Viscoplastic Flow Research Articles

Effect of Y2O3 Addition on Oxidation Behavior of W-Cr Alloys

A study has been carried out on non-isothermal and cyclic oxidation behavior of the W1−x Cr x –3 wt pct Y2O3 (x = 0.3 or 0.5) composite samples, and the results have been compared with those of binary W-Cr alloys. The microstructures of the sintered samples showed the presence of W-rich (β1) + Cr-rich (β2) regions and more or less uniformly distributed Y2O3 particles. Protection against high-temperature oxidation is possible due to the formation of a stable mixed oxide scale containing both Cr2WO6 and Y2W3O12 at the oxide–air interface. Melting of the eutectic composition of Y2W3O12 and WO3 leads to the formation of a liquid phase, which helps in closure of pores by sintering and viscoplastic flow of the oxide scale, thereby enhancing its resistance to spallation and further oxidation.

Micromechanical modeling of hardening mechanisms in commercially pure α-titanium in tensile condition

Tensile tests on commercially pure α-titanium show a three-stage behavior giving rise to a well on the strain dependence of the work hardening. An opposite strain rate effect on the well depth is found whether specimens are elongated along the rolling or the transverse direction. Slip lines analysis reveals an initial predominance of prismatic slip, particularly pronounced in specimens strained along the rolling direction. The relative activity of prismatic slip is then observed to decrease with the samples deformation. These results provide grounds for elaboration of an elasto-viscoplastic self-consistent model based on the translated field method and an affine linearization of the viscoplastic flow rule, and capable of explaining such peculiar work hardening behavior. The model considers crystal plasticity and deals separately with mobile dislocation density and dislocation velocity. It assumes lower strain rate sensitivity as well as higher dislocation multiplication rate for prismatic systems. Based on these assumptions, the model reproduces correctly the stress–strain curves and gives sound estimates of Lankford coefficients, prismatic slip activity and textures evolution. Most importantly, the opposite effect of strain rate on the well depth with regard to the orientation of the tensile axis is qualitatively retrieved, which allows putting forward an explanation of the observed phenomena.

Nonisothermal motion of an elastoviscoplastic medium through a pipe under a changing pressure drop

The solution of a sequence of coupled problems of thermoelastic plasticity on the nucleation and development of medium flow in a cylindrical pipe in conditions of varying pressure drop and material heating due to friction on the pipe wall and subsequent stagnation of flow under slow load removal and cooling of the layer material is derived based on the theory of large elastoplastic deformations generalized for the nonisothermal case. The thermal and deformation processes are interrelated with the temperature dependence of the yield point. The conditions of nucleation of the viscoplastic flow and regularities of motion of the elastoplastic boundaries over the layer are noted, and the flow rates and large strains, both irreversible and reversible, are calculated.

Elementos finitos mixtos estabilizados para flujos confinados de Bingham y de Herschel-Bulkley. Parte I: Formulación

This work presents a methodology for the solution of the Navier-Stokes equations for Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. The theoretical formulation is developed and implemented in a computer code.Viscoplastic fluids are characterized by a minimum shear stress called yield stress. Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a quasi-rigid body, with zero strain-rate.First, the Navier-Stokes equations for incompressible fluid are presented. A review of the viscoplastic rheological models is included, with a detailed description of these models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed as an alternative to the models commonly used.The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization method, the Orthogonal Subgrid Scale (OSS) method and the split orthogonal subscales method are introduced.The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry.

Development of the strain–rate and temperature sensitive theory of microstrain

Plastic flow, caused by the dislocation glide is closely related to the thermal activation mechanism in a wide range of strain rates. On the other hand, the high-rate plastic strain may lead to an apparent increase in temperature. Therefore, the influence of strain rate and temperature are usually related and should be considered both in the study of the materials behavior, depending on the strain rate. Over the past three decades, this approach has been implemented in a number of the continuum and physical theories of thermoviscoelasticity that lead to rather complicated constitutive relations and their use is restricted mainly by simple loading processes. A generalized version of the theory of microstrain, which is sufficiently simple and suitable to describe the finite visco-plastic strain in a wide range of strain rates and temperatures was proposed. Constitutive relations of the theory that are applicable not only under simple, but also complex loading were built. The algorithm for their numerical implementation, which allows to take into account not only the plurality of active microplastic strains but also possibility to set an arbitrary loading trajectory was proposed. A comparison of the charts of uniaxial tension at various strain rates obtained using the theory of microstrain with the known experimental data was performed. It is shown that the proposed option allows to achieve a satisfactory description of experiments with a small number of material constants, which simplifies the calibration of the theory. The results significantly extend the capabilities of the theory of microstrain and open up prospects for its use to describe the viscoplastic flow and solve applied tasks under complex loading.

