Numerical results achieved with an inverse computational method for determining the constitutive parameters using the hot torsion test results

It was demonstrated in a previous paper that to obtain a unique set of parameters for a constitutive relationship from the hot torsion test, two separate objective or error functions must be considered. They are based on the load-displacement and load-displacement rate data respectively. The algorithm described earlier, has been implemented in a rigid viscoplastic FE code. The best set of the constitutive parameters that minimizes the objective functions is determined by using an optimization scheme. To demonstrate the predictive capabilities of the analytical approximation described in the previous part and to simulate the problem of identification of material parameters, a set of pseudo-experimental load-displacement/displacement rate data has been used for calculating the objective functions. The results confirm the inadequacy of using only the load-displacement results for the identification of the constitutive parameters from the hot torsion results. This is in agreement with the theoretical results in the previous paper. It is shown subsequently that the newly proposed inverse computational method can be used successfully to determine a unique set of the constitutive parameters.     

Thermo-viscoplastic parameter identification formulated as an inverse finite element analysis of the hot torsion test

This paper deals with an inverse finite element approach applied to the analysis of the steel behaviour during a hot torsion test. The rheological test is simulated by a finite element model and the inverse analysis principle is to find the constitutive parameters which permit to compute the closest values of a set of experimental torques which are measured for different operating conditions. A least square deviation between computed and measured variables is minimized with respect to the Theological coefficients corresponding to an appropriate material constitutive equation. A numerical validation of the proposed method is illustrated in the case of a Norton-Hoff thermo-viscoplastic law. All the rheological parameters which defined the consistency and the strain rate sensitivity can be simultaneously determined for a chosen analytical expression.     

The effect of specimen geometry on the accuracy of the constitutive equation derived from the hot torsion test

A rigid-viscoplastic FE code has been used to simulate the isothermal hot torsion of specimens used in tests designed for determining the relationship governing constitutive behaviour. For a given constitutive equation, the torque-rotation data were derived from the FE analysis of specimens of various geometries. Subsequently, based on these data, the constitutive equation was regenerated using an existing analytical relationship relating torque and twist in a cylindrical specimen. The effect of geometry of hot torsion specimens on the accuracy of the constitutive equation derived from the analytical relationship was investigated. Recommendations on the preferred geometry of hot torsion specimens for high deformations were made.     

Application of the Coupled Local Minimizers Method to the Optimization Problem in the Spectral Analysis of Surface Waves Method

The spectral analysis of surface waves (SASW) method aims to determine the small strain dynamic soil characteristics of shallow soil layers. The method involves an in situ experiment, the determination of an experimental dispersion curve, and the solution of an inverse problem, formulated as a nonlinear least squares problem. The latter is usually solved with a gradient-based local optimization method, which converges fast, but does not guarantee to find the global minimum of the objective function. The method of coupled local minimizers (CLM) combines the advantage of gradient-based local algorithms with the global approach of genetic algorithms. A cooperative search mechanism is set up by simultaneously performing a number of local optimization runs that are coupled by pairs of synchronization constraints. A synthetic example with two design variables (the shear wave velocity of two top layers of a layered half-space consisting of three layers on a half-space), demonstrates that the CLM method succeeds in finding the global minimum of an objective function with multiple minima and can successfully be used to solve the inverse problem in the SASW method. This is further illustrated by a complete inversion of the shear wave velocity profile accounting for seven design variables (the thickness and shear wave velocity of the three layers and the shear wave velocity of the underlying half-space). The inversion algorithm based on the CLM method is subsequently applied to invert the experimental dispersion curve derived from in situ data collected at a test site in Saluggia, Italy, consisting mainly of alluvial sediments. Up to a depth of about 25?m, the results show a reasonably good correspondence with crosshole test results.     

A Coupled Electrical–Thermal–Mechanical Modeling of Gleeble Tensile Tests for Ultra-High-Strength (UHS) Steel at a High Temperature

A coupled electrical–thermal–mechanical model is proposed aimed at the numerical modeling of Gleeble tension tests at a high temperature. A multidomain, multifield coupling resolution strategy is used for the solution of electrical, energy, and momentum conservation equations by means of the finite element method. Its application to ultra-high-strength steel is considered. After calibration with instrumented experiments, numerical results reveal that significant thermal gradients prevail in Gleeble tensile steel specimen in both axial and radial directions. Such gradients lead to the heterogeneous deformation of the specimen, which is a major difficulty for simple identification techniques of constitutive parameters, based on direct estimations of strain, strain rate, and stress. The proposed direct finite element coupled model can be viewed as an important achievement for subsequent inverse identification methods, which should be used to identify constitutive parameters for steel at a high temperature in the solid state and in the mushy state.     

