Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled diff...Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and fiexural rigidity with the consideration of the effect of Poisson＇s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.展开更多
Thermal barrier coating(TBC)systems are widely used in industrial gas-turbine engines.However,premature failures have impaired the use of TBCs and cut down their lifetime,which requires a better understanding of their...Thermal barrier coating(TBC)systems are widely used in industrial gas-turbine engines.However,premature failures have impaired the use of TBCs and cut down their lifetime,which requires a better understanding of their failure mechanisms.In the present study,experimental studies of isothermal cycling are firstly carried out with the observation and estimation of microstructures.According to the experimental results,a finite element model is established for the analysis of stress perpendicular to the TBC/BC interface.Detailed residual stress distributions in TBC are obtained to reflect the influence of mechanical properties,oxidation,and interfacial roughness.The calculated results show that the maximum tensile stress concentration appears at the peak of TBC and continues to increase with thermal cycles.Because of the microstructural characteristics of plasma-sprayed TBCs,cracks initialize in tensile stress concentration(TSC)regions at the peaks of TBC and propagate along the TBC/BC interface resulting in the spallation of TBC.Also,the inclusion of creep is crucial to failure prediction and is more important than the inclusion of sintering in the simulation.展开更多
This paper investigates the effect of the location of testing area in residual stress measurement by Moiréinterferometry combined with hole-drilling method.The selection of the location of the testing area is ana...This paper investigates the effect of the location of testing area in residual stress measurement by Moiréinterferometry combined with hole-drilling method.The selection of the location of the testing area is analyzed from theory and experiment.In the theoretical study,the factors which affect the surface released radial strainεr were analyzed on the basis of the formulae of the hole-drilling method,and the relations between those factors andεr were established.By combining Moiréinterferometry with the hole-drilling method,the residual stress of interference-fit specimen was measured to verify the theoretical analysis.According to the analysis results,the testing area for minimizing the error of strain measurement is determined.Moreover,if the orientation of the maximum principal stress is known,the value of strain will be measured with higher precision by the Moiréinterferometry method.展开更多
Wrinkling and buckling of nano-films on the compliant substrate are always induced due to thermal deformation mismatch.This paper proposes effective means to control the surface wrinkling of thin film on the compliant...Wrinkling and buckling of nano-films on the compliant substrate are always induced due to thermal deformation mismatch.This paper proposes effective means to control the surface wrinkling of thin film on the compliant substrate,which exploits the curvatures of the curve cracks designed on the stiff film.The procedures of the method are summarized as:1)curve patterns are fabricated on the surface of PDMS(Polydimethylsiloxane)substrate and then the aluminum film with the thickness of several hundred nano-meters is deposited on the substrate;2)the curve patterns are transferred onto the aluminum film and lead to cracking of the film along the curves.The cracking redistributes the stress in the compressed film on the substrate;3)on the concave side of the curve,the wrinkling of the film surface is suppressed to be identified as shielding effect and on the convex side the wrinkling of the film surface is induced to be identified as inductive effect.The shielding and inductive effects make the dis-ordered wrinkling and buckling controllable.This phenomenon provides a potential application in the fabrication of flexible electronic devices.展开更多
In this paper,a new method combining focused ion beam(FIB)and scanning electron microscope(SEM)Moirétechnique for the measurement of residual stress at micro scale is proposed.The FIB is employed to introduce str...In this paper,a new method combining focused ion beam(FIB)and scanning electron microscope(SEM)Moirétechnique for the measurement of residual stress at micro scale is proposed.The FIB is employed to introduce stress relief like the macro ring-core method and fabricate gratings with a frequency of 5000 lines/mm on the measured area of the sample surface.Three groups of gratings in different radial directions are manufactured in order to form a micro-scale strain rosette.After milling ring-core by FIB,the deformation incurred by relief of the stress will be recorded with the strain rosette.The displacement/strain field can be measured using SEM scanning Moiréwith random phase-shifting algorithm.In this study,the Nickel alloy GH4169 sample(which was processed by laser shock peening)is selected as a study object to determine its residual stress.The results showed that the components of the in-plane principal stresses were-359 MPa and-207 MPa,respectively,which show good agreement with the results obtained from the available literature.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11402133,11620162,11321202,and 11532001)
文摘Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and fiexural rigidity with the consideration of the effect of Poisson＇s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11232008 and 11372118)the Tsinghua University Initiative Scientific Research Program
文摘Thermal barrier coating(TBC)systems are widely used in industrial gas-turbine engines.However,premature failures have impaired the use of TBCs and cut down their lifetime,which requires a better understanding of their failure mechanisms.In the present study,experimental studies of isothermal cycling are firstly carried out with the observation and estimation of microstructures.According to the experimental results,a finite element model is established for the analysis of stress perpendicular to the TBC/BC interface.Detailed residual stress distributions in TBC are obtained to reflect the influence of mechanical properties,oxidation,and interfacial roughness.The calculated results show that the maximum tensile stress concentration appears at the peak of TBC and continues to increase with thermal cycles.Because of the microstructural characteristics of plasma-sprayed TBCs,cracks initialize in tensile stress concentration(TSC)regions at the peaks of TBC and propagate along the TBC/BC interface resulting in the spallation of TBC.Also,the inclusion of creep is crucial to failure prediction and is more important than the inclusion of sintering in the simulation.
