Elastic Lattice Strains Research Articles

Texture and strain analysis of the ferroelastic behavior of Pb(Zr,Ti)O3 by in situ neutron diffraction

In situ uniaxial compression experiments on Pb(Zr,Ti)O3 or PZT-based polycrystalline electroceramics were conducted using time-of-flight neutron diffraction. Elastic lattice strain and texture evolution were observed in PZT’s near the edge of the morphotropic phase boundary (with tetragonal and rhombohedral phases present). Multiphase Rietveld analysis yielded anisotropic lattice strain evolution curves in directions parallel and perpendicular to the loading axis for both phases. A quantitative analysis of the domain switching under applied stress was possible through application of a March–Dollase model for texture.

On the mechanical behaviour of AA 7075-T6 during cyclic loading

The mechanical behavior of an aluminum alloy during uniaxial cyclic loading is examined using finite element simulations of aggregates with individually resolved crystals. The aggregates consist of face centered cubic (FCC) crystals with initial orientations assigned by sampling the orientation distribution function (ODF) determined from the measured crystallographic texture. The simulations show that the (elastic) lattice strains within the crystals evolve as the number of cycles increases. This evolution is attributed to the interactions between grains driven by the local plasticity. Under constant amplitude strain cycles, the average (macroscopic) stress decays with increasing number of cycles in concert with the evolution of the lattice strains. Further, the average number of active slip systems also decreases with increasing cycles, eventually reaching zero as the material response becomes totally elastic at the grain level. During much of the cyclic history only a single slip system is activated in most grains. The simulation results are compared to experimental data for the macroscopic stress and for lattice strains in the unloaded state after 1, 30 and 1000 cycles.

Prediction of intergranular strains in cubic metals using a multisite elastic-plastic model

A novel approach is adopted for determining the elastic and plastic strains of individual grains within a deformed polycrystalline aggregate. In this approach, termed “multisite modeling”, the deformation of a grain does not merely depend on the grain lattice orientation. It is also significantly influenced by the interaction with one or several of the surrounding grains. The elastic-plastic constitutive law is integrated by identifying iteratively which dislocation slip systems are activated within the grains, and the local stress tensor is shown to be the solution of a linear equation set. Several micro–macro averaging schemes are considered for the distribution of the macroscopic load over the polycrystalline aggregate. These averaging schemes are tested by simulating the development of intergranular strains during uniaxial tension of MONEL-400 as well as commercial purity aluminium. Neutron diffraction measurements of the elastic lattice strains are used as a reference in order to discriminate between the various predictions. The results demonstrate the relevance of “multisite” grain interactions in f.c.c. polycrystals.

Ferroelastic Behavior of PZT-Based Ferroelectric Ceramics

As a first step towards developing accurate constitutive relations for ferroelectrics, neutron diffraction experiments were conducted on Pb(Zr,Ti)O 3 (PZT)-based polycrystalline ceramics. Elastic lattice strain and texture evolution were monitored in situ during uniaxial compression experiments. Single phase (tetragonal) PZTs as well as those at the morphotropic phase boundary (with tetragonal and rhombohedral phases present) were investigated.

Modelling the Distribution of Lattice Strains Following Plastic Deformation of a Polycrystal. Application to Aluminum AA 7075 T6.

A modelling approach is described for computing the contribution to neutron diffraction peaks from variations in lattice strains in a polycrystalline material which has been subjected to plastic deformation. A grain-by-grain finite element formulation combined with crystal elastoplasticity was used to calculate the evolution of elastic lattice strains under loading conditions consistent with experiments performed on aluminum AA 7075 T6 samples. Eleven groups of crystals were associated with eleven measured neutron diffraction peaks. The full distribution of lattice strains was obtained for each of the crystal groups, thereby giving equivalent digital diffraction peaks. The model was able to incorporate various microstructural and material parameters. The impact of those parameters on the calculated diffraction peak profiles was studied, focusing on the Probability Distribution Functions best representing those profiles. It was found that Weibull and Gaussian distributions compete, with an advantage given to the former, due to its ability to account for skewness.

Bauschinger Effect in .ALPHA.-.GAMMA. Dual Phase Alloys Studied by In Situ Neutron Diffraction.

In situ neutron diffraction experiments during tension-compression deformation were performed on five Fe–Cr–Ni alloys with the volume fraction of ferrite (α) ranging from 0.0 to 100 %. Tensile deformation was applied in a step by step manner up to a strain of 1.3–2.0 % followed by compressive deformation, and neutron diffraction spectra were recorded during temporary stops of a deformation machine with fixed crosshead. (111) reflection of austenite and (110) of ferrite, respectively, were measured simultaneously by using a position sensitive detector. Elastic lattice strains in both constituent phases were evaluated from measured diffraction spectra as a function of external load. Based on these experimental results, heterogeneous deformation behavior in the α–γ dual phase alloys is discussed considering the Bauschinger effect. It is concluded that large compressive residual lattice strains detected in the γ phase after tensile pre-strain-ing, causes the large Bauschinger effect in α–γ dual phase alloys.

