Rigid-viscoplastic Model Research Articles

Numerical and experimental study on friction stir welding of aluminum alloy pipe

An attempt has been made in this work to study the temperature distribution, force variation, and material flow behavior by developing a rigid viscoplastic model for friction stir welding (FSW) of pipes. An optimum value of plunge depth is predicted through simulation to fabricate the weld. The weld defect has been predicted by using point tracking method and the same is compared with experimental observation. Influence of plunge depth on hardness and microstructure is studied to characterize the welded sample. Plunge depth of 0.3 mm results in sufficient contact at the interface of the pipe and tool shoulder, and produces a good weld. Lower grain size is observed for plunge depth of 0.3 mm as compared to 0.5 mm, but with negligible variation in hardness.

An alternative interpretation of axial friction test results for viscoplastic materials

A new friction test proposed elsewhere consists of pushing a cylindrical sample of material compressed by axial forces through a tube. This test is called the axial friction test. Friction induces plastic deformation in the sample. In general, plastic deformation is responsible for the evolution of material properties. Experiments demonstrate that a narrow layer with drastically changed material properties is often generated in the vicinity of the friction surface in the axial friction test. This suggests that plastic deformation is localized near the friction surface in this test. The capability of theoretical solutions to predict highly localized plastic deformation near frictional interfaces depends on the material model chosen. Since the thickness of the layer with drastically changed material properties is a measurable quantity, the axial friction test can be used for identifying material models. The present paper deals with rigid viscoplastic models. It is shown that there is a class of such models that predict the existence of a layer of highly localized plastic deformation near friction surfaces.

On the nonexistence of certain solutions for damage mechanics models

The objective of this paper is to demonstrate that elastic and rigid plastic boundary value problems in damage mechanics may not have a solution. Two classes of damage mechanics models are considered. The constitutive equations of one class of models consist of a pressure-independent yield criterion, its associated flow rule, Hooke’s law and a damage evolution equation. The damage parameter enters the yield criterion. Therefore, these models are partly coupled. The constitutive equations of the other class are the constitutive equations of the classical rigid perfectly plastic model (or a rigid viscoplastic model) supplemented with an empirical ductile fracture criterion. The viscoplastic model contains a saturation stress. These models are uncoupled. In the case of partly coupled models, a simple boundary value problem is formulated and solved. It is shown that the solution breaks down for certain values of input parameters. In the case of uncoupled models, it is shown that empirical ductile fracture criteria are not compatible with solution behavior in the vicinity of maximum friction surfaces. An approach to formulate a new type of empirical ductile damage models is outlined.

Motion of a rigid bar in a rigid-viscoplastic medium: The influence of the model type on the solution behavior

The paper deals with rigid-plastic materials satisfying the vonMises plasticity condition under the assumption that their yield point in pure shear depends only on the equivalent strain rate (rigid-viscoplastic material models). The rigid-viscoplastic models are classified by the yield point behavior in pure shear as the equivalent strain rate tends to zero or infinity. All in all, four classes of rigid-viscoplastic material models are distinguished. For each of these classes of material models, the solution is constructed for the translational motion of an axisymmetric rigid bar along its symmetry axis in a rigid-plastic medium. It is assumed that the maximum friction law acts on the surface of contact between the bar and the rigid-viscoplastic medium. It is shown that the solutions provided by models of different classes qualitatively differ from each other. A qualitative comparison with experimental results known in the literature is carried out. It is shown that predicting the formation of an intensive plastic deformation layer near the friction surface, which is observed in experiments, is possible if the rigid-viscoplastic model contains the saturation stress (the stress, bounded in magnitude, to which the yield point in pure shear tends as the equivalent strain rate tends to infinity).

Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold

The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The importance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the turbulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed.

An Efficient Approach for Identifying Constitutive Parameters of the Modified Oyane Ductile Fracture Criterion at High Temperature

The paper presents the theoretical part of a method for identifying constitutive parameters involved in the modified Oyane ductile fracture criterion at high temperature. Quite a general rigid viscoplastic model is adopted to describe material behavior. The ductile fracture criterion is in general path-dependent and involves stresses. Therefore, the identification of constitutive parameters of this criterion is a difficult task which usually includes experimental research and numerical simulation. The latter requires a precisely specified material model and boundary conditions. It is shown in the present paper that for a wide class of material models usually used to describe the behavior of materials at high temperatures, the criterion is significantly simplified when the site of fracture initiation is located on traction free surfaces. In particular, this reduced criterion does not involve stresses. Since there are well established experimental procedures to determine the input data for the reduced criterion, the result obtained can be considered as a theoretical basis for the efficient method for identifying constitutive parameters of the modified Oyane ductile fracture criterion at high temperature. The final expression can also be used in computational models to increase the accuracy of predictions.