Optimization of Temperature and Force Adaptation Algorithm in Hot Strip Mill

Abstract： In the hot strip rolling control system, the temperature distribution and deformation resistance are the main parameters affecting prediction of rolling force. In order to improve the model prediction precision, an optimiza- tion algorithm based on objective function was put forward, in which the penalty function index was adopted. During the adaptation process, the temperature distribution and deformation resistance were taken as the optimized parame ters, and the Nelder-Mead simplex algorithm was used to search the optimal solution of the objective function. Fur thermore, the temperature adaptation and force adaptation were solved simultaneously. Application results show that the method can improve the accuracy of the rolling force model obviously, and it can meet the demand of the indus trial production and has a good application prospect.     

Value of epicardial potential maps in localizing pre-excitation sites for radiofrequency ablation. A simulation study

Using computer simulations, we systematically investigated the limitations of an inverse solution that employs the potential distribution on the epicardial surface as an equivalent source model in localizing pre-excitation sites in Wolff-Parkinson-White syndrome. A model of the human ventricular myocardium that features an anatomically accurate geometry, an intramural rotating anisotropy and a computational implementation of the excitation process based on electrotonic interactions among cells, was used to simulate body surface potential maps (BSPMs) for 35 pre-excitation sites positioned along the atrioventricular ring. Two individualized torso models were used to account for variations in torso boundaries. Epicardial potential maps (EPMs) were computed using the L-curve inverse solution. The measure for accuracy of the localization was the distance between a position of the minimum in the inverse EPMs and the actual site of pre-excitation in the ventricular model. When the volume conductor properties and lead positions of the torso were precisely known and the measurement noise was added to the simulated BSPMs, the minimum in the inverse EPMs was at 12 ms after the onset on average within 0.65 +/- 0.26 cm of the pre-excitation site. When the standard torso model was used to localize the sites of onset of the pre-excitation sequence initiated in individualized male and female torso models, the mean distance between the minimum and the pre-excitation site was 0.67 +/- 0.31 cm for the male torso and 0.82 +/- 0.53 cm for the female torso. The findings of our study indicate that a location of the minimum in EPMs computed using the inverse solution can offer non-invasive means for pre-interventional planning of the ablative treatment.     

An inverse analysis of the hot uniaxial compression test by means of the finite element method

A computer simulation using the finite element method is carried out in the present work to model a hot compression test. Real constitutive equations of the hot flow behaviour of a medium carbon microalloyed steel, experimentally determined, are implemented in a commercial computer code and an inverse analysis is performed to determine under which conditions the experimental test can be considered as valid. In other words, the degree of strain and strain rate heterogeneity as well as the isothermatility of the test, for the given material, are verified. The effect of the friction coefficient is also included in the current analysis.     

Optimal Design and Operation of Irrigation Pumping Stations

A methodology based on solving a large-scale nonlinear programming problem is presented for the optimal design and operation of pumping stations. Optimum design and operation refers to the selection of pump type, capacity, and number of units as well as scheduling the operation of irrigation pumps that results in minimum design and operating cost for a given set of demand curves. The design criteria for such pumping stations are based fundamentally on some important and critical parameters, such as pump capacity, number of units, types of pumps, and civil works. The optimization process consists of three main steps: (1) determination of minimum yearly consumed energy; (2) minimization of the total cost for all sets of pumping stations; and (3) selection of the least-cost set among the feasible sets of pumping stations, recognizing a combination of the cited criteria. The computational analysis is based upon one major objective function and a computer program, which is developed to solve the generated equations. Application of the model to the Farabi Agricultural and Industrial Project, Iran, shows considerable savings, about 25% in total annual cost of the pumping station.     

