Localized necking criterion for strain-softening materials

The paper presents the development of a localized necking criterion based on the singularity of acoustic tensor This criterion is applicable to materials exhibiting strain-softening behavior The tensor form of the criterion is deployed in simple mathematical expressions, based on which the forming limit diagrams (FLDs) of strain-softening materials can be determined. At the left-hand side of a FLD, or the negative strain ratio region, a closed-form expression of localized band inclination is derived as a function of the strain-ratio value. At the right-hand side of a FLD, or the positive strain ratio regions, the localized band is assumed to be perpendicular to major strain according to the MK [Marciniak and Kuczynski (1967)] model. On both sides of the FLD, the localized necking criteria are analytically expressed by elements of tangent modulus matrix. For the sake of illustration of the proposed criterion, a special case of localized necking employing associative and isotropic plasticity is presented. The material chosen for the illustration is AA-6061 at an elevated temperature. The proposed criterion is also applicable to the formability of other metals at high temperatures and other strain-softening materials such as rocks.