Etienne Aernoudt

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.

Metallographic methods for revealing the multiphase microstructure of TRIP-assisted steels

Classical etching techniques used for the investigation of steel microstructures allow the simultaneous observation of only a restricted number of phases. So far, this limitation has not been too detrimental, because most low-carbon steel grades possess a quite simple microstructure. The recent interest in the so-called TRIP-assisted multiphase steels characterized by complex microstructures requires new developments in metallographic methods. This paper proposes an extension of already known techniques to allow the study of four kinds of TRIP-aided steels. The actual restrictions justifying the development of an improved method are emphasized. In spite of its simplicity, the procedure has the advantage of allowing the simultaneous observation of the four phases that generally compose the microstructure of TRIP-assisted steels; that is, ferrite, bainite, austenite, and martensite. Light and electron microscopy as well as diffraction techniques are used to demonstrate the interest of the method.

A crystal plasticity based work-hardening/softening model for b.c.c. metals under changing strain paths

Abstract Metal forming processes typically involve changes of strain paths, which are accompanied by transients in softening or hardening behaviour. The physical cause of these transients in stress–strain responses can be attributed to the evolution of the underlying microstructural details. A crystal plasticity based model is presented to capture the complex hardening/softening transients observed in deformation of b.c.c. polycrystals at low homologous temperatures. For each crystallite, the microstructure, i.e. the cell block boundaries and cell structure, is modelled with three dislocation densities. The cell block boundaries are treated as geometrical obstacles to slip on non-coplanar slip systems. This model is implemented in a Full Constraints Taylor model to obtain the response of a polycrystal from the response of the constituent single crystals. It was found that several important features observed in the experimental stress–strain curves of b.c.c. polycrystals during complex strain paths could be reproduced.

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.

The mechanical behaviour of intracondylar cancellous bone of the femur at different loading rates

The compressive properties of human cancellous bone of the distal intracondylar femur in its wet condition were determined. Specimens were obtained from six cadaveric femora and were tested at a strain rate of 0.002, 0.10 and 9.16 sec−1. It was found that the compressive strength decreases with an increasing vertical distance from the joint. The highest compressive strength level was recorded in the posterior medial condyle. Correlations among the mechanical properties, the bulk specimen density and the bone mineral content yield (i) highly significant correlations between the compressive strength and the elastic modulus (ii) highly significant correlations between the compressive strength or the modulus of elasticity and the bulk specimen density (iii) a doubtful correlation between the compressive strength and the bone mineral content. All recorded graphs of the impact loaded specimens displayed several well defined stress peaks, unlike the graphs recorded at low loading rates. It can be concluded that upon impact loading the localized trabecular failure which is associated with each peak, does not affect the spongy bones stress capacity in a detrimental way.

Neutron diffraction measurement of the residual stress in the cementite and ferrite phases of cold-drawn steel wires

Abstract The residual stress state in both the cementite and ferrite phases of cold-drawn pearlitic wires has been measured by neutron diffraction. The phase microstress in the axial direction is obtained. It is found that the cementite lamellae are subjected to a high tensile stress, up to 2000 MPa, after cold drawing. Measurements on etched wires showed that the phase microstress is nearly constant with the distance to the wire axis. Combination of these data with complementary X-ray diffraction measurements on the ferrite determines the response of each phase to the macrostress or an applied stress. Additionally, the peak broadening and texture of both phases have been studied using the neutron diffraction technique. The texture is less sharp in the cementite than in the ferrite. In the cold-drawn samples the diffraction peaks are very broad, which suggests plastic deformation of the cementite lamellae.

Low energy dislocation structures in highly deformed materials

Abstract Gross low temperature plastic deformation of metals results from the movement of large numbers of dislocations. This movement is characterized by dislocation-dislocation interaction events statistically distributed in time and space and by the continuing trend of the dislocation density to rearrange into low energy configurations. The various approaches proposed to link flow stress and strain hardening with the evolving substructure may be grouped into families, emphasizing one or the other of those aspects. The first examines possible low energy dislocation configurations and derives the observed flow stress and strain hardening from the characteristics of the proposed dislocation architecture. The second phase relates flow stress evolution to the kinetics of dislocation movement, i.e. the build-up of the substructure as resulting from successive interaction events. The two approaches have been developed independently. It is the aim of the present paper to examine to what extent experimental observations fit into the framework of the existing models (the “kinetic” model being somewhat modified by an addition proposed in this paper) and to what extent the models are complementary in covering different aspects of the one same truth or are mutually exclusive.

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.

Influence of rolling of TRIP steel in the intercritical region on the stability of retained austenite

Abstract Deformation in the intercritical region—or two-phase ( α + γ ) area—has a substantial effect on the microstructures and mechanical properties of TRIP-aided steel. It indeed increases dislocation density, arranging it in a subgrain substructure which in its turn affects the mechanisms occurring during the ageing treatment that is given on the run-out table. The first purpose of the present work is to investigate the effect of increasing amounts of prior rolling deformation at a given temperature in the intercritical area upon the resulting microstructure. Rolling in the intercritical region stabilizes retained austenite against strain induced transformation on room temperature straining. Increased dislocation density, grain refinement and carbon enrichment are the main factors that govern the retained austenite stability, and consequently the strength and work-hardening behaviour of the material. The second purpose of the study, hence, is the understanding of these stabilising effects. It was found that the morphology of the retained austenite and of the surrounding phase should also be involved as factors that dictate the retained austenite transformation to martensite. These two factors are related to the internal stress state.

Considerations on the crystal and the strain symmetry in the calculation of deformation textures with the taylor theory

Abstract In recent years, it has become possible to use the Taylor analysis for the simulation of cold deformation textures in polycrystalline cubic metals. More complicated deformation processes than wire drawing, compression or cold rolling have also been studied. It is necessary then to know in advance the symmetry of the texture, in order to reduce computer time. This problem involves the choice of the fundamental area in orientation space, to which the evolution of the crystallite orientation can be constricted during the simulation. A full analysis of the above problem is presented here. The symmetry of the deformation texture and the size of the fundamental area are related to the properties of the displacement gradient which describes the strain. In this way a new classification of cold deformation textures has become possible. Euler angles as well as a new type of inverse pole figure are used to describe the fundamental area in orientation space.