Viscoplastic Material Behavior Research Articles

Numerical study of hydrodynamic forces of nonlinear fluid flow in a channel-driven cavity: Finite element-based simulation

This communication is aimed at presenting the flow behavior of viscoplastic materials in a channel driven-cavity by utilizing the Bingham constitutive equation in conjunction with the modification proposed by Papanastasiou. The whole system has been represented by a model consisting of coupled nonlinear partial differential equations. In addition, the governing equations were nondimensionalized by making use of the appropriate set of variables and the computations were carried out using the finite element method. A finite element space including quadratic polynomial [Formula: see text] is chosen for the approximation of velocity profiles whilst a space containing linear polynomials is used for the estimation of pressure [Formula: see text]. The hydrodynamics forces like drag and lift values on cylindrical obstacle whose center is located at (1.5, 1.5) are computed against various values of Bingham number. Moreover, pressure drop values between the back and front of the square obstacle have also been tabulated.

Chaboche viscoplastic material model for process simulation of additively manufactured Ti-6Al-4 V parts

For the estimation and further optimization of the residual stress and distortion state in additively manufactured structures during and after the wire arc additive manufacturing (WAAM) process, thermomechanical simulation can be applied as a numerical tool. In addition to the detailed modelling of key process parameters, the used material model and material data have a major influence on the accuracy of the numerical analysis. The material behaviour, in particular the viscoplastic behaviour of the titanium alloy Ti-6Al-4 V which is commonly used in aerospace, is investigated within this work. An extensive material characterization of the viscoplastic material behaviour of the WAAM round specimen is carried out conducting low cycle fatigue (LCF) and complex low cycle fatigue (CLCF) tests in a wide temperature range. An elasto-viscoplastic Chaboche material model is parameterised, fitted, and validated to the experimental data in the investigated temperature range. Subsequently, the material model is implemented in the thermomechanical simulation of a representative, linear ten-layer WAAM structure. To finally determine the effect of the fitted material model on the estimation accuracy of residual stress and distortion, simulation results using the standard material model and the elaborated Chaboche model from this study are compared to experimental data in the substrate. The thermomechanical simulation with the Chaboche model reveals a better agreement with the experimental distortion and residual stress state, whereby the standard material model tends to an overestimation. The estimation accuracy with respect to the maximum distortion is improved from an error of 60% with the standard model to an acceptable error of about 6% using the elaborated model. Additionally, the estimated residual stress state shows a sound agreement to the experimental residual stress in the substrate.

Experimental determination of cyclically stabilized material properties of the Mo-based alloy MHC in stress-relieved condition from room temperature to 1400 °C

The aim of the current study was the determination of the time-dependent visco-plastic material behavior of the molybdenum alloy MHC (Molybdenum-Hafnium-Carbon) in stress-relieved condition with cyclic strain-controlled low cycle fatigue experiments at room temperature, 800 °C and 1400 °C. To ensure high data quality, a servohydraulic testing machine modified with a vacuum chamber was utilized to avoid material oxidation. The long-time strain-controlled experiments were conducted with a laser extensometer with high accuracy up to the highest applied test temperature of 1400 °C. The determined data were appropriate to generate cyclic stress-strain curves, strain-Wöhler curves, and their descriptive parameters. Furthermore, the strain rate dependency of the cyclic stress response and the stress relaxation behavior of the cyclically stabilized material were also investigated at the mentioned temperatures. The current study indicates that MHC in stress-relieved condition has a softening ability during cyclic loading, especially at 800 °C and 1400 °C. The strain rate sensitivity of the stress amplitude for the case of cyclic stabilization shows similar behavior as described in the literature for the case of monotonously increasing loading conditions, with a minimum at 800 °C. An interesting effect was identified in relaxation tests with loading at different strain rates. A kind of rebound effect was observed at the highest utilized strain rate of 10−2 s−1, which disappears with decreasing strain rate. Elastic strain proportions can be converted into plastic strain proportions during the application of the slow strain rate.

