In hot deformation, the flow stress curves of steels always present as two typical types: at relatively high temperature and low strain rate, the flow stress may first increase and then attain a steady value without r...In hot deformation, the flow stress curves of steels always present as two typical types: at relatively high temperature and low strain rate, the flow stress may first increase and then attain a steady value without reaching an obvious peak stress; in other situations, the flow stress decreases after reaching peak stress and then attains a steady value. A new phenomenological model,described by a sine-function equation, is proposed to define the relationship between flow stress and deformation parameters. A series of isothermal compressions for a carbon steel were carried out, as a case study, to obtain basic experimental data.Parameters of the new model were sequentially determined. The predicted results of the proposed model were compared with actual measured data. Good accuracy was found in the standard statistical parameters of correlation coefficient, root mean square error, and average absolute relative error with the values of 0.935, 7.137 MPa and 4.352%, respectively. Discussion of applications of different models in finite-element simulation demonstrated the benefit of the new model. When comparing the simulation results of three different deformation patterns with large strain, the new model showed 10%–20% lower predicted forming load than the original Arrhenius equation, and better applicability and reliability than modified Arrhenius equations.展开更多
A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equation...A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable's triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable's triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable's responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable's triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable's triad resonance, and the second characterizes the degree of difficulty for activating cable's triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51475294)
文摘In hot deformation, the flow stress curves of steels always present as two typical types: at relatively high temperature and low strain rate, the flow stress may first increase and then attain a steady value without reaching an obvious peak stress; in other situations, the flow stress decreases after reaching peak stress and then attains a steady value. A new phenomenological model,described by a sine-function equation, is proposed to define the relationship between flow stress and deformation parameters. A series of isothermal compressions for a carbon steel were carried out, as a case study, to obtain basic experimental data.Parameters of the new model were sequentially determined. The predicted results of the proposed model were compared with actual measured data. Good accuracy was found in the standard statistical parameters of correlation coefficient, root mean square error, and average absolute relative error with the values of 0.935, 7.137 MPa and 4.352%, respectively. Discussion of applications of different models in finite-element simulation demonstrated the benefit of the new model. When comparing the simulation results of three different deformation patterns with large strain, the new model showed 10%–20% lower predicted forming load than the original Arrhenius equation, and better applicability and reliability than modified Arrhenius equations.
基金Supporting Program for Young Investigators,Hunan UniversityNational Science Foundation of China(Grant Nos.11502076 and 11572117)
文摘A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable's triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable's triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable's responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable's triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable's triad resonance, and the second characterizes the degree of difficulty for activating cable's triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.
