Parameter determination of Chaboche kinematic hardening model using a multi objective Genetic Algorithm

Chaboche model is a powerful tool to evaluate the cyclic behavior under different loading conditions using kinematic hardening theory. It can also predict the ratcheting phenomenon. To predict the ratcheting, it is required to determine the material parameters under strain control conditions. Although, these parameters can model the hysteresis loop fairly accurately, their ratcheting prediction does not have the same quality. A set of material parameters that could accurately predict both ratcheting and hysteresis loop is of great importance. The available models, generally for low cycle fatigue, are mostly complex and nonlinear. Therefore, an optimization procedure can be used for parameter determination and consequently improving the prediction of these models.Genetic Algorithm is a numerical approach for optimization of nonlinear problems. Using a multi objective Genetic Algorithm for Chaboche model, a set of parameters was obtained which improved both ratcheting prediction and hysteresis loop model. Two fitness functions were used for this approach. The proposed model was verified using Hassan and Corona’s experimental data conducted on CS 1026 low carbon steel. The model indicated a very good agreement in the case of uniaxial loading with the experimental data. The results of proposed model for biaxial loading histories are similar to the model by Hassan and his co-workers.     

Nondestructive Characterization of Microstructure and Mechanical Properties of Heat Treated H13 Tool Steel Using Magnetic Hysteresis Loop Methodology

ABSTRACT

The aim in this article is to evaluate microstructural changes, hardness variations, and wear behavior of H13 hot work tool steel as a function of austenitizing and tempering temperature using nondestructive magnetic hysteresis loop method. To obtain different microstructural characteristics in the H13 specimens, austenitizing and tempering temperatures were varied in the range of 1,050–1,100°C and 200–650°C, respectively. The microstructural features, hardness, and wear loss were characterized using X-ray diffraction/metallographic examinations, hardness measurements, and a pin-on-disk wear tester, respectively. The relations between features obtained from the conventional methods and parameters extracted from the magnetic hysteresis loops were established. Results demonstrate that the proposed nondestructive method is able to assess the wear behavior of the heat treated H13 tool steels. Besides, a standard Generalized Regression Neural Network (GRNN) was trained with a training dataset and then used to estimate the hardness of a given sample with its measured values of magnetic parameters. Experimental results indicate that, if the training dataset has sufficient samples, the proposed method will have a very high accuracy to estimate hardness of the sample, nondestructively.     

Fatigue Hysteresis Behavior of 2.5D Woven C/SiC Composites: Theory and Experiments

This paper presents an intriguing fatigue hysteresis behavior of 2.5 dimensional woven C/SiC composites via the integration tool of advanced experimental techniques with a multiscale theoretical model. Tension-tension fatigue experiment has been carried out to predict the fatigue hysteresis properties of 2.5D woven C/SiC composite at room temperature, accompanied with the fracture of specimens to investigate the mechanism of fatigue damage. Meanwhile, a multiscale fatigue model of 2.5D woven C/SiC composites, which encompasses a micro-scale model of fiber/matrix/porosity in fiber tows and a macro-scale model of unit-cell, has been proposed to provide a reliable validation of the experimental results based on fiber damages resulting from relative slip motion with respect to matrix at interfaces and the architecture of 2.5D woven C/SiC composites. The predicted hysteresis loop from theoretical model at room temperature holds great agreement with that from tension-tension fatigue experiments. Also, effects of fatigue load, braided structural parameters and material properties at micro scale on fatigue hysteresis behavior have been investigated.     

Description of the process of magnetization of hollow cylindrical rods from soft magnetic materials in a homogeneous quasi-static magnetic field of a solenoid. Hysteresis loop

On the basis of the arctangential approximation of the magnetic hysteresis loop of the material and the expression for the central demagnetization coefficient of hollow cylindrical rods from soft magnetic materials, a method for calculating the hysteresis loops of these rods in a homogeneous quasi-static field of a solenoid is proposed. Calculation and comparison to experimental data of the basic parameters of the magnetic loops hysteresis of hollow cylindrical rods with a different value of the demagnetization coefficient have been made. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 6, pp. 181–188, November–December, 2007.     

