Strain-dependent Coefficients Research Articles

Specific of the Recrystallization Driving Force Calculation on the early Stages of Thermomechanical Treatment of Aluminum Alloys

The article investigates the effect of the strain rate on the driving force of recrystallization during hot working of the as-cast structure. For the study, we applied previously obtained experimental data of recrystallization kinetics during this stage of thermomechanical treatment. In addition, hot laboratory rolling, followed by saltpeter bath soaking, were performed in order to obtain supplemental data on grain structure size and orientations. Grain structure size was examined by optical microscopy, and its orientation was examined by X-ray texture analysis. The studies demonstrated, that overestimated recrystallization driving force not only results in erroneous kinetics estimation, but also gives excessive number of recrystallization centers and undersized grain structure. Besides, unaccounted effect of recrystallization driving force on grain size leads to distorted predictions of texture composition. In order to avoid this, it was recommended to apply an special exponential accumulated strain dependent coefficient.

Wall-distance-free formulation for SSTk-ωmodel

Abstract Two different wdf (wall-distance-free) approaches are devised using local wall-distance and dissipation based representations to obtain consistency formulations for blending functions associated with the SST model. The strain-dependent coefficient C μ assists the SST model in constructing the functions such as to benefit complex flows with non-equilibrium turbulence, while retaining the predictive quality of unmodified SST closure. Naturally, the proposed methods allow the original SST model to be modified accurately and alleviate the free-stream dependency. Comparisons with the original SST k - ω model demonstrate that the newly developed alternatives to actual wall-distance usually improve the response of SST model to non-equilibrium effects.

Jamming transition in a two-dimensional open granular pile with rolling resistance

We present a molecular dynamics study of the jamming/unjamming transition in two-dimensional granular piles with open boundaries. The grains are modeled by viscoelastic forces, Coulomb friction and resistance to rolling. Two models for the rolling resistance interaction were assessed: one considers a constant rolling friction coefficient, and the other one a strain dependent coefficient. The piles are grown on a finite size substrate and subsequently discharged through an orifice opened at the center of the substrate. Varying the orifice width and taking the final height of the pile after the discharge as the order parameter, one can devise a transition from a jammed regime (when the grain flux is always clogged by an arch) to a catastrophic regime, in which the pile is completely destroyed by an avalanche as large as the system size. A finite size analysis shows that there is a finite orifice width associated with the threshold for the unjamming transition, no matter the model used for the microscopic interactions. As expected, the value of this threshold width increases when rolling resistance is considered, and it depends on the model used for the rolling friction.Received: 14 June 2014, Accepted: 7 October 2014; Reviewed by: R. Arévalo, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore; Edited by: L. A. Pugnaloni; DOI: http://dx.doi.org/10.4279/PIP.060007Cite as: C F M. Magalhaes, A P F Atman, G Combe, J G Moreira, Papers in Physics 6, 060007 (2014)

Modelling direction-dependent hardening in magnesium sheet forming simulations

In this work, a model capturing anisotropic hardening during plastic deformation under monotonic loading is proposed. For this purpose, the anisotropic plastic potential coefficients are assumed to be functions of a measure of the accumulated plastic strain. This model is applied to describe the plastic behavior of a magnesium alloy (ZM21) sheet at room temperature. The selected plastic potential accounts for the main features of Mg alloy plasticity, i.e., anisotropy and strength-differential (SD) effects. All the accumulated plastic strain dependent coefficients of the phenomenological model are determined from input data generated with a crystal plasticity approach. They are optimized to best capture the accumulated strain dependent potentials computed with crystal plasticity. The R-value (Lankford coefficient) anisotropy is used as an independent measure for the assessment of the approximation quality. This model is implemented into a finite element (FE) code and successfully validated through the numerical simulations of the cup drawing test. The calculated earing profile obtained with the proposed hardening model is compared to results assuming isotropic hardening for various plausible shapes of the plastic potential. Although the ear and valley numbers and positions are similar in all cases, the height differences between peaks and valleys are strongly dependent on the type of constitutive approach used in the simulation.

