An improved dislocation model for the stress-strain behaviour of polycrystalline α-Fe

A physically based gradient plasticity theory

“…(6) shows that the rate of SSDs, _ q S , depends on the strain rate, which means that dislocations are less mobile when the material hardens. Therefore, one can assume that the mobile dislocation density is much smaller than the immobile dislocation density and it is strain independent (Bergstrom and Hallen, 1982).…”

Numerical and experimental investigations of forming limit diagrams in metal sheets

“…(2) and (3) can now be combined to express the equivalent stress,σ, in terms of variations iṅ ε andε. This model gives a good description for the deep drawing quality steel (DDQS) [28], while for the aluminum more advanced models are sometimes advocated. Eqs.…”

Analysis of Nonisothermal Deep Drawing of Aluminum Alloy Sheet With Induced Anisotropy and Rate Sensitivity at Elevated Temperatures

“…They also showed that the modified Khan-Huang-Liang constitutive model [23] is able to predict the strain-rate and temperature dependent responses reasonably well. The reported constitutive fitting exercises have identified the Bergstrom and Hallen [24] or Nes [25] models as appropriate hardening models for use in numerical simulation of warm forming, van den Boogaard et al [7] showed that Bergstrom and Hallen [24] model is able to model fiow stress of 5000-series aluminum alloys at elevated temperatures up to 200 °C and medium strain rates. McKinley et al [8] used the Bergstrom and Hallen [24] model for a 3000 series aluminum alloy sheet and showed that the strain rate and temperature dependence of the fiow stress is captured well.…”

“…A number of previous efforts have reported the application of the Nes/Bergstrom model and also the Barlat-2000 yield surface separately; however, in the current work, a novel constitutive model is implemented that captures the Barlat YLD2000 yield surface [28] in conjunction with the Bergstrom and Hallen [24] hardening model to accurately model aluminum alloy sheet dtiring warm forming.…”

“…Here, the Barlat YLD2000 anisotropic yield criterion [28] is used to capture the plastic induced anisotropy and the Bergstrom [24] isotropic hardening rule to predict the temperature and strain rate sensitivity. The model is implemented as a user material subroutine (UMAT) in LS-DYNA.…”