A field experiment was conducted in a manural loesial soil in middle of Shaanxi Province ofChina, a sub-humid area prone to drought, to study the effects of rainwater-harvestingcultivation on water use efficiency (WUE...A field experiment was conducted in a manural loesial soil in middle of Shaanxi Province ofChina, a sub-humid area prone to drought, to study the effects of rainwater-harvestingcultivation on water use efficiency (WUE) and yield of winter wheat. Ridge-furrow tillage wasused, the ridge being mulched by plastic sheets for rainwater harvesting while seeding in thefurrows. Results showed that from sowing to reviving stage of winter wheat, water stored in 0-100 cm layer was significantly decreased whereas that in 100-200 cm layer did not change.Compared to the non-mulching, plastic mulch retained 6.5 mm more water as an average of the twoN rate treatments, having a certain effect on conservation of soil moisture. In contrast, atharvest, water was remarkably reduced in both the 0-100 cm and the 100-200 cm layers, andmulched plots consumed 34.8 mm more water as an average of the two treatments: low N rate (75kg N ha-1) with low plant density (2 300 000 plants ha-1) and high N rate (225 kg N ha-1)with highplant density (2 800 000 plants ha-1), in 0-200 cm layer than those without mulching, the formerbeing beneficial to plants in utilization of deep layer water. Mulching was significant inharvesting water and in increase of yield. Mulched with plastic sheets, biological and grainyields were 22.5 and 22.6% higher for the average of the high N rate than for the low N rate,and the high N rate with low plant density was 29.8 and 29.1% higher in both biological andgrain yields than that of the low N rate with low plant density. With high N rate and high plantdensity, the mulched biological and grain yields were 39.5 and 28.9% higher than the correspondingtreatments without mulching. Of the treatments, that with high N rate and low plant density wasthe highest in both biological and grain yields, and the water use efficiency reached 43.7 kgmm-1 ha-1 for biological yield and 22 kg mm-1 ha-1 for grain yield, being the highest WUE reportedin the world up to now.展开更多
The increasing demand of water in the country highlights the need to introduce low-input and water saving technologies for agricultural sustainability and crop production,mainly in semi-arid region.A study was conduct...The increasing demand of water in the country highlights the need to introduce low-input and water saving technologies for agricultural sustainability and crop production,mainly in semi-arid region.A study was conducted to minimize deep percolation losses from the furrow bottom under two different irrigation treatments viz.(1)furrow bottom with plastic sheet(T1)and(2)furrow bottom without plastic Sheet(T0).The physical and chemical analyses of soil profile were taken at a depth of 0-80 cm before and after crop harvesting.The dry density of soil slightly increased(0.01 g/cm^(3))under both treatments,while soil pH decreased under T1.The average yield was 8332 kg/hm^(2) and 7575 kg/hm^(2),with 21.56 m^(3) and 31.09 m^(3) total volume of irrigation water applied under T1and T0,respectively.The saving percentages of water under treatments were 52.22% and 31.00% under T1 and T0 respectively as compared to the saving of water under traditional irrigation practice.Overall,better performance,in terms of crop production and water saving,was obtained with use of plastic sheet integrated with bottom of furrows.Hence,it is suggested that the furrow irrigation method with plastic sheet may be used to preventing moisture and minimize deep percolation losses from furrow bottom.展开更多
Twenty-one square concrete columns were constructed and tested. The testing results indicate that bonded carbon fiber reinforced plastics(CFRP) sheets can be used to increase the strength and improve the serviceabilit...Twenty-one square concrete columns were constructed and tested. The testing results indicate that bonded carbon fiber reinforced plastics(CFRP) sheets can be used to increase the strength and improve the serviceability of damaged concrete columns at low temperatures. The failure of the specimens,in most cases,takes place within the middle half of the columns. And the failure of strengthened columns is sudden and explosive. The CFRP sheets increase both the axial load capacity and the ultimate concrete compressive strain of the columns. The ultimate loads of strengthened columns at-10,0 and 10 ℃ increase averagely by 9.09%,6.63% and 17.83%,respectively,as compared with those of the control specimens. The axial compressive strength of strengthened columns is related to the curing temperatures. The improvement of axial compressive strength decreases with reducing temperature,and when the temperature drops to a certain value,the improvement increases with falling temperature.展开更多
