Papers by Keyword: Constitutive Equation

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Authors: Lei Chen, Xiao Cong Ma, Ming Jia Wang, Hua Gui Huang
Abstract: The flow behavior and microstructural evolution of an as-wrought duplex stainless steel has been investigated by Gleeble-3500 thermal-mechanical simulator within the temperature range of 950-1200°C and the strain rate range of 0.1-10s-1. The flow curves exhibited a peak stress characteristic followed by dynamic softening and the strain for appearance of steady stress is bigger at higher strain rate than at lower strain rate. The apparent activation energy (Q) and the apparent stress exponent (n) of the test steel are obtained to be about 462 kj/mol and 3.95, respectively. The relationship between peak stress (σp) and Zener-Holomon parameter (Z) is obtained, whereby the σp can be predicted at differern hot working conditons. The results of microstructural observation show that the austenite softens by the dynamic recrystallization (DRX) which can be dominantly responsib le for dynamic softening, while the ferrite phase mainly continues to exhibit dynamic recovery (DRV).
Authors: Jiao Luo, Miao Quan Li, Y.Q. Hu
Abstract: A constitutive equation has been established to describe the effect of grain size on the deformation behavior of Ti-6.62Al-5.14Sn-1.82Zr alloy during the high temperature. In this paper, firstly a steady flow stress model is proposed, and a function relating to the grain size is introduced to modify the steady flow stress model. Meanwhile, a microstructure model established by the fuzzy neural network method is applied to calculate the grain size of prior α phase during the high temperature deformation of Ti-6.62Al-5.14Sn-1.82Zr alloy. The calculated flow stress using the present constitutive equation shows a good agreement with the experimental flow stress of the Ti-6.62Al-5.14Sn-1.82Zr alloy. The relative maximum error was not more than 15%.
Authors: Kazunari Shinagawa, Y. Hirashima
Authors: Zoltán Pálmai
Abstract: The common feature of the different forming technologies is that the deformation is concentrated into a relatively narrow shear zone. The behaviour of the material can be defined only by specific material properties, the definition of which is difficult and costly. We have developed a new method for the comparatively simple and cheap definition of these specific material properties based on the well known theory and the sophisticated measuring technology of cutting. To achieve this we have developed our previous dynamic technological model, which is described by evolution and delay differential equations. As an example, in the case of a steel with 13% Cr content T, C555520−≈8.26.2−≈=φεγ, the thermal softening 4410−−≈=sφεγ&&≈κ0.98±0.016 MPa/K, the strain rate sensitivity constant k≈0.034±0.009 and the strain hardening exponent n0.170.005.
Authors: Nicholas J. Politis, Denis J. Politis, Catrin Mair Davies, Jian Guo Lin
Abstract: Constitutive equations have been used extensively to accurately describe material properties over a wide range of temperatures and strain rates in numerical simulations. In this paper, an algorithmic method of determining the constants of such constitutive equations is presented. The Genetic Algorithm implementation utilising MATLAB is described, and example fits to experimental data are presented.
Authors: Ji Ming Zhou, Le Hua Qi, Guo Ding Chen
Abstract: This paper describes a new integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inelastic strain rate in HSCE so that the inelastic strain rate can be solved indirectly from the Lambda. The proposed integration algorithm is based on the stress update concept and the effect of normal stress updating on the material compression is also discussed thoroughly in this paper. The investigation results show that the new algorithm can integrate the HSCE efficiently and the normal stress should keep constant as the deviatoric stress updating. An example of semi-solid extruding was given in the paper at last to illustrate the implementation of new algorithm and effect of normal stress updating on the compression of material.
Authors: Yong Zhi Hua, Li Wen Guan, Xin Jun Liu, Yu Hui Zhang
Abstract: These methods that extract parameters of constitutive equations can be divided into three groups: direct search-based strategies, gradient-based methods and evolutionary algorithms. By analyzing these strategies, a new method based on iteration algorithm was proposed. To obtain parameters of JC and ZA model for Ti-6Al-4V, the error between prediction data and SHPB experiment data was set as objective function, then initial value was calculated using iteration algorithm. The effect of convergence rate and precision at various steps and experiment data was invested. The main advantage of the method are as follows:fast calculation; compatible with SHPB data and orthogonal cutting data; compatible with the decoupling and coupling constitutive equations. Finally, it has shown that the algorithm is stable, and acceptable results can be obtained.
Authors: Fu Guo Li, Xiao Na Wang, Xiao Lu Yu
Abstract: This paper advances a new optimization method about material constitutive equation on the basis of physical simulation and numerical simulation results which basic thinking can be described as the following: through comparing the results of the material deformation process under actual experimental conditions and virtually simulated by the finite element numerical simulation method with the constitutive equation established on the basis of the physical simulation, the constitutive equation established by the experimental data is optimized in turn. Based on it, this paper advances a visco/plastic constitutive equation to depict the semi-solid thixo-forming and the constitutive equation is analyzed and optimized through coupling of the physical simulation and numerical simulation. It is observed that this method can effectively eliminate the influence of the factor outside material itself on the constitutive equation. So, it can exactly depict the deformation behavior of the materials and improve the accuracy and reliability of the numerical simulation.
Authors: Zhong Guo Huang, Shun Yao Jin, Qing Hua Yuan
Abstract: An elevated temperature deformation test of industrial coarse-grained Ti-6Al-4V(TC4), which is for gas forming process, was conducted under the temperature of 880 ~ 980°C and the strain rate of 5×10-4mm/s, 1×10-3 mm /s, 5×10-3 mm /s, 1×10-2 mm /s. Based on the stress-strain curve of that material, the Johnson-Cook model, Exponential model, Series model, Parallel model and the Kumar model were established by using the regression analysis on stable deformation stage and whole strain stage (strain hardening stage plus stable deformation stage) respectively. The appropriate application circumstances of those models are analyzed. By using statistic analysis and aiming at minimizing the error rate between actual value and regression value, Kumar model is selected as the constitutive model of that material for gas forming test. Based on Kumar model, the industrial coarse-grained TC4 gas forming test was simulated by nonlinear finite element software Msc.Marc. The simulation results agree well with the actual parts. The Kumar model was appropriate and accurate.
Authors: Ming Tu Ma, Yan Zhao, Gang Fang, Yi Feng
Abstract: In this paper, the high speed tension experiments have been performed on ultra high strength bullet proof steel. The samples were cut from the bullet proof steel plate after hard-module quenching with thickness of 3.7 mm. The mechanical properties at strain rates of 0.001 s-1, 0.01 s-1, 0.1 s-1 and 1 s-1 were carried out on MTS810, while those at higher strain rates of 200 s-1, 500s-1 and 1000s-1 were tested on HTM5020 high speed tension tester and Hopkinson bar. The data from the high-speed tension experiments were fitted via Johnson-Cook constitutive equation, and the fracture surface of each sample was analyzed by SEM. The results indicate that, the shoot-resistance capability of bullet proof steel is closely related to its strength, thickness and flow behaviors under high strain rate. The shoot-resistance will be improved in the case of higher strength and better matching between strength and elongation. The Johnson-Cook equation fitted via experimental data provides fundament to numerical simulation. With the increase of strain rate, the size and depth of dimple trend to decrease and the depth of dimple changes less in steel with lower strength and higher elongation. The SEM analysis of fracture is benefit for further understanding of deformation and fracture mode under high strain rate.
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