A mesoscopic approach for predicting sheet metal formability

Abstract

A mesoscopic approach for constructing a forming limit diagram (FLD) is developed. The approach is based on the concept of a unit cell. The unit cell is macroscopically infinitely small and thus represents a material point in the sheet, and is microscopically finitely large and thus contains a sufficiently large number of grains. The responses of the unit cell under biaxial tension are calculated using the finite element method. Each element of a mesh/unit cell represents an orientation and the constitutive response at an integration point is described by the single crystal plasticity theory. It is demonstrated that the limit strains are the natural outcomes of the mesoscopic approach, and the artificial initial imperfection necessitated by the macroscopic M-K approach is not relevant in the mesoscopic approach. The effects of strain-rate sensitivity, single slip hardening and latent hardening, texture evolution, crystal elasticity and spatial orientation distribution on necking are discussed. Numerical results based on the mesoscopic approach are compared with experimental data.

Experimental analysis and theoretical predictions of the limit strains of a hot-dip galvanized interstitial-free steel sheet

“…A quasi-random arrangement of hard elastic inclusions was also considered in finite element (FE) calculations to generate inhomogeneous strain fields leading to necking of the representative volume element 24,25 . Wu et al 26 performed FE computations of the response of a macroscopically infinitely small unit cell made of an assembly of elements, where each element represents a grain following the constitutive laws of crystal plasticity. The orientation distribution of grains is representative of a given texture.…”

Prediction of Forming Limit Diagrams in Sheet Metals Using Different Yield Criteria

“…When the condition described by Eq. [9] is satisfied, phase I terminates. The termination point is named H.…”

“…Therefore, the Considere condition (Eq. [9]) not only specifies phase I termination but remains valid throughout phase II at the critical cross sections that are deforming faster than the others.…”

“…Although they are not totally independent from each other, they are distinguishable from deformation localization and failure mode view points. Different models such as Marciniak-Kuczynski (MK) [4] and crystal plasticity [5][6][7][8][9][10] are considered in the literature. In the MK model, the assumption of the existence of an initial imperfection is necessary.…”

Self-Consistent Homogenization Methods for Predicting Forming Limits of Sheet Metal

“…They claim that the development of texture causes deterioration of the material. On the other hand, Wu et al (2004b) use a mesoscopic approach and a Taylor homogenization scheme to show that texture evolution increases the limit-strains in the biaxial zone. Finally, Inal et al (2005) recently analyzed these two studies and their opposite conclusions, adding a study of how texture evolution in BCC materials affects the FLD.…”