Cristian Teodosiu

Work-hardening/softening behaviour of B.C.C. Polycrystals during changing strain paths : I. An integrated model based on substructure and texture evolution, and its prediction of the stress-strain behaviour of an if steel during two-stage strain paths

Abstract For many years polycrystalline deformation models have been used as a physical approach to predict the anisotropic mechanical behaviour of materials during deformation, e.g. the r -values and yield loci. The crystallographic texture was then considered to be the main contributor to the overall anisotropy. However, recent studies have shown that the intragranular microstructural features influence strongly the anisotropic behaviour of b.c.c. polycrystals, as revealed by strain-path change tests (e.g. cross effect, Bauschinger effect). This paper addresses a method of incorporating dislocation ensembles in the crystal plasticity constitutive framework, while accounting for their evolution during changing strain paths. Kinetic equations are formulated for the evolution of spatially inhomogeneous distributions of dislocations represented by three dislocation densities. This microstructural model is incorporated into a full-constraints Taylor model. The resulting model achieves for each crystallite a coupled calculation of slip activity and dislocation structure evolution, as a function of the crystallite orientation. Texture evolution and macroscopic flow stress are obtained as well. It is shown that this intragranular–microstructure based Taylor model is capable of predicting quantitatively the complex features displayed by stress–strain curves during various two-stage strain paths.

Finite element modeling of plastic anisotropy induced by texture and strain-path change

Abstract Consideration of plastic anisotropy is essential in accurate simulations of metal forming processes. In this study, finite element (FE) simulations have been performed to predict the plastic anisotropy of sheet metals using a texture- and microstructure-based constitutive model. The effect of crystallographic texture is incorporated through the use of an anisotropic plastic potential in strain-rate space, which gives the shape of the yield locus. The effect of dislocation is captured by use of a hardening model with four internal variables, which characterize the position and the size of the yield locus. Two applications are presented to evaluate the accuracy and the efficiency of the model: a cup drawing test and a two-stage pseudo-orthogonal sequential test (biaxial stretching in hydraulic bulging followed by uniaxial tension), using an interstitial-free steel sheet. The experimental results of earing behavior in the cup drawing test, maximum pressure and strain distribution in bulging, and transient hardening in the sequential test are compared against the FE predictions. It is shown that the current model is capable of predicting the plastic anisotropy induced by both the texture and the strain-path change. The relative significance of texture and strain-path change in the predictions is discussed.

Work-hardening/softening behaviour of B.C.C. polycrystals during changing strain paths: II. TEM observations of dislocation sheets in an if steel during two-stage strain paths and their representation in terms of dislocation densities

Abstract The relationship between the developed intragranular microstructure and the deformation history of a grain in a low-carbon IF steel is comprehensively investigated during monotonic deformation and two-stage strain paths. TEM micrographs show that dislocation sheets are currently generated parallel to the active slip planes. In the extended Taylor model developed in Part 1 of this paper, such substructural features are modelled and updated dynamically for each strain increment. The actual structure bears some memory of the deformation history. This paper shows the capability of the extended Taylor model to reproduce several features of the substructural developments observed in transmission electron micrographs after monotonic deformation and two-stage strain paths. The evolution of the mesostructural features in stable and unstable crystals are discussed in the context of the work-hardening/softening behaviour of the IF steel. It is demonstrated that the model can be used to predict qualitatively the intensity and the polarity of the dislocation sheets in a grain during any deformation path.

Prediction of forming limit strains under strain-path changes: Application of an anisotropic model based on texture and dislocation structure

Abstract Strain-path changes strongly influence the forming limit strains of sheet metals. The value of the limit strains is greatly affected by material-related effects such as initial anisotropy, transient. hardening, Bauschinger effect and cross hardening. A model which can describe these mechanical behaviours has been developed on the physical basis of texture and dislocation structure, and applied in conjunction with the Marciniak-Kuczynski analysis of the forming limit strains. The results are represented in forming limit diagrams (FLDs) in which the forming limit strains are indicated. The calculation successfully predicts some of the experimental tendencies which cannot be reproduced by conventional phenomenological models. Furthermore, the model has been used to discuss the effects of texture and dislocation structure on the FLDs. Especially, it is suggested that transient hardening caused by the latent part of the persistent dislocation structure significantly reduces the forming limit strain for a strain-path change from equi-biaxial stretching to uniaxial tension.