Improvement of stability conditions, accuracy and uniqueness of penalty approach in contact modeling

The main objective of this paper is to improve stability conditions, uniqueness and convergence of numerical analysis of metal forming processes with contact constraints enforced by the penalty method. A commonly known drawback of this approach is the choice of penalty factor values. When assumed too low, they result in inaccurate fulfillment of the constraints while when assumed too high, they lead to ill-conditioning of the equations system which affects stability and uniqueness of the solution. The proposed modification of the penalty algorithm consists in adaptive estimation of the penalty factor values for the particular system of finite element equations and for the assumed allowed inaccuracy in fulfillment of the contact constraints. The algorithm is tested on realistic examples of sheet metal forming. The finite element code based on flow approach formulation (for rigid-plastic and rigid-viscoplastic material model) has been used.

Numerical and experimental investigations of semi-solid AZ91D magnesium alloy in thixoforming process

Abstract Many complicated factors affect thixoforming fluidity in thixoforming process of semi-solid metal (SSM). So, it is important to forecast the flow property of SSM. Rigid visco-plastic constitutive model of semi-solid AZ91D Mg alloy was established at different strain rate. The thixoforming process of semi-solid AZ91D Mg alloy was simulated using commercial finite element software DEFORM-3D™. The fluid and effective stress–strain fields in the thixoforming process were obtained and the relationships among stress, strain rate and temperature also were analyzed. The thixoforming experiments were performed at 570 °C with different holding time. Finite element analysis results were compared with experimental ones, and experimental data has good agreements with the simulation results.

Numerical modeling of projectile penetration into compressible rigid viscoplastic media

AbstractWe develop computational methods for modeling penetration of a rigid projectile into porous media. Compressible rigid viscoplastic models are used to capture the solid–fluid transition in behavior at high strain rates and account for damage/plasticity couplings and viscous effects that are observed in geological and cementitious materials.A hybrid time discretization is used to model the non‐stationary flow of the target material and the projectile–target interaction, i.e. an explicit Euler method for the projectile equation and a forward (implicit) method for the target boundary value problem. At each time step, a mixed finite element and finite‐volume strategy is used to solve the ‘target’ boundary value problem. Specifically, the non‐linear variational inequality for the velocity field is discretized using the finite element method while a finite‐volume method is used for the hyperbolic mass conservation and damage evolution equations. To solve the velocity problem, a decomposition–coordination formulation coupled with the augmented Lagrangian method is adopted.Numerical simulations of penetration into concrete were performed. By conducting a time step sensitivity study, it was shown that the numerical model is robust and computationally inexpensive. For the constants involved in the model (shear and volumetric viscosities, cut‐off yield limit, and exponential weakening parameter for friction) that cannot be determined from data, a parametric study was performed. It is shown that using the material model and numerical algorithms that developed the evolution of the density changes around the penetration tunnel, the shape and location of the rigid/plastic boundary, the compaction zones, and the extent of damage due to air‐void collapse are described accurately. Copyright © 2007 John Wiley & Sons, Ltd.

Superplastic Deforming Analysis Based on Element Free Galerkin Method

Superplastic large deformation problems always meet handicaps associated with severe mesh distortion and iterative remeshing when traditional mesh-based numerical approaches are used. To eliminate these difficulties, meshless simulation of element free Galerkin method (EFGM) for rigid-viscoplastic(RVP) model and incompressible materials is built upon the Moving Least Squares (MLS) approximation and modified Markov variational principles. Also, a numerical quadrature that aligns integration cells with the local supports of shape functions is presented to compute integrations involved in the objective functions. Satisfying results of a superplastic upsetting example with very large compression ratio demonstrate the feasibility and accuracy for the meshfree method to simulate superplastic large deformation process.

Grain size dependence of strength of nanocrystalline materials as exemplified by copper: an elastic-viscoplastic modelling approach

The purpose of this work is to model the mechanical behavior of nanocrystalline materials. Based on previous rigid viscoplastic models proposed by Kim et al. (Acta Mater, 48: 493, 2000) and Kim and Estrin (Acta Mater, 53: 765, 2005), the nanocrystalline material is described as a two phase composite material. Using the Taylor–Lin homogenisation scheme in order to account for elasticity, the yield stress of nanocrystalline materials can be evaluated. The transition from a Hall–Petch relation to an inverse Hall–Petch relation is defined and is related to a change in plastic deformation mode in the crystallite phase from a dislocation glide driven mechanism to a diffusion-controlled process.

Material flow in FSW of AA7075–T6 butt joints: numerical simulations and experimental verifications

Friction stir welding (FSW) has reached a large interest in the scientific community and in the recent years also in the industrial environment, owing to the advantages of such solid state welding process with respect to the classic ones. Advanced finite element method tools are needed in order to develop an effective engineering of the processes; quantitative results can be acquired from numerical simulations once the basic information such as the material flow is certain. A 3D Lagrangian implicit coupled rigid viscoplastic model has already been developed by the authors to simulate FSW of butt joints. In the present paper the material flow in the FSW of AA7075–T6 butt joints is investigated on the varying of the most relevant technological and geometrical parameters with numerical simulations and experiments. In particular to investigate the metal flow a wide campaign of experimental tests and observations has been developed utilising a thin foil of copper as marker.