Development and deceleration of viscoplastic flow in a layer heated by friction on a rough plane

This paper presents a solution of a sequence of coupled problems of thermoelastoplasticity which study the occurrence and development of flow in a material layer under pure shear conditions, and its subsequent deceleration by slowly removing the load. The homogeneity of the stress state of the layer is excluded due to the coupling of thermal and deformation processes in the presence of a temperature dependence of the yield point. An additional source of heat is taken to be its production by friction of the material layer on a rough plane. The conditions for the occurrence of viscoplastic flow in the deformable material layer and the laws of motion of the boundaries between the elastic and plastic regions in this layer are determined, and the flow velocities and large irreversible and reversible deformations are calculated. It is shown that reversible deformations cause stresses in the flow region and the moving elastically deformed core.

Elementos finitos mixtos estabilizados para flujos confinados de Bingham y de Herschel-Bulkley Parte II: soluciones numéricas

The objective of this work is to model computationally Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. Numerical solutions for these viscoplastic flows are presented and assessed. The regularized viscoplastic models due to Papanastasiou is used. In the discrete model, the Orthogonal Subgrid scale (OSS) method is used.In this part II, numerical solutions for two problems of Bingham and Herschel-Bulkley confined flows are presented. The solutions obtained validate the methodology proposed in part I of this work.

Accounting for the elastic properties of viscoplastic lubricant between coaxial rotating cylinders

This paper presents a solution of the boundary-value problem of the stress–strain state of a friction unit placed in the gap between rigid rotating cylinders. It is assumed that the two-layer incompressible material of these unit has elastic, viscous, and plastic properties and different values of the elastic moduli, stress limit, and viscosity. The conditions of the occurrence of viscoplastic flow, motion of the elastoplastic boundary in a deformable medium, and interaction of the latter with the contact boundary of the materials were determined. Limiting values of the characteristic rotation parameters at which the damping layer of the friction unit is not deformed plastically are given. The velocity and stress fields for acceleration and deceleration of the lubricant flow are calculated.

A new application of unified constitutive equations for cross wedge rolling of a high-speed railway axle steel

The mechanical properties of 25CrMo4 steel for high-speed railway axles depend on its microstructural evolution during hot cross wedge rolling (CWR). In this paper a set of mechanism-based unified constitutive equations has been determined for the prediction of elastic-viscoplastic material behaviour and microstructural evolution of the 25CrMo4 steel during hot CWR processes. Hot compression tests were conducted using a Gleeble thermo-mechanical simulator at temperatures in a range of 1223–1433K and at strain rates in a range of 1.0–10.0/s. A set of equations was determined from experimental data of static grain growth, grain refinement and viscoplastic flow using a genetic algorithm (GA) method. Good agreements between the experimental and predicted data were obtained. The determined constitutive equations were implemented into the commercial FE code, DEFORM-3D, via a user defined subroutine and CWR processes were modelled. CWR tests were also carried out and microstructure examinations were conducted. FE simulation results, such as grain size, were compared with those of CWRed parts. Good agreements have been obtained, which shows that the determined constitutive model enables microstructure evolution in CWR processes to be well predicted.

A scalable, matrix-free multigrid preconditioner for finite element discretizations of heterogeneous Stokes flow

Abstract In this paper we describe a computational methodology that is specifically designed for studying three-dimensional geodynamic processes governed by heterogeneous visco-plastic Stokes flow. The method employs a hybrid spatial discretization consisting of a Q 2 - P 1 disc mixed finite element formulation for the Stokes problem, coupled to a material-point formulation which is used for representing material state and history-dependent variables. The applicability and practicality of this methodology is realized through the development of an efficient, scalable and robust variable viscosity Stokes preconditioner. In this work, these objectives are achieved through exploiting matrix-free operators and a geometric multigrid preconditioner employing hybrid coarse level operators, Chebyshev smoothers and hybrid Krylov coarse level solvers. The robustness and parallel efficiency of this strategy is demonstrated using an idealized geodynamic model. Lastly, we apply the new methodology to study geodynamic models of continental rifting and break-up in order to understand the diverse range of passive continental margins we observe on Earth today.

