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Selective laser melted Titanium grade 23 was characterized by low porosity, relatively large surface roughness and pronounced surface texture (i.e. surface grooves orientation). The band/layer microstructure was built of mixed α and β phases. The as printed structure exhibited very high compressive residual stresses with strong anisotropy (i.e., − 512 ± 17 MPa and − 282 ± 14 MPa along the laser scanning direction and along the transverse direction, respectively) and strong fiber crystallographic texture. The latter one is responsible for the anisotropy of hardness in the material. Annealing at 600 °C during four hours significantly removed residual stresses (i.e. to − 14 ± 2.8 MPa) and slightly weakened the texture. Yield strength, 1120 ± 50 MPa, and ultimate tensile strength, 1210 ± 50 MPa, of the annealed material are significantly higher and tensile elongation, 3.9%, lower than for commercial Titanium grade 23. Final mechanical polishing to obtain flat and relatively smooth surface induced desired compression residual stress in the subsurface (i.e., equal to about − 90 MPa). Low absorbed gas contents (oxygen, nitrogen, hydrogen) and low porosity of the printed material indicates the correctness of the technology and allows the printed material to be classified as meeting the requirements of ASTM standards for Titanium grade 23. Besides traditional testing techniques, the optical profilometry, X-ray analysis (texture and residual stresses measurement) and infrared absorption method were applied for the product characterization and some potential of these testing methods and usefulness in technological practice was discussed, what can be particularly interesting both to practitioners from industry and researches from scientific laboratories.

Characterisation of the residual stresses at a scale of polycrystalline grains is the main topic of this work. The grazing incidence X-ray diffraction during “in situ” tensile test and a novel method of experimental data interpretation allowed to determine the evolution of macroscopic and intergranular stresses (the second order stresses) during elastic-plastic deformation and elastic unloading of AZ31 alloy sample. Additionally, the values of the critical resolved shear stresses were determined for slip systems activated during plastic deformation. A new important finding of this work is the determination of significant residual intergranular stresses in textured magnesium alloy subjected to plastic deformation. These stresses are correlated with the orientation of basal plane with respect to the applied stress, and they can be explained by a large difference between critical resolved shear stress values for basal and non-basal slip systems. In contrast to the magnesium alloy studied in this work, low values of the second order stresses were found previously in a two-phase Ti alloy due to the small difference between critical resolved stresses in both phases.

The goal work of this work is to describe the qualitative and quantitative behaviour of titanium T40 during tensile test. Material characteristics were determined using EBSD and X-ray techniques. Textures, twin boundary fractions, residual stresses and coherent domain size were determined. It was found that deformation mechanisms and microstructure characteristics are different in the samples stretched along rolling and transverse directions. For example the average grain size, as determined from EBSD measurements, is higher in the sample stretched along rolling direction. Also smaller coherent domains form and residual stress is more easily relaxed in this sample. A strong appearance of tensile twins was observed in the samples deformed along transverse direction. In the present paper a complex study of material characteristics and deformation mechanisms is presented. A special emphasis is done on residual stress characteristics determined in the samples stretched in two perpendicular directions.

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.

The multireflection grazing incident X-ray diffraction (MGIXD) is used to determine a stress gradient in thin surface layers (about 1-20 μm for metals). In this work two theoretical developments of this method are presented. The first procedure enables determination of c/a parameter in hexagonal polycrystalline materials exhibiting residual stresses. In the second method, the influence of stacking faults on the experimental data is considered. The results of both procedures were verified using X-rays diffraction.

Asymmetric rolling can be used in order to modify material properties and to decrease 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 EBSD technique and X-ray diffraction. The rolling asymmetry was realized using two identical rolls, driven by independent motors, rotating with different angular velocities w1 and w2. It was found that asymmetric rolling leads to microstructure refinement, texture homogenization and lowering of residual stress.

The results of three-dimensional simulation of asymmetric rolling, using Finite Elements Method, are presented. The example case of low carbon steel is considered. The rolling asymmetry, considered in the present work, results from different angular velocities of two identical working rolls. The effects of asymmetry on stress and strain distributions, material bending and variations of normal force and torque exerted by rolls are calculated and discussed. A special emphasis is done on the influence of inclined entry of a rolled material, which can appear in sequential rolling. Such the entry can partly compensate the material bending during. The results of the present simulations show that optimum parameters can be found in order to minimize the effect of sheet curvature and to reduce the applied torque and normal rolling force. The predicted internal stress distributions were applied next in the crystallographic deformation model; the predicted textures of symmetric and asymmetric rolling are in good agreement with experimental results.