Compressible rigid viscoplastic fluids

In this paper, a general methodology for constructing fluid-type constitutive equations for description of the behavior of porous media when subjected to large deformations and high strain rates is proposed. The elastic deformations are neglected and the representation of the dynamic state of stress in the material is obtained from classic yield conditions for plastic solids using the viscoplastic regularization and/or a stress superposition method. Examples of constitutive equations obtained using both procedures are presented. We show that irrespective of the method used, it is not possible to obtain consistent viscoplastic fluid formulations starting from certain yield functions. Comparisons between the response of the proposed models for uniaxial compression conditions is provided. Extensions of these models that include coupling between damage, plastic and viscous effects are proposed. Finally, some results of numerical modeling of penetration into concrete using a compressible rigid-viscoplastic model are presented.

Material Flow in FSW of AA7075-T6 Butt Joints: Continuous Dynamic Recrystallization Phenomena

In the paper the continuous dynamic recrystallization (CDRX) phenomena occurring in the FSW of AA7075-T6 butt joints is investigated at the varying of the most relevant technological and geometrical parameters. In particular, both experiments and numerical simulations obtained utilizing a 3D Lagrangian implicit, coupled, rigid-viscoplastic model have been developed on FSW butt joints. The resulting microstructure at the core of the weldings is correlated to the material flow occurring during the FSW process.

A new rigid‐viscoplastic model for simulating thermal strain effects in metal‐forming processes

AbstractA new rigid‐viscoplastic model that includes the effect of thermal strains when modelling steady‐state metal‐forming processes was developed. A symmetric approximation to the resulting non‐symmetric stiffness matrix was derived. The thermo‐mechanical flow formulation was implemented using the pseudo‐concentrations technique. The new formulation was numerically tested showing that it provides reliable results. Copyright © 2003 John Wiley & Sons, Ltd.

Finite element simulation of the steel plates hot rolling process

AbstractIn this paper we discuss our finite element procedure for simulating the hot rolling of flat steel products. We couple an Eulerian rigid‐viscoplastic model of the steel plates deformation to a Lagrangian elastic model of the rolls deformation. This latter model incorporates the bending deformation of the work rolls supported by the back‐up rolls and the flattening of the contact areas (Hertz problem) via an enhanced beam model.The finite element model is validated comparing its predictions with actual industrial measurements and then it is used to analyse different rolling set‐ups. Copyright © 2001 John Wiley & Sons, Ltd.

Modeling of metal forming processes: implementation of an iterative solver in the flow formulation

Rigid-viscoplastic models of metal forming processes are mathematically formulated as non-linear Stokes problems: incompressible flows with variable viscosity, function of the point velocities. When discretizing those mathematical models using either u-p or velocity interpolated finite element formulations with the incompressibility imposed via penalty techniques, bad conditioned matrices are obtained. In this paper we discuss the implementation of an iterative solver for the efficient solution of the resulting equation systems.

On the maximum friction law in viscoplasticity

Assuming a rigid viscoplastic material model, it is shown thatthe velocity fields adjacent to surfaces of maximum friction mustsatisfy sticking conditions. This means that the stress boundarycondition, the maximum friction law, may be replaced by the velocityboundary condition. Axisymmetric flows without rotation and planar flowsare considered. Applications of the upper bound theorem are discussed.

Study on the Warpage of Plastics Vacuum-Forming Process

A series of experiments was carried out to comprehensively study the effect of technological parameters including mold geometry (depths of draw, the shape of impression), initial forming temperature and material properties on the warpage of plastics vacuum-formed parts. During the process of plastics vacuum-forming, the thermoelastic FEM model was adopted to analyze the warpage at the cooling stage and the rigid visco-plastic FEM model was adopted to analyze the deformation at the deforming stage. The 3-D temperature fields are computated using Calerkin FEM code with proper selection of the parison's thermal properties and appropriate disposals of dynamic heat conclusion boundary condition, latent heat and deformation heat. The simulation results of warpage match the experimental results of the sample part quite well.

A finite-element analysis on the upsetting process of semi-solid aluminum material

The behavior of alloys in the semi-solid state depends strongly on the imposed stress state and on the morphology of the phase, which can vary from dendritic to globular. A finite-element model for semi-solid material in the upsetting process is presented. The semi-solid material is assumed to be described by compressible rigid visco-plastic model for the solid region and by Darcy's law for the liquid flow saturated in the interstitial space. The variation of the distribution of the solid fraction and the material behavior under the upsetting process is investigated for the various values of friction and die speed, the computed results being compared with experimental data. The semi-solid materials of the experiments are fabricated by mixing and cooling of the molten metal. The application validity of the yield criteria for semi-solid material is investigated in the upsetting process analysis.