Papers by Keyword: Constitutive Equation

Abstract: The aim of this work is to analyze the effect of the anisotropy on the formability of the third generation of advanced high strength steel (3genAHSS) from experimental and theoretical point of view. The reference material is the USS CR980XG3TM️ AHSS, a 3genAHSS 980T/600Y-retained austenite bearing-high elongation steel grade. A careful experimental work on the selected 3genAHSS characterization has been performed. The anisotropy factors and the yield stresses have been identified from tensile tests at several orientations with respect to the rolling direction. The experimental forming limit diagram under linear strain paths has been determined using Nakajima tests and the Erichson test for the equibiaxial stretching, respectively. The Marciniak-Kuczynski analysis is used to simulate the onset of localized necking through an advanced sheet metal forming limit model. YLD00-2d yield condition gives the initial shape of the yield locus. Swift strain–hardening power law is used to describe the strain hardening of the material. The effect of the anisotropy on the forming limits of 3genAHSS steel is analyzed. It was achieved proper reproducibility of the experimental tendencies of anisotropic factor distribution and the yield stress as a function of the tensile loading axis by the selected constitutive equations. A good accuracy of the FLDmodel on the prediction of the experimental results is found.

Abstract: The hot deformation of TA15 titanium alloy was studied by the hot compression test on the Gleeble-3800 thermal simulation equipment. The true stress-strain curves of TA15 titanium alloy at the temperature of 1123-1223K and the strain rate of 0.001-1s^-1 were obtained.. The results show that the flow stress increases with decreasing temperature, and increases as the strain rate increases. And the deformation process is accompanied by work hardening and dynamic recovery and dynamic recrystallization. Based on the true stress-strain curves of TA15 titanium alloy, the Arrhenius-typed constitutive equation was established. The thermal deformation activation energy of TA15 titanium alloy with a strain of 0.2 is 746.27kJ/mol.

Abstract: The hot deformation behavior of Ti-Al-Nb-Zr-Mo-Cr titanium alloy has been investigated using a Gleeble-1500D thermal simulation test machine in the temperature range of 855°C~1015°C,at constant strain rate from 0.01 s^-1 to 10s^-1 and with height reduction of 45%. The flow curves characteristic under different deformation parameters show significant difference. According to the stress-strain curves of the alloy and its stress characteristics, the Arrhenius constitutive equation was obtained. The average activation energy is about 541 kJ/mol in the α+β field, and about 243 kJ/mol in the β field, respectively. Based on the dynamic materials model, the processing map is generated, which shows that the peak efficiency domain appears at the temperature of 874°C~900°C and the strain rate of 0.001 s^-1~0.06s^-1 with a peak efficiency of 0.58 at about 887°C/0.001s^-1.

Abstract: The hot deformation behavior of spray-formed AlSn20Cu alloy during hot compression deformation was studied, and the constitutive equation of AlSn20Cu alloy was established. The samples of spray-formed AlSn20Cu alloy were compressed on Gleeble-3500 thermal simulation test machine. The error of the true stress caused by adiabatic heating effect in the experiment was corrected. The constitutive equation of spray-formed AlSn20Cu alloy could be represented by Zener-Hollomon parameter in a hyperbolic sine function. The results showed that the deformation temperatures and strain rates had a notable effect on the true stress of the alloy. At the identical deformation temperature, the true stress increased with the increase of strain rate. When the strain rate was constant, the stress decreased with the increase of deformation temperature. After hot compression deformation, the tin phase was elongated along the direction perpendicular to the compression axis with short strips and blocks. With the increase of deformation temperature and the decrease of strain rate, Sn phase distribution became more homogeneous.

Abstract: The thermal deformation behavior of a new metastable beta titanium alloy composed of Ti-Al-Mo-V-Nb-Cr was studied under different experimental conditions of varying temperatures (760°C~ 970°C) and strain rates (0.001s⁻¹, 0.01s⁻¹, 0.1s⁻¹, 1s⁻¹ and 10s⁻¹) up to deformation amount of 60%. The hot compression experiments were completed on a Gleeble-3500 thermal analogue. The experimental results showed that the true stress of the Ti-Al-Mo-V-Nb-Cr titanium alloy decreased with increasing the temperature and decreasing the strain rate, the stress peaks and the steady-state stress values were higher with the decreasing of temperature at the same strain rate. The calculated values of the deformation activation energy were 187.87 kJ/mol in the two-phase region and 165.17kJ/mol in beta single-phase region. The corresponding constitutive equation was determined by the multiple linear regression calculation on the hot compression experimental data, on the base of Arrhenius equations.

Abstract: Aiming at the plastic shrinkage cracking of cement mortar, the constitutive equations of it in laboratory were established by testing plastic tensile strength, plastic capillary shrinkage stress and water loss evaporation rate of mortar under different composition parameters, environmental parameters, initial structural parameters and constraints condition parameters. And the early warning system of it was explored. The results showed that the seven-element constitutive equation of plain mortar and the nine-element constitutive equation of mortar with polyvinyl alcohol (PVA) fiber can effectively predict the plastic shrinkage cracking state of mortar outdoors. An early warning system for it was initially established.

Abstract: The hot deformation behavior and microstructure evolution of Al-3.5Cu-1.0Li-0.4Mg- 0.6Zn-0.3Ag aluminum lithium alloy were investigated by hot tensile tests on Gleeble-1500 thermal simulator at 480-510 °C and strain rates 0.0001-0.1 s^-1. The results show that obvious flow steady-state phenomena occur during hot stretching and the main mechanism changes from dynamic recovery to dynamic recrystallization with the increase of temperature and decrease of strain rate. The constitutive equation was calculated using the true stress-strain curve obtained by the hyperbolic sinusoidal pair of deformation activation energy Q and temperature T proposed by Sellars and Tegart. The deformation heat activation energy is 226.783 KJ/mol.

Abstract: The hot deformation behavior of Ti-Al-Nb-Zr-Mo-Cr titanium alloy was studied by hot compressive method in this paper, and the flow stress constitutive equation and activation energy also calculated. The results show that the flow stress increased with deformation temperature dropping and strain rate increasing. The flow behavior of the sample hot-deformaed exhibited a peak value of stress in the α+β field, whereas, the true stress attained a steady state in the β field. According to the stress-strain curves of the alloy and its stress characteristics, the Arrhenius constitutive equation was obtained. The average activation energy was about 654.228 KJ/mol in the α+β field, and about 272.196 KJ/mol in the β field, respectively.

Abstract: The high-elastic Cu-20.0Ni-5.0Sn-0.25Zn-0.22Mn alloy was designed and prepared using a 830°C/2h+850°C/2h dual-stage homogenization annealing process. The true stress-strain curves of well annealed Cu-20.0Ni-5.0Sn-0.25Zn-0.22Mn alloy were plotted as a function of compressive temperature and strain rate. The results showed that the stage division of thermal compression deformation is temperature dependent, which involves work hardening, dynamic recovery and recrystallization stages. The maximum value of the true stress increases as the strain rate gets larger, but decreases as the deformation temperature rises. The high temperature compression deformation process of the alloy is a thermal activated process, and the corresponding constitutive equation of the true stress-strain is established.

Abstract: A plane stress yield function which is described by multi-segment spline curve is proposed. This model is able to consider an arbitrary number of multi-axial stress states and its normal directions on the yield surface. Moreover by using interpolation based on cubic spline function, planar anisotropy is also described precisely. To show the applicability of the model, some evaluation of material properties and simulation results of hole expansion test are discussed.