K. Inal

Finite element analysis of localization in FCC polycrystalline sheets under plane stress tension

Abstract Localization phenomena in thin sheets subjected to plane stress tension are investigated. The sheet is modelled as a polycrystalline aggregate, and a finite element analysis based on rate-dependent crystal plasticity is developed to simulate large strain behaviour. Accordingly, each material point in the specimen is considered to be a polycrystalline aggregate consisting of a large number of FCC grains. The Taylor model of crystal plasticity theory is assumed. This analysis accounts for initial textures as well as texture evolution during large plastic deformations. The numerical analysis incorporates certain parallel computing features. Simulations have been carried out for an aluminum sheet alloy, and the effects of various parameters on the formation and prediction of localized deformation (in the form of necking and/or in-plane shear bands) are examined.

Instability and localized deformation in polycrystalline solids under plane-strain tension

In this paper we investigate the nonuniform and localized deformation of a polycrystalline aggregate under plane-strain tension. A finite element analysis based on rate-dependent crystal plasticity has been developed to simulate large strain behaviour. Each material point in the specimen is considered to be a polycrystalline aggregate of a large number of FCC grains. The Taylor theory of crystal plasticity is assumed. This analysis accounts for initial textures, as well as texture evolution during large plastic deformations. The numerical analysis incorporates certain parallel computing features. Simulations have been carried out for a commercial aluminium sheet alloy (AA3004-H19), and the effects of various parameters on the formation and prediction of localized deformation (in the form of necking and/or shear bands) are examined.

Simulation of earing in textured aluminum sheets

Abstract In this paper we investigate the phenomenon of earing, which is a troublesome defect often observed during the deep drawing of rolled aluminum sheets. A special finite element analysis for this problem has been developed where only the flange area of the sheet is modelled. A polycrystal and a phenomenological model are used for the numerical simulations of earing. For the polycrystal model, the material behaviour is described using crystal plasticity theory where each material point in the sheet is considered to be a polycrystalline aggregate of a very large number of FCC grains. The Taylor theory of crystal plasticity is assumed. This analysis accounts for initial sheet textures, as well as texture evolution during large plastic deformations. The numerical analysis incorporates certain parallel computing features. For the phenomenological model, a six component yield function proposed by Barlat, Panchanadeeswaran and Richmond, 1991a , Barlat, Lege and Brern, 1991b is used. The numerical simulation of earing has been carried out for two textures typical of rolled aluminum sheets. The effects of these textures are discussed, and comparisons are made with experimental data.

Large strain behaviour of aluminium sheets subjected to in-plane simple shear

In this paper, we investigate the nonuniform and localized deformation of thin rolled aluminium sheets subjected to in-plane simple shear. A finite element analysis based on a rate-dependent crystal plasticity model has been developed to simulate the planar shear test and large strain behaviour. Each material point in the specimen is considered to be a polycrystalline aggregate consisting of a large number of FCC grains. The Taylor theory of crystal plasticity is assumed. This analysis accounts for initial textures, as well as texture evolution during large plastic deformations. The numerical analysis incorporates certain parallel computing features. Both plane stress and plane strain analyses have been carried out for the aluminium sheet alloy AA3004-H19, and the initiation and propagation of shear bands are investigated.

Numerical Simulations of Formability of Multiphase Steels

In this paper we investigate the formability of multiphase steels. A new model based on crystal plasticity has been developed to investigate large strain phenomena in multiphase steels. The approach is based on the concept of a unit cell. The unit cell is defined as a globally small region of the sheet that contains all the essential micro‐structural and textural features that characterize the sheet. Orientations within the measured texture data are randomly assigned in the mesh/unit cell. In other words, each element of the mesh represents an orientation from the measured texture and the constitutive response at a material point is given by the single crystal constitutive model. This model is employed to construct forming limit diagrams for multiphase steels.

Parallel finite element algorithms for the analysis of multiscale plasticity problems

Parallel computing algorithms for the finite element method have been developed to simulate multiscale large deformation plasticity problems. Due to the nature of these problems and the computational methods involved, different parallel computing techniques must be employed for the Taylor-type crystal plasticity (TFE) and the so-called “finite element per single crystal” (FESC) models. For the FESC model, the global stiffness matrix is formed in parallel and a parallel solver employing a number of Krylov iterative methods is used to solve the systems of equations. For the TFE model, a data parallel implementation technique is employed. This technique provides a large reduction in the storage required on a single processor and thus allows for an effective solution of computationally demanding crystal plasticity problems. The efficiency and the performance of the parallel finite element models that have been developed are investigated by comparing simulations performed on an IBM POWER3 SP parallel supercomputer.

Numerical Modelling of Large Strain Deformation in Magnesium

In this paper, a new constitutive framework based on a rate-dependent crystal plasticity theory is presented to simulate large strain deformation phenomena in HCP metals such as magnesium. In this new model the principal deformation mechanisms considered are crystallographic slip and deformation twinning. The new framework is incorporated into in-house finite element (FE) codes. Simulations of uniaxial tension and compression for the magnesium alloy AM30 are performed and the results are compared with experimental observations of the specimens deformed at 200°C. Limitations of the current modelling approaches are also discussed.

Multiscale Modelling of Texture Gradient Effects on Localization in FCC Polycrystals

The effects of through-thickness texture gradients on instabilities and localized deformation in FCC polycrystals are investigated. In-house finite element analyses based on a rate-dependent crystal plasticity model have been developed to simulate large strain behaviour for sheet specimens subjected to plane strain tension. Modelling of the polycrystalline aggregates is carried out at various scales, and predictions of localized deformation are compared against each other.