Multiscale viscoplastic modeling of recycled glass fiber-reinforced thermoplastic composites: Experimental and numerical investigations

One of the main challenges facing fiber-reinforced polymer composites is the lack of options for end-of-life recycling. The environmental impact of waste materials disposed of at landfill sites, by incineration, or by erratic dispersion in the environment is accelerating the need to find innovative solutions to increase the value of recycled materials. This research aims to investigate the relationship between microstructural parameters and the mechanical properties of a recycled thermoplastic composite material. The latter is processed by thermocompression molding of a polyamide (PA66) matrix reinforced with chopped glass strands. An innovative approach is proposed to link the local microstructure of the composite to the mechanical behavior of the recycled material. It exploits an experimental characterization of the material microstructure using optical microscopy and X-ray micro-computed tomography (mCT). The experimental findings are implemented into a numerical modeling strategy to mimic the flexural behavior, based on a micromechanical approach coupling mean and full-field analysis. The region of interest is reconstructed from detailed 3D images using a modified random sequential adsorption (MRSA) algorithm, while other regions are modeled as homogenized macro-scale continua. Furthermore, the abilities of the proposed approach are proven by incorporating the viscoplastic behavior of the random heterogeneous material induced by the polymer matrix. The originality of the present research consists of the multi-scale FE analysis and the experimental validation for the viscoplastic behavior of the recycled composite material, taking into account influences from the microstructure.

Regularized variational formulation for nonlinear dynamics of viscoplastic plates

In this work we present novel approach to Reissner–Mindlin plates, targeting the nonlinear dynamics applications and in particular robust scheme for improved performance in vibration and wave propagation computations, where the standard finite element isoparametric interpolations no longer provide the best approximation property. The first key ingredient of the present development is regularized variational formulation, recast in terms of stress resultants (bending moments and shear forces), which allows any convenient interpolations. The discrete approximation is here constructed by using the lowest order Raviart–Thomas vector space employed to discretize bending moment and shear force fields, providing the continuity of the stress resultants projections across the boundary between adjacent plate elements. The latter is of particular interest for dynamic analysis for it can capture smooth approximation for wave propagation phenomena. This particular space discrete approximation is further combined with the most appropriate time-integration schemes capable of enforcing either energy conservation or decay of high frequency modes, which delivers the schemes with higher stability and robustness in long-term computations. The developments are carried out for viscoplastic constitutive behavior of plate material, where the corresponding evolution equations are obtained by appealing to the penalty-like form of the principle of maximum plastic dissipation. The choice of viscoplasticity (rather than plasticity) is crucial in that allows development of second-order scheme by integrating simultaneously the momentum balance and viscoplastic strains evolution equations. Several numerical simulations are given to illustrate a very satisfying performance of the proposed hybrid-stress discrete approximation for thick plate element and of the energy conserving/decaying schemes.

A multifield variational formulation of viscoplasticity suitable to deal with singularities and non-smooth functions

In the present paper a multifield variational formulation of non-smooth viscoplasticity is illustrated which is well suited to deal with multivalued operators and non-smooth functions characterized by singularities. The adopted approach proves to be helpful in describing a geometrical framework of the non-smooth viscoplastic problem and in guiding to enhancements towards other kinds of plastic and viscoplastic material behavior. Alternative equivalent expressions of evolutive laws are discussed. The formulation shows to include Koiter’s theory as a special case. In addition, a multifield variational formulation of non-smooth viscoplasticity is illustrated. A procedure for deriving a parent potential in all the unknown variables is illustrated for non-smooth viscoplasticity problems. From the parent potential a set of associated multifield potentials is furtherly derived in one or more unknown fields and the relevant extremum properties are illustrated so that the non-smooth viscoplasticity structural problem is provided with a complete variational formulation suitable for developments in finite element applications.

The direct impact method for studying dynamic behavior of viscoplastic materials

Equipping mathematical models of deformation of viscoplastic materials with the necessary parameters and constants requires comprehensive experimental data meeting the requirements of the problem being analyzed. For problems of evaluating strength of dynamically loaded structures, it is important to account for the strain rate effect on the yield surface radius. Experimental schemes for studying such an effect can be constructed based on the measuring rod technique. Such methods include, for instance, the well-known Kolsky method. The methodological limitations of the above experimental scheme necessitated the development of its alternative versions to widen the range of realized strain rates studied. The present paper gives the description and the results of numerical analysis of an experimental method implementing the socalled direct impact scheme that is also constructed based on the measuring bar technique. The method is used for determining deformation diagrams of viscoplastic structural materials loaded in high-rate compression with strain rates higher than those in the traditional Kolsky method. Using the Kolsky method and the direct impact method, deformation diagrams of copper S101 and aluminum alloy D16Т in the strain rate range of 1000 to 10000 s-1 have been obtained.

