Transactions of Nanjing University of Aeronautics & Astronautics
Volume 0,Issue 5,2024 Table of Contents
1 Numerical Analysis for High-Throughput Elastic Modulus Measurement of Substrate-Supported Thin Films
2024(5):555-563.
DOI: 10.16356/j.1005-1120.2024.05.001
Abstract:
Micro/nano-thin films are widely used in the fields of micro/nano-electromechanical system （MEMS/NEMS） and flexible electronics， and their mechanical properties have an important impact on the stability and reliability of components. However， accurate characterization of the mechanical properties of thin films still faces challenges due to the complexity of film-substrate structure， and the characterization efficiency of traditional techniques is insufficient. In this paper， a high-throughput determination method of the elastic modulus of thin films is proposed based on the strain variance method， the feasibility of which is analyzed by the finite element method （FEM）， and the specific tensile configuration with array-distributed thin films is designed and optimized. Based on the strain difference between the film-substrate region and the uncoated region， the elastic modulus of multiple films is obtained simultaneously， and the influences of film width， spacing， thickness， and distribution on the measurement of elastic modulus are elucidated. The results show that the change in film width has a more obvious effect on the elastic modulus determination than film spacing and thickness， i.e.， the larger the film width is， the closer the calculation results are to the theoretical value， and the change in calculation results tends to be stabilized when the film width increases to a certain length. Specifically， the simultaneous measurement of the elastic modulus of eight metal films on a polyimide （PI） substrate with a length of 110 mm and a width of 30 mm can be realized， and the testing throughput can be further increased with the extension of the substrate length. This study provides an efficient and low-cost method for measuring the elastic modulus of thin films， which is expected to accelerate the development of new thin film materials.
Micro/nano-thin films are widely used in the fields of micro/nano-electromechanical system （MEMS/NEMS） and flexible electronics， and their mechanical properties have an important impact on the stability and reliability of components. However， accurate characterization of the mechanical properties of thin films still faces challenges due to the complexity of film-substrate structure， and the characterization efficiency of traditional techniques is insufficient. In this paper， a high-throughput determination method of the elastic modulus of thin films is proposed based on the strain variance method， the feasibility of which is analyzed by the finite element method （FEM）， and the specific tensile configuration with array-distributed thin films is designed and optimized. Based on the strain difference between the film-substrate region and the uncoated region， the elastic modulus of multiple films is obtained simultaneously， and the influences of film width， spacing， thickness， and distribution on the measurement of elastic modulus are elucidated. The results show that the change in film width has a more obvious effect on the elastic modulus determination than film spacing and thickness， i.e.， the larger the film width is， the closer the calculation results are to the theoretical value， and the change in calculation results tends to be stabilized when the film width increases to a certain length. Specifically， the simultaneous measurement of the elastic modulus of eight metal films on a polyimide （PI） substrate with a length of 110 mm and a width of 30 mm can be realized， and the testing throughput can be further increased with the extension of the substrate length. This study provides an efficient and low-cost method for measuring the elastic modulus of thin films， which is expected to accelerate the development of new thin film materials.
2024(5):564-574.
DOI: 10.16356/j.1005-1120.2024.05.002
Abstract:
In comparison to discrete descriptions of fracture process， the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids， which enables the numerical implement simplification. An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids. This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity， embracing plasticization， cracks initiation， propagation， branching and merging while fulfilling the basic principle of thermodynamics. Herein， we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code. The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks， and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.
In comparison to discrete descriptions of fracture process， the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids， which enables the numerical implement simplification. An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids. This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity， embracing plasticization， cracks initiation， propagation， branching and merging while fulfilling the basic principle of thermodynamics. Herein， we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code. The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks， and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.
2024(5):575-588.
DOI: 10.16356/j.1005-1120.2024.05.003
Abstract:
Molecular dynamics （MD） simulations are employed to delve into the multifaceted effects of TiB2 nanoparticles on the intricate grain refinement mechanism， microstructural evolution， and tensile performance of Inconel 718 superalloys during the rapid directional solidification. Specifically， the study focuses on elucidating the role of TiB2 nanoparticles in augmenting the nucleation rate during the rapid directional solidification process of Ni60Cr21Fe19 alloy system. Furthermore， subsequent tensile simulations are conducted to comprehensively evaluate the anisotropic behavior of tensile properties within the solidified microstructures. The MD results reveal that the incorporation of TiB? nanoparticles during the rapid directional solidification of the Ni60Cr21Fe19 significantly enhances the average nucleation rate， escalating it from 1.27×1034 m-3·s-1 to 2.55×1034 m-3·s-1. Notably， within the face centered cube（FCC）structure， Ni atoms exhibit pronounced compositional segregation， and the solidified alloy maintains an exceptionally high dislocation density reaching up to 1016 m-2. Crucially， the rapid directional solidification process imparts a distinct microstructural anisotropy， leading to a notable disparity in tensile strength. Specifically， the tensile strength along the solidification direction is markedly superior to that perpendicular to it. This disparity arises from different deformation mechanisms under varying loading orientations. Tensile stress perpendicular to the solidification direction encourages the formation of smooth and organized mechanical twins. These twins act as slip planes， enhancing dislocation mobility and thereby improving stress relaxation and dispersion. Moreover， the results underscore the profound strengthening effect of TiB2 nanoparticles， particularly in enhancing the tensile strength along the rapid directional solidification direction.
