In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials out...In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.展开更多
The single hot thermocouple technique （SHTT） and high temperature equilibrium technique were combined to investigate the phase diagram of the CaO-SiO2-5%MgO-20%AlzO3-TiO2 system. The 1300 ℃ to 1500 ℃ liquidus line...The single hot thermocouple technique （SHTT） and high temperature equilibrium technique were combined to investigate the phase diagram of the CaO-SiO2-5%MgO-20%AlzO3-TiO2 system. The 1300 ℃ to 1500 ℃ liquidus lines are calculated according to the thermodynamic equations based on the pseudo-melting temperatures measured by the single hot thermocouple technique. The phase equilibria relationships are experimentally determined at 1400 ℃ using the high temperature equilibria technique followed by X-ray fluorescence （XRF）, X-ray diffraction（XRD）, scanning electron microscopy （SEM） and energy dispersive X-ray spectroscopy （EDX） analysis. The liquid phase（L）, melilite solid solution phase （（C2MSz,C2AS）ss）, diopside phase（CMS2） and perovskite phase （CaO·TiO2） are found. Coupled with the liquidus lines and equilibria results, the phase diagram is constructed for the specified region of the CaO-SiO2-5%MgO-20%Al2O3-TiO2 system.展开更多
基金Project(2007CB714001) supported by the National Basic Research Program of China (973 Program)
文摘In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.
基金Projects(51104039,51374059,51304042)supported by the National Natural Science Foundation of ChinaProject(L2013114)supported by Scientific Research Fund of Liaoning Provincial Education Department,China+1 种基金Project(2012221013)supported by Programs of Liaoning Province for Science and Technology Development,ChinaProject(N130602002)supported by the Fundamental Research Funds for the Central Universities China
文摘The single hot thermocouple technique （SHTT） and high temperature equilibrium technique were combined to investigate the phase diagram of the CaO-SiO2-5%MgO-20%AlzO3-TiO2 system. The 1300 ℃ to 1500 ℃ liquidus lines are calculated according to the thermodynamic equations based on the pseudo-melting temperatures measured by the single hot thermocouple technique. The phase equilibria relationships are experimentally determined at 1400 ℃ using the high temperature equilibria technique followed by X-ray fluorescence （XRF）, X-ray diffraction（XRD）, scanning electron microscopy （SEM） and energy dispersive X-ray spectroscopy （EDX） analysis. The liquid phase（L）, melilite solid solution phase （（C2MSz,C2AS）ss）, diopside phase（CMS2） and perovskite phase （CaO·TiO2） are found. Coupled with the liquidus lines and equilibria results, the phase diagram is constructed for the specified region of the CaO-SiO2-5%MgO-20%Al2O3-TiO2 system.
