Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and...Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and useful tool to predict the forming limit in the sheet metal forming processes. In the present study, FLD has been determined experimentally for Ti?6Al?4V alloy at 400 °C by conducting a Nakazima test with specimens of different widths. Additionally, for theoretical FLD prediction, various anisotropic yield criteria (Barlat 1989, Barlat 1996, Hill 1993) and different hardening models viz., Hollomon power law (HPL), Johnson?Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-Arr) models have been developed. Theoretical FLDs have been determined using Marciniak and Kuczynski (M?K) theory incorporating the developed yield criteria and constitutive models. It has been observed that the effect of yield model is more pronounced than the effect of constitutive model for theoretical FLDs prediction. However, the value of thickness imperfection factor (f0) is solely dependent on hardening model. Hill (1993) yield criterion is best suited for FLD prediction in the right hand side region. Moreover, Barlat (1989) yield criterion is best suited for FLD prediction in left hand side region. Therefore, the proposed hybrid FLD in combination with Barlat (1989) and Hill (1993) yield models with m-Arr hardening model is in the best agreement with experimental FLD.展开更多
Forming limit of metal foil is an important index to evaluate its formability,and is of considerable significance to improve the quality of products.The ductile fracture(DF)behavior in microscale plastic deformation i...Forming limit of metal foil is an important index to evaluate its formability,and is of considerable significance to improve the quality of products.The ductile fracture(DF)behavior in microscale plastic deformation is remarkably affected by the geometry and grain size.To explore the size-dependent forming limit curve(FLC),the Holmberg and Marciniak tests of SUS304 foils with the thicknesses of less than 0.1 mm and diverse grain sizes were performed.In addition,the validity and feasibility of three types of existing failure models including Swift/Hill,MarciniakKuczynski(M-K)and DF criteria for predicting the micro-scaled FLCs were discussed.It is found that the Swift/Hill model possesses the worst accuracy with predicting deviation above 50%.Four classical DF criteria including Freudenthal,Ayada,Brozzo and Oh show great difference,and Oh model considering plastic anisotropy presents the best precision.The predicted deviation of M-K model is aggravated with increasing grain size and decreasing foil thickness,which is attributed to the intensified free surface roughening and transformation of fracture mechanism with miniaturization.This research thus provides a deeper understanding and valuable reference for the widespread application of FLC in microforming.展开更多
基金The financial support received for this research work from Department of Science and Technology (DST), Government of India, SERB-DST, SR/FTP/ETA0056/2011
文摘Forming limit diagram (FLD) is an important performance index to describe the maximum limit of principal strains that can be sustained by sheet metals till to the onset of localized necking. It offers a convenient and useful tool to predict the forming limit in the sheet metal forming processes. In the present study, FLD has been determined experimentally for Ti?6Al?4V alloy at 400 °C by conducting a Nakazima test with specimens of different widths. Additionally, for theoretical FLD prediction, various anisotropic yield criteria (Barlat 1989, Barlat 1996, Hill 1993) and different hardening models viz., Hollomon power law (HPL), Johnson?Cook (JC), modified Zerilli–Armstrong (m-ZA), modified Arrhenius (m-Arr) models have been developed. Theoretical FLDs have been determined using Marciniak and Kuczynski (M?K) theory incorporating the developed yield criteria and constitutive models. It has been observed that the effect of yield model is more pronounced than the effect of constitutive model for theoretical FLDs prediction. However, the value of thickness imperfection factor (f0) is solely dependent on hardening model. Hill (1993) yield criterion is best suited for FLD prediction in the right hand side region. Moreover, Barlat (1989) yield criterion is best suited for FLD prediction in left hand side region. Therefore, the proposed hybrid FLD in combination with Barlat (1989) and Hill (1993) yield models with m-Arr hardening model is in the best agreement with experimental FLD.
基金funding support to this research from the National Natural Science Foundation of China(Nos.51605018 and 51635005)Beijing Municipal Natural Science Foundation of China(No.3172022)。
文摘Forming limit of metal foil is an important index to evaluate its formability,and is of considerable significance to improve the quality of products.The ductile fracture(DF)behavior in microscale plastic deformation is remarkably affected by the geometry and grain size.To explore the size-dependent forming limit curve(FLC),the Holmberg and Marciniak tests of SUS304 foils with the thicknesses of less than 0.1 mm and diverse grain sizes were performed.In addition,the validity and feasibility of three types of existing failure models including Swift/Hill,MarciniakKuczynski(M-K)and DF criteria for predicting the micro-scaled FLCs were discussed.It is found that the Swift/Hill model possesses the worst accuracy with predicting deviation above 50%.Four classical DF criteria including Freudenthal,Ayada,Brozzo and Oh show great difference,and Oh model considering plastic anisotropy presents the best precision.The predicted deviation of M-K model is aggravated with increasing grain size and decreasing foil thickness,which is attributed to the intensified free surface roughening and transformation of fracture mechanism with miniaturization.This research thus provides a deeper understanding and valuable reference for the widespread application of FLC in microforming.