Molecular dynamics （MD） simulations are employed to delve into the multifaceted effects of TiB2 nanoparticles on the intricate grain refinement mechanism， microstructural evolution， and tensile performance of Inconel 718 superalloys during the rapid directional solidification. Specifically， the study focuses on elucidating the role of TiB2 nanoparticles in augmenting the nucleation rate during the rapid directional solidification process of Ni60Cr21Fe19 alloy system. Furthermore， subsequent tensile simulations are conducted to comprehensively evaluate the anisotropic behavior of tensile properties within the solidified microstructures. The MD results reveal that the incorporation of TiB? nanoparticles during the rapid directional solidification of the Ni60Cr21Fe19 significantly enhances the average nucleation rate， escalating it from 1.27×1034 m-3·s-1 to 2.55×1034 m-3·s-1. Notably， within the face centered cube（FCC）structure， Ni atoms exhibit pronounced compositional segregation， and the solidified alloy maintains an exceptionally high dislocation density reaching up to 1016 m-2. Crucially， the rapid directional solidification process imparts a distinct microstructural anisotropy， leading to a notable disparity in tensile strength. Specifically， the tensile strength along the solidification direction is markedly superior to that perpendicular to it. This disparity arises from different deformation mechanisms under varying loading orientations. Tensile stress perpendicular to the solidification direction encourages the formation of smooth and organized mechanical twins. These twins act as slip planes， enhancing dislocation mobility and thereby improving stress relaxation and dispersion. Moreover， the results underscore the profound strengthening effect of TiB2 nanoparticles， particularly in enhancing the tensile strength along the rapid directional solidification direction.
2024(5):589-598.
DOI: 10.16356/j.1005-1120.2024.05.004
Abstract:
To achieve full-surface strain measurement of variable curvature objects， a 360° 3D digital image correlation （DIC） system is proposed. The measurement system consists of four double-camera systems， which capture the object’s entire surface from multiple angles， enabling comprehensive full-surface measurement. To increase the stitching quality， a hierarchical coordinate matching method is proposed. Initially， a 3D rigid body calibration auxiliary block is employed to track motion trajectory， which enables preliminary matching of four 3D-DIC sub-systems. Subsequently， secondary precise matching is performed based on feature points on the test specimen’s surface. Through the hierarchical coordinate matching method， the local 3D coordinate systems of each double-camera system are unified into a global coordinate system， achieving 3D surface reconstruction of the variable curvature cylindrical shell， and error analysis is conducted on the results. Furthermore， axial compression buckling experiment is conducted to measure the displacement and strain fields on the cylindrical shell’s surface. The experimental results are compared with the finite element analysis， validating the accuracy and effectiveness of the proposed multi-camera 3D-DIC measuring system.
To achieve full-surface strain measurement of variable curvature objects， a 360° 3D digital image correlation （DIC） system is proposed. The measurement system consists of four double-camera systems， which capture the object’s entire surface from multiple angles， enabling comprehensive full-surface measurement. To increase the stitching quality， a hierarchical coordinate matching method is proposed. Initially， a 3D rigid body calibration auxiliary block is employed to track motion trajectory， which enables preliminary matching of four 3D-DIC sub-systems. Subsequently， secondary precise matching is performed based on feature points on the test specimen’s surface. Through the hierarchical coordinate matching method， the local 3D coordinate systems of each double-camera system are unified into a global coordinate system， achieving 3D surface reconstruction of the variable curvature cylindrical shell， and error analysis is conducted on the results. Furthermore， axial compression buckling experiment is conducted to measure the displacement and strain fields on the cylindrical shell’s surface. The experimental results are compared with the finite element analysis， validating the accuracy and effectiveness of the proposed multi-camera 3D-DIC measuring system.
2024(5):599-608.