The multi-reflection grazing incidence X-ray diffrection was used to determine residual stress gradient in the mechanically polished Al-Mg alloy and CrN coating. Also, the root mean square values of the third order lattice strain was determined using Wiliamson-Hall method. The results obtained for Al-Mg alloy show that the stress field in the surface layer as well as the microstructure (density of dislocation) depend strongly on the sample preparation. A very high residual compressive stress, which does not change significantly with depth, was measured in the CrN coating. Moreover, a large value of the measured third order strains in the coating was found.

Asymmetric rolling is a promising forming technique offering numerous possibilities of material properties modification and the improvement of technological process parameters. This geometry of deformation is relatively easy to implement on existing industrial rolling mills. Moreover, it can provide large volume of a material with modified properties. 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 EBSD technique and X-ray diffraction. The rolling asymmetry was realized using two identical rolls, driven by independent motors, rotating with different angular velocities ω1 and ω2. This ensured a wide range of rolling asymmetry: A=ω1/ω2. It was found that a strong shear stress induced in the asymmetrically rolled material allowed to obtain a microstructure refinement, texture homogenization and lowering of residual stress.

The relation between residual stresses occurring in plastically deformed material and after subsequent annealing is of practical and theoretical importance. In the present work the X-ray multi-reflection method was applied to determine residual stresses and their orientation distribution in rolled and annealed ferrite and austenite steel samples. An important decrease of the first- and the second-order residual stresses was observed during recovery and recrystallization processes. Diffraction peak width was also studied and correlated with stress variation during annealing. Different kinetics of stress relaxation in ferrite and austenite were explained by different levels of stacking fault energy and different types of intergranular interactions occurring in these materials.

The aim of the present work is to study effects occurring during elatoplastic deformation and unloading of Al/SiCp metal–matrix composite material. We have measured lattice strains for both phases independently using two separated diffraction peaks (the 111 reflections of Al and SiC) during in situ tensile testing. Lattice strains were measured in the direction parallel to the applied load. The results were compared with an elastoplastic model in order to find parameters determining the plastic deformation of Al matrix (critical resolved shear stress and hardening parameter). We have found that during initial deformation relaxation of the thermal stresses occurs in both phases. Afterwards, the distribution of strains measured during the in situ test and unloading of the sample agree very well with self-consistent model prediction.

Rotation of grain crystal lattice is the basic mechanism of texture formation and of anisotropic behavior of metals during plastic deformation. The classical definition of crystal lattice rotation leads in some cases to different texture and residual stress predictions than the definition based on the orientation preservation of selected sample planes and/or directions. Also the intensity of grain-matrix interaction plays an important role in the prediction of the above quantities. These problems were studied using elasto-plastic deformation model of polycrystalline materials. Examples of austenite and ferrite steels were considered.

The geometry based on the multireflection grazing incidence X-ray diffraction (called the MGIXD method) can be applied to measure residual stresses. Using this method, it is possible to perform a non-destructive analysis of the heterogeneous stresses for different and well defined volumes below the surface of the sample (range of several mm). As the result the average values of stresses weighted by absorption of X-ray radiation are measured. In this work the stress profile as a function of depth for mechanically polished Ti and Al samples were calculated from MGIXD data using inverse Laplace transform.

Multireflection grazing incidence X-ray diffraction (MGIXD) was applied to measure residual stresses in thin surface layers and the problem of X-ray elastic constants (XEC) used for the interpretation of results was studied. To show the influence of the X-ray elastic constants on the interpretation of MGIDX results, polycrystalline materials having low (Ti alloy) and high elastic anisotropy of crystallites (Ni alloy) were investigated.

The results of crystallographic textures and residual stress measurement in cross-rolled low carbon ferrite steel and polycrystalline copper of commercial purity are presented. It was found that cross-rolling significantly modifies crystallographic texture, residual stresses, and finally the plastic strain anisotropy. The cross-rolling provides a tool to modify the final properties of the material.