Analysis, evaluation and interpretation of measured signals become important components in engineering research and practice, especially for material characteristic parameters which can not be obtained directly by exp...Analysis, evaluation and interpretation of measured signals become important components in engineering research and practice, especially for material characteristic parameters which can not be obtained directly by experimental measurements. The present paper proposes a hybrid-inverse analysis method for the identification of the nonlinear material parameters of any individual component from the mechanical responses of a global composite. The method couples experimental approach, numerical simulation with inverse search method. The experimental approach is used to provide basic data. Then parameter identification and numerical simulation are utilized to identify elasto-plastic material properties by the experimental data obtained and inverse searching algorithm. A numerical example of a stainless steel clad copper sheet is consid- ered to verify and show the applicability of the proposed hybrid-inverse method. In this example, a set of material parameters in an elasto-plastic constitutive model have been identified by using the obtained experimental data.展开更多
A rate-independent polycrystalline plasticity constitutive model considering self and latent hardening was developed. Next, a new orientation probability assignment method was proposed and the crystal orientations wer...A rate-independent polycrystalline plasticity constitutive model considering self and latent hardening was developed. Next, a new orientation probability assignment method was proposed and the crystal orientations were assigned to FE integration points, which represent crystals and can rotate individually. Then cup drawing of FCC aluminum sheet was studied using crystalline plasticity finite element analysis. The results show that the validity of proposed model is proved through comparison between numerical results and experimental ones. {001}<110> texture can lead to earing at 45° direction, while {124}<211> texture at 0° and 90° directions. For the rolled aluminum sheet, which contains strong {001}<110> texture, earing is formed at 45° direction after cup drawing. For the annealing aluminum sheet, due to the balance between two main textures, the flange earing tendency is not obvious.展开更多
Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper.Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its...Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper.Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its applications on the prediction of sheet forming process. Then, a new macroscopic constitutive model is introduced, which possesses an enhanced description capacity of tension/compression anisotropy and anisotropic hardening. In order to take into account the twinning process of hexagonal close-packed material, a modified hierarchical multi-scale model is also established with adequate accuracy in a shorter computational time. The advanced forming limit of sheet metal, mainly about aluminum alloy, is also investigated. Besides the above theory developments, some new sheet metal forming technologies are reviewed simultaneously. The warm forming technology of Mg alloy is discussed. New processes to form sheet parts and to bend tubes are proposed by using hard granules. On the other hand, a new kind of ultra-high-strength steel based on typical22 Mn B5 by introducing more residual austenite and Cu-rich phase to increase the elongation and strength and its novel forming method that integrates hot stamping and quenching participation are proposed. Progresses in sheet hydroforming,press forging and electromagnetic forming of sheet metal parts are also summarized.展开更多
A thorough understanding of the texture evolution of near-αtitanium alloys during the hot metal forming can help obtain an optimal crystallographic texture and material performance.The strain state has an obvious eff...A thorough understanding of the texture evolution of near-αtitanium alloys during the hot metal forming can help obtain an optimal crystallographic texture and material performance.The strain state has an obvious effect on the texture evolution of near-αtitanium alloys during the hot metal forming.In this paper,the texture evolution of a near-αTA15 titanium alloy during the hot metal forming under different strain states were discussed based on the crystal plasticity finite element method.It is found that the basal and prismatic slip systems are regarded as the dominant slip modes due to the similar low critical resolved shear stress during the hot metal forming of the TA15 sheet rotating the lattice around the[1010]and 0001 axis,respectively.Once both of them cannot be activated,the pyramidal-2 slipping occurs rotating the lattice around the[1010]axis.The relationship between the texture evolution and strain state is established.All the(0001)orientations form a band perpendicular to the direction of the first principal strain.The width of the band along the direction of the second principal strain depends on the ratio of the compressive effect to the tensile effect of the second principal strain.This relationship can help control the crystallographic texture and mechanical properties of the titanium alloys component during the hot metal forming.展开更多
