Viscoplastic boundary layer

Boundary layer (BL) solutions around a flat plate for viscoplastic fluids are re-examined, after the precursory study by Oldroyd of low inertia Bingham fluid mechanics. Due consideration is paid to the admissible stress fields far from the obstacle. Normalized Cauchy equations are introduced in the flowing regions. They initially contain inertia, pressure, and viscoplastic terms obtained by adding the yield value and a viscous stress excess in the flowing regions. New similarity solutions for the BL along a flat plate are derived, and the VPBL properties are given, in the limiting case of creeping flows with a dominant yield value. Improvements with respect to Oldroyd solution and relevant aspects are presented and discussed.     

Creeping flow of viscoplastic materials through a planar expansion followed by a contraction

In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed.     

Rehodynamics of nonlinear viscoplastic media

It is known that the rheological behavior of many non-Newtonian media (including clay and cement suspensions) is best described by non-linear viscoplastic model.Exact results of the calculation of non-linear viscoplastic flows in circular, annular and plane transverse channels are given in terms of Saint-Venant numbers and non-linear parameters.     

Extensional dynamics of viscoplastic filaments: II. Drips and bridges

A model for the dynamics of slender filaments of Herschel–Bulkley fluid is used to explore viscoplastic dripping under gravity and thinning under controlled extension (liquid bridges). The conditions required for fluid to yield are delineated, and the subsequent thinning and progression to pinch-off are tracked numerically. Calculations varying the dimensionless parameters of the problem are presented to illustrate the effect of surface tension, rheology, inertia (for dripping) and gravity. The theoretical solutions are compared with laboratory experiments using aqueous solutions of Carbopol and Kaolin suspensions. For drips and bridges, experiments with Carbopol are well matched by the theory, using a surface tension equal to that of water, even in situations when the fluid is not slender. Experiments with Kaolin do not compare well with theory for physically plausible values of the surface tension. Implications for rheometry and surface-tension inference are discussed.     

Very slow flow of Bingham viscoplastic fluid around a circular cylinder

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.     

Instability and localization of plastic flow in shear at high strain rates

Shear band formation in a thermal viscoplastic heat conducting material is described in a simple shear test at high strain rate with inertia effects. The classical perturbation method is discussed, and a new relative perturbation method accounting for non-steadiness of plastic flow is presented. They respectively provide instability and localization criteria which are compared. Furthermore both are compared to available nonlinear exact results and to experimental data. The influence of material parameters, initial imperfections, and boundary conditions is described.     

Design sensitivity analysis for parameters affecting geometry,elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method

This paper presents a design sensitivity analysis method by the consistent tangent operator concept-based boundary element implicit algorithm. The design variables for sensitivity analysis include geometry parameters, elastic–viscoplastic material parameters and boundary condition parameters. Based on small strain theory, Perzyna’s elastic–viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis. The related elastic–viscoplastic radial return algorithm and the formula of elastic–viscoplastic consistent tangent operator are derived and discussed. Based on the direct differentiation approach, the incremental boundary integral equations and related algorithms for both geometric and elastic–viscoplastic sensitivity analysis are developed. A 2D boundary element program for geometry sensitivity, elastic–viscoplastic material constant sensitivity and boundary condition sensitivity has been developed. Comparison and discussion with the results of this paper, analytical solution and finite element code ANSYS for four plane strain numerical examples are presented finally.     

Asymmetric vibration effect on the flow of a thin layer of a viscoplastic fluid

The gravity field and vibration effect on the flow of a viscoplastic fluid layer along an inclined solid surface is investigated. The rheological properties of the fluid are described using the Williamson equation. The vibrations are shown to have a considerable effect on the fluid layer flow intensity and direction; in particular, they generate a considerable mean fluid flow even in the cases in which the fluid is at rest in the absence of the vibrations.     