基金supported by the National Basic Research Program of China(Grant Nos.2010CB631005 and 2011CB606105)the National Natural Science Foundation of China(Grant Nos.11232008,91216301,11227801 and 11172151)Tsinghua University Initiative Scientific Research Program
文摘This paper investigates the effect of the location of testing area in residual stress measurement by Moiréinterferometry combined with hole-drilling method.The selection of the location of the testing area is analyzed from theory and experiment.In the theoretical study,the factors which affect the surface released radial strainεr were analyzed on the basis of the formulae of the hole-drilling method,and the relations between those factors andεr were established.By combining Moiréinterferometry with the hole-drilling method,the residual stress of interference-fit specimen was measured to verify the theoretical analysis.According to the analysis results,the testing area for minimizing the error of strain measurement is determined.Moreover,if the orientation of the maximum principal stress is known,the value of strain will be measured with higher precision by the Moiréinterferometry method.
基金supported by the National Basic Research Program of China(Grant Nos.2010CB631005 and 2011CB606105)the National Natural Science Foundation of China(Grant Nos.11232008,91216301,11072125 and 11272175)Tsinghua University Initiative Scientific Research Program
文摘Wrinkling and buckling of nano-films on the compliant substrate are always induced due to thermal deformation mismatch.This paper proposes effective means to control the surface wrinkling of thin film on the compliant substrate,which exploits the curvatures of the curve cracks designed on the stiff film.The procedures of the method are summarized as:1)curve patterns are fabricated on the surface of PDMS(Polydimethylsiloxane)substrate and then the aluminum film with the thickness of several hundred nano-meters is deposited on the substrate;2)the curve patterns are transferred onto the aluminum film and lead to cracking of the film along the curves.The cracking redistributes the stress in the compressed film on the substrate;3)on the concave side of the curve,the wrinkling of the film surface is suppressed to be identified as shielding effect and on the convex side the wrinkling of the film surface is induced to be identified as inductive effect.The shielding and inductive effects make the dis-ordered wrinkling and buckling controllable.This phenomenon provides a potential application in the fabrication of flexible electronic devices.
基金supported by the National Basic Research Program of China(Grant Nos.2010CB631005 and 2011CB606105)the National Natural Science Foundation of China(Grant Nos.90916010,11172151 and 11232008)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20090002110048)Tsinghua University Initiative Scientific Research Program
文摘In this paper,a new method combining focused ion beam(FIB)and scanning electron microscope(SEM)Moirétechnique for the measurement of residual stress at micro scale is proposed.The FIB is employed to introduce stress relief like the macro ring-core method and fabricate gratings with a frequency of 5000 lines/mm on the measured area of the sample surface.Three groups of gratings in different radial directions are manufactured in order to form a micro-scale strain rosette.After milling ring-core by FIB,the deformation incurred by relief of the stress will be recorded with the strain rosette.The displacement/strain field can be measured using SEM scanning Moiréwith random phase-shifting algorithm.In this study,the Nickel alloy GH4169 sample(which was processed by laser shock peening)is selected as a study object to determine its residual stress.The results showed that the components of the in-plane principal stresses were-359 MPa and-207 MPa,respectively,which show good agreement with the results obtained from the available literature.