Viscoplastic behavior of bulk solder material under cyclic loading and compression of spherical joint-scale granules

Viscoplastic behavior of bulk solder material under cyclic loading and compression of spherical joint-scale granules

Simulating dense granular flow using the μ(I)‐rheology within a space‐time framework

AbstractA space‐time framework is applied to simulate dense granular flow. Two different numerical experiments are performed: a column collapse and a dam break on an inclined plane. The experiments are modeled as two‐phase flows. The dense granular material is represented by a constitutive model, the (I)‐rheology, that is based on the Coulomb's friction law, such that the normal stress applied by the pressure is related to the tangential stress. The model represents a complex viscoplastic material behavior. The interface between the dense granular material and the surrounding light fluid is captured with a level set function. Due to discontinuities close to the the interface, the mesh requires a sufficient resolution. The space‐time approach allows unstructured meshes in time and, therefore a well‐refined mesh in the temporal direction around the interface. In this study, results and performance of a flat and a simplex space time discretization are verified and analyzed.

A new stress-updating algorithm for viscoplasticity

Material behavior beyond the elastic limit can be rate-dependent, and this rate sensitivity can be captured by the viscoplastic material models. To describe the viscoplastic material behavior in structural analysis, an efficient numerical framework is necessary. In this paper an algorithm is proposed for metals for which von Mises yield surface along with Peric’s viscoplastic model is employed. The efficiency and accuracy of the technique is examined by comparison with different numerical studies. The convergence rate of the proposed algorithm is investigated. Characteristics of the viscoplastic behavior such as relaxation are illustrated in the selected case studies. Finally, application of the algorithm in practice is demonstrated by a boundary value problem.

On the interplay of friction and stress relaxation to improve stretch-flangeability of dual phase (DP600) steel

Industrial servo presses have been used to successfully demonstrate improved formability when deforming sheet metals. While the time dependent viscoplastic behavior of material is attributed to the observed formability improvement, much less effort has been devoted to understand and quantify the underlying mechanisms. In this context, the hole expansion test (HET) of a dual phase steel was interrupted at pre-defined punch travel heights to understand the time-dependent effects on stretch-flangeability. The effect of pre-strain, hold time and edge quality on hole expansion ratio (HER) improvement was studied. The present study shows that the HER improves significantly in interrupted HET. This improved HER is due to the combined effects of stress relaxation and friction on deformation behavior. The ductility improvement estimated from uniaxial stress relaxation tests was used to estimate the contribution of stress relaxation and friction, respectively, in HET. This study shows that friction plays a significant role in improving HER at high pre-strain. It was also demonstrated that frictional effects are largely influenced by edge quality.

A finite strain framework for steady-state problems: Hyperelasto-viscoplasticity

A numerical framework for analyzing steady-state elastic–plastic material deformation at finite strains is developed and demonstrated in the present work. The framework is an extension of the original method by Dean and Hutchinson (1980) develop to analyze steady-state crack propagation, under a small strain assumption, in which the history-dependent material response is captured through streamline integration. Steady-state problems are encountered in numerous engineering processes, and the original studies of crack growth have already been extended to include rolling and drawing, though within a small strain framework. However, the investigation of such manufacturing processes, where strains greater than 10% easily develop, requires a finite strain formulation to provide accurate results. The framework proposed in the present work offers an efficient and accurate method to extract the steady-state solution at finite strains without encountering the numerical issues related to traditional Lagrangian procedures. Furthermore, the framework also accounts for elastic unloading compared to many existing numerical steady-state schemes as they are often restricted to rigid plasticity. The new numerical framework employs a hyperelastic material model, in terms of a Neo-Hookean material, combined with an isotropic viscoplastic material behavior. However, the framework is not limited to any specific hyperelastic material model, nor any specific model for the plastic behavior. The finite strain steady-state framework has been verified through comparison to a traditional Lagrangian analysis conducted in ANSYS. The benchmark case constitutes a plane strain drawing process where the thickness of the specimen is reduced by drawing it between two circular cylindrical tools.