A New Damage Constitutive Model for Thermal Deformation of AA6111 Sheet

Hot tensile tests were conducted using a Gleeble 1500, at the temperature range of 623 K to 823 K (350 °C to 550 °C) and strain rate range of 0.1 to 10 s−1. Flow stress is significantly affected by temperature and strain rate. As strain increases; the flow stress first rapidly increases, subsequently maintains a steady state, and finally drops sharply because of damage evolution. The features and mechanism of the damage were studied utilizing a scanning electron microscope. Micro-void nucleation, growth, and coalescence result in the failure of the hot-formed specimen. A damage equation based on continuum damage mechanics and damage mechanism in hot metal forming was proposed. A unified viscoplastic damage model coupled with strain, strain rate, temperature, dislocation, hardening, damage, damage rate, and so on was developed and calibrated for AA6111 using Genetic Algorism Tool in three steps. This model can be used to describe viscoplastic flow behavior and damage evolution at various temperatures and strain rates. The model was implemented into the finite element (FE) model in ABAQUS platform via the variable user material subroutine. Thus, the FE model could be employed to study the damage distribution and the effects of blank holder force (BHF) and forming velocity on hot cylindrical deep drawing. It is revealed that lower BHF and higher velocity are beneficial for drawability. A good agreement between simulated and experimental results has been achieved.

Suddenly expanding recirculating and non-recirculating viscoplastic non-newtonian flows

Viscoplastic non-Newtonian flows through axisymmetric 1:5 and 1:2 sudden expansions have been studied numerically by solving the mass and momentum conservation equations and the Bingham constitutive equation. Two distinct viscoplastic flow regimes are observed. For a given Reynolds number, increasing the yield number, a non-dimensional yield stress results in transitioning from a recirculating to a non-recirculating viscoplastic flow regime. For Newtonian fluids, a typical separating and reattaching flow field with a large corner recirculation region and a reattachment point is observed. For a low yield number viscoplastic non-Newtonian flow, the incoming flow separates, creating a weak recirculation region, and unyielded attached-to-the wall, corner and impingement regions. For a high yield number, a non-separating viscoplastic flow field forms, resulting in the elimination of flow recirculation and the formation of significant unyielded region behind the expansion plane. For Newtonian and low yield number viscoplastic flows, axisymmetric 1:5 expansion flows result in more intense recirculation, larger reattachment, and flow redevelopment lengths in comparison with axisymmetric 1:2 expansion flows.

Some aspects of viscoplastic flow in blanks of tungsten-based heavy alloys

The paper gives some findings of the investigation of geometrical shape distortion of blanks made of a tungsten-based alloy with a nickel binder. Blanks are found to undergo a multistage form alteration due to a liquid-phase segregation in the material during its sintering in a multizone continuous furnace.

Solving the problem of Bingham fluid flow in cylindrical pipeline

We consider an elliptic variational inequality in a circular domain, which simulates viscoplastic Bingham flow in a pipe. This variational inequality is approximated by finite-difference scheme on a grid in polar coordinates. To solve the finite-dimensional problem we propose a generalized Uzawa-type iterative method. We prove the convergence of the iterative method.

РАЗВИТИЕ И ТОРМОЖЕНИЕ ВЯЗКОПЛАСТИЧЕСКОГО ТЕЧЕНИЯ В СЛОЕ ПРИ ЕГО НАГРЕВЕ ЗА СЧЕТ ТРЕНИЯ О ШЕРОХОВАТУЮ ПЛОСКОСТЬ

РАЗВИТИЕ И ТОРМОЖЕНИЕ ВЯЗКОПЛАСТИЧЕСКОГО ТЕЧЕНИЯ В СЛОЕ ПРИ ЕГО НАГРЕВЕ ЗА СЧЕТ ТРЕНИЯ О ШЕРОХОВАТУЮ ПЛОСКОСТЬ

Quasi-static axially symmetric viscoplastic flows near very rough walls

The paper deals with asymptotic behavior of viscous and viscoplastic solutions in the vicinity of very rough walls under conditions of axial symmetry. The constitutive equations adopted include a saturation stress. A distinguished feature of this model is that the regime of sticking at the wall may be incompatible with other boundary conditions. In this case the regime of sliding must occur and solutions are singular in the vicinity of such surfaces. The exact asymptotic representation of the singular solutions is controlled by the dependence of the equivalent stress on the equivalent strain rate as the latter approaches infinity. There exist such dependences that the viscoplastic model possesses a smooth transition of qualitative behavior between rigid perfectly plastic and viscoplastic solutions, and this may prove to be advantageous for some applications.

