The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plo...The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.展开更多
This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control poin...This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.展开更多
In order to establish a restoring-force model for modified concrete columns with recycled aggregates concrete(RAC), cyclic loading tests were carried out on five concretes with RAC columns and ordinary concrete frame ...In order to establish a restoring-force model for modified concrete columns with recycled aggregates concrete(RAC), cyclic loading tests were carried out on five concretes with RAC columns and ordinary concrete frame columns under the combined influence with different admixtures and admixtures ratios(silica fume and hybrid fiber). The expressions for characteristic nodes of the skeleton curve were given by the analysis and numerical regression of the test results. In addition, the hysteretic rules of the restoring-force model and the expression for unloading stiffness were presented. Finally, we summed up the complete calculation method of the hysteretic restoring force, whose results were in good agreement with experiment. The results demonstrated that the proposed model could simulate and reflect the corresponding hysteretic behaviors, and the calculation method can provide the theoretical basis for the engineering application.展开更多
The mechanical properties of modified sea water sea sand coral concrete(SWSSCC)under axial compression were experimentally studied.Two different parameters were considered in this test:types of cement and fiber.An exp...The mechanical properties of modified sea water sea sand coral concrete(SWSSCC)under axial compression were experimentally studied.Two different parameters were considered in this test:types of cement and fiber.An experimental campaign was developed involving uniaxial compression tests and the use of digital image correlation(DIC)method to analyze the strain distribution and crack propagation of specimen.Test results indicated that the compressive strength and elastic modulus of SWSSCC were improved by adding stainless steel fibers(SSF),while polypropylene fibers(PF)enhanced the SWSSCC peak deformation.It was found that the elastic modulus and strength of SWSSCC using ordinary Portland cement(OPC)were higher compared to specimen with low alkalinity sulphoaluminate cement(LAS).Typical strain distribution changed with the variation of fiber types.The propagation and characteristics of cracks in SWSSCC containing PF were similar to those of cracks in SWSSCC.However,the propagation of cracks and the development of plastic deformation in SWSSCC were effectively hindered by adopting SSF.Finally,an analytical stress-strain expression of specimen considering the influences of fibers was established.The obtained results would provide a basis for the application of SWSSCC.展开更多
Commercially pure titanium(CP Ti) has been actively used in the plate heat exchanger due to its light weight, high specific strength, and excellent corrosion resistance. However, researches for the plastic deformati...Commercially pure titanium(CP Ti) has been actively used in the plate heat exchanger due to its light weight, high specific strength, and excellent corrosion resistance. However, researches for the plastic deformation characteristics and press formability of the CP Ti sheet are not much in comparison with automotive steels and aluminum alloys. The mechanical properties and hardening behavior evaluated in stress-strain relation of the CP Ti sheet are clarified in relation with press formability. The flow curve denoting true stress-true strain relation for CP Ti sheet is fitted well by the Kim-Tuan hardening equation rather than Voce and Swift models. The forming limit curve(FLC) of CP Ti sheet as a criterion for press formability was experimentally evaluated by punch stretching test and analytically predicted via Hora's modified maximum force criterion. The predicted FLC by adopting Kim-Tuan hardening model and appropriate yield function shows good correlation with the experimental results of punch stretching test.展开更多
The idea of modified water masses is introduced and a cluster analysis is used for determining the boundary of modified water masses and its variety in the shallow water area of the Huanghai Sea (Yellow Sea) and the E...The idea of modified water masses is introduced and a cluster analysis is used for determining the boundary of modified water masses and its variety in the shallow water area of the Huanghai Sea (Yellow Sea) and the East China Sea. According to the specified standards to make the cluster, we have determined the number and boundary of the water masses and the mixed zones.The results obtained by the cluster method show that there are eight modified water masses in this area. According to the relative index of temperature and salinity,the modified water masses are divided into nine different characteristic parts. The water, masses may also be divided into three salinity types. On the TS-Diagram, the points concerning temperature and safinity of different modified mater masses are distributed around a curve, from which the characteristics of gradual modification may be embodied. The variation ranges of different modified water masses are all large, explaining the intensive modification of water masses in展开更多
