The longitude tensile properties of 3-Dimension-4-directional（3D-4d） braided C/Si C composites（CMCs） were investigated with the help of a double scale model. This model involves micro-scale and unit-cell scale. In...The longitude tensile properties of 3-Dimension-4-directional（3D-4d） braided C/Si C composites（CMCs） were investigated with the help of a double scale model. This model involves micro-scale and unit-cell scale. In micro-scale, the tensile properties of fiber tows which involves matrix cracking, interfacial debonding, and fiber failure are studied. The unit-cell scale model can reflect the braided structure and simulate the tensile properties of 3D-4d CMCs by introducing the tensile properties of fiber tows into it. Quasi-static tensile tests of 3D-4d braided CMCs were performed on a PWS-100 test system. The predicted tensile stressstrain curve by the double scale model is in good agreement with that of the experimental results.展开更多
Double-scale model for three-dimension-4 directional（3D-4d） braided C/SiC composites has been proposed to investigate its elastic properties. The double-scale model involves micro-scale that takes fiber/ matrix/poro...Double-scale model for three-dimension-4 directional（3D-4d） braided C/SiC composites has been proposed to investigate its elastic properties. The double-scale model involves micro-scale that takes fiber/ matrix/porosity in fibers tows into consideration with unit cell which considers the 3D-4d braiding structure. Micro-optical photographs of composites have been taken to study the braided structure. Then a parameterized finite element model that reflects the structure of 3D-4d braided composites is proposed. Double-scale elastic modulus prediction model is developed to predict the elastic properties of 3D-4d braided C/SiC composites. Stiffness and eompliance-averaging method and energy method are adopted to predict the elastic properties of composites. Static-tension experiments have been conducted to investigate the elastic modulus of 3D-4d braided C/SiC composites. Finally, the effect of micro-porosity in fibers tows on the elastic modulus of 3D-4d braided C/SiC composites has been studied. According to the conclusion of this thesis, elastic modulus predicted by energy method and stiffness-averaging method both find good agreement with the experimental values, when taking the micro-porosity in fibers tows into consideration. Differences between the theoretical and experimental values become smaller.展开更多
The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-la...The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.展开更多
The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air-water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optica...The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air-water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s^(-1)and gas superficial velocity ranging from 0.049 to 0.65 m·s^(-1). A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness Cδand nose shape CZ*were proposed to calculate aTB. In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate aLS, by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al., indicating that the new model was effective and applicable under the slug flow conditions.展开更多
A continuum model of solids with cylindrical microvoids is proposed based on the Taylor dislocation model. The model is an extension of Gurson model in the sense that the void size effect is accounted for. Beside the ...A continuum model of solids with cylindrical microvoids is proposed based on the Taylor dislocation model. The model is an extension of Gurson model in the sense that the void size effect is accounted for. Beside the void volume fraction f, the intrinsic material length l becomes a parameter representing voids since the void size comes into play in the Gurson model. Approximate yield functions in analytic forms are suggested for both solids with cylindrical microvoids and with spherical microvoids. The application to uniaxial tension curves shows a precise agreement between the approximate analytic yield function and the exact parametric form of integrals.展开更多
The void closure behavior in a central extra-thick plate during the gradient temperature rolling was simulated and a back propagation(BP)neural network model was established.The thermal–mechanical finite element mode...The void closure behavior in a central extra-thick plate during the gradient temperature rolling was simulated and a back propagation(BP)neural network model was established.The thermal–mechanical finite element model of the gradient temperature rolling process was first developed and validated.The prediction error of the model for the rolling force is less than 2.51%,which has provided the feasibility of imbedding a defect in it.Based on the relevant data obtained from the simulation,the BP neural network was used to establish a prediction model for the compression degree of a void defect.After statistical analysis,80%of the data had a hit rate higher than 95%,and the hit rate of all data was higher than 90%,which indicates that the BP neural network can accurately predict the compression degree.Meanwhile,the comparisons between the results with the gradient temperature rolling and uniform temperature rolling,and between the results with the single-pass rolling and multi-pass rolling were discussed,which provides a theoretical reference for developing process parameters in actual production.展开更多