DOI: 10.16356/j.1005-1120.2024.05.005
Abstract:
The appearance and accumulation of internal impact damage seriously influence overall performance of carbon fiber reinforced plastic（CFRP）. Thus， this study evaluates the change in impact damage number by using linear and nonlinear ultrasonic Lamb wave detection methods， and compares these two detection results. An ultrasonic wave simulation model for composite structure with impact damage is established using the finite element method， and the interaction between impact damage and the ultrasonic wave is simulated. Simulation results demonstrate that the ultrasonic amplitude linearly decreases， and the relative nonlinear parameter linearly increases in proportion to the impact number， respectively. The linear-fitting slope of nonlinear parameter is 0.38 per impact number at an input frequency of 1.0 MHz. It is far higher than that of the linear ultrasonic amplitude， which is only -0.12. However， with the increase of impact damage， the linear growth of nonlinear parameters mainly depends on the decrease in ultrasonic amplitude rather than the accumulation of second harmonic amplitude. In the linear ultrasonic amplitude detection， the linear fitting slope at 1.1 MHz is -0.14， which is lower than those at 0.9 MHz and 1.0 MHz. Meanwhile， in the nonlinear ultrasonic parameter detection， the linear fitting slope at 1.1 MHz is 0.92， which is higher than those at 0.9 MHz and 1.0 MHz. The results show that higher frequencies lead to greater attenuation of ultrasonic amplitude and a larger increase in nonlinear parameters， which can enhance the sensitivity of both linear and nonlinear ultrasonic detections. The accuracy of simulation results is demonstrated through the low-velocity impact and ultrasonic experiments. The results show that compared with nonlinear ultrasonic technology， the linear ultrasonic technology is more suitable for impact damage assessment of carbon fiber reinforced plastic because of its simpler detection process and higher sensitivity.
The appearance and accumulation of internal impact damage seriously influence overall performance of carbon fiber reinforced plastic（CFRP）. Thus， this study evaluates the change in impact damage number by using linear and nonlinear ultrasonic Lamb wave detection methods， and compares these two detection results. An ultrasonic wave simulation model for composite structure with impact damage is established using the finite element method， and the interaction between impact damage and the ultrasonic wave is simulated. Simulation results demonstrate that the ultrasonic amplitude linearly decreases， and the relative nonlinear parameter linearly increases in proportion to the impact number， respectively. The linear-fitting slope of nonlinear parameter is 0.38 per impact number at an input frequency of 1.0 MHz. It is far higher than that of the linear ultrasonic amplitude， which is only -0.12. However， with the increase of impact damage， the linear growth of nonlinear parameters mainly depends on the decrease in ultrasonic amplitude rather than the accumulation of second harmonic amplitude. In the linear ultrasonic amplitude detection， the linear fitting slope at 1.1 MHz is -0.14， which is lower than those at 0.9 MHz and 1.0 MHz. Meanwhile， in the nonlinear ultrasonic parameter detection， the linear fitting slope at 1.1 MHz is 0.92， which is higher than those at 0.9 MHz and 1.0 MHz. The results show that higher frequencies lead to greater attenuation of ultrasonic amplitude and a larger increase in nonlinear parameters， which can enhance the sensitivity of both linear and nonlinear ultrasonic detections. The accuracy of simulation results is demonstrated through the low-velocity impact and ultrasonic experiments. The results show that compared with nonlinear ultrasonic technology， the linear ultrasonic technology is more suitable for impact damage assessment of carbon fiber reinforced plastic because of its simpler detection process and higher sensitivity.
2024(5):609-620.
DOI: 10.16356/j.1005-1120.2024.05.006
Abstract:
In spacecraft electronic devices， the deformation of solder balls within ball grid array （BGA） packages poses a significant risk of system failure. Therefore， accurately measuring the mechanical behavior of solder balls is crucial for ensuring the safety and reliability of spacecraft. Although finite element simulations have been extensively used to study solder ball deformation， there is a significant lack of experimental validation， particularly under thermal cycling conditions. This is due to the challenges in accurately measuring the internal deformations of solder balls and eliminating the rigid body displacement introduced during ex-situ thermal cycling tests. In this work， an ex-situ three-dimensional deformation measurement method using X-ray computed tomography （CT） and digital volume correlation （DVC） is proposed to overcome these obstacles. By incorporating the layer-wise reliability-guided displacement tracking （LW-RGDT） DVC with a singular value decomposition （SVD） method， this method enables accurate assessment of solder ball mechanical behavior in BGA packages without the influence of rigid body displacement. Experimental results reveal that BGA structures exhibit progressive convex deformation with increased thermal cycling， particularly in peripheral solder balls. This method provides a reliable and effective tool for assessing internal deformations in electronic packages under ex-situ conditions， which is crucial for their design optimization and lifespan predictions.
