P.A. Turner

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.

An iterative approach to mechanical properties of MMCs at the onset of plastic deformation

Abstract The current work presents a generalized Eshelby model allowing interaction among reinforcing particles under a Mori-Tanaka like scheme. Different aspect ratios and geometries are studied in the elastic and incipient elasto-plastic regime for a model SiC Al composite. The fibers are taken as purely elastic and the matrix is regarded elastic perfectly plastic responding to a Von Mises yield criterion. The phenomenon of plastic localization in the vicinities of the inclusions is carefully described for different reinforcement volume fractions and thermo-mechanical loading. Equivalent stress, hydrostatic pressure and elastic and plastic strains are depicted as contour levels around a representative inclusion. Effective coefficients of thermal expansion of composites are calculated both under purely elastic composite response and at the onset of plastic localized deformation. The influence of plastic strain over those effective coefficients is shown to be detectable. The simulated stress-strain curves show the influence of interaction stresses over macroscopic yield stress by isolating this phenomenon from matrix hardening. Accumulated elastic energies and plastic work are calculated to show the different nature of purely thermal and mechanical loads.

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.