Casting magnesium alloys are highly heterogeneous materials inevitably containing numerous voids.These voids will evolve during material deformation and markedly affect material behaviors,so it is important to investi...Casting magnesium alloys are highly heterogeneous materials inevitably containing numerous voids.These voids will evolve during material deformation and markedly affect material behaviors,so it is important to investigate the equation of the void evolution and the constitutive relation involving the void evolution.By assuming the voids in casting magnesium alloys were spherical,the growth equation of the voids was obtained from the incompressibility and continuity conditions of material matrix. Through combining the obtained void-growth equation with the void-nucleation equation relative to the increment of intrinsic-time measure,the evolution equation of the voids was presented.By introducing the presented void-evolution equation to a nonclassical elastoplastic constitutive equation,a constitutive model involving the void evolution was put forward.The corresponding numerical algorithm and finite element procedure of the model were developed and applied to the analysis of the elastoplastic response and the porosity change of casting magnesium alloy ZL305.Computed results show satisfactory agreement with those of the corresponding experiments.展开更多
The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void gr...The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void growth equation was obtained based on the continuous supposition of the material matrix,and the void nucleation equation was derived by assuming that the void nucleation follows a normal distribution. A softening function related to the void evolution was given. After the softening function was embedded to a nonclassical elastoplastic constitutive equation,a constitutive model involving void evolution was obtained. The numerical algorithm and the finite element procedure related to the constitutive model were developed and applied to the analysis of the distributions of the stress and the porosity of the notched cylindrical specimens of casting magnesium alloy ZL305. The computed results show satisfactory agreement with the experimental data.展开更多
The conventional forming limit diagram （FLD） is described as a plot of major strain versus minor strain. However, FLD is dependent on forming history and strain path. In the present study, a forming limit stress-bas...The conventional forming limit diagram （FLD） is described as a plot of major strain versus minor strain. However, FLD is dependent on forming history and strain path. In the present study, a forming limit stress-based diagram （FLSD） has been adopted to predict the fracture limit of aluminum alloy （AA） 5052-O1 sheet. Nakazima test is simulated by plastic constitutive formula derived from the modified Gurson-Tvergaard-Needleman （GTN） model. An in situ tensile test with scanning electron microscope （SEM） is proposed to determine the parameters in GTN model. The damage evolution is observed and recorded, and the parameters of GTN model are identified through counting void fraction at three damage stages of AA5052-O 1. According to the experimental results, the original void volume fraction, the volume fraction of potential nucleated voids, the critical void volume fraction, the void volume fraction at the final failure of material are assigned as 0.002 918, 0.024 9, 0.030 103, 0.048 54, respectively. The stress and strain are obtained at the last loading step before crack. FLSD and FLD of AA5052-O 1 are plotted. Compared with the experimental Nakazima test and uniaxial tensile test, the predicted results show a good agreement. The parameters determined by in situ tensile test can be applied to the research of the forming limit for ductile metals.展开更多
The deterioration of the sleeper support on the ballasted track begins with the accumulation of sleeper voids.The increased dynamic loading in the voided zone and the ballast contact conditions cause the accelerated g...The deterioration of the sleeper support on the ballasted track begins with the accumulation of sleeper voids.The increased dynamic loading in the voided zone and the ballast contact conditions cause the accelerated growth of the settlements in the voided zones,which results in the appearance of local instabilities like ballast breakdown,white spots,subgrade defects,etc.The recent detection and quantification of the sleeper voids with track-side and onboard monitoring can help to avoid or delay the development of local instabilities.The present paper is devoted to the study of the dynamic behavior of railway track with sleeper voids in the ballast breakdown zone.The result of the experimental track-side measurements of rail acceleration and deflection is presented.The analysis shows the existence of the dynamic impact during wheel entry in the voided zone.However,the measured dynamic impact is subjected to the bias of the track-side measurement method.Both the mechanism of the impact and the measurement aspects are explained by using the one-beam model on viscoelastic foundation.The void features in the dynamic behavior are analyzed for the purpose of track-side and onboard monitoring.A practical method of the void parameter quantification is proposed.展开更多