The flow stress feature of aluminum sheet used for pressure can during plastic deformation at elevated temperature was studied by isothermal compression test using Gleeble 1 500 dynamic materials testing machine. The ...The flow stress feature of aluminum sheet used for pressure can during plastic deformation at elevated temperature was studied by isothermal compression test using Gleeble 1 500 dynamic materials testing machine. The experimental results show that the steady state deformation is remarkable when the material is deformed in the temperature range of 350～500 ℃ at strain rates within the range of 10 -2 ～10.0 s -1 . The material is sensitive to positive strain rate. A hyperbolic sine relationship is found to correlate well the flow stress with the strain rate, and an Arrhenius relationship with the temperature. Semi empirical constitutive equations of the flow stress are derived from all experimental data for tested material during plastic deformation at elevated temperature by polyelement linear regression analysis. [展开更多
A semi analytical method was proposed to solve the mechanics problem of stamping a sheet on elastic die. The sheet was divided into four parts according to its deformation and contact with the punch and elastic die. ...A semi analytical method was proposed to solve the mechanics problem of stamping a sheet on elastic die. The sheet was divided into four parts according to its deformation and contact with the punch and elastic die. Analytical solutions were derived individually for each part by using elastic large deflection and plastic large deformation. Solutions were found out with MATLAB by developing a numerical algorithm. Interface forces were obtained by iteration under the compatibility conditions between the neighboring parts of the sheet. Computation shows the method is efficient.展开更多
The behavior of flow stress of Al sheets used for pressure can prepared by different melt-treatment during plastic deformation at elevated temperature was studied by isothermal compression test using Gleeble1500 dynam...The behavior of flow stress of Al sheets used for pressure can prepared by different melt-treatment during plastic deformation at elevated temperature was studied by isothermal compression test using Gleeble1500 dynamic hot-simulation testing machine. The results show that the AI sheets possess the remarkable characteristic of steady state flow stress when they are deformed in the temperature range of 350-500℃ at strain rates within the range of 0.01-10.0s^-1. A hyperbolic sine relationship is found to correlate well the flow stress with the strain rate, and an Arrhenius relationship with the temperature, which implies that the process of plastic deformation at elevated temperature for this material is thermally activated. Compared with the AI pieces prepared by no or conventional melt-treatment, hot deformation activation energy of AI sheets prepared by high-efficient melt-treatment is the smallest （ Q= 168.0kJ/mol）, which reveals that the hot working formability of this material is very better, and has directly to do with the effective improvement of its metallurgical quality.展开更多
To investigate the influence of magnitude and distribution of the transverse normal pressure on deformation behavior of sheet metal,viscous pressure bulge test (VPB) of overlapping sheet metals is proposed,where the o...To investigate the influence of magnitude and distribution of the transverse normal pressure on deformation behavior of sheet metal,viscous pressure bulge test (VPB) of overlapping sheet metals is proposed,where the overlapped sheet metal is deformed under the dual-sided normal pressure provided by viscous medium and the overlapping sheet.The transverse normal pressure loading features provided by overlapping sheet metals are first simulated by DEFORM-2D.It shows that the magnitude and space distribution of transverse normal pressure are dependent on strain hardening exponent n-,strength coefficient K-and thickness t-values of the overlapping sheet metal.Based on the stress,deviator stress and strain distribution resulted from the finite element simulation,it indicated that the uniform transverse normal pressure has no effect on deviator stress,the figure and strain distribution of bulge specimens have no change.The non-uniform transverse normal pressure can remarkably change the figure and metal flow of specimens,and the formability of sheet metal can be improved by controlling the transverse normal pressure distribution.展开更多
This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool m...This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.展开更多
An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted in a failure prediction methodology that can be used to investigate the failure of sheet metals under forming operations. This...An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted in a failure prediction methodology that can be used to investigate the failure of sheet metals under forming operations. This failure prediction methodology is developed based on the Marciniak-Kuczynski approach by assuming a slightly higher void volume fraction inside randomly oriented imperfecte analysis. Here, a nonproportional deformation history including relative rotation of principal stretch directions is identified in a selected critical element of an aluminum sheet from a FEM fender forming simulation. Based on the failure prediction methodology, the failure of the critical sheet element is investigated under the non-proportional deformation history. The results show that thiven non-proportional deformation history.展开更多
基金part of the projects(49890330,30230230 and 30070429)supported by the National Natural Science Foundation of China(NSFC)project(G1999011707)supported by the National Key Basic Research Support Funds,China(NKBRSF).
