J.K. Lee

Modeling the Bauschinger effect for sheet metals, part I: theory

Abstract It is essential to model the Bauschinger effect correctly for sheet metal forming process simulation and subsequent springback prediction when material points are subjected to cyclic loading conditions. The combined nonlinear hardening model for time independent cyclic plasticity, proposed by Chaboche and co-workers, is examined and a simple modification is suggested for the isotropic part of the hardening rule to utilize the conventional tensile test data directly. This modification is useful for the materials whose reverse loading curves saturate to the monotonic loading curve. In addition, an anisotropic nonlinear kinematic hardening model (ANK model) is proposed in an attempt to represent the Bauschinger effect more realistically. Possible offset in flow stress is modeled by treating the back stress evolution during reverse loading differently from the initial loading. This strategy coupled with the modified isotropic hardening rule seems to provide a way to model the Bauschinger effect consistently over multiple cycles. Two types of auto-body alloys are examined in this paper. Associated material parameters are determined by employing available tension-compression test data and multi-cycle bend test data. A developed finite element formulation is applied to analyze simple validation type of problems. The cyclic stress–strain curves generated from the proposed ANK model match remarkably well with measured data.

Modeling the Bauschinger effect for sheet metals, part II: applications

Abstract The modified Chaboche and ANK model proposed in Part I are implemented into second order accurate user material routines for ABAQUS/Explicit and /Standard. A criterion to detect a load reversal for ANK model is also proposed. They are applied to investigate the role of Bauschinger effect in the simulation of sheet metal forming and springback prediction under multi-cyclic loading conditions. Reverse cup drawing and draw-bead tests are simulated and results are compared with available experimental data. The ANK model predicted the maximum punch forces more accurately with a correct trend for the reverse cup drawing process. The draw-bead test simulation results with the ANK model show encouragingly good comparisons with measured data. An accurate modeling of the Bauschinger effect appears to be more important when multiple cycles of bending and reverse bending loading conditions are expected.

Modeling mechanical response of intumescent mat material at room temperature

Abstract Intumescent mat material is widely used to support ceramic substrates in catalytic converters and behaves very much like hyper-foam material under compressive loading. Experiments show that compressive loading curves depend on the ram speed and the number of cycles. The unloading curves show different slopes and paths that depend less on the ram speed and number of cycles. The slopes of the unloading curves decrease as the plastic strain increases; this is referred to as “softening” in this study. The effects of rate, softening, and plastic deformation must be considered to model the mechanical response of intumescent mat material. Finite deformation theory is applied with a multiplicative decomposition of the deformation gradient tensor. The developed theory is implemented as an implicit finite element algorithm in ABAQUSTM/STANDARD. The necessary material parameters are extracted from experiments. Numerical simulations show good agreement with experiments.

Constitutive Modeling of Magnesium Alloy Sheets

Magnesium alloy sheets have unique mechanical properties: high in‐plane anisotropy/asymmetry of yield stress and hardening response, which have not been thoroughly studied. The unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of h.c.p metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A new hardening law based on two‐surface model was developed to consider the general stress‐strain response of metal sheets such as Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker‐Prager’s pressure dependent yield s...