An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shea...An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.展开更多
The effect of specimen thinkness on JR resistance curve has been investigated using low and middle strength steels. As the J dominance regime is reached, the initial J-integral values, J(i), are definite even if the e...The effect of specimen thinkness on JR resistance curve has been investigated using low and middle strength steels. As the J dominance regime is reached, the initial J-integral values, J(i), are definite even if the elastic component Ji(e) and plastic component Ji(p)vary with the thinkness of specimen. The wider the specimen width, the larger the Ji(e)/Ji and the smaller the Ji(p)/Ji. The crack propagation resistance, dJR/da and dJp/da, decreases, while dJe/da increases linearly with increasing specimen thinness.Based on the above experimental results, an empirical formula dJ/da = α+β. B is given, which can be used to evaluate the safety of practical structural components.A modified J-integral is presented, upon which a new view is Put forward that the increase in crack growth resistance is induced mainly by the increase in the plastic J-integral component with the crack propagation,展开更多
Reliable earthquake death toll estimate can provide valuable references for disaster relief headquarters and civil administration departments to make arrangement and deployment plan during post-earthquake relief work,...Reliable earthquake death toll estimate can provide valuable references for disaster relief headquarters and civil administration departments to make arrangement and deployment plan during post-earthquake relief work, thus increasing the efficiency of the relief work to a certain extent. In this study, we acquired the death toll data of Wenchuan earth- quake, fitted the data using modified exponential curve and compared the result with that of the exponential function. Experimental verification with Chi-Chi earthquake and Kobe earthquake data shows that the fitted result by modified exponential curve is more satisfactory. The final death toll resulting from future destructive earthquakes can be estimated by the acquired fitting function.展开更多
This paper studies electromagnetoelastic static investigation of a sandwich doubly curved microshell subjected to multi-field loading based on a new thickness stretching included refined higher order shear/normal defo...This paper studies electromagnetoelastic static investigation of a sandwich doubly curved microshell subjected to multi-field loading based on a new thickness stretching included refined higher order shear/normal deformable model.Modified-couple-stress-theory(MCST)is used for accounting small-scaledependency.The numerical results are derived using an analytical method.The effect of small scale parameter in micro scale,initial electric and magnetic potentials and foundation parameters is studied on the electromagnetoelastic bending results.It is confirmed an enhancing in stiffness of small scale shell with an increase in micro length scale parameter.展开更多
A new model of the modified Newtonian gravity called Compacted & Collapsing Gravity (CCG) is proposed. Similar to the Milgrom’s MOND, it allows explaining the flattening of rotation curve in spiral galaxies, thus...A new model of the modified Newtonian gravity called Compacted & Collapsing Gravity (CCG) is proposed. Similar to the Milgrom’s MOND, it allows explaining the flattening of rotation curve in spiral galaxies, thus eliminates the need for dark matter at this level. However, in contrast to MOND, it puts a distinct limit on effective gravity;thereby constraints the sizes of single galaxies in connection to their masses, which complies with observations. In the bigger than single galaxies structures such as galaxy clusters, CCG rather complements than replaces interpretations of the observational data based on dark matter. Besides, the new model provides a plausible explanation to the hierarchical structure of the universe.展开更多
Applying conventional analytical methods,the following results have been found:the satura-tion value of acid--modified multifunction copolyest fibre( acid-modified polyester fibre)is1.74,then this kind of fibre is goo...Applying conventional analytical methods,the following results have been found:the satura-tion value of acid--modified multifunction copolyest fibre( acid-modified polyester fibre)is1.74,then this kind of fibre is good for being dyed medium and light colours with cationicdyes;its level of erystalization is lower than of PET fibre;the third monomer(SIPM)con-tent in the fibre will be reduced by about 8% by the "alkali treatment"in dyeing and finishingprocess:through measuring and analysing the dye-up-take curves of time and temperature ofdyeing the fibre with cationic dyes,we indicate the key factors in dyeing are the 100℃ dyeingtemperature and the time for heat preservation;moveover,adding sodium sulphate will help leveldyeing but lower the dye-uptake.展开更多