Work-hardening behavior of mild steel under stress reversal at large strains

Abstract A physically based modeling and experimental investigation of the work-hardening behavior of AK-mild steel under stress reversal at large strains is presented. Internal variables describing the polarity of persistent dislocation structures, a “capacitor-like” behavior, and long-range internal stresses were introduced. By considering the evolution of dislocation substructures during reversed deformation, the model explains the strain-hardening stagnation, the type II recovery and the influence of the amount of prestress. The strain-hardening behavior at large strains (up to an amount of shear of 90%) has been investigated. A satisfactory quantitative agreement has been achieved between model predictions and experimental results.

A theoretical investigation of the influence of dislocation sheets on evolution of yield surfaces in single-phase B.C.C. polycrystals

Abstract Accurate and reliable predictions of yield surfaces and their evolution with deformation require a better physical representation of the important sources of anisotropy in the material. Until recently, the most physical approach employed in the current literature has been the use of polycrystalline deformation models, where it is assumed that crystallographic texture is the main contributor to the overall anisotropy. However, recent studies have revealed that the grain-scale mesostructural features (e.g. cell-block boundaries) may have a large impact on the anisotropic stress–strain behaviour, as evidenced during strain-path change tests (e.g. cross effect, Bauschinger effect). In previous papers, the authors formulated an extension of the Taylor-type crystal plasticity model by incorporating some details of the grain-scale mesostructural features. The main purpose of this paper is to study the evolution of yield surfaces in single-phase b.c.c. polycrystals during deformation and strain-path changes using this extended crystal plasticity model. It is demonstrated that the contribution of the grain-scale substructure in these metals on yield loci is comparable in magnitude to the effects caused by the differences in texture. Furthermore, it is shown that the shape of yield loci cannot be predicted accurately by the traditional polycrystalline deformation model with equal slip hardening. The trends predicted by the extended crystal plasticity model are in much better agreement with the experimental evidence reported in the literature than those represented in classical treatments by isotropic and kinematic hardening.

Interfacial misorientations and underlying slip activity of a shear microband in mild steel: TEM analysis and numerical simulation

A shear microband, formed in mild steel after an orthogonal strain-path change, has been examined. Based on the measured shear offsets at the intersection of the microband with preformed dislocation boundaries and on the interfacial misorientations, the localized slip activity has been reconstructed by numerical simulation. 2002 Published by Elsevier Science Ltd. on behalf of Acta Materialia Inc.

Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems

We present a new method for precise ray-tracing simulation considering form errors in the fabrication process of aspheric lenses. The Nagata patch, a quadratic interpolant for surface meshes using normal vectors, is adopted for representing the lens geometry with mid-spectral frequencies of surface profile errors. Several improvements in the ray-patch intersection calculation and its acceleration technique are also proposed. The developed algorithm is applied to ray-tracing simulation of optical disk pick-up aspheric objectives, and this technique requires 10(5) to 10(9) times fewer patches than a polygonal approximation. The simulation takes only several seconds on a standard PC.

Warpage simulation and the experimental verification of an L‐plate sand mold casting by using the thermo‐elastoplastic FEM code

The warpage of casting parts is a critical issue, especially for large industrial products. Besides, it is difficult to predict the warpage accurately in the casting process because of its complex dependence on mechanical and thermal factors such as the constitutive law of the high temperature metal, the temperature history of the entire part and the restrictions imposed on the deformation by the mold wall. In the present paper, a 3D finite element software V-Shrink developed within the VCAD System Research Program is used to simulate the warpage of an L-plate sand mold casting. It takes into account the thermal coupling between the cast and the mold with non-uniform heat transfer coefficient depending on the local air-gap thickness. 1) The thermo-elastoplastic constitutive law with the temperature dependency of the yield stress is used for the thermal contraction analysis. 2) The simulated warpage of the L-plate casting is in good agreement with the experimental data obtained by a 3D digitizer. Furthermore, the well-known technical finding that the inelastic strain caused by the temperature dependence of the yield stress and the local delay of the temperature drop is a dominant factor of the warpage, is confirmed by the simulation.

3D-analysis of the effect of interfacial debonding on the plastic behaviour of two-phase composites

The present paper deals with the interfacial debonding processes in Al/SiC metal matrix composites, by using 3D finite element calculations on representative cells. The reinforcements are considered as elastic, while the behaviour of the matrix is described by an elastoviscoplastic law. The debonding of the reinforcement is allowed for by using a non-linear elastic dependence between the stress vector and the separation vector at the interface. The results obtained show that the macroscopic behaviour of the composite depends to a large extent on the ratio between the the normal and tangential strength of the interface and the characteristic lengths defining the geometry of the reinforcements.