Javier Signorelli

Calculation of intergranular stresses based on a large-strain viscoplastic self-consistent polycrystal model

We present here an extension of the viscoplastic self-consistent (VPSC) polycrystal model for the calculation of the intergranular Cauchy stresses in an aggregate. This method, which is based on the self-consistent treatment of incompressible aggregates proposed in 1987 by Molinari et al, is formulated using the inclusion formalism and full anisotropy is incorporated into it. The complete stress state in the grains is obtained by computing the deviatoric and the hydrostatic local deviations with respect to the overall corresponding magnitudes applied to the polycrystal. The extended VPSC model, followed by an elastic self-consistent unloading, is used to obtain the intergranular residual strains in the aggregate after large plastic deformation. The texture evolution and the hardening of the material are explicitly taken into account in the model. As an application, the model is used to predict intergranular residual states in Incoloy-800 plate after uniaxial deformation.

A multiscale approach to model the anisotropic deformation of lithospheric plates

The association of experimental data showing that the plastic deformation of olivine, the main constituent of the upper mantle, is highly anisotropic and the ubiquitous seismic anisotropy in the upper mantle, which indicates that olivine crystals show coherent orientations over scales of tens to hundreds of kilometers, implies that the long-term deformation in the upper mantle is anisotropic. We propose a multiscale approach, based on a combination of finite element and homogenization techniques, to model the deformation of a lithospheric plate while fully considering the mechanical anisotropy stemming from a strain-induced orientation of olivine crystals in the mantle. This multiscale model explicitly takes into account the evolution of crystal preferred orientations (CPO) of olivine and of the mechanical anisotropy during the deformation. We performed a series of numerical experiments simulating the uniaxial extension of a homogeneous (100% olivine) but anisotropic plate to test the role of the olivine CPO on the plate mechanical behavior and the link between CPO and mechanical anisotropy evolution. Even for this simple solicitation, different orientations and intensity of the initial olivine CPO result in variable plate strengths and deformation regimes. A plate with an initial CPO where the olivine [100] and [010] axes are concentrated at 45 degrees to the extension direction has high resolved shear stresses on the easy (010)[100] and (001)[100] slip systems of olivine. This results in low strength and in deformation by transtension. Plates with an initial CPO where the maximum of [100] axes is parallel or normal to the extension direction show a high initial strength. Isotropic plates have an intermediate behavior. The progressive rotation of olivine [100] axes toward the imposed stretching direction results in hardening in all models, except in those characterized by an initial concentration of olivine [100] axes normal to the imposed extension, in which softening is followed by hardening.

Sensitivity of α-ZY4 high-temperature deformation textures to the β-quenched precipitate structure and to recrystallization: Application to hot extrusion

Hot extrusion of Zircaloy-4 tubes usually starts from β-quenched microstructures and induces strong textures. Individual crystallographic orientations were investigated by transmission electron microscopy using the electron backscatter pattern (EBSP) technique as well as Kikuchi patterns. Basal poles were found close to the tangential direction of the tubes in regions exhibiting fine and homogeneously distributed precipitates (FHDPs). In contrast, regions with large and isolated precipitates (LIPs) had more variable orientations. Laboratory plane strain compression tests were performed and the induced textures were compared with numerical simulations using a polycrystalline viscoplastic self-consistent model. The β-quenched material was modeled as a mixture of LIP and FHDP regions, each having a different set of slip system hardnesses, with a volume fraction depending on the previous thermal history. The model was subsequently applied to predict the texture evolution during extrusion with metadynamic recrystallization taking place thereafter. The calculation suggests that recrystallization modifies the orientation of those grains where 〈c+a〉 crystallographic slip has been significantly activated during deformation.

Parameter identification method for a polycrystalline viscoplastic selfconsistent model based on analytical derivatives of the direct model equations

An inverse method for automatic identification of the parameters involved in a polycrystalline viscoplastic selfconsistent (VPSC) model is presented. The parameters of the constitutive viscoplastic law at the single-crystal level, i.e. the critical resolved shear stresses (CRSS) of slip and twinning and the micro-hardening coefficients, can be identified using experimental data at the polycrystal level, i.e. stress-strain curves and deformation-induced textures. The minimization problem is solved by means of a Gauss-Newton scheme and the sensitivity matrix is evaluated by analytical differentiation of the direct model equations. As a particular case, the optimization procedure for the Taylor full constraints (FC) formulation is also presented. The convergence and stability of the identification scheme are analysed using several validation tests for different deformation paths imposed to a polycrystal of hexagonal structure. As an example of application of this inverse method, the relative CRSS of the active deformation systems of a Zircaloy-4 sheet are identified, based on several textures measured for different reductions and rolling directions.

K-S Relationship Identification Technique by EBSD

This paper focuses on the identification of activated slip system in flat specimens of hot- and cold-rolled UNS S32750 DSS plates subjected to low-cycle fatigue, paying particular attention on the existence of the K-S relationship. Electron Backscattered Diffraction (EBSD) technique was used to determine the local crystallographic properties of both phases. Although 27182 couples of α/γ grains were analyzed, the crystallographic K-S relationships were rarely observed between them. As a conclusion, it was observed that microcracks were mostly nucleated at grain boundaries and rarely at the extrusions.