文摘A field experiment was conducted in a manural loesial soil in middle of Shaanxi Province ofChina, a sub-humid area prone to drought, to study the effects of rainwater-harvestingcultivation on water use efficiency (WUE) and yield of winter wheat. Ridge-furrow tillage wasused, the ridge being mulched by plastic sheets for rainwater harvesting while seeding in thefurrows. Results showed that from sowing to reviving stage of winter wheat, water stored in 0-100 cm layer was significantly decreased whereas that in 100-200 cm layer did not change.Compared to the non-mulching, plastic mulch retained 6.5 mm more water as an average of the twoN rate treatments, having a certain effect on conservation of soil moisture. In contrast, atharvest, water was remarkably reduced in both the 0-100 cm and the 100-200 cm layers, andmulched plots consumed 34.8 mm more water as an average of the two treatments: low N rate (75kg N ha-1) with low plant density (2 300 000 plants ha-1) and high N rate (225 kg N ha-1)with highplant density (2 800 000 plants ha-1), in 0-200 cm layer than those without mulching, the formerbeing beneficial to plants in utilization of deep layer water. Mulching was significant inharvesting water and in increase of yield. Mulched with plastic sheets, biological and grainyields were 22.5 and 22.6% higher for the average of the high N rate than for the low N rate,and the high N rate with low plant density was 29.8 and 29.1% higher in both biological andgrain yields than that of the low N rate with low plant density. With high N rate and high plantdensity, the mulched biological and grain yields were 39.5 and 28.9% higher than the correspondingtreatments without mulching. Of the treatments, that with high N rate and low plant density wasthe highest in both biological and grain yields, and the water use efficiency reached 43.7 kgmm-1 ha-1 for biological yield and 22 kg mm-1 ha-1 for grain yield, being the highest WUE reportedin the world up to now.
基金Authors wish to thank the National Natural Science Foundation of China(Grant No.51275250)for supporting.
文摘The increasing demand of water in the country highlights the need to introduce low-input and water saving technologies for agricultural sustainability and crop production,mainly in semi-arid region.A study was conducted to minimize deep percolation losses from the furrow bottom under two different irrigation treatments viz.(1)furrow bottom with plastic sheet(T1)and(2)furrow bottom without plastic Sheet(T0).The physical and chemical analyses of soil profile were taken at a depth of 0-80 cm before and after crop harvesting.The dry density of soil slightly increased(0.01 g/cm^(3))under both treatments,while soil pH decreased under T1.The average yield was 8332 kg/hm^(2) and 7575 kg/hm^(2),with 21.56 m^(3) and 31.09 m^(3) total volume of irrigation water applied under T1and T0,respectively.The saving percentages of water under treatments were 52.22% and 31.00% under T1 and T0 respectively as compared to the saving of water under traditional irrigation practice.Overall,better performance,in terms of crop production and water saving,was obtained with use of plastic sheet integrated with bottom of furrows.Hence,it is suggested that the furrow irrigation method with plastic sheet may be used to preventing moisture and minimize deep percolation losses from furrow bottom.
基金Project(04043076) supported by the Outstanding Youth Foundation for Scientific and Technological Research of Anhui Province, ChinaProject(2007jq1035) supported by the Scientific Research Projects for Young College Teachers of Anhui Province, China
文摘Twenty-one square concrete columns were constructed and tested. The testing results indicate that bonded carbon fiber reinforced plastics(CFRP) sheets can be used to increase the strength and improve the serviceability of damaged concrete columns at low temperatures. The failure of the specimens,in most cases,takes place within the middle half of the columns. And the failure of strengthened columns is sudden and explosive. The CFRP sheets increase both the axial load capacity and the ultimate concrete compressive strain of the columns. The ultimate loads of strengthened columns at-10,0 and 10 ℃ increase averagely by 9.09%,6.63% and 17.83%,respectively,as compared with those of the control specimens. The axial compressive strength of strengthened columns is related to the curing temperatures. The improvement of axial compressive strength decreases with reducing temperature,and when the temperature drops to a certain value,the improvement increases with falling temperature.
