Papers by Keyword: Constitutive Equation

Abstract: Constitutive equation for metal plastic forming reflects the relationships among the parameters of stress, strain and strain rate. The accuracy of constitutive equation is a key factor in the research of material mechanism, finite element simulation accuracy and forming failure. The commonly used establishment methods of constitutive equation are summarized. Those methods include experiment method, theory analysis method, neural network method, regression method and inverse finite element method. The advantages and disadvantages of those methods are discussed, and application scope of those methods is summarized simultaneously.

Abstract: Taking the schist as investigative subject, which is the weak layer widely distributed in Yun Fu pyrite, Guangdong province, the deformation characteristics and strength properties of the schist rock mass are analyzed through laboratory uniaxial and triaxial compression tests. Based on the tests on natural and saturated schist, the elastic constitutive equations of the schist, considering the closing of micro cracks, are established; and the deformation characteristics and strength properties of water-weakening influence is analyzed. Through the tests, the deformation characteristics and strength properties of the schist are further understood, which can give some advices to the design of rock slope containing weak layers of the schist.

Abstract: In order to study the hot workability of TC21 titanium alloy, isothermal hot compression tests were conducted in the temperatures range of 1123~1203K and strain rates range of 0.01~10s-1. The influence of strain was incorporated in hyperbolic sine constitutive equation by considering the effect of strain on material constants. Correlation coefficient (R) and average absolute relative error (AARE) were introduced to verify the validity of the developed hyperbolic sine constitutive equation. The values of R and AARE were determined to be 0.9891 and 7.753% respectively, which indicated that the developed hyperbolic sine constitutive equation considering strain compensation could precisely predict the flow behavior of TC21 titanium alloy throughout the entire range of temperatures and strain rates.

Abstract: The hot deformation behavior of Mg-3.5Zn-0.6Y-0.5Zr alloy was investigated by compressive tests of strain rate ranges of 0.002~1 s^-1 and deformation temperature ranges of 300~450 °C using a Gleeble 1500D thermal simulator. The flow stresses in different deformation conditions are measured. The results show that flow stress is significantly affected by both deformation temperature and strain rate, the flow stress increases with increase in strain rate and decreases in deformation temperature during the hot compression process. The constitutive equation established on the basis of data of activation energy and stress exponent is a hyperbolic sine function.

Abstract: Thermal cycling of a unit Sn0.7Cu solder was studied based on the steady-state creep constitutive equation and Matlab software. The results show that there is a steady-state cycle for the thermal cycling of unit Sn0.7Cu eutectic solder. In steady-state thermal cycling, the shear stress is increased with the increase of temperature. There is a stage of stress relaxation during high temperature. A liner relationship between maximum shear stress and maximum shear strain is observed during thermal cycling. The metastable cycle number is declined greatly with the increase of maximum shear strain.

Abstract: This study investigated the constitutive flow behavior and hot workability of in-situ 5wt% TiB₂ reinforced 7050 Al alloy matrix composite by hot compression experiments. Based on the experimental results of flow curves, a constitutive model describing the relationship of the flow stress, true strain, strain rate and temperature is proposed. Substantially, it is found the constitutive equation of flow stress is dependent on the strain, strain rate and temperature. The coefficients (E.g., α, n, Q and lnA) in the equation are functions of true strains. The results of the calculated values from constitutive equation are verified to well agree with the experimental values. Furthermore, the processing map of the composite is created in order to determine the hot processing domains. The optimum zones for hot workability and instability regions are identified. In instability domain, the microstructures display the main failure modes as the particle cracking and interface debonding.

Abstract: The hot compression tests on a Gleeble-1500D thermal mechanics simulator were carried out under the strain rate range of 1~ 0.005s-1 at the temperature range of 873-1373K in order to evaluate the constitutive equation of 5Cr21Mn9Ni4N valve steel. All of the flow stress curves exhibit a single peak stress, after which the stress is followed by a steady state regime. The results indicate that the deforming behavior is strongly depending on the strain rate and the deforming temperature. According the experimental data, the hyperbolic law is used to develop the constitutive equations. In the constitutive equations, the effect of the deforming temperature and the strain rate are represented by the Zener-Hollomam parameter. And the flow stress curves are coinciding with the constitutive equation of .

Abstract: The multi-size Al₂O₃ particles dispersion strengthened copper base composite (i.e. Al₂O₃/Cu-0.6%Al₂O₃ composite) was prepared by the vacuum hot-press sintering-internal oxidizing method. The hot deformation behavior of Al₂O₃/Cu-0.6%Al₂O₃ composite was investigated by the isothermal compression tests at the temperature range from 600°C to 950°C and strain rates of 0.001 s^-1 and 1s^-1 respectively with a Gleeble-1500D thermal simulator system. The results show that the flow stress-strain curves of Al₂O₃/Cu-0.6%Al₂O₃ composites indicate the softening mechanism of recrystallization. The flow stress increases with the deformation strain increasing, then decreases and tends to be steady. The hot deformation activation energy is calculated as 116.46 kJ/mol for the Al₂O₃/Cu-0.6%Al₂O₃ composite. The strain-stress constitutive equation is established on the basis of above results.

Abstract: A study on the hot deformation behavior and microstructural changes of nickel based superalloy are presented. Constitutive equation allowing the calculation of peak stress was derived. A study of the effect of the temperature-deformation parameters on the kinetic of austenitic heat-resistant superalloy dynamic recrystallization and on the microstructure evolution was performed as well.

Abstract: In order to study the workability and optimize hot forming processing parameters for GH4169 superalloy, the hot deformation behaviors are investigated. The results show that the flow stress strongly depends on the strain rate, deformation temperature and strain. With the increase of strain rates and the decrease of deformation temperature, the flow stress increases. The flow stress exhibits an initial increase with the strain until a peak stress value, showing a obvious work hardening. After the peak stress, increasing strain results in the decrease of stress, indicating a dynamic flow softening. A revised constitutive equation incorporating the effects of temperature, strain rate and work-hardening rate of the material is established by compensation of strain. A good agreement between the measured and predicted results shows that the established model can give an accurate prediction of the flow behavior of GH4169 superalloy.