Simulation of low cycle fatigue stress‐strain response in 316LN stainless steel using non‐linear isotropic kinematic hardening model—A comparison of different approaches

Cyclic stress‐strain response of 316LN stainless steel subjected to low cycle fatigue at strain amplitude of ±0.4% and at 873 K is simulated using finite element analysis with non‐linear isotropic‐kinematic hardening Chaboche model. Four different approaches have been used in simulating cyclic stress response and hysteresis loops: 3 based on Chaboche model‐parameters and the fourth on direct experimental data (stabilized loop and cyclic stress‐strain curve [CSSC]). Among them, simulations performed with direct experimental data have not yielded expected initial cyclic response. The source of data used for evaluation of kinematic‐hardening (KH) parameters determined the extent of closeness between experimental results and Chaboche‐model predictions. KH parameters determined from first‐cycle loop and modified‐CSSC predicted the overall stress‐strain response (from initial to stabilized condition) with reasonable fit, compared with other approaches. All 4 approaches though predicted stabilized response, simulations based on “KH‐parameters from stabilized‐cycle” accurately described stabilized response with coefficient of determination (r²) 0.995.     

Hysteresis behaviour of reactive high power impulse magnetron sputtering

Hysteresis behaviour during reactive High Power Impulse Magnetron Sputtering (HIPIMS) has been investigated in detail. Such analysis has been made possible by the recently developed plasma emission monitoring based reactive HIPIMS monitoring and control technology. Hysteresis curves were recorded at frequencies of 300, 450 and 600 Hz at an average power of 3.0 kW during reactive HIPIMS of Ti in Ar/O₂ atmosphere. It is shown that the target pulsing parameters, such as frequency, pulse voltage, and duty cycle do affect the overall shape of the hysteresis loop. Analysis of the hysteresis behaviour at different target pulsing parameters reveals how different regions of the hysteresis loop are affected by different pulsing parameters. The outcomes of this work demonstrate trends and explain relationships between the pulsing parameters and the hysteresis behaviour. Although the overall picture is rather complicated, it is quite clear that the hysteresis effect is induced by the same processes as in direct current magnetron sputtering, while the influence of the reactive ion implantation oxidation mechanism appears to be far more significant in reactive HIPIMS.     

基于PSO算法的GMM改进J-A磁滞模型的参数辨识与验证

为了解决现有的GMM-FBG电流传感器的磁滞非线性问题,基于经典的J-A磁滞模型提出了一种改进的适用于低频(<120Hz)条件下的J-A模型。采用粒子群(PSO)算法对改进后的J-A模型进行了分段参数辨识与优化,提高了模型的预测精度。搭建了相应的GMM-FBG交流电流传感系统实验平台,运用所提出的改进的J-A模型对GMM-FBG电流传感器进行了磁滞建模和实验验证。实验及仿真结果证实该模型具有良好的预测性,模型的预测误差在2.5%以内,传感系统的电流测量灵敏度达到0.067nm/A。     

Analysis of minor loop behavior during alternating flux reversal in rectangular-loop toroidal cores

The analysis of minor hysteresis loop behavior during partial alternating flux reversal in toroidal cores with a rectangular hysteresis loop is considered. A simple flux-reversal model is proposed on the basis of which, with the aid of dimensionless units, the asymmetry of minor hysteresis loops is derived. The drift of minor hysteresis loops during alternating flux reversal is investigated on the basis of loop asymmetry and by means of a proposed indirect method. The method involves compensation of the minor-loop drift by means of a dc component of the exciting field, the magnitude and sense of which are a measure of the drift. The experimental section deals partly with a qualitative comparison of the character of the actual asymmetry of a minor loop with that derived from the flux reversal model, and partly with comparing the actual minor-loop drift to the drift derived theoretically on the basis of the indirect method. Experimental results indicate that in the case of the 50 percent nickel-iron alloy, cold-rolled at a great reduction, there appear additional factors which affect the instability of the minor loop. This effect is further investigated, and a simplified mechanism is proposed for its stimulation. Finally, the proposed mechanism is verified experimentally.     