スピンバルブ構造をもつ極薄ＣｏＦｅフリー層の磁歪

An ultrathin CoFe free layer is very important for future high density recording head such as those using specular spin-valve films, because a CoFe free layer gives a higher MR ratio than a conventional NiFe/CoFe free layer. In order to realize a single CoFe free layer, we investigated the magnetostriction (λs) of an ultrathin CoFe free layer in spin-valve films. We compared the magnetostriction dependence on the underlayer structure among Cu, Ru, and Ru/Cu underlayers on a Ta buffer layer. For an Ru/Cu double-layered underlayer, λs becomes positively large when the Ru underlayer thickness is increased; on the other hand, it becomes negatively large when the Cu underlayer thickness is increased. This tendency can be explained by a model in which the λs is changed by the lattice elastic strain, where the volume ratio of Ru/Cu changes the lattice strain of an ultrathin CoFe free layer. The sensitivity of λs to the Cu underlayer thickness becomes large with increasing Co concentration in the CoFe free layer. This indicates that λs of a CoFe free layer becomes sensitive to the elastic strain with increasing Co concentration.

Low-temperature diffusion of lithium in silicon-germanium solid solutions

The influence of germanium content on lithium diffusion in Si1−x Gex solid solutions is investigated at temperatures from 300 to 500°C. It is found that the diffusion coefficient and the solubility of lithium abruptly decrease with a decrease in the temperature and an increase in the germanium content. As the diffusion temperature increases, the decrease in the lithium diffusion coefficient slows down with a change in the solid solution composition due to the effect of lattice elastic strains induced by germanium isovalent impurities.

In situ neutron diffraction study of α–γ Fe–Cr–Ni alloys under tensile deformation

Neutron diffraction experiments were performed in situ upon tensile loading for five Fe–Cr–Ni alloys with different ferrite volume fractions ranging from 0 to 100%. The diffraction profiles were recorded along with the tensile deformation curves during temporary stops in a deformation machine (5 ks each) with the crosshead fixed. One reflection of each phase, (111) of austenite (γ) and (110) of ferrite (α), respectively, were measured simultaneously by using a position sensitive detector. Evolution of elastic lattice strains and dislocation densities in both constituent phases was evaluated from measured diffraction profiles as a function of external loading. Based on these experimental results, heterogeneous deformation behavior in the α–γ dual-phase alloys is discussed.

Laboratory multiple-crystal X-ray topography and reciprocal-space mapping of protein crystals: influence of impurities on crystal perfection.

Double-axis multiple-crystal X-ray topography, rocking-curve measurements and triple-axis reciprocal-space mapping have been combined to characterize protein crystals using a laboratory source. Crystals of lysozyme and lysozyme crystals doped with acetylated lysozyme impurities were examined. It was shown that the incorporation of acetylated lysozyme into crystals of lysozyme induces mosaic domains that are responsible for the broadening and/or splitting of rocking curves and diffraction-space maps along the direction normal to the reciprocal-lattice vector, while the overall elastic lattice strain of the impurity-doped crystals does not appear to be appreciable in high angular resolution reciprocal-space maps. Multiple-crystal monochromatic X-ray topography, which is highly sensitive to lattice distortions, was used to reveal the spatial distribution of mosaic domains in crystals which correlates with the diffraction features in reciprocal space. Discussions of the influence of acetylated lysozyme on crystal perfection are given in terms of our observations.

A two phase elastic–plastic self-consistent model for the accumulation of microstrains in Waspaloy

A two phase self-consistent scheme for the accumulation of elastic lattice strains in the nickel-base superalloy Waspaloy is presented. The microstructure is idealised as a set of randomly orientated anisotropic grains which are assumed to be spherical and embedded within a homogenous effective medium which is assigned the properties of the bulk. Each grain is modelled as a medium with the properties of identically aligned cubic γ-Ni with a spherical inclusion of γ′-Ni 3Al. The γ′ is treated as an elastic anisotropic solid, and the γ is modelled as an elastic–plastic single crystal according to the Taylor–Bishop–Hill plasticity theory. The diffraction elastic constants and microstrains accumulated are compared with those found experimentally using neutron diffraction, as previously reported by Stone et al. The predictions are found to be adequate, and in particular the shift of load, as reflected in the microstrain, from the matrix to the precipitate between 3 and 10% plastic strain is reproduced. The implications of these results for the development and use of Reitveld-derived schemes for the measurement of bulk residual stress at spallation sources are discussed.