International audience; Multi-reflection grazing incidence geometry, referred to as MGIXD, characterized by a small and constant incidence angle, was applied to measure low surface stresses in very thin layers of Al-Mg alloy and CrN coating. These two materials were selected in order to deal with the low and high levels of residual stress, respectively. The influence of different mechanical treatments on residual stresses was studied for Al-Mg samples. It was found that both rolling and mechanical polishing influence the distribution and amplitude of residual stress in surface layers. In the case of CrN coating, a very high compressive stress was generated during the deposition process. The stress distributions determined by the MGIXD method is in good agreement with the classic sin2 technique results for all studied samples. In performing stress measurements for a powder sample, it was found that the application of the Göbel mirror in the incident beam strongly reduces statistical and misalignment errors. Additionally, the root mean square values of the third order lattice strain within diffracting grains were determined.

Formation of residual stresses and crystallographic textures during rolling have been studied using elasto-plastic deformation for polycrystalline material (Leffers-Wierzbanowski model). The rotation of grain crystal lattices is the basic mechanism of texture formation and anisotropic behavior of metals during plastic deformation. The classical definition of crystal lattice rotation leads in some cases to different texture predictions than the definition based on the orientation preservation of selected sample planes and/or directions (preservation condition). Also predicted residual stresses can be influenced by a choice of rotation definition. In the used deformation model of polycrystalline material, the intensity of grain-matrix interaction is described by the parameter L= aG, where G is shear modulus and a is elasto-plastic accommodation parameter. Model calculations have been done for different values of this parameter and for two definitions of lattice rotation. The predicted second order residual stresses and crystallographic textures for cold rolled ferrite steel are compared with experimental ones.

X-ray diffraction method was applied to measure residual stresses in deformed and annealed polycrystalline austenitic steel. An elastoplastic deformation model was used in analysis of experimental data. As the result, the orientation distribution function of grain stresses, created during elastoplastic deformation was determined and presented in the Euler space. An important decrease of the first and the second order residual stresses was observed during recovery process. It was found that the magnitude of the stresses decreases, while their distribution between different grain orientations remains almost unchanged.

Diffraction method was applied to determine the residual stresses in deformed and annealed polycrystalline samples of ferritic steel. The specific stored elastic energy corresponding to the grain stresses was calculated and presented in Euler space. An important decrease of the first and second order residual stresses and consequently stored elastic energy was observed during recovery and recrystallization. The evolution of stresses was correlated with the variation of diffraction peak width (related to dislocations density) and crystallographical texture.

ray diffraction method is used to determine the stress field in polycrystalline materials. The measurement of peak shifts enables the determination of the macrostresses and the plastic incompatibility stresses (intergranular stresses). In the interpretation of the experimental results self-consistent model of elatoplastic deformation is used. In the present work, the plastic incompatibility stresses and the elastic energy stored in cold rolled brass and ferritic steel were determinate. The results are discussed and presented in Euler space.

Using X-ray grazing incidence diffraction (GID) it is possible to perform a nondestructive 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 μm. The penetration depth of radiation is almost constant in a wide 2θ range for a given incidence angle α. It can be easily changed by an appropriate selection of α 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 wavelength and direction of the beam. Both effects modify a pick position. A corresponding correction was calculated and tested on ferrite powder and on 316L austenite stainless steel sample.

The X-ray diffraction method and theoretical model of elastoplastic deformation were used to examine the residual stresses in polycrystalline copper. To this end, the {2 2 0} strain pole figures were determined for samples subjected to different magnitudes of tensile deformation. Using diffraction data and the self-consistent model, the tensor of plastic incompatibility stress was found for each orientation of a polycrystalline grain. Crystallographic textures, macroscopic and second-order residual stresses were considered in the analysis. As a result, the distributions of elastic stored energy and von Mises equivalent stress were presented in Euler space and correlated with the preferred orientations of grains. Moreover, using the model prediction, the variation of the critical resolved shear stress with grain orientation was determined.

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.

The evolution of residual stress and crystallographic texture during thermal treatment was studied using X-ray diffraction. Polycrystalline α-brass samples were examined after cold rolling and afterwards after annealing at different temperatures in the range of 50 0C - 450 0C. Additionally, the width of the diffraction peak was measured in order to estimate the variation of the dislocation density. The interpretation of experimental data was based on a fitting procedure for which the anisotropic diffraction elastic constants calculated by a self-consistent approach were used. As the result of analysis, the values of the first order and second order stresses were determined in each sample.

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.

