Mitsutoshi Kuroda

Use of abrupt strain path change for determining subsequent yield surface : Experimental study with metal sheets

A basic idea for a method for determining the subsequent yield surface in the vicinity of a current loading point by using an abrupt strain path change has been proposed recently by Kuroda and Tvergaard (Acta mater., 1999, 47, 3879). The proposed method is applied to real experimental studies. In a biaxial tensile testing apparatus, a cruciform specimen is used, with the strains measured by a biaxial-strain gauge. Then, with the hydraulic pressure of two sets of opposing hydraulic cylinders servo-controlled independently, the testing apparatus can be used to prescribe an abrupt change of the strain path. Both a cold-rolled steel sheet and an aluminum alloy sheet are investigated. The differences between the yield surface shapes found by the strain path change procedure and the shapes found by probing the yield points from the elastic region are shown and discussed for different cases.

A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity

Abstract An abrupt strain path change has recently been used to determine the shape of the subsequent yield surface near a current loading point. Both polycrystal plasticity calculations and experiments have shown non-normality of plastic flow, with a vertex-type response on the apparently smooth yield surface. The physical reason for this observation is carefully discussed in the paper, with particular emphasis on the fact that the prediction appears in spite of the normality rule built into each slip system of the crystal plasticity model. To represent the observed non-linear material response, a phenomenological plasticity model is proposed, in which a smooth yield surface for an anisotropic solid is combined with a vertex-type plastic flow rule. As plastic instability results are particularly sensitive to accurate modeling of material response under abrupt stress path change, the material model is tested on predictions of the onset of necking in biaxially stretched metal sheets. It is shown that the phenomenological plasticity model gives a good approximation of critical strains predicted by direct application of the Taylor polycrystal plasticity model.

Shear band development predicted by a non-normality theory of plasticity and comparison to crystal plasticity predictions

A phenomenological plasticity model has recently been proposed, which combines a smooth yield surface for an anisotropic solid with a vertex-type plastic flow rule. Both polycrystal plasticity calculations and experiments have shown the type of non-normality of plastic flow, which is represented by this material model. The plasticity model is here implemented in a finite element programme and is used to analyze the plane strain tensile test, thus representing the formation of a neck and the subsequent evolution of shear bands in the neck region. To test the predictions of the phenomenological plasticity model the tensile test problem is also analyzed by polycrystal plasticity, based on the Taylor model for either b.c.c. or f.c.c. crystal structure. It is shown that the phenomenological plasticity model gives a good approximation of the crystal plasticity predictions.

Shear–band development in polycrystalline metal with strength–differential effect and plastic volume expansion

Experimental studies have shown that the flow stress of some metals is clearly influenced by superimposed hydrostatic pressure. Flow stress increases with the hydrostatic pressure, and consequently it is often observed that the flow stress is clearly larger in a uniaxial compression test than in a uniaxial tension test. This phenomenon is known as the strength–differential effect (SDE). In addition, metals undergoing uniaxial tension and compression show a permanent volume expansion (dilatancy) which is insensitive to the sign of the hydrostatic pressure. In this paper, shear–band development in polycrystalline metal with the SDE and dilatancy is studied, using a rate–dependent crystal–plasticity model with a full three–dimensional, body–centred–cubic, slip–system structure. It is postulated that the appearances of the SDE and dilatancy are consequences of non–Schmid effects existing in each slip system. In the finite–element analyses performed here, each Gaussian integration point in a finite element represents a polycrystal consisting of many of crystal grains having different orientations. As a boundary–value problem, a rectangular specimen subjected to plane–strain tension is considered. Although the finite–element geometry is chosen to be two dimensional, the constitutive model incorporates the full three–dimensional slip–system structure. As a polycrystal model to be embedded in each integration point, an extended Taylor model is employed. Thus, macroscopic manifestations of non–Schmid effects are studied. The influences of hydrostatic stress, internal friction, plastic volume expansion and strain–rate sensitivity on macroscopic shear–band formation in polycrystals are investigated. Results are directly compared with predictions from a classical Schmid–law–based crystal–plasticity theory.