Symmetry relations in viscoplastic drag laws.

The following note shows that the symmetry of various resistance formulae, often based on Lorentz reciprocity for linearly viscous fluids, applies to a wide class of nonlinear viscoplastic fluids. This follows from Edelen's nonlinear generalization of the Onsager relation for the special case of strongly dissipative rheology, where constitutive equations are derivable from his dissipation potential. For flow domains with strong dissipation in the interior and on a portion of the boundary, this implies strong dissipation on the remaining portion of the boundary, with strongly dissipative traction-velocity response given by a dissipation potential. This leads to a nonlinear generalization of Stokes resistance formulae for a wide class of viscoplastic fluid problems. We consider the application to nonlinear Darcy flow and to the effective slip for viscoplastic flow over textured surfaces.

Viscoplastic Poiseuille flow in a rectangular duct with wall slip

We solve numerically the Poiseuille flow of a Herschel–Bulkley fluid in a duct of rectangular cross section under the assumption that slip occurs along the wall following a slip law involving a non-zero slip yield stress. The constitutive equation is regularized as proposed by Papanastasiou. In addition, we propose a new regularized slip equation which is valid uniformly at any wall shear stress level by means of another regularization parameter. Four different flow regimes are observed defined by three critical values of the pressure gradient. Initially no slip occurs, in the second regime slip occurs only in the middle of the wider wall, in the third regime slip occurs partially at both walls, and eventually variable slip occurs everywhere. The performance of the regularized slip equation in the two intermediate regimes in which wall slip is partial has been tested for both Newtonian and Bingham flows. The convergence of the results with the Papanastasiou regularization parameter has been also studied. The combined effects of viscoplasticity and slip are then investigated. Results are presented for wide ranges of the Bingham and slip numbers and for various values of the power-law exponent and the duct aspect ratio. These compare favorably with available theoretical results and with numerical results in the literature obtained with both regularization and augmented Lagrangian methods.

Two-temperature continuum thermomechanics of deforming amorphous solids

There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent, finite-deformation, continuum framework for deforming amorphous solids. The basic premise is that the configurational degrees of freedom of the material – the part of the internal energy/entropy that corresponds to mechanically stable microscopic configurations – are characterized by a configurational temperature that might differ from that of the vibrational degrees of freedom, which equilibrate rapidly with an external heat bath. This results in an approximate internal energy decomposition into weakly interacting configurational and vibrational subsystems, which exchange energy following a Fourier-like law, leading to a thermomechanical framework permitting two well-defined temperatures. In this framework, internal variables, that carry information about the state of the material equilibrate with the configurational subsystem, are explicitly associated with energy and entropy of their own, and couple to a viscoplastic flow rule. The coefficients that determine the rate of flow of entropy and heat between different internal systems are proposed to explicitly depend on the rate of irreversible deformation. As an application of this framework, we discuss two constitutive models for the response of glassy materials, a simple phenomenological model and a model related to the concept of Shear-Transformation-Zones as the basis for internal variables. The models account for several salient features of glassy deformation phenomenology. Directions for future investigation are briefly discussed.

Mechanical behavior of electrochemically lithiated silicon

The time-independent and time-dependent mechanical behavior of electrochemically lithiated silicon was studied with nanoindentation. As indentation was performed with continuous stiffness measurements during loading and load-hold, new insight into the deformation behavior of lithiated silicon is furnished. Supporting other research, Young's modulus and the hardness of lithiated silicon are found to decline with increasing lithium content. However, the results of this study indicate that Young's modulus of the fully lithiated phase, at 41 GPa, is in fact somewhat larger than reported in some other studies. Nanoindentation creep experiments demonstrate that lithiated silicon creeps readily, with the observed viscoplastic flow governed by power law creep with large stress exponents (>20). Flow is thought to occur via local, shear-driven rearrangement at the scale of the Li15Si4 molecular unit volume. This research emphasizes the importance of incorporating viscoplasticity into lithiation/delithiation models. Additionally, more broadly, the work offers insight into nanoindentation creep methodology.