A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as void...A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution(rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.展开更多
Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of partic...Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of particle breakage on the CSL is mainly attributed to the change in GSD due to particle breakage.However,GSD has not been properly considered in modeling the CSL with influence of particle breakage.This study aims to propose a quantitative model to determine the CSL considering the effect of GSD.We hypothesize that the change of critical state void ratio with respect to GSD is caused by the same mechanism that influences of the change of minimum void ratio with respect to GSD.Consequently,the particle packing model for minimum void ratio proposed by Chang et al.(2017)is extended to predict critical state void ratio.The developed model is validated by experimental results of CSLs for several types of granular materials.Then the evolution of GSD due to particle breakage is incorporated into the model.The model is further evaluated using the experimental results on rockfill material,which illustrates the applicability of the model in predicting CSL for granular material with particle breakage.展开更多
Hydrostatic stresses of copper dual-damascene interconnects are calculated by a commercial finite element software in this paper.The analytical work is performed to examine the effects of different low-k(k is permitti...Hydrostatic stresses of copper dual-damascene interconnects are calculated by a commercial finite element software in this paper.The analytical work is performed to examine the effects of different low-k(k is permittivity)dielectrics,barrier layer and aspect ratio of via on hydrostatic stress distribution in the copper interconnects.The results of calculation indicate that the hydrostatic stresses are highly non-uniform throughout the copper interconnects and the highest tensile hydrostatic stress exists on the top interface of lower level interconnect near via.Both the high coefficient of thermal expansion and the low elastic modulus of the low-k dielectrics and barrier layer can decrease the highest hydrostatic stress on the top interface,which can improve the reliability of the copper interconnects.展开更多
基金Funded by the National Basic Research Program of Chinathe National Natural Science Foundation of China(51675266)+3 种基金the Aeronautical Science Foundation of China(2014ZB52024)the Fundamental Research Funds for the Central Universities(NJ20160038)the Jiangsu Innovation Program for Graduate Education(CXLX13_165)the Fundamental Research Funds for the Central Universities
文摘The longitude tensile properties of 3-Dimension-4-directional（3D-4d） braided C/Si C composites（CMCs） were investigated with the help of a double scale model. This model involves micro-scale and unit-cell scale. In micro-scale, the tensile properties of fiber tows which involves matrix cracking, interfacial debonding, and fiber failure are studied. The unit-cell scale model can reflect the braided structure and simulate the tensile properties of 3D-4d CMCs by introducing the tensile properties of fiber tows into it. Quasi-static tensile tests of 3D-4d braided CMCs were performed on a PWS-100 test system. The predicted tensile stressstrain curve by the double scale model is in good agreement with that of the experimental results.
基金Funded by the National Basic Research Program of China,National Natural Science Foundation of China(No.51075204)Funding of Jiangsu Innovation Program for Graduate Education(No.CXLX13_165)+2 种基金the Fundamental Research Funds for the Central Universities,Aeronautical Science Foundation of China(No.2012ZB52026)Research Fund for the Doctoral Program of Higher Education of China(No.20070287039)NUAA Research Funding(No.NZ2012106)
文摘Double-scale model for three-dimension-4 directional（3D-4d） braided C/SiC composites has been proposed to investigate its elastic properties. The double-scale model involves micro-scale that takes fiber/ matrix/porosity in fibers tows into consideration with unit cell which considers the 3D-4d braiding structure. Micro-optical photographs of composites have been taken to study the braided structure. Then a parameterized finite element model that reflects the structure of 3D-4d braided composites is proposed. Double-scale elastic modulus prediction model is developed to predict the elastic properties of 3D-4d braided C/SiC composites. Stiffness and eompliance-averaging method and energy method are adopted to predict the elastic properties of composites. Static-tension experiments have been conducted to investigate the elastic modulus of 3D-4d braided C/SiC composites. Finally, the effect of micro-porosity in fibers tows on the elastic modulus of 3D-4d braided C/SiC composites has been studied. According to the conclusion of this thesis, elastic modulus predicted by energy method and stiffness-averaging method both find good agreement with the experimental values, when taking the micro-porosity in fibers tows into consideration. Differences between the theoretical and experimental values become smaller.