Thermal strain in the mushy zone related to hot tearing

A volume-averaged two-phase model addressing the main transport phenomena associated with hot tearing in an isotropic mushy zone during solidification of metallic alloys has recently been presented elsewhere along with a new hot tearing criterion addressing both inadequate melt feeding and excessive deformation at relatively high solid fractions. The viscoplastic deformation in the mushy zone is addressed by a model in which the coherent mush is considered as a porous medium saturated with liquid. The thermal straining of the mush is accounted for by a recently developed model taking into account that there is no thermal strain in the mushy zone at low solid fractions because the dendrites then are free to move in the liquid, and that the thermal strain in the mushy zone tends toward the thermal strain in the fully solidified material when the solid fraction tends toward one. In the present work, the authors determined how variations in the parameters of the constitutive equation for thermal strain influence the hot tearing susceptibility calculated by the criterion. It turns out that varying the parameters in this equation has a signiicant effect on both liquid pressure drop and viscoplastic strain, which are key parameters in the hot tearing criterion. However, changing the parameters in this constitutive equation will result in changes in the viscoplastic strain and the liquid pressure drop that have opposite effects on the hot tearing susceptibility. The net effect on the hot tearing susceptibility is thus small.     

Simulating Three-Dimensional Free Surface Viscoelastic Flows using Moving Finite Difference Schemes

An efficient finite difference framework based on moving meshes methods is developed for the three-dimensional free surface viscoelastic flows. The basic model equations are based on the incompressible Navier-Stokes equations and the Oldroyd-B constitutive model for viscoelastic flows is adopted. A logical domain semi-Lagrangian scheme is designed for moving-mesh solution interpolation and convection. Numerical results show that harmonic map based moving mesh methods can achieve better accuracy for viscoelastic flows with free boundaries while using much less memory and computational time compared to the uniform mesh simulations.     

基于多目标满意优化的热轧非对称工作辊设计

热轧非对称工作辊可兼顾板形控制和自由规程轧制,其关键参数通常采用经验设计法,缺乏相应的依据.本文提出了热轧非对称工作辊关键参数的理论设计方法.由于设计过程中无法精确给定已知条件,因此把多目标满意优化引入到非对称工作辊的参数设计中,建立了综合满意度目标函数,并用模拟退火遗传算法进行满意度最优值求解.采用满意解代替最优解,使得辊形参数的优化设计结果更具科学性.在某热连轧生产线上的实际应用表明,优化设计的辊形在板形控制和自由规程轧制方面均取得了理想的效果.     

Modeling Flow Stress of 70Cr3Mo Steel Used for Back-Up Roll During Hot Deformation Considering Strain Compensation

A constitutive model incorporating the influence of strain developed based on the Arrhenius equation by considering the variation of material constants as a fifth polynomial function of strain is presented. Materials constants are fit to data from hot compression tests of 70Cr3Mo steel used for back-up roll at the temperatures from 1173 to 1473 K and strain rates from 0.01 to 10s^?1 by using a Gleeble-1500D thermo-mechanical simulator. The developed constitutive model is then used to predict the flow stress under all the tested conditions. The statistical parameters of correlation coefficient and average absolute relative error are used to analyze the predictable efficiency and the values are 0.997 and 3.64%, respectively. The results show a good agreement between experimental stress and predicted stress.     

Markov Chain Monte Carlo-Based Method for Flaw Detection in Beams

A Bayesian inference methodology using a Markov chain Monte Carlo (MCMC) sampling procedure is presented for estimating the parameters of computational structural models. This methodology combines prior information, measured data, and forward models to produce a posterior distribution for the system parameters of structural models that is most consistent with all available data. The MCMC procedure is based upon a Metropolis-Hastings algorithm that is shown to function effectively with noisy data, incomplete data sets, and mismatched computational nodes/measurement points. A series of numerical test cases based upon a cantilever beam is presented. The results demonstrate that the algorithm is able to estimate model parameters utilizing experimental data for the nodal displacements resulting from specified forces.     