T-wave alternans (TWA) in surface electrocardiograph (ECG) signal is considered a marker of abnormal ventricular function which may be associated with ventricular tachy- cardia. Several methods have been developed...T-wave alternans (TWA) in surface electrocardiograph (ECG) signal is considered a marker of abnormal ventricular function which may be associated with ventricular tachy- cardia. Several methods have been developed in recent years to evaluate the important feature. One such method is known as modified moving average (MMA) analysis, which performs well for different levels of TWA, but it is sensitive to the noise in T-waves. In this paper we propose an improved MMA algorithm, which adds a stage of T-wave curve fitting for the MMA method before intermediate averaging. The curve fitting is performed by means of least square method technique. Our assessment study demon- strates the improved performance.展开更多
There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been ...There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far: existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.展开更多
A new approach for predicting forming limit curves(FLCs)at elevated temperatures was proposed herein.FLCs are often used to predict failure and determine the optimal forming parameters of automotive parts.First,a grap...A new approach for predicting forming limit curves(FLCs)at elevated temperatures was proposed herein.FLCs are often used to predict failure and determine the optimal forming parameters of automotive parts.First,a graphical method based on a modified maximum force criterion was applied to estimate the FLCs of 22MnB5 boron steel sheets at room temperature using various hardening laws.Subsequently,the predicted FLC data at room temperature were compared with corresponding data obtained from Nakazima's tests to obtain the best prediction.To estimate the FLC at elevated temperatures,tensile tests were conducted at various temperatures to determine the ratios of equivalent fracture strains between the corresponding elevated temperatures and room temperature.FLCs at elevated temperatures could be established based on obtained ratios.However,the predicted FLCs at elevated temperatures did not agree well with the corresponding FLC experimental data of Zhou et al.A new method was proposed herein to improve the prediction of FLCs at elevated temperatures.An FLC calculated at room tem-perature was utilized to predict the failure of Nakazima's samples via finite element simulation.Based on the simulation results at room temperature,the mathematical relationships between the equivalent ductile fracture strain versus stress triaxiality and strain ratio were established and then combined with ratios between elevated and room temperatures to calculate the FLCs at different temperatures.The predicted FLCs at elevated temperatures agree well with the corresponding experimental FLC data.展开更多
基金funded by the National Natural Science Foundation of China(91025015,51178209)the Project of Arid Meteorological Science Research Foundation of China Meteorological Administration(IAM201608)
文摘The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.
文摘This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.
基金Project(51178388)supported by the National Natural Science Foundation of ChinaProject(2013SZS01-Z02)supported by Key Laboratory Fund of Shaanxi Province,China
文摘In order to establish a restoring-force model for modified concrete columns with recycled aggregates concrete(RAC), cyclic loading tests were carried out on five concretes with RAC columns and ordinary concrete frame columns under the combined influence with different admixtures and admixtures ratios(silica fume and hybrid fiber). The expressions for characteristic nodes of the skeleton curve were given by the analysis and numerical regression of the test results. In addition, the hysteretic rules of the restoring-force model and the expression for unloading stiffness were presented. Finally, we summed up the complete calculation method of the hysteretic restoring force, whose results were in good agreement with experiment. The results demonstrated that the proposed model could simulate and reflect the corresponding hysteretic behaviors, and the calculation method can provide the theoretical basis for the engineering application.
基金supported by the National Natural Science Foundation of China(Nos.51408346,51978389)the China Postdoctoral Science Foundation Funded Project(No.2015M572584,No.2016T0914)+3 种基金the Shandong Provincial Natural Science Foundation(No.ZR2019PEE044)the Opening Foundation of Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation(CDPM2019KF12)the Systematic Project of Guangxi Key Laboratory of Disaster Prevention and Structural Safety(2019ZDK035)the Shandong University of Science and Technology(SDKDYC190358).
