Application of Case I and Case II of Hill’s 1979 Yield Criterion to Predict FLD

Forming limit diagrams (FLDs) are calculated based on both the Marciniak and Kuczynski (M-K)  model and the analysis proposed by Jones and Gillis (J-G). J-G analysis consisted of plastic deformation approximation by three deformation phases. These phases consisted of homogeneous deformation up to the maximum load (Phase I), deformation localization under constant load (phase II) and local necking with a precipitous drop in load (phase III). In the present study, case I and case II of Hill’s non-quadratic yield function were used for the first time. It is assumed that sheets obey the power-law flow rule and in-plane isotropy is satisfied. Calculated FLDs from this analysis are compared with the experimental data of aluminum alloys 3003-O, 2036-T4 and AK steel reported by other references.  Calculated FLDs showed that limit strain predictions based on case I and case II of the Hill’s non-quadratic yield function are fairly well correlated to experiments when J-G model is used.