Development of a nonlinear near-wall turbulence model for turbulent flow and heat transfer

A new nonlinear near-wall turbulence model is developed on the basis of realizability constraints to predict turbulent flow and heat transfer in strongly nonequilibrium flows. The linear k– ε– f μ model of Park and Sung (Fluid Dyn. Res., 20 (1997) 97) is extended to a nonlinear formulation. The stress–strain relationship is derived from the Cayley–Hamilton theorem in a homogeneous flow. The ratio of production to dissipation ( P k/ ε) is employed to solve an algebraic equation of the strain dependent coefficients. A near-wall treatment is dealt with by reproducing the model coefficients from a modified strain variable. An improved explicit heat flux model is proposed with the aid of Cayley–Hamilton theorem, which includes the quadratic effects of flow deformations. The near-wall asymptotic behavior is incorporated by modifying the f λ function. Emphasis is placed on the model performance on the truncated strain terms. The model performance is shown to be generally satisfactory.

Modifications for an explicit algebraic stress model

An extension of the explicit algebraic stress model, developed by Gatski and Speziale [Gatski TB, Speziale CG. On the explicit algebraic stress models for complex turbulent flows. Journal of Fluid Mechanics 1993; 254: 59–78] is proposed. The extension implicates some essential characteristics of second-order closure models. The strain-dependent coefficients are modified, resulting in an alleviation of the numerical instabilities involved in the model. A new near-wall damping function fμ in the eddy viscosity relation is introduced. To enhance dissipation in near-wall regions, the model constant Cϵ1 is modified and an extra positive source term is included in the dissipation equation. In addition, a realizable time scale is incorporated to remove the wall singularity. Computed results show that the modified Gatski–Speziale (MGS) model predictions are in better agreement with the direct numerical simulation (DNS) and experimental data than those of the original Gatski–Speziale (OGS) model. Copyright © 2001 John Wiley & Sons, Ltd.

Development of a Nonlinear Near-Wall Model for Turbulent Flow and Heat Transfer

A new nonlinear near-wall turbulence model is developed to predict turbulent flow and heat transfer in strongly nonequilibrium flows. The k--f/, model of Park and Sung(1)/ is extended to a nonlinear formulation. The stress-strain relationship is the thrid-order in the mean velocity gradients. The strain dependent coefficients are obatined from the realizability constraints and the singular behavior at large strains. An improved explicit heat flux model is proposed with the aid of Cayley-Hamilton theorem. This new model includes the quadratic effects of flow deformations. The near-wall asymptotic behavior is incorporated by modifying the fλ/ function. The model performance is shown to be satisfactory.

Modifications for an explicit algebraic stress model

An extension of the explicit algebraic stress model, developed by Gatski and Speziale is proposed. The extension implicates some essential characteristics of second-order closure models. The strain-dependent coefficients are modified, resulting in an alleviation of the numerical instabilities involved in the model. A new near-wall damping function f μ in the eddy viscosity relation is introduced. To enhance dissipation in near-wall regions, the model constant C e1 is modified and an extra positive source term is included in the dissipation equation. In addition, a realizable time scale is incorporated to remove the wall singularity

Advanced Turbulence Modelling of Separated Flow in a Diffuser

The paper describes an investigation into the predictive performance of linear and non-linear eddy-viscosity models and differential stress-transport closures for separated flow in a nominally two-dimensional, asymmetric diffuser. The test case forms part of a broader collaborative exercise between academic and industrial partners. It is demonstrated that advanced turbulence models using strain-dependent coefficients and anisotropy-resolving closure offer tangible advantages in predictive capability, although the quality of their performance can vary significantly, depending on the details of closure approximations adopted. Certain features of the flow defy resolution by any of the closures investigated. In particular, no model resolves correctly the flow near the diffuser's inclined wall immediately downstream of the inlet corner, which may reflect the presence of a “flapping” motion associated with a highly-localised process of unsteady separation and reattachment.