two maximum friction surfaces and, accordingly, two distributions of the strain rate intensity factor. Since, according to the theory [5], the strain rate intensity factor is related to the thickness of the intensive strain layer near the friction surface, the solution of this problem may serve as a starting point for experimental confirmations of the theory. Note that the intensive strain layer thickness can be determined experimentally without any difficulties [6, 7] and the flow in an infinite channel of the shape under study can successfully model the tube drawing process [8].     

Strain-rate intensity factor in compression of a layer of a plastic material between cylindrical surfaces

A model problem for a rigid perfectly/plastic material is obtained. Based on this solution, it is possible to estimate the influence of the friction surface curvature and one of the types of additional rotational motion of the friction surface on the strain-rate intensity factor. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 171–180, May–June, 2009.     

Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.     

Thermoelastic stress intensity factors for a cracked layer between two different anisotropic solids

Steady-state anisotropic thermoelasticity equations are used to obtain the stress intensity factors for a cracked layer sandwiched between two different anisotropic elastic solids. The anisotropy is assumed to arise from discrete fibers whose orientation could alter with reference to the crack edges. A generalized plane deformation prevails in the dissimilar media domain with a line of discontinuity disturbing a uniform heat flow. The flexibility/stiffness matrix approach is used such that the crack problem reduces to solving two sets of singular integral equations. Numerical values of the crack tip stress-intensity factors are obtained for various crack size, crack location, crack surface insulation, fiber volume fraction and orientation angles. The results are displayed graphically.     

Koiter-boundary layer singular perturbation method for axial compressed stiffened cylindrical shells

I.IntroductionStiffenedandunstiffenedcircularcylindricalshellsfoundwideusesasprimarystructuralcomponentsinunderwatervehicles,offshoreplatformsandotherstructuralconfigurations.Theinitialinvestigationofthebucklingofstiffenedandunstiffenedcircularcylindrical…     

Stress intensity factors for an interface crack with impermeable surfaces between dissimilar electrostrictive materials

The asymptotic problem of a semi-infinite interface crack between dissimilar electrostrictive materials that are subjected to electric loading is numerically analyzed by using the finite element method. Numerical results of electric displacement fields are obtained on the basis of the mathematical equivalence of the mode III problem and an electrostatic problem. The shape and the size of saturation zones are explored as a function of the ratio of the saturated electric displacements of dissimilar electrostrictive materials. In contrast with conventional wisdom, the ratio of the permittivities is shown to exert a negligibly small influence on electric displacement fields. For various combinations of the material properties of dissimilar electrostrictive materials, stress fields and stress intensity factors are systemically calculated by using the numerical results of electric displacement fields. The effects of the electric, elastic, and electrostrictive properties on stress intensity factors are demonstrated.     

Compression of a plastic porous material between rotating plates

The problem of a plane flow of a rigid-plastic porous material between two rotating rough plates with no material flux through the point of their rotation and with a uniform distribution of porosity at the initial instant is considered under the assumption that the material behavior follows the cylindrical yield condition and the associated flow rule. The solution reduces to consecutive calculation of several ordinary integrals. It is demonstrated that the solution behavior depends on the angle between the plates, and the value of porosity at a certain stage of the deformation process can be equal to zero. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 128–135, July–August, 2009.     

Dynamic intensity factors for an interface flaw extending at a non-uniform rate

Two initially undisturbed dissimilar elastic half-spaces are perfectly bonded along half of their interface and separated by a semi-infinite flaw along the remainder. Induced by time-independent anti-plane tractions applied at the flaw edge and subsequently distributed over the newly-created surfaces, the flaw starts from rest and extends along the interface at a non-uniform rate, giving rise to wave motion in the half-spaces. By first examining the same flaw extending at a constant rate and then suddenly halting, conclusions are reached which lead to the derivation of the dynamic intensity factors for the stress and difference in the particle velocities at the edge of the non-uniformly extending flaw.

---

Zusammenfassung Zwei anfänglich ungestörte verschiedene elastische Halbräume sind vollkommen verbunden entlang der Hälfte der Grenzfläche und getrennt bei einem Schnitt in dem restlichen unendlichen Halbraum. Induzient bei einer zeitunabhänglicher Schubspannung angewandt an der Risskante und nachfolgend uber die nuerschaffene Fläche verteilt, der Riss fangt von der Ruhelage an und ausbreitet sich in einer ungleichmassiger Geschwindigkeit und verursacht eine Wellenberregung in den Halbräumen. Durch eine anfänglich Untersuchung das selben Risses der sich mit gleichmässiger Geschwindigkeit ausdehnt und dann plötzlich anhalt werden Schlussfolgerungen erreicht melche zu der Ableitung von dem dynamischen intensitätsfaktor für die Spannung und der Unterschied in der Teilchengeschwindigkeit an der Kante das ungleichmassig langgestrecktem Riss.

     

Acceleration waves in rate type plastic material with general work-hardening

The acceleration waves propagating in the rate type plastic material are investigated, where the material has isotropic and kinematic work-hardening. The waves are classified into unloading and loading waves, and have, in general, different propagation velocities. The propagation velocities of the principal waves are obtained for the Prandtl-Reuss material and the T material.     

Integral formulation for a circular cylindrical cavity in infinite solid and a finite length coaxial cylindrical crack compressed axially

A method for solving problems of fracture of an infinite solid with a circular cylindrical cavity and a coaxial cylindrical crack near the surface under an uniform axial compression is proposed using a non-classical criterial approach associated with a mechanism of a local stability loss near the defect. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a system of linear algebraic equations with respect to the contraction parameter.     

Stress intensity factors around a cylindrical crack in an interfacial zone in composite materials

Axisymmetric stresses around a cylindrical crack in an interfacial cylindrical layer between an infinite elastic medium with a cylindrical cavity and a circular elastic cylinder made of another material have been determined. The material constants of the layer vary continuously from those of the infinite medium to those of the cylinder. Tension surrounding the cylinder and perpendicular to the axis of the cylinder is applied to the composite materials. To solve this problem, the interfacial layer is divided into several layers with different material properties. The boundary conditions are reduced to dual integral equations. The differences in the crack faces are expanded in a series so as to satisfy the conditions outside the crack. The unknown coefficients in the series are solved using the conditions inside the crack. Numerical calculations are performed for several thicknesses of the interfacial layer. Using these numerical results, the stress intensity factors are evaluated for infinitesimal thickness of the layer.     

On the application of boundary layer method in the large deflection plastic buckling of a cylindrical shell

Using a cylindrical shell under axial loading as an example, we discuss the possibility of applying the membrane theory together with the boundary layer correction to analyze the large deflection plastic buckling problem. In the cases of fixed ends and simply-supported ends, the conditions to be satisfied for using the boundary layer method (also called the composite-expansion method) are given and discussed.     

Analytical investigation of boundary layer growth and swirl intensity decay rate in a pipe

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed that the free vortex velocity profile can better predict the boundary layer parameters in the entrance region than in the forced one. Also, effects of pressure gradient inside the boundary layer is investigated and showed that if pressure gradient is ignored inside the boundary layer, results deviate greatly from the experimental data.     

Mass optimization of a compressed cylindrical shell with limited life

A new optimization model is proposed to design corrosion-affected structures with limited life. The optimization problem is stated as a nonlinear-programming problem. The mass of the structure is minimized. The design is considered optimal when physical wear and obsolescence arrive simultaneously. A smooth cylindrical shell compressed in the longitudinal direction is used to illustrate the model __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 97–101, March 2006.