Effect of material damage on forming limits of voided anisotropic sheet metals
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Effect of Material Damage on Forming Limits of Voided Anisotropic Sheet Metals YOUNG-SUK KIM, SUNG-YEUN WON, and KYOUNG-HOAN NA Most failures of ductile materials in metal-forming processes occur due to material damage evolution (void nucleation, growth, and coalescence). The current article examines the modified yield function of Liao et al., in conjunction with Hosford’s yield criterion, to clarify the plastic-deformation characteristic of voided anisotropic sheet metals. As such, the void growth of an anisotropic sheet under biaxial tensile loading and the damage effect of void growth on the forming limits of sheet metals are investigated. Plus, the process length defining the neck geometry is included in the Marciniak and Kuczynski (M-K) model to incorporate the effect of triaxial stress in a necked region on the forming limits. The predicted forming limits were compared with experimental data, and a satisfactory agreement was obtained.
I. THEORETICAL ANALYSIS
IN sheet metal–forming processes, the formability of sheet metals is limited by the occurrence of internal damage evolution, which eventually yields a localized necking failure. The formability of sheet metals is often evaluated by using a strain analysis based on the concept of forming-limit diagrams (FLDs), which defines the maximum deformable strains before a localized neck and final failure occur. Marciniak and Kuczynski (M-K)[1] analyzed the causes of necking failure and proposed an analytical model, the M-K model, to theoretically predict the forming limit of a sheet with an initial local inhomogeneity. Azrin and Backofen[2] also performed experiments to investigate the M-K model of localized necking. The experiments showed that as the deformation proceeds, the strain state in the necking zone shifts to the plane-strain state, yet required an unrealistically large imperfection for a meaningful prediction of FLDs based on the M-K model. Moreover, when the M-K model uses a quadratic anisotropic yield criterion, this produces discrepancies between the predicted and measured forming-limit strains for a rolled sheet material with a normal anisotropy (R) less than unity, e.g., aluminum alloys and brass. To overcome this drawback, Stroen and Rice[3] developed a localized-necking model based on the bifurcation theory for a material with a vertex formation on its yield surface. Zhao et al.[4] also calculated the limit strains using the limit-stress concept. A qualitative improvement in predicting the forminglimit strains for materials where R < 1 was exhibited when using the nonquadratic anisotropic yield criterion.[5–8] Other experimental research[9,10,11] has shown that the density of a sheet material changes with straining, and there is some correlation between the density changes and the limit strains. The change in density or void volume fraction, which may govern the necking process, can result from the growth of initially existing voids and nucleation of voids in the early stages of deformation. Commonly, microvoids nucleate at YOUNG-SUK KIM, Profes
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