Stored energy is generally considered as a main driving force of recrystallization process. After plastic deformation a high dislocation density and residual stress field remain in a material. Both quantities are at the origin of the stored energy and we call them as the “plastic” and “elastic” parts of this energy. Their orientation distributions can be determined using diffraction and deformation models. Both components of the stored energy are studied in the present work. Their distributions and characteristics are studied for f.c.c. and b.c.c. materials.

A new method for determining the residual stresses in two-phase material is proposed. The method is based on the diffraction measurements analysed using a model of elasto-plastic deformation. The time-of-flight neutron diffraction technique was applied to determine lattice strains and a self-consistent rate-independent model was used to predict the second-order stresses in austeno-ferritic duplex steel. As the result of analysis, the stress state and elastic energy for each polycrystalline grain was found. Finally, the influence of different parameters characterizing elastoplastic deformation on the second-order stresses was studied.

Plastic deformation induces the dislocation and residual stress fields, which rest in a material after releasing of applied external forces. One can distinguish the stored energy connected with dislocation density and that with residual stresses. The stored energy distributions can be determined experimentally by diffraction experiments and also can be predicted by deformation models. The so obtained distributions of the stored energy versus crystal orientation were correlated with deformation and recrystallization textures of low carbon steel.

Residual stresses in cross-rolled polycrystalline copper and low carbon steel are studied. Cross-rolling modifies both residual stresses and crystallographic texture. Consequently, it can be used in order to improve the final properties of a material by introducing a given state of internal stress and by imposing more symmetry to the texture.

Residual stress fields induces elastic energy, stored in a material. Another kind of stored energy is due to dislocation density and this energy is mainly localized inside grains. The latter one is considered as a main driving force of recrystallization. However, the stored energy connected with the residual stresses can also have some influence on this process. Both types of energy can be determined experimentally and predicted by deformation models. Using recrystallization models and stored energy distribution, important features of the recrystallization process in cold rolled steel and polycrystalline copper can be explained.

Stored energy plays a crucial role in recrystallization process. One can distinguish two contributions to this energy. The first one is the elastic energy, connected with residual stresses, i.e., with grain-grain interaction. Another part of the stored energy is due to dislocation density, which is mainly localized inside grains. The latter one is considered as a main driving force of recrystallization. However, the stored energy connected with residual stresses can also have some influence on this process. Both types of energy can be determined experimentally and predicted by deformation models. Taking into account both types of the stored energy, some features of recrystallization textures can be explained.

The aim of this work is to study the influence of residual stresses on the properties of textured duplex stainless steel (DSS). The properties of both phases in DSS were studied using Xray diffraction whilst external load was applied “in situ” to the sample. The interpretation of experimental data is based on the diffraction elastic constants calculated by the self-consistent model taking into account the anisotropy of the studied material. Carrying out measurements in both compression and tension by using neutron diffraction, important differences in the evolution of lattice strains were noticed. An elastoplastic model is used to predict the evolution of the internal stresses during loading and to identify critical resolved shear stresses and strain hardening parameters of the material. The influence of the initial residual stresses on the yield stresses of the phases is considered. The difference between tensile and compressive behaviour of the steel is explained when the initial stresses (measured in the as received non-loaded sample by diffraction methods) are taken into account in model calculations. The yield stresses in each phase of the studied steel have been experimentally determined and successfully compared with the results of the elastoplastic self-consistent model.

A general X-ray multireflection method was applied to determine the stress level in deformed and recrystallised polycrystalline copper samples. Different reflections hkl were simultaneously used in the fitting procedure. The anisotropic diffraction elastic constants were calculated using the self consistent model and crystallographic texture. A significant decrease of the first order residual stresses was observed during recovery and recrystallisation. Diffraction peak widths and intensities were also examined for a few characteristic texture components during the recrystallisation process. Independently, synchrotron radiation and electron backscatter diffraction techniques were used to determine the stored energy in the examined material. The main result is that residual stress components start to reduce already before the recrystallisation process. The stored energy is strongly orientation dependent. It has the lowest value in the cubic texture component, which is dominating one in recrystalisation texture.

A general multi-reflection method was applied to determine the stress level in deformed and recrystallized polycrystalline copper samples. Different reflections hkl were simultaneously used in the fitting procedure. The anisotropic diffraction elastic constants were calculated using the self-consistent model and crystallographic texture. Important decrease of the first order residual stresses was observed during recovery and recrystallization. Independently, diffraction peak widths and intensities were examined for a few characteristic texture components during the recrystallization process. The importance of cubic orientation grains in the recrystallization process was confirmed.