Deep convolutional neural networks in structural dynamics under consideration of viscoplastic material behaviour

The aim of the present study is to develop a deep convolutional neural network (DCNN) to predict geometrically and physically nonlinear structural deformations. Training data is obtained by short-time measurements in shock tubes, wherein metal plates are subjected to impulsive loadings, leading to viscoplastic vibrations and inelastic deflections. Due to the fact that, in literature, feed forward neural networks (FFNN) are more distributed for applications in structural mechanics, comparative calculations are presented between structural deformations based on DCNNs and FFNNs. Special attention is focused on the ability of DCNNs to capture also path-dependent deformations inside the network, which is an essential feature for inelastic material behaviour.

On the change of the reference configuration and its application within FEM simulations

AbstractWithin numerical simulations of mechanical systems, not only the geometry, boundary conditions, the material behavior and the included material parameters have to defined. Beyond that, initial conditions have to be set properly in order to define the initial state of the material. In this contribution, two different examples of proper definition of initial values are regarded and their impact on the simulation results is discussed. The first example is devoted to models including elasto‐ or viscoplastic material behavior. Here initial values of plastic internal variables enable the consideration of the loading history. Thereby, a change of the reference configuration has to be taken into account. The second example highlights the impact of initial values for the temperature and similar physical properties that control the initial volume of a material with volume‐changing capabilities (like heat expansion, swelling or polymerization shrinkage).

An asynchronous integration method for accelerated finite element analysis

Elasto-plastic boundary value problems involving heterogeneous geometry, material properties and/or loading can have localized deformation, stress, and, plastic flow. The Finite Element Method (FEM) finds wide spread usage to solve such boundary value problems. However due to localized deformation, the speed of FEM simulation can be extremely slow owing to the need of small time steps to ensure convergence. The difficulty in convergence can arise due to the large spatio-temporal gradient and strong non-linearity in the region of localization. The issue of increased computational time can be alleviated by the use of asynchronous integration wherein different sub-domains are evolved with different time step sizes and synchronization after certain time interval. However, the speedup and accuracy of the solution is strongly influenced by the interface constraint condition, sub-domain selection and the disparity in time step sizes required in the sub-domains. In the present work, an asynchronous integration method is proposed for quasi-static problems with material non-linearity and geometric imperfection. The interfaces between the sub-domains are constrained such that the incremental energy is balanced over the largest time increment. The performance of the method is evaluated for one and two-dimensional boundary value problems with viscoplastic material behavior. In both the cases geometric imperfections are introduced to obtain localization. Different sub-domain sizes and tolerance values are considered to evaluate their impact on accuracy and computational speed up.

Enhancement of stiffness and dynamic mechanical properties of polymers using single-walled-carbon-nanotube – a multiscale finite element formulation study

The static and dynamic mechanical properties of polymeric materials can greatly be enhanced by using carbon nanotubes as reinforcement material. However, studies still need to be carried out to characterize the dynamic mechanical properties of the Carbon-Nanotube-Reinforced-Polymer (CNRP) material. Experimental investigations for this purpose have severe limitations and, in most cases, appropriate and reliable experimental work could not be carried out. Computational modelling and simulation encompassing multiscale material behavior provides an alternate approach to study the material behavior. The objective of the present work is to study the enhancement of stiffness and dynamic mechanical properties of Carbon-Nanotube-Reinforced-Polymer (CNRP) material by using a 3D multiscale finite-element model of the representative volume element of the CNRP material. A composite material model consisting of a polymer matrix, an interface region, and a Single-Walled Carbon Nanotube (SWCNT) is constructed for this purpose. The polymer matrix is modeled with the Mooney-Rivlin strain energy function to calculate its non-linear response and the interface region is modeled via van der Waals links. The SWCNT is modeled as a space frame structure by using the Morse potential and as a thin shell model based on Donnell’s Shell Theory. The stiffness response of the CNRP is calculated and the natural frequencies of the CNRP are also determined. The viscoplastic behavior of the polymer matrix material is considered and the rate-dependent characteristics of the CNRP are studied. The damping properties of the CNRP are investigated based on its viscous and structural damping mechanisms. The effectiveness of the SWCNT reinforcement is quantified and characterized.