Lattice plane response during tensile loading of an aluminum 2 percent magnesium alloy

In-situ neutron diffraction measurements of plane specific elastic lattice strains were made during a tensile test of an aluminum 2 pct magnesium alloy. The macroscopic response exhibited a serrated flow curve, evidence of dynamic strain aging. The neutron results are compared to calculations using a self-consistent polycrystal deformation model. The relatively poor agreement with the measured data may suggest that the model has limitations with respect to face-centered cubic (fcc) alloys with low elastic anisotropy.

In-situ X-ray diffraction study on LaNi 5 and LaNi 4.75Al 0.25 in the initial activation process

We investigated the hydriding mechanism of LaNi 5 and LaNi 4.75Al 0.25 by means of in-situ X-ray diffraction (XRD) measurements during their activation process. The XRD profiles were analyzed by the Rietveld method to evaluate the lattice strain and the crystallite size for both the solid solution phase and the hydride phase. The change of the crystallite size and the formation of lattice strain in the initial hydrogen absorption and desorption were studied. In LaNi 5, the lattice strain of the solid solution phase did not increase through the plateau region while large anisotropic lattice strain was introduced in the hydride phase formed. The crystallite size of both phases was around 100 nm, which did not change significantly during the first cycle. These results indicate that lattice strain introduced in the hydride phase did not influence the coexisting solid solution phase in the activation process. The hydride phase is produced within a coherent domain of about 100 nm independently of neighboring domains, forming anisotropic lattice strain only in itself. In LaNi 4.75Al 0.25, anisotropic lattice strain of the same type as in LaNi 5 was not observed over the first absorption and desorption processes. However, a lattice strain that forms only in the hydride phase in the plateau region was observed. The two phases have some contact and exert elastic lattice strain on each other.

Residual strains in HY100 polycrystals: Comparisons of experiments and simulations

Residual stresses commonly arise in metallic components following plastic deformation and can have a significant effect on the mechanical properties. At the scale of the crystals, stresses are directly related to changes in lattice spacing. Neutron diffraction provides an effective method of measuring the spacing of atomic planes in crystal lattices with sufficient precision to determine the elastic (lattice) strains. In this work, tensile specimens were loaded and unloaded in situ to progressively larger amounts of plastic strain. Neutron diffraction measurements were taken at various points in the loading history, and the data were reduced to give the average elastic strains in subsets of the crystals characterized by common crystallographic directions.

In Situ High-Resolution Neutron Diffraction Study of Stress Induced Martensitic Transformations in CuAlZnMn Shape Memory Alloy

Stress induced martensitic transformation in Cu-10Al-5Zn-5Mn [wt.%] shape memory alloy (SMA) was investigated in situ by neutron diffraction technique. The SMA specimen was deformed step by step at room temperature and neutron diffraction spectra were recorded during the temporary stops. The analysis of the neutron diffraction profiles gathered along the reversible σ-e curve yields accurate bulk information on the structural changes associated with the martensitic transformations and elastic lattice strains. It is shown that, in spite of the almost complete reverse transformation from the martensite to the austenite phase upon unloading, the crystal lattice of the austenite phase becomes slightly distorted compared to the virgin state following just a single pseudoelastic cycle. It is suggested that this slight oriented distortion assists the stress induced martensitic transformation in successive tensile load cycles. It can play an important role in functional fatigue of SMA's and two-way shape memory effect.

In situ neutron diffraction study of metals under external mechanical loading

High-resolution neutron strain scanners in NPI were recently equipped with a deformation rig enabling both tensile and compressive tests of materials. Employing this instrumentation can bring new information concerning deformation process in various polycrystalline materials. Multiphase materials are particularly suitable for such experiments because strain states could be determined in situ by diffraction in each individual phase yielding thus frequently a scheme of phase interaction in deformation process [1]. Microstructural characteristics of individual phases such as elastic lattice strain or microstrain can be determined from the profile analysis (position, width and shape of the diffraction peaks corresponding to each phase). These characteristics can be associated with macroscopic stresses and strains. In this paper, results of the investigation of the CuAlZnMn shape memory alloy exhibiting stress-induced martensitic transformation is shown to demonstrate the applicability of the experimental technique.