基金supported by the National Natural Science Foundation of China (Nos.10732080 and 10572102)National Basic Research Program of China (No.2007CB714000)
文摘Analysis, evaluation and interpretation of measured signals become important components in engineering research and practice, especially for material characteristic parameters which can not be obtained directly by experimental measurements. The present paper proposes a hybrid-inverse analysis method for the identification of the nonlinear material parameters of any individual component from the mechanical responses of a global composite. The method couples experimental approach, numerical simulation with inverse search method. The experimental approach is used to provide basic data. Then parameter identification and numerical simulation are utilized to identify elasto-plastic material properties by the experimental data obtained and inverse searching algorithm. A numerical example of a stainless steel clad copper sheet is consid- ered to verify and show the applicability of the proposed hybrid-inverse method. In this example, a set of material parameters in an elasto-plastic constitutive model have been identified by using the obtained experimental data.
文摘A rate-independent polycrystalline plasticity constitutive model considering self and latent hardening was developed. Next, a new orientation probability assignment method was proposed and the crystal orientations were assigned to FE integration points, which represent crystals and can rotate individually. Then cup drawing of FCC aluminum sheet was studied using crystalline plasticity finite element analysis. The results show that the validity of proposed model is proved through comparison between numerical results and experimental ones. {001}<110> texture can lead to earing at 45° direction, while {124}<211> texture at 0° and 90° directions. For the rolled aluminum sheet, which contains strong {001}<110> texture, earing is formed at 45° direction after cup drawing. For the annealing aluminum sheet, due to the balance between two main textures, the flange earing tendency is not obvious.
文摘Developments of new sheet metal forming technology and theory in China are reviewed in detail in this paper.Advances of crystal plasticity on the deformation mechanism of Mg alloy are firstly described, especially its applications on the prediction of sheet forming process. Then, a new macroscopic constitutive model is introduced, which possesses an enhanced description capacity of tension/compression anisotropy and anisotropic hardening. In order to take into account the twinning process of hexagonal close-packed material, a modified hierarchical multi-scale model is also established with adequate accuracy in a shorter computational time. The advanced forming limit of sheet metal, mainly about aluminum alloy, is also investigated. Besides the above theory developments, some new sheet metal forming technologies are reviewed simultaneously. The warm forming technology of Mg alloy is discussed. New processes to form sheet parts and to bend tubes are proposed by using hard granules. On the other hand, a new kind of ultra-high-strength steel based on typical22 Mn B5 by introducing more residual austenite and Cu-rich phase to increase the elongation and strength and its novel forming method that integrates hot stamping and quenching participation are proposed. Progresses in sheet hydroforming,press forging and electromagnetic forming of sheet metal parts are also summarized.
基金financially supported by the National Natural Science Foundation of China(No.51401065).
文摘A thorough understanding of the texture evolution of near-αtitanium alloys during the hot metal forming can help obtain an optimal crystallographic texture and material performance.The strain state has an obvious effect on the texture evolution of near-αtitanium alloys during the hot metal forming.In this paper,the texture evolution of a near-αTA15 titanium alloy during the hot metal forming under different strain states were discussed based on the crystal plasticity finite element method.It is found that the basal and prismatic slip systems are regarded as the dominant slip modes due to the similar low critical resolved shear stress during the hot metal forming of the TA15 sheet rotating the lattice around the[1010]and 0001 axis,respectively.Once both of them cannot be activated,the pyramidal-2 slipping occurs rotating the lattice around the[1010]axis.The relationship between the texture evolution and strain state is established.All the(0001)orientations form a band perpendicular to the direction of the first principal strain.The width of the band along the direction of the second principal strain depends on the ratio of the compressive effect to the tensile effect of the second principal strain.This relationship can help control the crystallographic texture and mechanical properties of the titanium alloys component during the hot metal forming.