文摘The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.
基金supported by National Key Research and Development Program of China ( 2018YFE011061)。
文摘The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air-water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s^(-1)and gas superficial velocity ranging from 0.049 to 0.65 m·s^(-1). A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness Cδand nose shape CZ*were proposed to calculate aTB. In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate aLS, by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al., indicating that the new model was effective and applicable under the slug flow conditions.
基金The project supported by the National Natural Science Foundation of China(20020003023)the Ministry of Education(key grant 0306)
文摘A continuum model of solids with cylindrical microvoids is proposed based on the Taylor dislocation model. The model is an extension of Gurson model in the sense that the void size effect is accounted for. Beside the void volume fraction f, the intrinsic material length l becomes a parameter representing voids since the void size comes into play in the Gurson model. Approximate yield functions in analytic forms are suggested for both solids with cylindrical microvoids and with spherical microvoids. The application to uniaxial tension curves shows a precise agreement between the approximate analytic yield function and the exact parametric form of integrals.
基金supported by the National Natural Science Foundation of China(Grant Nos.U1960105,52074187,and 52274388).
文摘The void closure behavior in a central extra-thick plate during the gradient temperature rolling was simulated and a back propagation(BP)neural network model was established.The thermal–mechanical finite element model of the gradient temperature rolling process was first developed and validated.The prediction error of the model for the rolling force is less than 2.51%,which has provided the feasibility of imbedding a defect in it.Based on the relevant data obtained from the simulation,the BP neural network was used to establish a prediction model for the compression degree of a void defect.After statistical analysis,80%of the data had a hit rate higher than 95%,and the hit rate of all data was higher than 90%,which indicates that the BP neural network can accurately predict the compression degree.Meanwhile,the comparisons between the results with the gradient temperature rolling and uniform temperature rolling,and between the results with the single-pass rolling and multi-pass rolling were discussed,which provides a theoretical reference for developing process parameters in actual production.
基金Project(10872221)supported by the National Natural Science Foundation of China
文摘Casting magnesium alloys are highly heterogeneous materials inevitably containing numerous voids.These voids will evolve during material deformation and markedly affect material behaviors,so it is important to investigate the equation of the void evolution and the constitutive relation involving the void evolution.By assuming the voids in casting magnesium alloys were spherical,the growth equation of the voids was obtained from the incompressibility and continuity conditions of material matrix. Through combining the obtained void-growth equation with the void-nucleation equation relative to the increment of intrinsic-time measure,the evolution equation of the voids was presented.By introducing the presented void-evolution equation to a nonclassical elastoplastic constitutive equation,a constitutive model involving the void evolution was put forward.The corresponding numerical algorithm and finite element procedure of the model were developed and applied to the analysis of the elastoplastic response and the porosity change of casting magnesium alloy ZL305.Computed results show satisfactory agreement with those of the corresponding experiments.
基金Project(10572157) supported by the National Natural Science Foundation of China
文摘The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void growth equation was obtained based on the continuous supposition of the material matrix,and the void nucleation equation was derived by assuming that the void nucleation follows a normal distribution. A softening function related to the void evolution was given. After the softening function was embedded to a nonclassical elastoplastic constitutive equation,a constitutive model involving void evolution was obtained. The numerical algorithm and the finite element procedure related to the constitutive model were developed and applied to the analysis of the distributions of the stress and the porosity of the notched cylindrical specimens of casting magnesium alloy ZL305. The computed results show satisfactory agreement with the experimental data.