Onset and dynamic shallow flow of a viscoplastic fluid on a plane slope

The shallow flow of a viscoplastic fluid on a plane slope is investigated. The material constitutive law may include two plasticity (flow/no-flow) criteria: Von-Mises (Bingham fluid) and Drucker–Prager (Mohr–Coulomb). Coulomb frictional conditions on the bottom are included, which implies that the shear stresses are small and the extensional and in-plane shear stress becomes important. A stress analysis is used to deduce a Saint-Venant type asymptotic model for small thickness aspect ratio. The 2D (asymptotic) constitutive law, which relates the average plane stresses to the horizontal rate of deformation, is obtained from the initial (3D) viscoplastic model.The “safety factor” (limit load) is introduced to model the link between the yield limit (material resistance) and the external forces distribution which could generate or not the shallow flow of the viscoplastic fluid. The DVDS method, developed in [I.R. Ionescu, E. Oudet, Discontinuous velocity domain splitting method in limit load analysis, Int. J. Solids Struct., doi:10.1016/j.ijsolstr.2010.02.012], is used to evaluate the safety factor and to find the onset of an avalanche flow.A mixed finite element and finite volume strategy is developed. Specifically, the variational inequality for the velocity field is discretized using the finite element method while a finite volume method is adopted for the hyperbolic equation related to the thickness variable. To solve the velocity problem, a decomposition–coordination formulation coupled with the augmented lagrangian method, is adapted here for the asymptotic model. The finite volume method makes use of an upwind strategy in the choice of the flux.Several boundary value problems, modeling shallow dense avalanches, for different visoplastic laws are selected to illustrate the predictive capabilities of the model.     

Extensional dynamics of viscoplastic filaments: I. Long-wave approximation and the Rayleigh instability

We derive an asymptotic reduced model for the extensional dynamics of long, slender, axisymmetric threads of incompressible Herschel–Bulkley fluids. The model describes the competition between viscoplasticity, gravity, surface tension and inertia, and is used to explore the viscoplastic Rayleigh instability. A finite-amplitude initial perturbation is required to yield the fluid and initiate capillary-induced thinning. The critical amplitude necessary for thinning depends on both the wavelength of the perturbation and on the yield stress. We also numerically examine the inertialess growth of the instability and the progression towards pinch-off. The final self-similar form of inertialess pinch-off is similar to that for a power-law fluid.     

A phase field model incorporating strain gradient viscoplasticity: Application to rafting in Ni-base superalloys

The first formulation of a phase field model accounting for size-dependent viscoplasticity is developed to study materials in which microstructure evolution and viscoplastic behavior are strongly coupled. Plasticity is introduced using a continuum strain gradient formalism which captures the size effect of the viscoplastic behavior. First, the influence of this size effect on the mechanical behavior of the material is discussed in static microstructures. Then, the dynamic coupling between microstructure evolution and viscoplastic activity is addressed and illustrated by the rafting of the microstructure observed in Ni-base superalloys under creep conditions. It is found that the plastic size effect has only a moderate impact on the shape of the rafts but is crucial to reproduce the macroscopic mechanical behavior of that particular material.     

Crossflow of viscoplastic materials through tube bundles

The flow of viscoplastic materials through staggered arrays of tubes is analyzed. The mechanical behavior of the materials is assumed to obey the generalized Newtonian liquid (GNL) model, with a viscosity function given by the biviscosity law. The governing equations of this flow are solved numerically using a finite-volume method with a non-orthogonal mesh. For a representative range of the relevant parameters, results are presented in the form of velocity, pressure and viscosity fields. The pressure drop is also given as a function of rheological and geometric parameters.     

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

We present the results of lattice Boltzmann (LB) simulations for the planar-flow of viscoplastic fluids through complex flow channels. In this study, the Bingham and Casson model fluids are covered as viscoplastic fluid. The Papanastasiou (modified Bingham) model and the modified Casson model are employed in our LB simulations. The Bingham number is an essential physical parameter when considering viscoplastic fluid flows and the modified Bingham number is proposed for modified viscoplastic models. When the value of the modified Bingham number agrees with that of the “normal” Bingham number, viscoplastic fluid flows formulated by modified viscoplastic models strictly reproduce the flow behavior of the ideal viscoplastic fluids. LB simulations are extensively performed for viscoplastic fluid flows through complex flow channels with rectangular and circular obstacles. It is shown that the LB method (LBM) allows us to successfully compute the flow behavior of viscoplastic fluids in various complicated-flow channels with rectangular and circular obstacles. For even low Re and high Bn numbers corresponding to plastic-property dominant condition, it is clearly manifested that the viscosity for both the viscoplastic fluids is largely decreased around solid obstacles. Also, it is shown that the viscosity profile is quite different between both the viscoplastic fluids due to the inherent nature of the models. The viscosity of the Bingham fluid sharply drops down close to the plastic viscosity, whereas the viscosity of the Casson fluid does not rapidly fall. From this study, it is demonstrated that the LBM can be also an effective methodology for computing viscoplastic fluid flows through complex channels including circular obstacles.     