In spacecraft electronic devices， the deformation of solder balls within ball grid array （BGA） packages poses a significant risk of system failure. Therefore， accurately measuring the mechanical behavior of solder balls is crucial for ensuring the safety and reliability of spacecraft. Although finite element simulations have been extensively used to study solder ball deformation， there is a significant lack of experimental validation， particularly under thermal cycling conditions. This is due to the challenges in accurately measuring the internal deformations of solder balls and eliminating the rigid body displacement introduced during ex-situ thermal cycling tests. In this work， an ex-situ three-dimensional deformation measurement method using X-ray computed tomography （CT） and digital volume correlation （DVC） is proposed to overcome these obstacles. By incorporating the layer-wise reliability-guided displacement tracking （LW-RGDT） DVC with a singular value decomposition （SVD） method， this method enables accurate assessment of solder ball mechanical behavior in BGA packages without the influence of rigid body displacement. Experimental results reveal that BGA structures exhibit progressive convex deformation with increased thermal cycling， particularly in peripheral solder balls. This method provides a reliable and effective tool for assessing internal deformations in electronic packages under ex-situ conditions， which is crucial for their design optimization and lifespan predictions.
2024(5):621-631.
DOI: 10.16356/j.1005-1120.2024.05.007
Abstract:
The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs， emits， and involves non-gray creates more complex radiative heat transfer problems. Furthermore， it adds difficulty to solving the coupled conduction， convection， and radiation problem， leading to suboptimal efficiency that fails to meet real-time control demands. To overcome this difficulty， comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem. However， the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency. It is necessary to present an efficient method for the equivalence. The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer， and the gray-equivalent radiative characteristics are successfully recovered. It is our intention that the issue of low inverse efficiency， which has been observed when the least-squares method is employed， will be resolved. To enhance the performance of the Levenberg-Marquardt algorithm， a modification is implemented for determining the damping factor. Detailed investigations are also conducted to evaluate its accuracy， stability of convergence， efficiency， and robustness of the algorithm. Subsequently， a comparison is made between the results achieved using each method.
The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs， emits， and involves non-gray creates more complex radiative heat transfer problems. Furthermore， it adds difficulty to solving the coupled conduction， convection， and radiation problem， leading to suboptimal efficiency that fails to meet real-time control demands. To overcome this difficulty， comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem. However， the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency. It is necessary to present an efficient method for the equivalence. The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer， and the gray-equivalent radiative characteristics are successfully recovered. It is our intention that the issue of low inverse efficiency， which has been observed when the least-squares method is employed， will be resolved. To enhance the performance of the Levenberg-Marquardt algorithm， a modification is implemented for determining the damping factor. Detailed investigations are also conducted to evaluate its accuracy， stability of convergence， efficiency， and robustness of the algorithm. Subsequently， a comparison is made between the results achieved using each method.
2024(5):632-644.
DOI: 10.16356/j.1005-1120.2024.05.008
Abstract:
This paper presents the design and verification of the dual-mode core driven fan stage （CDFS） and high-load compressor with a large flow regulation range. In view of the characteristics of large flow regulation range of the two modes and high average stage load coefficient， this paper investigates the design technology of the dual-mode high-efficiency compressor with a large flow regulation range and high-load compressor with an average stage load coefficient of 0.504. Building upon this research， the design of the dual-mode CDFS and four-stage compressor is completed， and three-dimensional numerical simulation of the two modes is carried out. Finally， performance experiment is conducted to verify the result of three-dimensional numerical simulation. The experiment results show that the compressor performance is improved for the whole working conditions by using the new design method， which realizes the complete fusion design of the CDFS and high-pressure compressor （HPC）. The matching mechanism of stage characteristics of single and double bypass modes and the variation rule of different adjustment angles on performance are studied comprehensively. Furthermore， it effectively reduces the length and weight of compressor， and breaks through the key technologies such as high-load compressor with the average load factor of 0.504. These findings provide valuable data and a methodological foundation for the development of the next generation aeroengine.
This paper presents the design and verification of the dual-mode core driven fan stage （CDFS） and high-load compressor with a large flow regulation range. In view of the characteristics of large flow regulation range of the two modes and high average stage load coefficient， this paper investigates the design technology of the dual-mode high-efficiency compressor with a large flow regulation range and high-load compressor with an average stage load coefficient of 0.504. Building upon this research， the design of the dual-mode CDFS and four-stage compressor is completed， and three-dimensional numerical simulation of the two modes is carried out. Finally， performance experiment is conducted to verify the result of three-dimensional numerical simulation. The experiment results show that the compressor performance is improved for the whole working conditions by using the new design method， which realizes the complete fusion design of the CDFS and high-pressure compressor （HPC）. The matching mechanism of stage characteristics of single and double bypass modes and the variation rule of different adjustment angles on performance are studied comprehensively. Furthermore， it effectively reduces the length and weight of compressor， and breaks through the key technologies such as high-load compressor with the average load factor of 0.504. These findings provide valuable data and a methodological foundation for the development of the next generation aeroengine.