Life prediction of stainless steels by cyclic and stable hysteresis curves

Abstract

This study develops an analytical expression to describe the cyclic stress‐strain curve obtained from a series of fully‐reversed fatigue tests. A set of stress‐strain relationships is proposed to simulate the tensile branch of the stable hysteresis loop. The complete shape of the stable hysteresis loop is then constructed and the associated theoretical plastic work calculated by integrating the area within the enclosed curve. The theoretical plastic work is employed to predict the fatigue lives of the investigated materials on the basis of their respective stable plastic work per cyclelife curves. In this paper, the current mathematical derivations are based upon the endochronic theory of plasticity. The accuracy of the proposed set of stress‐strain relationships is verified by conducting fully‐reversed constant strain amplitude fatigue tests on AISI 316 and AISI 304 stainless steels. The experimental and simulation results are found to be in good agreement, hence confirming the accuracy of the proposed analytical stress‐strain relationships. Again, comparing the obverted and predicted fatigue lives, a good agreement is found between the two sets of results.     

冷弯薄壁型钢组合墙体非线性滑移滞回模型研究

为了研究冷弯薄壁型钢组合墙体的滞回性能,对4 片3m×2.4m(高×宽)不同构造的冷弯薄壁型钢组合墙体足尺试件进行了拟静力试验。根据试验所得的滞回规律,采用Richard-Abbott 曲线,建立了能反映其滞回曲线非线性、滑移捏缩、强度和刚度退化特征的三段式非线性滑移滞回模型,并在Origin8.0软件里辨识了各试件模型中的待定参数。研究结果表明:影响滞回曲线的主要因素为墙体先前经历的最大位移;典型捏缩滞回环的上升或下降段曲线可分为刚度单调变化的三段;用参数辨识结果得到的仿真滞回曲线与试验滞回曲线吻合较好,三段式非线性滑移滞回模型能较全面地反映冷弯薄壁型钢结构组合墙体的滞回特征、模型表达式直观、各参数物理意义明确且易于识别。     

Application of Magnetic Information Parameters for Nondestructive Testing of the Hardness of Medium-Carbon Alloy Steels

Measurement Techniques - It is proposed that magnetic information parameters constructed from the parameters of the full magnetic hysteresis loop of steels be used for nondestructive testing of...     

A novel approach for predetermination of magnetization characteristics of transformers including hysteresis

A new method has been suggested for determining an analytical expression for the hysteresis loop of the transformers and non-linear reactors from the manufacturer's data giving the conventional RMS saturation curve and no load loss. The accuracy of the technique is verified by the experimental results. The analytical expression thus proposed also exhibits the hysteretic property of increasing the loop area with increase of frequency of operation. Furthermore the energy loss expression associated with the hysteresis loop is derived from the suggested expression.     

动态磁性能测试仪的研究

研制出频率范围 5 0Hz～ 5 0kHz的动态磁性能测量仪样机 ,该仪器是基于 16位微处理器的便携式仪器 ,包含信号源、功率放大器、电压表、电流表和功率表。采用准同步采样方法和数值积分算法 ,计算磁滞回线和损耗、磁导率等参数。     

The equation of a contour and the form factor of a hysteresis loop

A procedure for the determination of the parameters of actual diagrams of cyclic deformation is developed on the basis of experimental and theoretical investigations of cyclic stress-strain diagrams for steels. This diagram characterizes the dependence of strains on stresses in a loading cycle in the region of the transition from low-cycle fatigue to multicycle and proper multicycle fatigues. The correspondence between the amplitudes of plastic and residual deformations is established and the formula for the determination of the form factor of a hysteresis loop is proposed. Numerical data are compared with experimental results for 45 and 15313 steels and with data obtained by other authors. Translated from Problemy Prochnosti, No. 3, pp. 30–38, May–June, 1997.     