Self-Consistent Homogenization Methods for Predicting Forming Limits of Sheet Metal

© 2012 Signorelli and Bertinetti, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Self-Consistent Homogenization Methods for Predicting Forming Limits of Sheet Metal

A Theoretical Study on Forming Limit Diagram Predictions Using Viscoplastic Polycrystalline Plasticity Models

The Forming Limit Diagrams (FLDs) of textured polycrystalline sheet metals were investigated using micro-macro averaging and two types of grain-interaction models: Full-Constraint (FC) and Self-consistent (SC) schemes, in conjunction with the Marciniak–Kuczynski (MK) approach. By referring to previous FLD studies based on the FC-Taylor model ─ Wu and coworkers [Effect of an initial cube texture on sheet metal formability, Materials Science and Engineering A, 364:182–7, 2004] and Inal and coworkers [Forming Limit comparison for FCC and BCC sheets, International Journal of Plasticity, 21:1255-1266, 2005] ─ we found that the MK-FC strategy leads to unrealistic results. In the former case, the researchers found that an increasing spread about the cube texture produces unexpectedly high limit strains. In the latter work, Inal et al. predicted a remarkably low forming-limit curve for a FCC material and an extremely high forming-limit curve for a BCC material, in the biaxial-stretching range. Our investigations show that simulations performed with the MK-VPSC approach successfully predict more reliable results. For the BCC structure, the MK-VPSC predictions do not give the extreme values predicted when calculations are carried out with the MK-FC approach. In the FCC case, with decreasing textural intensity ─ from the ideal cube texture, through dispersions around the cube texture with increasing cut-off angles, to a random texture ─ a smooth transition in increasing limit strains was obtained. Furthermore, these results suggest that the selected constitutive model is critical for predicting the behavior of materials that exhibit a qualitative change in crystallographic texture, and hence, evolve anisotropically during mechanical deformation.

ECAE of Al-4%Cu Alloys: Experimental Study Assisted by Polycrystalline-FEM Simulations

The present work reports on the results obtained on equal channel angular extrusion experiments (ECAE) done on a laboratory-cast Al-4%Cu alloy, in the T4 condition, and the use of Polycrystalline-FEM simulations to assist in the interpretation of the experiments. The experimental setup consists on a die of approximately 15 x 15 mm2 sections intersecting at 120o. Deformation at room temperature consisted of up to 5 passes with no rotation between passes. After each extrusion pass, the samples were cut from the deformed billet along planes parallel to the extrusion direction and the preferential orientations were measured on surface and middle layers. Three pole figures, (111), (200) and (220) were measured by conventional x-ray diffraction techniques and used for Orientation Distribution Function calculation and analysis. In addition tensile tests and optical microscopy have been performed in each sample to provide a good estimation of the parameters that enter in the modeling process. A finite element code specially developed to model large deformation processes (Forge3Ò) was used with tetrahedral elements and an elastic-viscoplastic material model to investigate the influence of the different strain paths sustained by different areas of the samples. The calculated distribution of deformations agrees well with the theoretical result. The simulation was used to assist in the selection of sample-cutting procedures for texture measurements and to provide the strain paths needed for self-consistent polycrystal modeling of texture development.

Electron backscatter diffraction study of orientation gradients at the grain boundaries of a polycrystalline steel sheet deformed along different loading paths

In a polycrystal, the heterogeneity of plastic deformation in a particular grain is greatly enhanced by adjacent grains that constrain the grains local behavior, often imposing orientation gradients. This work aims to characterize and quantify the local orientation gradients near grain boundaries (GBs). Electron backscatter diffraction (EBSD) measurements were made on a 0.67 mm thick aluminium-killed drawing quality (AKDQ) steel sheet subjected to different loading paths that are typical of forming operations. A statistical analysis shows that a considerable fraction of the analyzed GB profiles can be described by an orientation profile with a constant slope near the GB. In order to quantify this behavior, as well as the degree of localization, two new parameters, based on the local orientation gradient assessed by EBSD, are proposed: BET (boundary effective thickness) and GAS (gradient average severity). These parameters should be considered together, the BET as an effective thickness of the GB zone where the orientation gradient takes place and the GAS as a measure of the magnitude or severity of the orientation gradient. Additionally, the GAS parameter shows a strong correlation with the accumulated macroscopic strain for the investigated deformation levels and loading paths, while the BET profile clearly reveals the influence of the GB on the misorientation profiles. Tension and biaxial stretching results lead to a BET value between 1.5 and 2 µm. Finally, it is shown that the local misorientation in the GB zone, on both sides of the GB line, is disperse and it does not correlate simply with misorientation or even the slip-transfer geometry across the GB. Moreover, the observed average local misorientation dispersions in GB zones are different for each loading condition.

Simulation of Recrystallization Textures in fcc Materials Starting from Self-Consistent Modelling Results

Recrystallization (RX) textures in FCC materials have defied modelling for quite a long time despite the major micro-mechanisms influencing the texture development are currently considered understood. FCC materials are coarsely classified in high and low stacking fault energy materials with a rather continuous transition between them. Both extreme kinds will give rise, after rolling deformation and later RX, to what are called Cube and Brass texture patterns. Besides long discussions, not still settled, about the influence of twinning on deformation textures, attempts of simulating RX textures have been unsuccessful. The current contribution will show SelfConsistent (SC) plus RX modelling taking into account accumulated deformation energy and misorientation angles between neighbouring crystals. Starting from grains characterized by previous SelfConsistent simulations, nucleation is probabilistically allowed on each crystal whenever the accumulated energy is larger than certain threshold. Grain boundary mobility is commanded by a probability function of the misorientation angles also calculated by the SC model. The modelling is able to predict the right trend for many of the literature experimental data without resorting to other more sophisticated variables.