Analysis of landslides employing a space–time single-phase level-set method

Landslide dynamics are characterized by a phase transition from a solid like behavior to a fluid one. Since the material is moving through space special discretization techniques are required. Four-dimensional space–time finite elements for fluid–structure interactions are applied together with the single-phase level-set method to investigate the dynamics of 3D landslides interacting with flexible walls. The wall is modeled as a geometric nonlinear solid with elastic–viscoplastic material behavior, whereas the liquefied soil is described with the Navier–Stokes equations for incompressible Bingham fluids. Between fluid and solid advanced coupling conditions are taken into account incorporating friction. In order to solve the governing equations of the multi-field problem, the weighted-residuals method is applied, which is discretized by time-discontinuous space–time elements. Within the monolithic solution procedure for the coupled problem, the kinematics of both solid and fluid are described using velocities as primary variables. A pseudo-structure adapts the coordinates of the fluid mesh to the deformations of adjacent structures. The single-phase level-set method describes the motion of the free surface of the sliding material. To accurately transport the free surface a pde-based extrapolation is used for the velocities. Various effects in 3D landslide dynamics are investigated.

A multiscale two-way thermomechanically coupled micromechanics analysis of the impact response of thermo-elastic-viscoplastic composites

A dynamic multiscale micromechanics model that accounts for two-way thermomechanical coupling in composites is presented. It predicts not only the standard deformation that results from a temperature change, but also the temperature change that results from mechanical deformation. In addition, viscoplastic material behavior is included at the scale of the fiber/matrix constituents in a local High-Fidelity Generalized Method of Cells analysis, which is conducted at each material point of a global analysis on a composite specimen. The global analysis of the composite considers time-dependent thermomechanical boundary conditions capable of simulating impact loading while solving the coupled transient thermal problem and the dynamic mechanical problem. Effective thermoelastic and physical properties, as well as homogenized inelastic strains are provided to the global model from the local scale. The multiscale model was employed to examine the impact response of carbon/epoxy and SiC/Ti composites with emphasis on the temperature changes and inelastic strains induced by the impact loading. It was found that the behavior of the two types of composites was quite different, with the differences traceable to the effect of the matrix material properties on the terms within the energy equation, which governs the heat generation.

Thermo-mechanical modeling and microstructure evolution of friction-assisted tube-straining method

A thermo-mechanical model of friction-assisted tube-straining method is presented for commercially pure copper. A dislocation-based mechanical property model is embedded to commercial FE code ABAQUS/Standard to simulate Lagrangian, thermo-mechanically coupled with visco-plastic material behavior. A python script was added to FE code to automatically re-mesh the distorted elements in the deformation area. The friction coefficient was obtained from the combined experimental tests and numerical simulations. The load and temperature histories in both of the numerical and the experimental tests were compared and a good agreement was found. Microstructure and microhardness analysis of processed samples show the considerable changes in which the initial grain size 63 μm for the annealed sample was refined to 6.5 μm and the microhardness increases 200% greater than the initial value.

A Dislocation Density-Based Viscoplasticity Model for Cyclic Deformation: Application to P91 Steel

To describe the viscoplastic behavior of materials under cyclic loading, a dislocation density-based constitutive model is developed based on the unified constitutive theory in which both the creep and plastic strain are integrated into an inelastic strain tensor. The stress evolution during cyclic deformation is caused by the mutual competition and interaction between hardening and recovery. To incorporate the physical mechanisms of cyclic deformation, the change of mobile dislocation density is associated with inelastic stain in the proposed model. The evolution of immobile dislocation density induced by strain hardening, dynamic recovery, static recovery and strain-induced recovery are simulated separately. The deterioration of yield strength following the hardening in tension (or compression) and subsequently in compression (or tension) is described by the Bauschinger effect and reduction of immobile dislocation density, the latter is induced by static- and strain-induced recovery. A kinematic hardening law based on dislocation density is proposed, both isotropic hardening and softening are described by determining the evolution of hardening parameters. The experimental data of P91 steel under different strain rates and temperatures are adopted to verify the proposed model. In general, the numerical predictions agree well with the experimental results. It is demonstrated that the developed model can accurately describe the hardening rate change, the yield strength deterioration and the softening under cyclic loading.