Constitutive and damage modelling of H11 subjected to low‐cycle fatigue at high temperature

Hot‐work tool steel H11 is extensively applied in extrusion industries as extrusion tools. The understanding of its mechanical properties and damage evolution as well as failure is crucial for its implementation. In this paper, a finite element (FE) model employing Chaboche unified constitutive model and ductile damage rule is proposed to simulate the mechanical responses of H11 subjected to low‐cycle fatigue (LCF). Accumulated inelastic hysteresis energy is adopted to demonstrate the impact on damage initiation and evolution rules. A series of tension and LCF experiments were conducted to investigate H11's mechanical properties and its deterioration processes. In addition, to deeply understand the deformation and damage mechanism, scanning electron microscope (SEM) investigations were performed on the fracture section of gauge‐length part of the specimen after failure. Furthermore, the parameters in both constitutive model and damage rule are identified based on experimental data. The comparison of the hysteresis loop of the first cycle and stable cycle with different strain amplitudes demonstrates that the Chaboche constitutive model provides high precision to predict the evolution of mechanical properties. Based on the reliable achieved constitutive model, LCF behaviour prediction with damage rule was executed successfully using FE model and gains a good agreement with the experiments. It is believed that the proposed FE method lays the foundation of structure analysis and rapid design optimization in further applications.     

Viscosity-based magnetodynamic model of soft magnetic materials

A time-stepping method based on the concept of magnetic viscosity developed to reproduce the excess loss in electrical steel is proposed. A numerical scheme for simultaneous solution of Maxwell equations and equations describing the magnetic viscosity has been developed. The method is suitable for describing arbitrary magnetization regimes such as waveforms associated with pulsewidth modulation (PWM) voltage excitation, and the model differential equations can be conveniently combined with equations of an external electric circuit. The accuracy of the proposed dynamic model is shown using three nonoriented electrical steel as examples. Fitting of the magnetic viscosity parameters for one sinusoidal flux regime enables dynamic hysteresis loops and losses to be predicted with high accuracy over a wide range of frequencies and amplitudes of sinusoidal or nonsinusoidal flux densities.     

压电驱动器的非对称迟滞模型

为了补偿压电驱动器的非对称迟滞,提出了改进型Maxwell迟滞模型.Goldfarb提出的经典Maxwell迟滞模型由多个基础单元并联叠加而成,其基础单元为单个弹簧-物块单元,迟滞特性为平行四边形,故只能描述对称迟滞.为了能描述压电驱动器非对称迟滞,提出了基础单元迟滞特性为梯形的模型.为了简化算法程序,将梯形单元优化为两个三角形单元组合而成.为了验证该模型,以压电工作台为实验对象,运用该迟滞模型的逆模型进行迟滞补偿控制.单独的迟滞逆模型前馈开环控制实验结果表明,位移跟踪相对误差从7.37％降到了1.56％,输入输出基本呈线性关系.逆模型结合PID复合反馈闭环控制实验结果表明,位移跟踪相对误差进一步降低到0.53％,输入输出呈很好的线性关系.这表明本文所建立的迟滞模型能很好地描述压电驱动器非对称迟滞特性.     

Parameters Identification of Interface Friction Model for Ceramic Matrix Composites Based on Stress-Strain Response

An approach to identify parameters of interface friction model for Ceramic Matrix composites based on stress-strain response was developed. The stress distribution of fibers in the interface slip region and intact region of the damaged composite was determined by adopting the interface friction model. The relation between maximum strain, secant moduli of hysteresis loop and interface shear stress, interface de-bonding stress was established respectively with the method of symbolic-graphic combination. By comparing the experimental strain, secant moduli of hysteresis loop with computation values, the interface shear stress and interface de-bonding stress corresponding to first cycle were identified. Substituting the identification of parameters into interface friction model, the stress-strain curves were predicted and the predicted results fit experiments well. Besides, the influence of number of data points on identifying the value of interface parameters was discussed. And the approach was compared with the method based on the area of hysteresis loop.     

气动肌肉的最小二乘支持向量机迟滞模型

针对传统迟滞模型存在的待辨识参数多、参数辨识过程复杂和辨识精度低等问题,采用最小二乘支持向量机对气动肌肉的位移/气压迟滞开展建模研究。通过非线性映射将原始数据空间映射到高维空间,将原系统的非线性问题变成高维空间中的线性问题,借助于最小二乘法求解该线性方程组,从而提高其求解速度及收敛精度。在气动肌肉迟滞特性实验的基础上,采用所建数学模型,与经典的PI模型进行对比。结果表明,采用最小二乘支持向量机建立的数学模型具有更高的建模精度,均方差和平均误差相比PI模型分别减小了99.21%和99.1%,该方法可为后续气动肌肉的迟滞补偿控制提供有效的手段。