Papers by Keyword: Constitutive Equation

Abstract: The constitutive equations may properly describe the flow behavior of the materials. In the present study, the constitutive equation of Mg-13Al-3Ca-3Zn-1Nd-0.2Mn alloy were investigated using hot compression tests at the temperatures range of 200, 250, 300, 350 and 400°Cwith the constant strain rates of 0.001, 0.01, 0.1, 1 and 10s^-1.The hot working constitutive base analysis has been conducted on the experimental alloy. The related material constants n, α and β, as well as the activation energy Q for each temperature regime have been determined. At last, the constitutive equations is given.

Abstract: In order to precisely describe superplastic flow behavior of H62 alloy, a empirical constitutive equation was established based on the experimental data, which were obtained from the constant strain rate tensions (2.0×10^-4~4.0×10^-2 s^-1) at 720 °C. Through verification of the constitutive equation with the experimental data in constant strain rate tensions and constant velocity tensions, it was indicated that the empirical constitutive equation has high accuracy and comprehensive reliability in a wide range of strain rates (2.0×10^-4~2.0×10^-2 s^-1) and strains (0~1.8). In addition, the empirical constitutive equation has a good ability to model the superplastic flow behavior of H62 alloy at 720 °C under other deformation conditions besides constant strain rate tension.

Abstract: In this article, firstly, the strain hardening index and the strain rate sensitivity index were deducted from the general state equation and the mechanical meaning of the two indexes were correspondingly depicted, and then constitutive equations, where both/either of the two indexes appear as constants, were theoretically deducted from the same state equation. Secondly, constitutive equations where both/either of the two indexes present as variables were put forward by numerical simulation. Next, constitutive equations were built, where mechanical variables are replaced by test data obtained on an electronic universal tensile tester with the capacity to carry out a true constant strain rate path. Finally, based on the test data of Zn-5%Al during superplastic tension, it is proved that the theoretical results in this article are valid.

Abstract: With the development of numerical calculation and precision forming, constitutive equations are required to possess high accuracy and good reliability, rather than simplicity of mathematical form. Due to simple algorithm and constant parameters, the conventional constitutive models can not be suited to describing superplastic flow behavior which represents complex responses with a large strain. In this study, through surface fitting on experimental data from tension tests performed over a wide range of strain rates, tensile velocities and loads, an empirical approach was proposed to establish constitutive equation for complex superplastic behavior of Zn-5%Al alloy at 340 °C. The empirical constitutive equation not only represents the strain dependence and the strain rate dependence of stress, but also reflects the coupling effects of strain and strain rate on stress, which can not be achieved by traditional models. A comparison between the predicted flow stresses and the experimental data verified that the empirical constitutive equation has high accuracy and good reliability on modeling superplastic flow behavior of Zn-5%Al alloy at 340 °C in a wide range of strains 0~2.5 and strain rates 7.0×10^-5~8.0×10^-2 s^-1.

Abstract: The increasing use of finite element simulation in the field of composite material forming involved in the past few years a large among of research on the constitutive modelling of textile material at the mesoscopic scale (i.e. the scale of individual fibre tow). Up to now, a consensus does not exist on the most appropriate approach. The present contribution aims on the comparison between hypo-and hyper-elastic approaches to describe the mechanical behaviour of a single tow in the framework of nonlinear continuum mechanics. A particular attention is paid to the ease of implementation in standard finite element codes.

Abstract: In order to analyze the mechanical behaviour of ultra-low carbon steel in warm rolling, the flow stress and pyroplastric behaviour were investigated on the Gleeble-3500 with the deformation temperatures in the warm range. The strain rates of 0.1, 1 and 10s^-1 were applied to the temperatures above. A series of stress-strain curves were obtained after the compression Gleeble tests with different parameters. The result indicates the flow stress increases with the decreasing deformation temperatures during the compression. And it increases with the increasing strain rate as well. The constitutive equation, which includes the deformation activation energy Q and the Kelvin temperature T, was developed by using the concept that proposed by C. M. Sellars and W.J. M. Tegart. These equation results can be verified by the results of Gleeble compression test. It indicates the average error is reasonable and acceptable for predicting the flow stress and pyroplastic deformation behaviour of ultra-low carbon steel in warm temperature range. The achieved constitutive equation provides theoretical fundaments for designing the warm rolling process of ultra-low carbon steel. The experimental data also can be used as material property parameters for the establishment of finite element (FE) model.

Abstract: The elevated temperature flow stress behavior of Mg-9Gd-2.5Y-1Nd-0.5Zr magnesium alloy was carried out by Gleeble-1500 thermal mechanical simulator in the temperature range of 460-520°C and in strain rates of 0.0005~1s-1 at a strain of 0.6. The optical microscopy was used for microstructure characterization. The results showed that the flow stress increases with increasing strain rates and decreasing temperature. All the deformed magnesium alloy specimens show a dynamic recovery characters in the temperature range from 460~500°C, and show dynamic recrystallization characters at 520°C. The flow stress of this alloy can be represented by Zener-Hollomon parameter function, and values of related parameters A, α and n, are 2.24×1013s-1、0.027MPa-1 and 2.93, respectively. Its activation energy for hot deformation Q is 212.6kJ/mol.

Abstract: Superalloy GH4169 as one of high temperature structural material is widely used in aviation industry. Isothermal compression of superalloy GH4169 has been conducted on Gleebe-1500D hot simulation at the deformation temperatures ranging from 950°C to 1100°C,the strain rates ranging from 0.01s^-1 to 10s^-1, and the height reduction of 50%. Effect of processing parameters ,i.e. deformation temperature, strain rate and strain, on the hot deformation behaviors of superalloy GH4169 was studied. The research shows that the fine dynamic recystallization grains could be obtained at the condition of high deformation temperature and low strain rate. Constitutive equation of superalloy GH4169 was established by experimental data. Error analysis showed that calculated stress values by the established constitutive equation were coincident with experimental data well, and it provided the theory basis to optimize forging processing of superalloy GH4169.

Abstract: Using lower-convected Maxwell constitutive model, the control equation of the steady flow of viscous-elastic fluid in the eccentric annulus with inner rod moving axially in the bipolar coordinates system is established, and discreted by control-volume method, the velocity profile is solved by ADI methods, which lays theory basis for further analyzing the stress field and the reason of pumping rod eccentric wear. The result shows: eccentric ratio is the most important factor to the velocity profile.

Abstract: This study derived the five parameters in Johnson-Cook equation of CP titanium Gr2. Quasi-static and dynamic compression tests were designed to measure mechanical properties at strain rates of 10^-3s^-1 and 6000s^-1. In order to secure the validity of tested data, a novel fixture was proposed to reduce the displacement measurement error in MTS testing system and the signal processing procedure of compressive split Hopkinson pressure bar for the present study was demonstrated. With the tested data and calculated adiabatic heating temperature rise, parameters A, B, n, m, C have been derived based on mathematical deduction and solve. It was found that the constructed constitutive model fit the tested data well and was able to restore the yield strength value at high strain rate.