文摘The mechanical properties of modified sea water sea sand coral concrete(SWSSCC)under axial compression were experimentally studied.Two different parameters were considered in this test:types of cement and fiber.An experimental campaign was developed involving uniaxial compression tests and the use of digital image correlation(DIC)method to analyze the strain distribution and crack propagation of specimen.Test results indicated that the compressive strength and elastic modulus of SWSSCC were improved by adding stainless steel fibers(SSF),while polypropylene fibers(PF)enhanced the SWSSCC peak deformation.It was found that the elastic modulus and strength of SWSSCC using ordinary Portland cement(OPC)were higher compared to specimen with low alkalinity sulphoaluminate cement(LAS).Typical strain distribution changed with the variation of fiber types.The propagation and characteristics of cracks in SWSSCC containing PF were similar to those of cracks in SWSSCC.However,the propagation of cracks and the development of plastic deformation in SWSSCC were effectively hindered by adopting SSF.Finally,an analytical stress-strain expression of specimen considering the influences of fibers was established.The obtained results would provide a basis for the application of SWSSCC.
基金supported by the National Research Foundation of Korea (NRF) granted by the Korea government [2014R1A2A2A01005903]Priority Research Centers Program (2010-0020089)support from a grant [R0003356] (Tuning Professional Support Center in Daegu Metropolitan City) funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea)
文摘Commercially pure titanium(CP Ti) has been actively used in the plate heat exchanger due to its light weight, high specific strength, and excellent corrosion resistance. However, researches for the plastic deformation characteristics and press formability of the CP Ti sheet are not much in comparison with automotive steels and aluminum alloys. The mechanical properties and hardening behavior evaluated in stress-strain relation of the CP Ti sheet are clarified in relation with press formability. The flow curve denoting true stress-true strain relation for CP Ti sheet is fitted well by the Kim-Tuan hardening equation rather than Voce and Swift models. The forming limit curve(FLC) of CP Ti sheet as a criterion for press formability was experimentally evaluated by punch stretching test and analytically predicted via Hora's modified maximum force criterion. The predicted FLC by adopting Kim-Tuan hardening model and appropriate yield function shows good correlation with the experimental results of punch stretching test.
文摘The idea of modified water masses is introduced and a cluster analysis is used for determining the boundary of modified water masses and its variety in the shallow water area of the Huanghai Sea (Yellow Sea) and the East China Sea. According to the specified standards to make the cluster, we have determined the number and boundary of the water masses and the mixed zones.The results obtained by the cluster method show that there are eight modified water masses in this area. According to the relative index of temperature and salinity,the modified water masses are divided into nine different characteristic parts. The water, masses may also be divided into three salinity types. On the TS-Diagram, the points concerning temperature and safinity of different modified mater masses are distributed around a curve, from which the characteristics of gradual modification may be embodied. The variation ranges of different modified water masses are all large, explaining the intensive modification of water masses in
文摘An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.
文摘The effect of specimen thinkness on JR resistance curve has been investigated using low and middle strength steels. As the J dominance regime is reached, the initial J-integral values, J(i), are definite even if the elastic component Ji(e) and plastic component Ji(p)vary with the thinkness of specimen. The wider the specimen width, the larger the Ji(e)/Ji and the smaller the Ji(p)/Ji. The crack propagation resistance, dJR/da and dJp/da, decreases, while dJe/da increases linearly with increasing specimen thinness.Based on the above experimental results, an empirical formula dJ/da = α+β. B is given, which can be used to evaluate the safety of practical structural components.A modified J-integral is presented, upon which a new view is Put forward that the increase in crack growth resistance is induced mainly by the increase in the plastic J-integral component with the crack propagation,
文摘Reliable earthquake death toll estimate can provide valuable references for disaster relief headquarters and civil administration departments to make arrangement and deployment plan during post-earthquake relief work, thus increasing the efficiency of the relief work to a certain extent. In this study, we acquired the death toll data of Wenchuan earth- quake, fitted the data using modified exponential curve and compared the result with that of the exponential function. Experimental verification with Chi-Chi earthquake and Kobe earthquake data shows that the fitted result by modified exponential curve is more satisfactory. The final death toll resulting from future destructive earthquakes can be estimated by the acquired fitting function.
