Norton-Hoff Model Research Articles

Non-smooth evolution of non-Newtonian flows influenced by thermal effects

Abstract Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff model coupled with the unsteady heat system govern the fluid motion. This contribution is an extension of the previous established works. The novelty of this paper is to supply a close scrutiny result of the spawned interface through the medium of the pervasive Schauder fixed point. Numerical results are exhibited to illustrate the effectiveness of the advocated approach.

Effective Viscoplastic-Softening Model Suitable for Brain Impact Modelling

In this paper, we address the numerical aspects and implementation of a nonlinear viscoplastic model of the mechanical behaviour of brain tissue to simulate the dynamic responses related to impact loads which may cause traumatic injury. Among the various viscoelastic models available, we deliberately considered modifying the Norton–Hoff model in order to introduce non-typical viscoplastic softening behaviour that imitates a brain’s response just several milliseconds after a rapid impact. We describe the discretisation and three dimensional implementation of the model, with the aim of obtaining accurate numerical results in a reasonable computational time. Due to the large scale and complexity of the problem, a parallel computation technique, using a space–time finite element method, was used to facilitate the computation boost. It is proven that, after calibrating, the introduced viscoplastic-softening model is better suited for modelling brain tissue behaviour for the specific case of rapid impact loading rather than the commonly used viscoelastic models.

Norton-Hoff model for deformation of growing solid shell of thin slab casting in funnel-shape mold

A funnel-type mold is commonly used to provide necessary clearance for the submerged entry nozzle in the thin slab casting (TSC). The partially solidified shell is subjected to the mechanical deformations, which can lead to the defects formation and, as a results, to a breakout. Traditionally, the results of the flow simulation, performed by the finite volume method (FVM), are fed to the external package for the finite element analysis of stress and strain. A coupled model was assembled using “creeping solid” approach by blending the Norton-Hoff viscoplastic stress for the solidifying shell with the Newtonian viscous stress of the liquid melt. The FVM was used to combine both liquid and solid stress models within a single solver. The iterative procedure based on the improved both side diffusion method was introduced to treat the nonlinear relation between the viscoplastic stress and the strain rate. The modeled shell thickness was verified by previously published breakout measurements and the simulation results. Temperature distribution, obtained during the TSC simulation, dominantly corresponds to the viscoplastic range. Developed numerical approach is robust and has direct industrial application.

Shape optimisation with the level set method for contact problems in linearised elasticity

This article is devoted to shape optimisation of contact problems in linearised elasticity, thanks to the level set method. We circumvent the shape non-differentiability, due to the contact boundary conditions, by using penalised and regularised versions of the mechanical problem. This approach is applied to five different contact models: the frictionless model, the Tresca model, the Coulomb model, the normal compliance model and the Norton-Hoff model. We consider two types of optimisation problems in our applications: first, we minimise volume under a compliance constraint, second, we optimise the normal force, with a volume constraint, which is useful to design compliant mechanisms. To illustrate the validity of the method, 2D and 3D examples are performed, the 3D examples being computed with an industrial software.

Pumping of dewatered sludge: Slipping or flowing behavior?

The current design of dewatered sludge pumping devices is based on material flowing properties assuming it is a non-Newtonian highly viscous fluid. From rheological analysis, we first clearly established that current rheological models are no longer valid for this purpose. By using parallel-plates geometry, it was shown that the apparent behavior is dependent on the gap between the plates: results are less representative of sludge intrinsic properties that of the interface interactions between sludge and rotating surfaces. By reproducing dewatered sludge pipe flow at lab-scale, it was highlighted that sludge does not flow but slips along the wall of the pipe. The existence of a thin lubrication layer is suspected and the behavior law to be considered is a slippery law, similar to a Norton–Hoff model.

Approximation of the Norton–Hoff plasticity model with isotropic hardening through Cosserat plasticity

In this paper the regularizing properties of Cosserat elasto-plastic models in a geometrically linear setting are investigated. For vanishing Cosserat effects it is shown that the Norton–Hoff model with isotropic hardening is approximated by the model with microrotations.