OptiLam:Design of Optimised Rolling Schedules

Nowadays it is known that the thermomechanical schedules applied during hot rolling of flat products provide the steel with improved mechanical properties.In this work an optimisation tool,OptiLam (OptiLam v.1),based on a predictive software and capable of generating optimised rolling schedules to obtain the desired mechanical properties in the final product is described.OptiLam includes some well-known metallurgical models which predict microstructural evolution during hot rolling and the transformation austenite/ferrite during the cooling.Furthermore,an optimisation algorithm,which is based on the gradient method,has been added,in order to design thermomechanical sequences when a specific final grain size is desired.OptiLam has been used to optimise rolling parameters,such as strain and temperature.Here,some of the results of the software validation performed by means of hot torsion tests are presented,showing also the functionality of the tool.Finally,the application of classical optimisation models,based on the gradient method,to hot rolling operations,is also discussed.     

Calibration of Soil Constitutive Models with Spatially Varying Parameters

Soil constitutive models are frequently calibrated from laboratory tests that utilize global boundary measurements, which necessarily relegate soil response to that of a homogenized equivalent medium. This paper demonstrates the applicability of advanced experimental technologies to enhance the state of model-based predictions in soil mechanics by taking into account the possibility of material heterogeneity during model calibration. By utilizing the full-field displacement measurement technique of three-dimensional digital image correlation, displacements of the surfaces of deforming triaxial sand specimens are measured throughout deformation. These displacements are assimilated into finite-element (FE) models of the test specimen through solution of an inverse problem. During optimization, in which the difference between measured and predicted displacements across the specimen surface form the basis for the objective function, model parameters are allowed to vary spatially throughout the specimen volume. FE models allowing three different levels of spatial variability are tested. Results indicate that accommodating consideration of material heterogeneity during calibration leads to more accurate predictions of global stress-strain behavior that are more faithful to observed full-field response.     

基于改进差分进化算法的加热炉调度方法

提出一种以燃料消耗量最小为优化目标的加热炉生产调度新方法。首先基于热力学第一定律分析了流入及流出加热炉的各项能量,并对燃料消耗量的计算式进行了理论推导。进而根据加热炉区实际生产调度特点归纳各约束条件,以多台加热炉总燃料消耗量最小为优化目标,构建调度优化数学模型。采用自适应差分进化算法搭配禁忌搜索算法进行综合求解,并通过9组实际钢坯生产案例模拟验证了该算法的可行性和有效性。同时,为了探究加热炉燃料消耗量的影响因素,提出了分别衡量加热炉区缓冲等待、炉内加热两部分时间同理想生产时间匹配程度的评价参数μ₁和μ₂,并分析了燃料消耗量对二者的敏感性,结果表明:当连铸坯到达加热炉节奏与热轧工序出坯节奏之比由0.5增至2时,燃料消耗量对两评价参数的敏感性逐渐减弱。      

Deformation mechanism maps based on grain size

A new form of deformation mechanism map is introduced based on grain size. Maps are developed for pure aluminum at two different homologous temperatures, and the relative contributions of the various deformation processes are estimated as a function of stress at different grain sizes. A simple method of constructing these maps is presented, requiring only a knowledge of the relevant constitutive equations for the various mechanisms and a minimum of calculation.     

Cr-Co-Mo-Ni齿轮钢的热变形行为及模锻工艺的有限元模拟

在Gleeble-3800热模拟试验机上进行大变形等温压缩试验,研究Cr-Co-Mo-Ni齿轮钢的高温热变形行为和显微组织,分析材料流变应力与变形温度和应变速率的关系,建立热变形过程的本构方程和热加工图.该材料的流变应力随着温度的升高而下降,随应变速率的增加而增加;用双曲正弦函数式可描述其在热变形过程中的流变应力,热变形活化能为487.21k J·mol^-1;热加工图显示的适宜加工区间为温度1000-1100℃,应变速率0.1-1 s^-1.在热模拟试验基础上进行该钢种锻造工艺的有限元模拟,并结合热加工图分析初锻温度和加工道次对于锻件温度和应变速率的影响,得出适宜的模锻工艺参数为初锻温度1000-1100℃,锻造道次15次.     

炉子优化控制中真实目标函数的研究

通过了计算加热炉最佳加热制度的一种新方法。该方法采用完全基于能量平衡的精确模型来构成真实目标函数,并且运用最优控制理论中的上值原理进行求解。从理论上解决了在线模型的简化和目标函数保真之间的矛盾,为进一步实现炉子热工理论与现代控制理论的交叉与衔接奠定了基础。