Deformation models are used for predictions of deformation characteristics, crystallographic textures and for interpretation of residual stress measurements. A basic element of any model is a law defining the interaction between a grain and a surrounding material. The level of interaction is very different in various models. The aim of the present work is to find the value of interaction parameter in a given material, using residual stress measurements. The estimation has been done for highly rolled steel via examination of the second order stress. In particular the "snake type" behaviour (in e 33 vs. sin2 ψ plot) was useful in this study.

The residual stress field in a titanium nitride coating was determined using the X-ray diffraction method based on grazing incident angle geometry. The first order stress components were determined in TiN coating on WC and on steel substrates. The diffraction elastic constants calculated by the self-consistent method were used for the interpretation of the results. The advantages of the grazing incidence geometry are pointed out in the case of the examination of heterogeneous residual stresses in thin layers.

In this work the residual stress field in surface layer of titanium sample is determined using the X-ray diffraction method based on grazing incident angle geometry. The surface of the sample was thermally treated by laser beam causing a high level of macro and microstresses. The experimental results were analysed with help of the self-consistent model and a new method for estimation of the first and second order stresses was proposed.

Deformed samples have in general a heterogeneous structure, e.g., the texture and the stress state vary with distance across the sample. It is very useful to study these heterogeneities in a non-destructive way. Such a method for the study of texture heterogeneity is presented in this work. It was tested on model samples having two distinct layers with different textures. Textures of two layers were separated by a numerical treatment of the total diffraction signal. Neutron and X-ray diffraction techniques were used. The results are very promising.

We present an original method for the determination of residual stresses in plastically deformed polycrystalline material (1, 2). The advantage of our method is that the anisotropy of residual stress field can be determined. Moreover, the principles of the diffraction experiment for internal stress measurement are recalled. Using the neutron and X-ray techniques, we have determined the first and the second order stresses for cold rolled steel.

International audience; The geometry based on the multireflection grazing incidence X-ray diffraction can be applied to measure residual stresses. Using this method, it is possible to perform a non-destructive analysis of the heterogeneous stresses for different and well defined volumes below the surface of the sample (range of several μm). As the result, the average values of stresses weighted by absorption of X-ray radiation are measured. In this work the stress profiles as a function of penetration depth were determined for mechanically polished Al sample. Measurements and verification of the method were performed using classical X-ray diffractometer and synchrotron radiation with different wavelengths.

There exists a large spectrum of plastic deformation models for polycrystalline materials. Each model describes the interaction between a grain and a surrounding average matrix. In this work, two models were used for the interpretation of standard diffraction experiments to determine the residual stresses in plastically deformed polycrystalline materials. The advantage of the presented method is that both the first and the second order stresses can be estimated.

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.

Asymmetric rolling is a promising forming technique offering numerous possibilities of material properties modification and the improvement of technological process parameters. This geometry of deformation is relatively easy to implement on existing industrial rolling mills. Moreover, it can provide large volume of a material with modified properties. The study of microstructure, crystallographic texture and mechanical properties of asymmetrically rolled aluminium is presented in this work. The above characteristics were examined using 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 refinement, texture homogenization and decreasing of residual stress.

The mechanical properties of both phases in duplex stainless steel have been studied in situ using neutron diffraction during mechanical loading. Important differences in the evolution of lattice strains are observed between tests carried out in tension and compression. An elastoplastic self-consistent model is used to predict the evolution of internal stresses during loading and to identify critical resolved shear stresses and strain hardening parameters of the material. The differences between tensile and compressive behaviours of the phases are explained when the initial stresses are taken into account in model calculations. The yield stresses in each phase of the studied steel have been experimentally determined and successfully compared with the results of the elastoplastic self-consistent model.

Deformation by rolling induces in general a strong crystallographic texture, hence an important material anisotropy. This is a reason why the cross-rolling is sometimes applied in order to symmetrize the crystallographic texture. Such an operation modifies also residual stresses. The goal of this study was to characterize residual stress and texture changes during simple and crossrolling in polycrystalline copper and ferritic steel. The obtained results show that important modification of the first order residual stresses occurs during cross-rolling, while the level of the second order ones is approximately constant. Experimental results were analysed using an elastoplastic deformation model.