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 is useful tool to access the forming severity of a drawing or stamping processes. In the present work, FLD has been determined experimentally for Ti-6Al-4 V alloy at 400 °C by conducting a hemispherical dome test with specimens of different widths. Additionally, theoretical FLDs have been determined using Marciniak Kuczynski (M-K) model. Various yield criteria namely: Von Mises, Hill 1948, Hill 1993 and Cazacu Barlat in combination with different hardening models viz., Hollomon power law (HPL), Johnson-Cook (JC), modified Johnson-Cook (m-JC), modified Arrhenius (m-Arr.), modified Zerilli–Armstrong (m-ZA) have been used in M-K analysis for theoretical FLD prediction. The material properties required for determination of yield criteria and hardening models constants have been calculated using uniaxial tensile tests. The predicted theoretical FLDs results are compared with experimental FLD. It can be observed that influence of yield criterion in M-K analysis for theoretical FLD prediction is predominant than the hardening model. Based on the results; it is observed that the theoretical FLD using Cazacu Barlat and Hill 1993 yield criteria with m-Arr. hardening model has a very good agreement with experimental FLD.

Experimental and theoretical investigation of forming limit diagram for Ti-6Al-4 V alloy at warm condition

The forming limit diagram of ferritic stainless steel sheets: Experiments and modeling

Formability analysis of pre-strained AA5754-O sheet metal using Yld96 plasticity theory : role of amount and direction of uni-axial pre-strain

The microstructure and material properties of continuous cast 5052 alloy sheet in as-received condition (as-received sheet) and laboratory cold rolled condition (lab-processed sheet) were investigated after annealing treatment. Microstructural examinations show that the cold rolling process increases the extent of centerline segregation of second-phase particles. The increase in rolling reduction results in a decrease of grain size and a more random distribution of crystallite orientations. Tensile test results indicate that all the sheets exhibit two-stage strain-hardening behavior. Cold rolling increases the total elongation and n2-value in the transverse direction of the lab-processed sheet with a thickness of 1.6 mm. However, further increase in the rolling reduction leads to an increase of UTS with a decrease of elongation and n2-value. Furthermore, from the determined forming limit curves (FLCs), it is found that the 1.6 mm thick lab-processed sheet has better stretchability than the as-received sheet, whereas further cold rolling reduces the level of FLC. The effects of cold rolling on the mechanical property and formability are discussed in terms of the microstructural changes.

Effect of cold rolling on microstructure and material properties of 5052 alloy sheet produced by continuous casting

The limiting value of strain describing necking/failure during a sheet stamping operation is quantified, predicted by the forming limit curve (FLC). The main aim of the present work is to analyse the applicability of the few existing necking criteria, namely the effective strain rate based criterion (ESRC - RC1), major strain rate based criterion (MSRC - RC2), thickness strain rate based criterion (TSRC - RC3), and thickness gradient based criterion (TGNC - RC4), in predicting the forming limit of unwelded and tailor-welded blanks. In the case of unwelded blanks, dry (m 50.12) and low-friction (m 50.02) conditions are simulated and forming limit results are predicted. In the case of tailor-welded blanks, the forming limits of laser-welded steel blanks and friction-stir-welded blanks made of aluminium alloy are predicted using the chosen necking criteria and then compared with results in the literature. The influence of friction on the whole forming limit curve and the non-linearity of strain paths in the stretching side of the forming limit diagram (FLD) are also predicted and discussed. It is found that the FLCs predicted by ESRC, MSRC, TSRC, and TGNC are comparable with experimental FLCs. The predictions are accurate in the low-friction condition, indicating that the necking criteria are also valid under changing friction conditions. Moreover, the overall FLC does not change much with changing friction conditions. The strain paths are non-linear in the dry friction condition, but they become linear in the low-friction condition. In the case of laser- welded blanks, the original strain rate based criteria defined for unwelded blanks under- estimate limit strains on the stretching side of the FLD, where failure near the weld region is witnessed. Hence they are modified as RC1 >25, RC2 >32, and RC3 >32, which show a better prediction level compared with the original criteria. The original and modified limit strain criteria show better correlation with results in the literature and the TGNC in the case of friction-stir-welded blanks modelled using the Hollomon and Swift strain-hardening laws.

S. Mansorzadeh

Papers

Determination of the forming limit diagram for Al 3105 sheet