재료역학 연구실

A novel elasto-visco-plastic self-consistent (EVPSC) formulation based on the scheme of the homogeneous effective medium is presented. The constitutive behavior of a polycrystal is described as that of an elasto-visco-plastic effective medium interacting with grains treated as elasto-visco-plastic ellipsoidal inclusions. The formulation is based on the definition of a unique elasto-visco-plastic compliance, so avoiding the inconsistency arising from assuming superimposed elastic and visco-plastic interaction laws, as made in similar elasto-visco-plastic models. In addition, the elasto-visco-plastic constitutive equation of crystal and aggregate is formulated in terms of stress increments, which leads naturally to a semi implicit solution scheme. The superior numerical stability and computational efficiency of the new incremental EVPSC model (denoted as \DeltaEVPSC) are demonstrated by applying the model to a 316L austenitic stainless steel and comparing against other elasto-plastic models. The modeling capability for predicting texture, stress-strain response, and Bauschinger effect are demonstrated using a dislocation-density based hardening law applied to low carbon (LC) steel subjected to deformation histories that involve strain-path changes.

The EVPSC model is a general elasto-visco-plastic self-consistent constitutive formalism based on a Homogeneous Effective Medium (HEM) approach that accounts explicitly for microstructural features such as slip, twinning, and crystallographic texture. \DeltaEVPSC is improved with respect to the original model reported in (Jeong and Tomé, 2020) by introducing an intermediate linearization scheme, which leads to better predictive accuracy of intergranular stress and strain distributions in the polycrystal. The \DeltaEVPSC model is interfaced with a commercial finite element solver Abaqus/standard as a user-defined material subroutine (EVPSC-FE). EVPSC-FE shows superior numerical stability and, when using parallel computation and 40 CPU core units, it reduces the computation time by a factor 20 compared to using a single CPU core unit for a structure consisting of 512 solid elements. The \DeltaEVPSC-FE model is applied to FE analyses of Zr and low-carbon steel bars subjected to a sequence of bending, stress-relaxation, and unloading. It is shown that the hereditary effect is responsible for the spring-forward motion during the early stage of unloading, while the elastic recovery mainly drives the subsequent spring-back.

An incremental elasto-visco-plastic self-consistent polycrystal model was directly interfaced with a finite element (FE) code and applied to simulations of a mild steel sample subjected to 3-point-bending (3 PB). Emphasis is put in applying this strategy, for the first time, to predict springback responses after various amounts of prestrains. The crystallographic orientation distribution obtained from an EBSD scan was used to assign the initial polycrystalline aggregate for each FE integration point. The RGVB dislocation-density-based hardening model was adopted as the constitutive law, and the parameters were characterized by fitting uniaxial tension and tension-compression flow stress curves. The numerical reliability of the FE simulation results was evaluated via a systematic numerical study in terms of the mesh size, the numbers of grains sampled per each FE integration point and the cross-section points. The model successfully predicts the effect of prestrain on the springback, thus implying that the current modeling approach can be directly applied to industrial forming and springback predictions.

The incremental elasto-visco-plastic self-consistent polycrystal model (\DeltaEVPSC) was utilized to describe the constitutive behavior of dual-phase 980 (DP980) steel. A simple baseline modeling approach was chosen: the hardening behavior of each constituent phase in the DP980 steel was described by a simple Voce hardening law without explicitly considering the back stress; and it was assumed that using the same single crystal elastic modulus for ferrite and martensite is sufficiently representative. The adequacy of this baseline modeling approach was evaluated by comparing various mechanical experimental data with model predictions in terms of the stress vs. strain curves obtained from uniaxial tension, tension-compression, and loading-unloading-loading (LUL) tests. Additionally, the evolution of experimental lattice strain data reported in literature was used to validate the phase-specific Voce hardening parameters. Despite its minimalistic modeling description, the baseline \DeltaEVPSC model successfully captured key features: 1) the Bauschinger effect, 2) the decrease in chord modulus, and 3) the non-linearity in the stress vs. strain curves resulting from the LUL test. All three mentioned characteristics are crucial for accurate prediction of springback in sheet metals. The \DeltaEVPSC model, interfaced with a finite element solver (Abaqus/standard) as the user material subroutine, was employed to simulate the Numisheet93 benchmark problem. The strip of DP980 was first U-drawn followed by springback. The model-predicted springback profile aligned well with the experimental results only when stress relaxation was properly considered, resulting in improved predictive accuracy compared to predictions based on a distortional plasticity model.