K. Wierzbanowski

Examination of the residual stress field in plastically deformed polycrystalline material

Abstract A new method for the determination of residual stresses in plastically deformed polycrystalline materials is presented. This method is based on standard X-ray and neutron diffraction measurements of the 〈d hkl〉 interplanar spacings in different directions. Until now the estimation of the residual stresses was limited to those of the first-order but the method presented takes into account both the first-and second-order stresses.

Quantitative estimation of incompatibility stresses and elastic energy stored in ferritic steel

Plastic incompatibility second-order stresses were determined for different orientations of a polycrystalline grain, using X-ray diffraction data and results of the self-consistent elasto-plastic model. The stresses in cold rolled ferritic steel were determined both in as-received and under tensile loaded conditions. It has been shown that the Reuss model and the self-consistent model applied to near surface volume provide the best approaches to determine diffraction elastic constants. For the first time, the elastic energy in an anisotropic material (arising from plastic incompatibilities between grains having various lattice orientations) has been determined. The second-order incompatibility stresses and stored elastic energy are presented in Euler space.

Recrystallization textures-two types of modelling

Dislocation density is assumed to be the stored energy in a deformed material, i.e, the driving force in recrystallization. It can be estimated in diffraction experiments and it can also be predicted. Model calculations for b.c.c. structure give higher dislocation density for the orientations of the γ fibre compared with those of the α one. This explains the observed increase of γ fibre intensity (and decrease of α intensity) in the recrystallization texture of low-carbon steels, because nuclei appear preferentially in high stored energy regions. Hence, the oriented nucleation behaviour explains the texture change in this case. In other materials the oriented growth behaviour dominates. Phenomenological laws state that only these nuclei grow intensively which have a given misorientation with the deformed matrix. This description is frequently verified in f.c.c. metals and generally reported misorientations are 30°–50° rotations around the <111> axis. The above approach leads to good predictions of recrystallization textures in copper, brass and aluminium. The predicted results are still improved assuming that only these nuclei which are able to consume many deformed grains simultaneously (with different crystal orientations) grow effectively. Consequently, so-calledcompromise criterion andcompromise functions are defined.

New Type of Diffraction Elastic Constants for Stress Determination

A new method for calculation of the diffraction elastic constants, based on the selfconsistent model, is proposed and tested. This method is especially useful in the interpretation of the results of X-ray measurements since the ellipsoidal inclusion near the sample surface is considered. In X-ray diffraction the information volume of the sample is defined by absorption, causing unequal contribution of different crystallites to the intensity of the measured peak. Consequently, the surface grains participate more effectively in diffraction than the grains which are deeper in the sample.

FCC Rolling Textures Reviewed in the Light of Quantitative Comparisons between Simulated and Experimental Textures

The crystallographic texture of metallic materials has a very strong effect on the properties of the materials. In the present article, we look at the rolling textures of fcc metals and alloys, where the classical problem is the existence of two different types of texture, the “copper-type texture” and the “brass-type texture.” The type of texture developed is determined by the stacking fault energy of the material, the rolling temperature and the strain rate of the rolling process. Recent texture simulations by the present authors provide the basis for a renewed discussion of the whole field of fcc rolling texture. We simulate the texture development with a model which allows us to vary the strength of the interaction between the grains and to vary the scheme for the calculation of the lattice rotation in the individual grains (type CL/MA or PR/PSA). For the deformation pattern we focus on {111}<110> slip without or with deformation twinning, but we also consider slip on other slip planes and slip by partial dislocations. We consistently make quantitative comparison of the simulation results and the experimental textures by means of a scalar correlation factor. We find that the development of the copper-type texture is best simulated with {111}<110> slip combined with type CL/PR lattice rotation and relatively strong interaction between the grains — but not with the full-constraint Taylor model and neither with the classical relaxed-constraint models. The development of the brass-type texture is best simulated with {111}<110> slip combined with PR/PSA lattice rotation and weak interaction between the grains. The possible volume effect of deformation twins on the formation of the brass-type texture is a controversial question which we discuss on the basis of our simulations as seen together with other investigations.