基金the Programs for Science and Technology Development of Henan province(No.202102210020)Basic research plan of key scientific research projects of Henan universities(No.20B430011).
文摘This paper studies electromagnetoelastic static investigation of a sandwich doubly curved microshell subjected to multi-field loading based on a new thickness stretching included refined higher order shear/normal deformable model.Modified-couple-stress-theory(MCST)is used for accounting small-scaledependency.The numerical results are derived using an analytical method.The effect of small scale parameter in micro scale,initial electric and magnetic potentials and foundation parameters is studied on the electromagnetoelastic bending results.It is confirmed an enhancing in stiffness of small scale shell with an increase in micro length scale parameter.
文摘A new model of the modified Newtonian gravity called Compacted & Collapsing Gravity (CCG) is proposed. Similar to the Milgrom’s MOND, it allows explaining the flattening of rotation curve in spiral galaxies, thus eliminates the need for dark matter at this level. However, in contrast to MOND, it puts a distinct limit on effective gravity;thereby constraints the sizes of single galaxies in connection to their masses, which complies with observations. In the bigger than single galaxies structures such as galaxy clusters, CCG rather complements than replaces interpretations of the observational data based on dark matter. Besides, the new model provides a plausible explanation to the hierarchical structure of the universe.
文摘Applying conventional analytical methods,the following results have been found:the satura-tion value of acid--modified multifunction copolyest fibre( acid-modified polyester fibre)is1.74,then this kind of fibre is good for being dyed medium and light colours with cationicdyes;its level of erystalization is lower than of PET fibre;the third monomer(SIPM)con-tent in the fibre will be reduced by about 8% by the "alkali treatment"in dyeing and finishingprocess:through measuring and analysing the dye-up-take curves of time and temperature ofdyeing the fibre with cationic dyes,we indicate the key factors in dyeing are the 100℃ dyeingtemperature and the time for heat preservation;moveover,adding sodium sulphate will help leveldyeing but lower the dye-uptake.
文摘T-wave alternans (TWA) in surface electrocardiograph (ECG) signal is considered a marker of abnormal ventricular function which may be associated with ventricular tachy- cardia. Several methods have been developed in recent years to evaluate the important feature. One such method is known as modified moving average (MMA) analysis, which performs well for different levels of TWA, but it is sensitive to the noise in T-waves. In this paper we propose an improved MMA algorithm, which adds a stage of T-wave curve fitting for the MMA method before intermediate averaging. The curve fitting is performed by means of least square method technique. Our assessment study demon- strates the improved performance.
文摘There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far: existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.
基金funded by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant Number 107.02-2019.300.
文摘A new approach for predicting forming limit curves(FLCs)at elevated temperatures was proposed herein.FLCs are often used to predict failure and determine the optimal forming parameters of automotive parts.First,a graphical method based on a modified maximum force criterion was applied to estimate the FLCs of 22MnB5 boron steel sheets at room temperature using various hardening laws.Subsequently,the predicted FLC data at room temperature were compared with corresponding data obtained from Nakazima's tests to obtain the best prediction.To estimate the FLC at elevated temperatures,tensile tests were conducted at various temperatures to determine the ratios of equivalent fracture strains between the corresponding elevated temperatures and room temperature.FLCs at elevated temperatures could be established based on obtained ratios.However,the predicted FLCs at elevated temperatures did not agree well with the corresponding FLC experimental data of Zhou et al.A new method was proposed herein to improve the prediction of FLCs at elevated temperatures.An FLC calculated at room tem-perature was utilized to predict the failure of Nakazima's samples via finite element simulation.Based on the simulation results at room temperature,the mathematical relationships between the equivalent ductile fracture strain versus stress triaxiality and strain ratio were established and then combined with ratios between elevated and room temperatures to calculate the FLCs at different temperatures.The predicted FLCs at elevated temperatures agree well with the corresponding experimental FLC data.