Complex Unloading Model for Springback Prediction

Springback behavior is an important issue for the automobile industry, particularly with the usage of Advanced High Strength Steels (AHSS).For an accurate prediction of springback, the evolution of Young's modulus and the Bauschinger effect must be considered in the numerical simulations of metal sheet forming processes.The principal objective of this work is to establish a new constitutive model in which the incorporation of nonlinear unloading behavior and the Bauschinger effect enable the model to predict non-proportional hardening and spingback for dual phase steels. Monotonic tension and compression, coaxial tension-compression (T-C), coaxial compression-tension (C-T), and two-stage/non-coaxial tensile tests have been performedfor three grades of dual phase steels: DP590, DP780, and DP980.The reverse or secondstage flow curves have three characteristics: reduced yield stress (Bauschinger effect), rapid transient strain hardening over a few percent strain, and long-term or "permanent" softening.The departure of reverse hardening curves from monotonic ones is larger than with other typical sheet forming alloys, presumably because of the large second-phase martensite particles in dual-phase steels.A Modified constitutive model based on the Chaboche approach (M-C) was used to describe above experimental phenomenon.In addition to one or more standard nonlinear components of the back stress, a linear term was added to represent the "permanent" offset of hardening following a stress reversal.iii The parameters for the model were fit using the monotonic and reverse tensile test results, and the model predictions were then compared with large-strain balanced biaxial bulge test results and with non-coaxial, two-stage tensile tests.All of the effects are captured with reasonable, but not perfect, accuracy.Complex unloading behavior following plastic straining has been reported as a significant challenge to accurate springback prediction.More fundamentally, the nature of the unloading deformation has not been resolved, being variously attributed to nonlinear / reduced modulus elasticity or to inelastic / "microplastic" effects.Unloading-andreloading experiments following tensile deformation showed that a special component of strain, deemed here "Quasi-Plastic-Elastic" ("QPE") strain, has three characteristics.1) It is recoverable, like elastic deformation.2) It dissipates work, like plastic deformation.3) It is rate-independent, contrary to some models of anelasticity to which the unloading modulus effect has been attributed.These characteristics are consistent with dislocation pile-up and relaxation.A consistent, general, continuum constitutive model was derived incorporating elastic, plastic, and QPE deformation.Using some aspects of two-yieldfunction approaches with unique modifications to incorporate QPE, the model was implemented in a finite element program with parameters determined for dual-phase steel and applied to draw-bend springback.Significant improvements of accuracy differences were found compared with standard simulations or ones incorporating modulus reduction.The proposed constitutive approach can be used with a variety of elastic and plastic models to treat the nonlinear unloading and reloading of metals consistently for general three-dimensional problems.