X-ray grazing incidence technique—corrections in residual stress measurement—a review

Using X-ray grazing incidence diffraction (GID) it is possible to perform a non-destructive analysis of the heterogeneous stress field for different volumes below the surface of the sample. The stress can be measured at very small depths, of the order of a few m. The penetration depth of radiation is almost constant in a wide 2  range for a given incidence angle . It can be easily changed by an appropriate selection of  angle (or also by using a different type of radiation). There are, however, some factors which have to be corrected in this technique. The most important is the refraction of X-ray wave: it changes the wave length and direction of the beam. The both effects modify a pick position. A corresponding correction was calculated and tested on ferrite powder and on 316L austenite stainless steel sample.

Crystallographic Textures Variation in Asymmetrically Rolled Steel

The crystallographic texture formation in low carbon steel during asymmetric rolling was studied experimentally and analysed numerically. Modelling of plastic deformation was done in two scales: in the macro-scale using the finite element method ( FEM) and in crystallographic scale using the polycrystalline deformation model (LW model). The stress distribution in the rolling gap was calculated using FEM and next these stresses were applied in LW model of polycrystalline plastic deformation. In general, the predicted textures agree very well with experimental ones.

Effect of rolling asymmetry on selected properties of grade 2 titanium sheet

Asymmetric rolling can be used in order to modify material properties and to reduce forces and torques applied during deformation. This geometry of deformation is relatively easy to implement on existing industrial rolling mills and it can provide large volumes of a material. The study of microstructure, crystallographic texture and residual stress in asymmetrically rolled titanium (grade 2) is presented in this work. The above characteristics were examined using the EBSD technique and X-ray diffraction. The rolling asymmetry was realized using two identical rolls, driven by independent motors, rotating with different angular velocities. It was found that asymmetric rolling leads to microstructure modification and refinement. At low deformations one observes a process of grain size decrease caused by the asymmetry of rolling process. In contrast, at the medium range of deformations the microstructure refinement consists mainly in subgrain formation and grain fragmentation. Another observation is that for low to intermediate rolling reductions (≤40%) the predominant mechanisms are slip and twinning, while for higher deformation (>40%) the main mechanism is slip. It was found that grain refinement effect, caused by the rolling asymmetry, persists also after recrystallization annealing. And finally, texture homogenization and reduction of residual stress were confirmed for asymmetrically rolled samples.

Residual stress field in steel samples during plastic deformation and recovery processes

An X-ray diffraction method was applied to measure residual stresses and stored elastic energy in deformed and annealed polycrystalline ferritic and austenitic steel samples. The orientation distribution of plastic incompatibility second-order stresses created during elastoplastic deformation was determined and presented in Euler space. Using deformation models, these stresses were correlated with different types of intergranular interactions occurring in the studied materials. An important decrease of the first- and the second-order residual stresses was observed during recovery and recrystallisation processes. Diffraction peak widths, related to dislocation density, were studied and correlated with stress variation during annealing process. Differences in stress relaxation between ferritic and austenitic samples were explained by different values of the stacking fault energy, which influences dislocation climb and cross-slip.

Corrections for residual stress in X-ray grazing incidence technique

Grazing incidence technique can be used to study samples with important stress gradients. The stress can be measured at very small depths, of the order of a few μm. The penetration depth of radiation is almost constant in a wide 2θ range for a given incidence angle α. It can be changed by an appropriate selection of α angle. This enables the investigation of stress variation with depth below the sample surface. There are, however, some factors which have to be corrected in this technique. The most important one is the X-ray wave refraction: it changes the wave length and direction of the beam inside a sample. These two effects cause some shift of a peak position and they have to be taken into account. For small incidence angles (α≤100) the corrections are significant and can modify the measured stress even of 70 MPa. The refraction correction decreases with increasing of the incidence angle. The corrections were tested on ferrite powder and on the ground AISI316L steel samples.