基金Aeronautical Science Foundation of China （03H53048）
文摘The conventional forming limit diagram （FLD） is described as a plot of major strain versus minor strain. However, FLD is dependent on forming history and strain path. In the present study, a forming limit stress-based diagram （FLSD） has been adopted to predict the fracture limit of aluminum alloy （AA） 5052-O1 sheet. Nakazima test is simulated by plastic constitutive formula derived from the modified Gurson-Tvergaard-Needleman （GTN） model. An in situ tensile test with scanning electron microscope （SEM） is proposed to determine the parameters in GTN model. The damage evolution is observed and recorded, and the parameters of GTN model are identified through counting void fraction at three damage stages of AA5052-O 1. According to the experimental results, the original void volume fraction, the volume fraction of potential nucleated voids, the critical void volume fraction, the void volume fraction at the final failure of material are assigned as 0.002 918, 0.024 9, 0.030 103, 0.048 54, respectively. The stress and strain are obtained at the last loading step before crack. FLSD and FLD of AA5052-O 1 are plotted. Compared with the experimental Nakazima test and uniaxial tensile test, the predicted results show a good agreement. The parameters determined by in situ tensile test can be applied to the research of the forming limit for ductile metals.
基金The authors acknowledge the support of Swiss Federal Railways with the experimental measurements.
文摘The deterioration of the sleeper support on the ballasted track begins with the accumulation of sleeper voids.The increased dynamic loading in the voided zone and the ballast contact conditions cause the accelerated growth of the settlements in the voided zones,which results in the appearance of local instabilities like ballast breakdown,white spots,subgrade defects,etc.The recent detection and quantification of the sleeper voids with track-side and onboard monitoring can help to avoid or delay the development of local instabilities.The present paper is devoted to the study of the dynamic behavior of railway track with sleeper voids in the ballast breakdown zone.The result of the experimental track-side measurements of rail acceleration and deflection is presented.The analysis shows the existence of the dynamic impact during wheel entry in the voided zone.However,the measured dynamic impact is subjected to the bias of the track-side measurement method.Both the mechanism of the impact and the measurement aspects are explained by using the one-beam model on viscoelastic foundation.The void features in the dynamic behavior are analyzed for the purpose of track-side and onboard monitoring.A practical method of the void parameter quantification is proposed.
基金support of this work by the National Science Foundation (CMMI Award no.1932975)。
文摘A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution(rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.
基金supported by the National Science Foundation of the United States under a research grant (CMMI-1917238)
文摘Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of particle breakage on the CSL is mainly attributed to the change in GSD due to particle breakage.However,GSD has not been properly considered in modeling the CSL with influence of particle breakage.This study aims to propose a quantitative model to determine the CSL considering the effect of GSD.We hypothesize that the change of critical state void ratio with respect to GSD is caused by the same mechanism that influences of the change of minimum void ratio with respect to GSD.Consequently,the particle packing model for minimum void ratio proposed by Chang et al.(2017)is extended to predict critical state void ratio.The developed model is validated by experimental results of CSLs for several types of granular materials.Then the evolution of GSD due to particle breakage is incorporated into the model.The model is further evaluated using the experimental results on rockfill material,which illustrates the applicability of the model in predicting CSL for granular material with particle breakage.
基金the National Natural Science Foundation of China(No.50871016)
文摘Hydrostatic stresses of copper dual-damascene interconnects are calculated by a commercial finite element software in this paper.The analytical work is performed to examine the effects of different low-k(k is permittivity)dielectrics,barrier layer and aspect ratio of via on hydrostatic stress distribution in the copper interconnects.The results of calculation indicate that the hydrostatic stresses are highly non-uniform throughout the copper interconnects and the highest tensile hydrostatic stress exists on the top interface of lower level interconnect near via.Both the high coefficient of thermal expansion and the low elastic modulus of the low-k dielectrics and barrier layer can decrease the highest hydrostatic stress on the top interface,which can improve the reliability of the copper interconnects.