Deep Drawing of Ti6Al4V: Experiments and Modeling over a Wide Range of Strain Rates and Temperatures

A combined experimental-numerical approach using digital image correlation (DIC) and finite element simulation in order to get the temperature dependent mechanical behaviour is presented. Results from a series of experiments on a Ti6Al4V titanium alloy sheet are shown. Tensile tests were carried out on specimens along 3 different orientations in order to characterise the material anisotropy. The strain-rates are varied from 10-1 to 10-2 s-1 while observations are made at temperatures from 903 to 1003 K. The samples are heated by Joule effect, which allows to use the image correlation in order to obtain the deformation fields and thus the coefficients of Lankford [1]. Differences in the responses of this alloy are observed in terms of work hardening, strain rate and temperature sensitivities. The Norton-Hoff model and the Hill [2] criterion are used to effectively simulate the observed responses obtained from these experiments. An inverse analysis model using kriging meta-model [3] is applied to determine each parameter of the mechanical behaviour law. The model, with the constants determined from these experiments, is then used to predict the mechanical behaviour of Ti6Al4V. Thus, the model is implemented into the implicit finite element code Forge® to model forming of thin-walled structures. The predictions are found to be very close to the observations.

Problèmes capacitaires en viscoplasticité avec effets de torsion

We study the homogenization of elasticity problems like (1) when f, g are strictly convex functions satisfying a growth condition of order p∈(1,+∞), g is positively homogeneous of degree p, kε→+∞, and Trε consists of an ε-periodic distribution of parallel fibers of cross sections of size rε≪ε. The problem (1) corresponds to a simplified model of small deformation nonlinear elasticity describing, for instance, the small deformations of an Ogdenʼs material (Ogden, 1972 [8]). When 1<p<2, it may also characterize the viscoplastic creep experienced, at high temperatures, by a metallic composite governed by the Norton–Hoff model (Friaâ, 1979 [7]). In this case, uε represents the velocity vector field. We show that if p⩽2, a concentration of strain energy appears in a small region of space surrounding the fibers. This extra contribution is characterized by a local density of the sections of the fibers with respect to some appropriate capacity depending, if p<2, on the angles of rotation of the fibers with respect to their principal axis. This rotating behavior generates, in parallel, the emergence of torsional strain energy within the fibers.

Modelization and comparison of Norton-Hoff and Arrhenius constitutive laws to predict hot tensile behavior of Ti–6Al–4V alloy

In order to study the workability of Ti–6Al–4V alloy in the hot forming process for sheets and profiles, the stress-strain experimental data from isothermal hot tensile tests of flat specimens, in the temperature range of 923-1023 K and strain rate range of 0.0005-0.05 s−1 were used to develop the constitutive equation. Arrhenius and Norton-Hoff constitutive models were proposed to characterize the tensile behavior. The fitting results suggest that both Arrhenius constitutive equation (material constants consider the compensation of strain) and modified Norton-Hoff one can predict flow stress of Ti–6Al–4V alloy under most experimental conditions. Further, the modified Norton-Hoff model is more accurate and precise than Arrhenius model.

Identification of a free boundary in Norton–Hoff flows with thermal effects

This work deals with a free boundary identification problem in a steady viscoplastic flow. We provide a novel identification model based on a non-linear optimization. The fluid motion is governed by the incompressible Norton–Hoff model coupled with the heat equation. The viscosity of the fluid is modeled by the non-linear Arrhenius law. Our point of view is to treat the problem as a shape sensitivity of a cost functional formulated on the free boundary and governed by the normal component of the velocity of the flow. We analyze the mathematical statement of the forward problem. The equations related to the free boundary are simplified. Various properties of this optimization are proved. Since the state of Norton–Hoff model is not regular enough we introduce a parameter penalization. The shape gradient of the considered cost functional is given in the strong sense up to the parameter of penalization. We supply the expression of the shape gradient in a weak sense.

Study of the Norton–Hoff operator coupled with the evolutive heat equation

We are interested in the study of quasistatic visco-plastic flows with thermal effects. The fluid motion is governed by the incompressible Norton–Hoff model coupled with the time-dependent heat equation where the dissipated mechanical power is the source term. The viscosity of the fluid is modeled by the non-linear Arrhenius law. The well-posedness of each decoupled system is given. The optimal regularities of the heat solution and of the scale factor are supplied. A non-linear operator describing the stand coupling is provided. The existence of a solution to the considered problem is established. We prove the compactness result of the set solutions.

A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity

A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity