Heterogeneity of Plastic Flow of Zirconium Alloys with a Parabolic Law of Strain Hardening

The specific features of plastic–strain macrolocalization at the stage of the parabolic law of strain hardening in samples from industrial zirconium–based alloys are considered. It is shown that in predeformed blanks, zones with a different character of plastic–strain localization are formed. It is also shown that the strain–localization macropattern can be used as a characteristic of the susceptibility of a material to further plastic form–changing, for example, upon tube rolling. The sign of fracture of alloys upon plastic deformation is revealed. The scale effect in the formation of localizedplastic–flow zones is shown and studied.     

Generalized rheological model of cavitating condensed media

It is shown that development of cavitation in solid–plastic, liquid–plastic, and liquid media can be modeled using a rheologically equivalent, cavitating viscoelastoplastic body containing microcavities in the initial state. An energy inequality is derived that defines the loading conditions for a body with microcavities under which the body enters a cavitating state, i.e., the concentration of microcavities increases by more than an order of magnitude. A generalized rheological equation of state is formulated; analytical dependences of the modulus of volume elasticity, volumetric (second) viscosity, and the relaxation time of tensile stresses on the volume concentration of cavitational hollows in the model viscoelastoplastic body are derived.     

Relationship between plastic and intrinsic dissipations

In this paper, the relationship between the plastic and intrinsic dissipations is addressed within the normality structure of [Rice, J.R., 1971. Inelastic constitutive relations for solids: an integral variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455; Rice, J.R., 1975. Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In: Argon, A.S. (Ed.), Constitutive Equations in Plasticity. MIT Press, Cambridge, MA, pp. 23–79.] It is shown that the plastic dissipation is generally not equal to the intrinsic dissipation. Within the normality structure, the microscale and macroscale thermodynamic fluxes and forces are related by the conditions of energy and dissipation equivalence. If the plastic dissipation is required to be equal to the intrinsic dissipation, J₂ potential and the Levy–Mises equation are recovered from the condition of dissipation equivalence for incompressible plastic flows.     

Elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with progressive debonding damage

This paper deals with elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with debonding damage of particle-matrix interface. Numerical analyses are carried out on a crack-tip field in elastic-matrix and elastic–plastic-matrix composites reinforced with elastic particles, using a finite element method developed based on an incremental damage theory of particulate-reinforced composites. A particle volume fraction and interfacial strength between particles and matrix of the composites are parametrically changed. In the elastic-matrix composites, a unique elastic singular field is created on the complete damage zone in the vicinity of a crack-tip in addition to the conventional elastic singular field on the no damage zone. The macroscopic stress level around a crack-tip is reduced by the debonding damage while the microscopic stress level of the matrix remains unchanged. In the elastic–plastic-matrix composites, the damage zone develops in addition to the plastic zone due to matrix plasticity, and both the macroscopic and microscopic stress revels around a crack-tip are reduced by the debonding damage. It is concluded from the numerical results that the toughening due to damage could be expected in the elastic–plastic-matrix composites, while it is questionable in the elastic-matrix composites.     

Estimate of the Latent Free Energy and Damage at the Tip of an Opening–Mode Crack

A method of estimating the latent elastic energy associated with the microinhomogeneity of the stress and plastic–strain fields inside the plastic zone localized near the tip of an opening–mode crack (Dugdale zone) under conditions of plane stresses is proposed. The microinhomogeneity of plastic flow upon small strain hardening is taken into account only in the form of considerable distortion of the geometry of the free surfaces of the plastic zone. The damage that developes because of release of the latent free energy is estimated depending on the magnitude of the crack opening.     

Elastoplastic deformations of rotating parabolic solid disks using Tresca''s yield criterion

Analytical solutions for the stress distribution in rotating parabolic solid disks are obtained. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening. It is shown that, the deformation behavior of the convex parabolic disk is similar to that of the uniform thickness disk, but in the case of concave parabolic solid disk, it is different. In the latter, the plastic core consists of three different plastic regions with different mathematical forms of the yield criteria. Accordingly, three different stages of elastic–plastic deformation occur. All these stages of elastic–plastic deformation are studied in detail. It is also shown mathematically that in the limiting case the parabolic disk solution reduces to the solution of rotating uniform thickness solid disk.     

Dynamics of a cavitational cavity in a non-newtonian fluid

The dynamics of a spherical cavity in a non-Newtonian fluid, described by the Reiner-Rivlin rheological equation [1], is investigated. The equation of radial cavity motion is obtained, where the gas in the cavity is subject to a polytropic law and surface tension is taken into account. The equation of cavity motion is solved numerically for a number of values of the transverse viscosity coefficient. The influence of the transverse viscosity on the collapse process of vapor and gas-filled cavities is shown. Numerical computations are also carried out for the rate of energy dissipation and the pressure distribution in the fluid.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–173, July–August, 1973.The authors are grateful to A. T. Listrove for attention to the research.     

Strain localization analysis using a large deformation anisotropic elastic–plastic model coupled with damage

Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic–plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice’s localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic–plastic-damage model has been implemented in Abaqus/implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully three-dimensional formulation adopted in the numerical development allowed for some new results – e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.     

Experimental determination of the speed ratio in free-molecular flow of nitrogen

The results are given for measurements of the speed ratio carried out in free-molecular flow of nitrogen. It is shown that hypersonic flow is achieved; the values of the speed ratio are close to theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 184–186, July–August, 1973.     

On rupture attributable to creep

The results of creep rupture tests carried out in a plane-stressed state are presented; the experiments confirm the validity of an earlier energy approach as regards the time to rupture under creep conditions [1],Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 140–143, November–December, 1973.     

Behavior of a rigidly plastic cylindrical shell exposed to internal pressure

A law for conservation of energy is used in solving a system of equations describing the one-dimensional motion of an ideally plastic incompressible shell exposed to an expanding polytropic gas in equilibrium. Analytic expressions are obtained for determining the stress and velocity fields in the shell as a function of the displacement of the internal shell boundary.Translated from Zhurual Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 172–176, May–June, 1975.     

Matching of discharge circuit with shell motion in noncylindrical Z-pinch

Model computations of the two-dimensional motion of a shell in a noncylindrical Z-pinch are carried out according to the scheme proposed in [1, 2]. In this two-dimensional snowplow model the configuration of the shell is determined at each instant of time and the shell is assumed to be infinitely thin. The computations are in good agreement with the available experimental data and permit one to predict the dimensions of the chamber and inductance of the discharge circuit necessary for an efficient use of the energy of the condenser battery.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 160–162, March–April, 1973.     

Inelastic Deformation of Flexible Spherical Shells with Two Circular Openings

Elastoplastic analysis of thin-walled spherical shells with two identical circular openings is carried out with allowance for finite deflections. The shells are made of an isotropic homogeneous material and subjected to internal pressure of known intensity. The distributions of stresses (strains or displacements) along the contours of the openings and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for only physical nonlinearity (plastic deformations) and only geometrical nonlinearity (finite deflections) and with a numerical solution of the linearly elastic problem. The stress–strain state near the two openings is analyzed depending on the distance between the openings and the nonlinear factors accounted for     

Gradient elasticity and nonstandard boundary conditions

Gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality. The pertinent thermodynamic restrictions upon the gradient constitutive equations are derived, which are shown to include, besides the field (differential) stress–strain laws, a set of nonstandard boundary conditions. Consistently with the latter thermodynamic requirements, a surface layer with membrane stresses is envisioned in the strained body, which together with the above nonstandard boundary conditions make the body constitutively insulated (i.e. no long distance energy flows out of the boundary surface due to nonlocality). The total strain energy is shown to include a bulk and surface strain energy. A minimum total potential energy principle is provided for the related structural boundary-value problem. The Toupin–Mindlin polar-type strain gradient material model is also addressed and compared with the above one, their substantial differences are pointed out, particularly for what regards the constitutive equations and the boundary conditions accompanying the solving displacement equilibrium equations. A gradient one-dimensional bar sample in tension is considered for a few applications of the proposed theory.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

Elastic–plastic and elastic anti-plane shear of two parallel cracks

Two infinite interacting parallel cracks in an elastic–plastic and in an elastic body under anti-plane strain (mode III) loading conditions are considered. The body is subjected to vanishing remote loading and the cracks are traction free. Closed-form solution is found for the elastic–plastic problem in terms of elementary functions, where the shape of the plastic boundary is obtained. The complete stress distribution is obtained in an inverse form i.e. physical coordinates are functions of stresses.     

Spectrum of developed turbulence of incompressible viscoelastic fluids

It is shown that fine-scale turbulent motions of a viscoelastic fluid damp out as in a viscous fluid with some effective viscosity dependent on the scale of the motion. The elasticity of deformation results in a diminution in the dissipativity of the turbulence, and hence, to an elongation of the high-frequency tail of the spectrum for a given energy influx.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–33, January–February, 1972.     

An energy approach to the link-up of multiple cracks in thin aluminum alloy sheets

An energy approach has been used in the study of the coalescence or linkage of multiple cracks in aluminum alloy sheets. The study was motivated by concern for the structural integrity of aging aircraft. Forty reported tests for 2024-T3 aluminum panels with a major crack and several multiple-site damage (MSD) cracks have been analyzed via a simple computational model with a Dugdale–Barenblatt [D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–104; G.I. Barenblatt, in: H.L. Dryden, Th. VonKarman (Eds.), Advances in Applied Mechanics, vol. II, 1962, pp. 55–130] type of plastic or inelastic deformation. For simplicity, the computational model considers only the plastic interaction between the major crack and two symmetrically adjacent MSD cracks in an infinite sheet under remote tensile stress. By following the approach given in [B. Cotterell, J. K. Reddel, Int. J. Fract. 13 (1977) 267–277], the specific work to cause ligament failure is found to be a linear function of the normal extent of the confined plastic region for most tests considered. A few exceptions to this linear relation are attributed to the limitation of the employed computational model. A new criterion and an engineering method to predict crack link-up in an MSD sheet are proposed based on this specific work concept, and they have been demonstrated through application to stiffened panels.     

Experimental investigation of laminar flow of a liquid with a free surface in triangular-shaped channels

Results are given of an experimental study of laminar flow of a liquid in triangular-shaped open channels with tangential frictional stress at the free surface. Experiments were carried out when the liquid flow in inclined triangular-shaped channels had Reynolds numbers R < 10 and the working range of Reynolds numbers of the approach air stream was R = (1.6–3.6)·10⁴. The data are presented in relative coordinates as a dependence of the hydraulic resistance coefficient of the liquid on the tangential frictional stress at the free surface. It is shown that with an increase of the tangential frictional stress the hydraulic resistance coefficient considerably increases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 168–170, January–February, 1977.     

Optimization of Dynamic Plastic Deformation of Plates with a Complex Contour

A method for studying dynamic deformation of ideal rigid–plastic plates with a complex contour on a viscoelastic foundation is proposed. The method allows one to optimize the process of pulsed forming. The optimization parameters are the amplitude of the pulsed load, viscoelastic damping coefficients of the foundation, the surface density of the plate material, and the shape and supporting conditions of the edges. Numerical examples of simply– and doubly–connected plates are given. It is shown that different combinations of the control parameters of the process can ensure the same final shape of the plate formed.