基金Project (E981 0 0 0 3)supportedbytheNaturalScienceFoundationofFujianProvince P .R .China
文摘The flow stress feature of aluminum sheet used for pressure can during plastic deformation at elevated temperature was studied by isothermal compression test using Gleeble 1 500 dynamic materials testing machine. The experimental results show that the steady state deformation is remarkable when the material is deformed in the temperature range of 350～500 ℃ at strain rates within the range of 10 -2 ～10.0 s -1 . The material is sensitive to positive strain rate. A hyperbolic sine relationship is found to correlate well the flow stress with the strain rate, and an Arrhenius relationship with the temperature. Semi empirical constitutive equations of the flow stress are derived from all experimental data for tested material during plastic deformation at elevated temperature by polyelement linear regression analysis. [
文摘A semi analytical method was proposed to solve the mechanics problem of stamping a sheet on elastic die. The sheet was divided into four parts according to its deformation and contact with the punch and elastic die. Analytical solutions were derived individually for each part by using elastic large deflection and plastic large deformation. Solutions were found out with MATLAB by developing a numerical algorithm. Interface forces were obtained by iteration under the compatibility conditions between the neighboring parts of the sheet. Computation shows the method is efficient.
基金supported by the Fujian Provincial Natural Science Foundation(No.E0210011)the Educational Commission of Fujian province(No.K20014).
文摘The behavior of flow stress of Al sheets used for pressure can prepared by different melt-treatment during plastic deformation at elevated temperature was studied by isothermal compression test using Gleeble1500 dynamic hot-simulation testing machine. The results show that the AI sheets possess the remarkable characteristic of steady state flow stress when they are deformed in the temperature range of 350-500℃ at strain rates within the range of 0.01-10.0s^-1. A hyperbolic sine relationship is found to correlate well the flow stress with the strain rate, and an Arrhenius relationship with the temperature, which implies that the process of plastic deformation at elevated temperature for this material is thermally activated. Compared with the AI pieces prepared by no or conventional melt-treatment, hot deformation activation energy of AI sheets prepared by high-efficient melt-treatment is the smallest （ Q= 168.0kJ/mol）, which reveals that the hot working formability of this material is very better, and has directly to do with the effective improvement of its metallurgical quality.
文摘To investigate the influence of magnitude and distribution of the transverse normal pressure on deformation behavior of sheet metal,viscous pressure bulge test (VPB) of overlapping sheet metals is proposed,where the overlapped sheet metal is deformed under the dual-sided normal pressure provided by viscous medium and the overlapping sheet.The transverse normal pressure loading features provided by overlapping sheet metals are first simulated by DEFORM-2D.It shows that the magnitude and space distribution of transverse normal pressure are dependent on strain hardening exponent n-,strength coefficient K-and thickness t-values of the overlapping sheet metal.Based on the stress,deviator stress and strain distribution resulted from the finite element simulation,it indicated that the uniform transverse normal pressure has no effect on deviator stress,the figure and strain distribution of bulge specimens have no change.The non-uniform transverse normal pressure can remarkably change the figure and metal flow of specimens,and the formability of sheet metal can be improved by controlling the transverse normal pressure distribution.
文摘This study is concerned with the problems of contact in the process of numerical simulation of sheet metal forming in rigid visco-plastic shell FEM. In respect of analysis of sheet deep drawing process,for the tool model described by triangular elements, a kind of contact judging algorithm about the correlation between the node of deformed mesh and the triangular element of a tool is presented. In SPF/DB Lagrangian multiplier method is adopted to solve the contact problem between deformed meshes, and a new reliable practical dynamic contact checking algorithm is presented. As computation examples, the simulation results of metal sheet deep drawing and SPF/DB are introduced in this paper.
文摘An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted in a failure prediction methodology that can be used to investigate the failure of sheet metals under forming operations. This failure prediction methodology is developed based on the Marciniak-Kuczynski approach by assuming a slightly higher void volume fraction inside randomly oriented imperfecte analysis. Here, a nonproportional deformation history including relative rotation of principal stretch directions is identified in a selected critical element of an aluminum sheet from a FEM fender forming simulation. Based on the failure prediction methodology, the failure of the critical sheet element is investigated under the non-proportional deformation history. The results show that thiven non-proportional deformation history.