The study of structural properties of 100 keV hydrogen ion implanted semi-insulating GaAs single crystals

100 keV hydrogen ion implantation has been carried out on undoped semi-insulating 〈1 0 0〉 gallium arsenide single crystals for various ion doses at room temperature. The structural properties due to high dose, low energy hydrogen ion implantation has been investigated using X-ray double crystal diffractometry (DCD) analysis, Rutherford backscattering spectrometry and channeling (RBS/C) experiments and transmission electron microscopy (TEM) analysis. By using DCD analysis, the value of elastic lattice strain for the ion doses of 1 × 10 16, 1 × 10 18 ions/cm 2 has been estimated to be 2.1 × 10 −3 and 3.2 × 10 -3, respectively. The RBS spectra in the channeling mode for the high dose implantations (10 17 and 10 18 ions/cm 2) show a high yield indicating a highly damaged region near the range of the implanted hydrogen ions. Particularly, for the dose 10 18 ions/cm 2, a heavily damaged region at the surface can be observed. The TEM results evidenced that no amorphisation occurred for the dose 10 18 ions/cm 2. From TEM characterisation, it is also observed that there are no hydrogen bubbles present in the implanted region. But small dislocation loops have been identified. The projected range of implanted hydrogen ions and the thickness of the implanted layer obtained by RBS and TEM analysis are compared with the TRIM calculations.

Self-consistent modelling of the plastic deformation of f.c.c. polycrystals and its implications for diffraction measurements of internal stresses

Using a self consistent scheme we model the development of elastic lattice strains during uniaxial loading for selected families of grains with specific orientations. These lattice strains vary dramatically for the different grain orientations, and most families of grains show a high degree of non-linearity at the start of the plastic regime. The 311 reflection does, however, respond almost linearly to loading, and therefore it constitutes a suitable reflection for characterization of macroscopic stresses and strains by diffraction for the given conditions. As a consequence of the high degree of non-linearity in the lattice strain response during loading highly anisotropic intergranular residual lattice strains develop during unloading. The evaluation of the model predictions by neutron diffraction is exemplified by selected results from in-situ loading experiments performed on austenitic stainless steel specimens. As a necessary condition for the proper understanding of the results we have included a description of the slip pattern resulting from the model applied and its relation to the slip patterns derived from the upper-bound Taylor model and the lower-bound Sachs model.

Röntgenographische Untersuchung von Spannungszuständen in Werkstoffen Teil IV. Fortsetzung von Matwiss. und Werkstofftechn. Heft 3/1995, S. 148–160, Heft 4/1995, S. 199–216 und Heft 9/1996, S. 426–437

X‐Ray Investigation of Stress States in MaterialsX‐ray stress analyses of crystalline or partially crystalline materials are based on the determination of elastic lattice strains which are converted to stresses by means of theory of elasticity. The development of the sin2Ψ‐method of X‐ray stress analysis and of diffractometers substituting film chambers during the 1960s initiated an enormous progress in X‐ray stress analysis during the following three decades both in respect of the knowledge of the underlying principles and in respect of the practical application.This report sketches the historical development of X‐ray stress analyses and describes the actual state of the art of this important tool for materials science and engineering. Besides some important elements of X‐ray physics and theory of elasticity, experimental aspects of practical applications are outlined. Standard measuring procedures and special measuring problems are described and hints for practical solutions are given. In particular, examples of destructive and non‐destructive depth profiling of residual stresses of residual stress analyses in thin coatings, in multilayer structures of thin coatings and in chemically graded coatings, of residual stress analyses in presence of textures, of residual and loading stress analyses in heterogeneous materials, in coarse grained, and in single crystalline materials are presented. The methods established up to now are explained and possible future developments are pointed out.

Röntgenographische Untersuchung von Spannungszuständen in Werkstoffen. Teil III. Fortsetzung von Matwiss. und Werkstofftechn. Heft 3/1995, S. 148–160 und Heft 4/1995, S. 199–216

AbstractX‐Ray Investigation of Stress States in materialsX‐ray stress analyses on crystalline or partially crystalline materials are based on the determination of elastic lattice strains which are converted to stresses by means of theory of elasticity. The development of the sin2Ψ‐method of X‐ray stress analysis and of diffractometers substituting film chambers during the 1960s initiated an enormcus progress in X‐ray stress analysis during the following three decades both in respect of the knowledge of the underlying principles and in respect of the practical applicationThis report sketches the historical development of X‐ray stress analyses and describes the actual state of the art of this important tool for materials science and engineering. Besides some important elements of X‐ray physics and theory of elasticity, experimental aspects of practical applications are outlined. Standard measuring procedures and special measuring problems are described and hints for practical solutions are given. In particular, examples of destructive and non‐destructive depth profiling of residual stresses, of residual stress analyses in thin coatings, in multilayer structures of thin coatings and in chemically graded coatings, of residual stress analyses in presence of textures, of residual and loading stress analyses in heterogeneous materials, in coarse grained, and in single crystalline materials are presented. The methods established up to now are explained and possible future developments are pointed out.