2024(5):645-655.
DOI: 10.16356/j.1005-1120.2024.05.009
Abstract:
The working environment of aerospace engines is extremely harsh with temperature exceeding 1 700 ℃ and accompanied by thermal coupling effects. In this condition， the materials employed in hypersonic aircraft undergo ablation issues， which can cause catastrophic accidents. Due to the excellent high-temperature stability and ablation resistance， HfC exhibits outstanding thermal expansion coefficient matching that of C/SiC composites. 2.5D needle-punched C/SiC composites coated with HfC are prepared using a plasma spraying process， and a high-enthalpy arc-heated wind tunnel is employed to simulate the re-entry environment of aircraft at 8 Mach and an altitude of 32 km. The plasma-sprayed HfC-coated 2.5D needle-punched C/SiC composites are subjected to long-term dynamic testing， and their properties are investigated. Specifically， after the thermal assessment ablation experiment， the composite retains its overall structure and profile； the total mass ablation rate is 0.074 45 g/s， the average linear ablation rate in the thickness direction is -0.067 5 μm/s， and the average linear ablation rate in the length direction is 13.907 μm/s. Results verify that plasma-sprayed HfC coating exhibits excellent anti-oxidation and ablation resistance properties. Besides， the microstructure and ablation mechanism of the C/SiC composites are studied. It is believed that this work will offer guideline for the development of thermal protection materials and the assessment of structural thermal performance.
The working environment of aerospace engines is extremely harsh with temperature exceeding 1 700 ℃ and accompanied by thermal coupling effects. In this condition， the materials employed in hypersonic aircraft undergo ablation issues
10 Stochastic Air Traffic Flow Management for Demand and Capacity Balancing Under Capacity Uncertainty
2024(5):656-674.
DOI: 10.16356/j.1005-1120.2024.05.010
Abstract:
This paper introduces an innovative approach to the synchronized demand-capacity balance with special focus on sector capacity uncertainty within a centrally controlled collaborative air traffic flow management （ATFM） framework. Further with previous study， the uncertainty in capacity is considered as a non-negligible issue regarding multiple reasons， like the impact of weather， the strike of air traffic controllers （ATCOs）， the military use of airspace and the spatiotemporal distribution of nonscheduled flights， etc. These recessive factors affect the outcome of traffic flow optimization. In this research， the focus is placed on the impact of sector capacity uncertainty on demand and capacity balancing （DCB） optimization and ATFM， and multiple options， such as delay assignment and rerouting， are intended for regulating the traffic flow. A scenario optimization method for sector capacity in the presence of uncertainties is used to find the approximately optimal solution. The results show that the proposed approach can achieve better demand and capacity balancing and determine perfect integer solutions to ATFM problems， solving large-scale instances （24 h on seven capacity scenarios， with 6 255 flights and 8 949 trajectories） in 5—15 min. To the best of our knowledge， our experiment is the first to tackle large-scale instances of stochastic ATFM problems within the collaborative ATFM framework.
This paper introduces an innovative approach to the synchronized demand-capacity balance with special focus on sector capacity uncertainty within a centrally controlled collaborative air traffic flow management （ATFM） framework. Further with previous study， the uncertainty in capacity is considered as a non-negligible issue regarding multiple reasons， like the impact of weather， the strike of air traffic controllers （ATCOs）， the military use of airspace and the spatiotemporal distribution of nonscheduled flights， etc. These recessive factors affect the outcome of traffic flow optimization. In this research， the focus is placed on the impact of sector capacity uncertainty on demand and capacity balancing （DCB） optimization and ATFM， and multiple options， such as delay assignment and rerouting， are intended for regulating the traffic flow. A scenario optimization method for sector capacity in the presence of uncertainties is used to find the approximately optimal solution. The results show that the proposed approach can achieve better demand and capacity balancing and determine perfect integer solutions to ATFM problems， solving large-scale instances （24 h on seven capacity scenarios， with 6 255 flights and 8 949 trajectories） in 5—15 min. To the best of our knowledge， our experiment is the first to tackle large-scale instances of stochastic ATFM problems within the collaborative ATFM framework.
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