Fluid boundary of a viscoplastic Bingham flow for finite solid deformations

The modelling of viscoplastic Bingham fluids often relies on a rheological constitutive law based on a “plastic rule function” often identical to the yield criterion of the solid state. It is also often assumed that this plastic rule function vanishes at the boundary between the solid and fluid states, based on the fact that it is true in the limit of small deformations of the solid state or for simple yield criteria. We show that this is not the case for finite deformations by considering the example of a two state flow on a tilted plane where the solid state is described by a Neo-Hookean model with a Von Mises yield criterion. This opens new approaches for the modelling and the computation of the fluid state boundaries.     

Simulation of curing-induced viscoplastic deformation: a new approach considering chemo-thermomechanical coupling

A modelling and simulation approach for plastic deformation effects in curing resins is presented. For this purpose known rheological models of viscoelasticity and viscoplasticity are combined and a thermochemical element is added to account for chemical shrinkage and thermal expansion. The degree of cure of the resin has a major influence on the behaviour of the curing material, and therefore, the material model is formulated depending on the degree of cure. It affects the viscoelastic behaviour as well as the chemical shrinkage and the yield function of the viscoplastic part of the model. For the yield function a von Mises approach with isotropic hardening is chosen, where the initial yield stress as well as the yield surface depends on the degree of cure and the temperature.     

Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling – Speckle measurements and high-speed photography

A methodology based on inverse modelling for estimating viscoplastic material parameters at high strain-rate conditions is presented. The methodology is demonstrated for a mild steel exposed for compression loading in a split Hopkinson pressure bar arrangement. By using dog-bone shaped specimens nonhomogeneous states of deformation are obtained throughout the entire deformation process. The resulting nonhomogeneous deformation of the specimens is evaluated using digital speckle photography (DSP) to give in-plane point-wise displacement and strain fields. The photographs are captured with a high-speed camera of image converter type, which acquire time resolved images during the impact loading. The experiments are simulated using finite element analysis (FEA), where the material model suggested by Johnson–Cook for high-strain rate conditions are utilised. Experimental and FE-calculated field information are compared in order to estimate the viscoplastic parameter in the Johnson–Cook material model. The estimation is performed by minimising least-square functions that contain the differences in displacements and strains, respectively. The quality of the estimated parameters is studied from statistical point of view.     

SnPb钎料合金的粘塑性Anand本构方程

采用统一型粘塑性本构 Anand方程描述了电子封装焊点 Sn Pb钎料合金的非弹性变形行为 ,基于 Sn Pb 合金的弹塑性蠕变本构方程和实验数据 ,确定了6 2 Sn36 Pb2 Ag、6 0 Sn40 Pb、96 .5 Sn3.5 Ag和 97.5 Pb2 .5 Sn四种钎料合金 Anand方程的材料参数 ,验证了粘塑性 Anand本构方程对 Sn Pb合金在恒应变速率和稳态塑性流动条件下应力应变行为的预测能力。结果表明 ,Anand方程能有效描述 Sn Pb钎料的粘塑性本构行为 ,并可应用于电子封装 Sn Pb焊点的可靠性模拟和失效分析     

New integral formulation and self-consistent modeling of elastic–viscoplastic heterogeneous materials

Predicting the overall behavior of heterogeneous materials, from their local properties at the scale of heterogeneities, represents a critical step in the design and modeling of new materials. Within this framework, an internal variables approach for scale transition problem in elastic–viscoplastic case is introduced. The proposed micromechanical model is based on establishing a new system of field equations from which two Navier’s equations are obtained. Combining these equations leads to a single integral equation which contains, on the one hand, modified Green operators associated with elastic and viscoplastic reference homogeneous media, and secondly, elastic and viscoplastic fluctuations. This new integral equation is thus adapted to self-consistent scale transition methods. By using the self-consistent approximation we obtain the concentration law and the overall elastic–viscoplastic behavior of the material. The model is first applied to the case of two-phase materials with isotropic, linear and compressible viscoelastic properties. Results for elastic–viscoplastic two-phase materials are also presented and compared with exact results and variational methods.     

A thermodynamics based damage mechanics model for particulate composites

A micro-mechanical damage model is proposed to predict the overall viscoplastic behavior and damage evolution in a particle filled polymer matrix composite. Particulate composite consists of polymer matrix, particle fillers, and an interfacial transition interphase around the filler particles. Yet the composite is treated as a two distinct phase material, namely the matrix and the equivalent particle-interface assembly. The CTE mismatch between the matrix and the filler particles is introduced into the model. A damage evolution function based on irreversible thermodynamics is also introduced into the constitutive model to describe the degradation of the composite. The efficient general return-mapping algorithm is exploited to implement the proposed unified damage coupled viscoplastic model into finite element formulation. Furthermore, the model predictions for uniaxial loading conditions are compared with the experimental data.