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
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 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 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
Accurate prediction of ductile fracture requires determining the material properties,including the parameters of the constitutive and ductile fracture model,which represent the true material response.Conventional cali...Accurate prediction of ductile fracture requires determining the material properties,including the parameters of the constitutive and ductile fracture model,which represent the true material response.Conventional calibration of material parameters often relies on a trial-and-error approach,in which the parameters are manually adjusted until the corresponding finite element model results in a response matching the experimental global response.The parameter estimates are often subjective.To address this issue,in this paper we treat the identification of material parameters as an optimization problem and introduce the particle swarm optimization(PSO)algorithm as the optimization approach.We provide material parameters of two uncoupled ductile fracture models—the Rice and Tracey void growth model(RT-VGM)and the micro-mechanical void growth model(MM-VGM),and a coupled model—the gurson-Tvergaard-Needleman(GTN)model for ASTM A36,A572 Gr.50,and A992 structural steels using an automated PSO method.By minimizing the difference between the experimental results and finite element simulations of the load-displacement curves for a set of tests of circumferentially notched tensile(CNT)bars,the calibration procedure automatically determines the parameters of the strain hardening law as well as the uncoupled models and the coupled GTN constitutive model.Validation studies show accurate prediction of the load-displacement response and ductile fracture initiation in V-notch specimens,and confirm the PSO algorithm as an effective and robust algorithm for seeking ductile fracture model parameters.PSO has excellent potential for identifying other fracture models(e.g.,shear modified GTN)with many parameters that can give rise to more accurate predictions of ductile fracture.Limitations of the PSO algorithm and the current calibrated ductile fracture models are also discussed in this paper.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
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
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
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.
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the National Natural Science Foundation of China(No.51908416)the Shanghai Pujiang Program(No.19PJ1409500)the Fundamental Research Funds for the Central Universities,China。
文摘Accurate prediction of ductile fracture requires determining the material properties,including the parameters of the constitutive and ductile fracture model,which represent the true material response.Conventional calibration of material parameters often relies on a trial-and-error approach,in which the parameters are manually adjusted until the corresponding finite element model results in a response matching the experimental global response.The parameter estimates are often subjective.To address this issue,in this paper we treat the identification of material parameters as an optimization problem and introduce the particle swarm optimization(PSO)algorithm as the optimization approach.We provide material parameters of two uncoupled ductile fracture models—the Rice and Tracey void growth model(RT-VGM)and the micro-mechanical void growth model(MM-VGM),and a coupled model—the gurson-Tvergaard-Needleman(GTN)model for ASTM A36,A572 Gr.50,and A992 structural steels using an automated PSO method.By minimizing the difference between the experimental results and finite element simulations of the load-displacement curves for a set of tests of circumferentially notched tensile(CNT)bars,the calibration procedure automatically determines the parameters of the strain hardening law as well as the uncoupled models and the coupled GTN constitutive model.Validation studies show accurate prediction of the load-displacement response and ductile fracture initiation in V-notch specimens,and confirm the PSO algorithm as an effective and robust algorithm for seeking ductile fracture model parameters.PSO has excellent potential for identifying other fracture models(e.g.,shear modified GTN)with many parameters that can give rise to more accurate predictions of ductile fracture.Limitations of the PSO algorithm and the current calibrated ductile fracture models are also discussed in this paper.
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.
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.