Plastic spin associated with a non-normality theory of plasticity

A plasticity model using a vertex-type plastic flow rule on a smooth yield surface for an anisotropic solid has been proposed recently. This model is here completed by incorporating the effect of plastic spin. Simple shear with a large shear strain is one of the hardest tests on finite strain anisotropic plasticity models, and it is here shown which plastic spin expression is needed to avoid unrealistic oscillatory behavior of the shear stress under large shear strains. The idea of using non-normality with a smooth yield surface originates from a recent proposal of using an abrupt strain path change to determine the subsequent yield surface shape. For this method both polycrystal plasticity calculations and experiments have shown a vertex-type response on the apparently smooth yield surface.

Effects of plastic anisotropy on crack-tip behaviour

For a crack in a homogeneous material the effect of plastic anisotropy on crack-tip blunting and on the near-tip stress and strain fields is analyzed numerically. The full finite strain analyses are carried out for plane strain under small scale yielding conditions, with purely symmetric mode I loading remote from the crack-tip. In cases where the principal axes of the anisotropy are inclined to the plane of the crack it is found that the plastic zones as well as the stress and strain fields just around the blunted tip of the crack become non-symmetric. In these cases the peak strain on the blunted tip occurs off the center line of the crack, thus indicating that the crack may want to grow in a different direction. When the anisotropic axes are parallel to the crack symmetry is retained, but the plastic zones and the near-tip fields still differ from those predicted by standard isotropic plasticity.

Forming Limit Stresses of Sheet Metal under Proportional and Combined Loadings

The effects of changing strain paths on forming limit stresses of sheet metals are investigated using the Marciniak‐Kuczynski model. Forming limits are analyzed for proportional loading and two types of combined loadings: combined loading which includes unloading between the first and second loadings and that which includes an abrupt strain path change without unloading between the first and second loadings. The forming limit stress curves in stress space calculated for the combined loading with unloading are in good agreement with those calculated for the proportional loading, while the forming limit curves in strain space are strongly dependent on the strain paths. The forming limit stresses calculated for combined loading with an abrupt strain path change, however, do not coincide with those calculated for proportional loading. The strain path dependence of the forming limit stresses is discussed in detail.

A Polycrystalline Analysis of Hexagonal Metal Based on the Homogenized Method

In this study, a three-dimensional finite element formulation for polycrystalline plasticity model based on the homogenization method has been presented. The homogenization method is one of the useful procedures, which can evaluate the homogenized macroscopic material properties with a periodical microstructure, so-called a unit cell. The present study focuses on hexagonal metals such as titanium or magnesium. An assessment of flow stress by the presented method is conducted and it is clarified how the method can reproduce the behavior of hexagonal metal.

Effects of Texture on Mechanical Properties of Aluminum Alloy Sheets and Texture Optimization Strategy

It is known that the crystallographic texture affects very much the mechanical properties of sheet metals. In this paper, rolled aluminum alloy sheets are considered as target materials. Typical texture components usually observed in rolled aluminum alloy sheets are the deformation textures of Cu, Brass and S, and the recrystallization textures of Cube and Goss. First, the effects of these components on mechanical properties, such as variations of Lankford’s r‐value for different tensile directions and forming limit strains, are investigated using full crystal plasticity analyses. In general, the most appropriate volume fractions of the texture components for a user‐defined particular requirement, e.g. the smallest possible in‐plane anisotropy, or the largest possible formability for a particular strain path, are unknown. Then, a texture optimization strategy is considered, i.e. a genetic algorithm is adopted to solve texture optimization problems. We describe a genetic algorithm with real‐valued genes, w...

On scale-dependent crystal plasticity models

An extended crystal plasticity theory that accounts for the length-scale effects in plastic strain gradient fields is presented. First, foundations and kinematics of crystal plasticity theory is reviewed. Then, experimental evidences for the size-effects in small-sized bent single crystals are presented. Total amounts of apparent strain hardening, which were experimentally observed, are decomposed into isotropic and kinematic hardening components. Physically-based models are formulated to describe the size-dependent isotropic and kinematic hardening behaviors, utilizing possible micromechanical information with respect to dislocations and their motions. Roles of the geometrically necessary dislocations (GNDs) in strain hardening behavior are studied in detail. Furthermore, some aspects of numerical computations of the extended size-dependent crystal plasticity theory are presented. The developed theory involves extra boundary conditions for crystallographic slips and/or the GND densities. Effects of these extra boundary conditions are demonstrated through numerical simulations for some basic boundary value problems. Finally, a phenomenological strain gradient plasticity theory is revisited, based on the knowledge from the present size-dependent crystal plasticity theory.