M.R. Daymond

USE OF RIETVELD REFINEMENT FOR ELASTIC MACROSTRAIN DETERMINATION AND FOR EVALUATION OF PLASTIC STRAIN HISTORY FROM DIFFRACTION SPECTRA

Macrostrain variations in engineering components are frequently examined using neutron diffraction, at both reactors and pulsed sources. It is desirable to minimize the sampling volume in order to maximize the spatial resolution, although this increases the required measurement time. At reactors, macrostrain behavior is inferred from a single lattice reflection (deemed to be representative of the bulk response). At a pulsed source, a complete diffraction pattern is recorded and accordingly it is natural to fit the entire diffraction spectra using a Rietveld [J. Appl. Cryst. 2, 65 (1969)] refinement. This means that an idealized crystal structure is fit to the measured distorted crystal structure, which includes deviation of the measured lattice reflections from the ideal due to elastoplastic strain anisotropies, which are dependent on the particular lattice reflection (hkl) considered. We show that elastic macrostrains calculated from lattice parameter changes in Rietveld refinements (without accounting for hkl dependent anisotropies) are almost identical to the bulk elastic response and are comparable to the response obtained from a single lattice reflection typically used by practitioners at a steady state source. Moreover good refinements on the complete pattern are obtained with short measurement times compared to what is required for good statistics for single reflections. By incorporating a description of the elastic strain anisotropy expected in cubic materials into the Rietveld code, an empirical prediction of plastic strain history is possible. The validity of these arguments is demonstrated by analysis of a uniaxial tensile load test and a reanalysis of previously reported data taken on a deformed stainless steel ring. The plastic strain predictions compare favorably with a finite element model.

ENGIN-X: A third-generation neutron strain scanner

ENGIN-X, a new time-of-flight (TOF) neutron diffractometer optimized to measure elastic strains at precise locations in bulky specimens recently commissioned at the ISIS Facility in the Rutherford Laboratory, UK, is described. Fast counting times, together with a flexible and accurate definition of the instrumental gauge volume are the main requirements of neutron strain scanning and have been addressed on ENGIN-X through the design of a novel TOF diffractometer with a tuneable resolution and interchangeable radial collimators. Further, the routine operation of the instrument has been optimized by creating a virtual instrument, i.e. a three-dimensional computer representation of the diffractometer and samples, which assists in the planning and execution of experiments. On comparing ENGIN-X with its predecessor ENGIN, a 25× gain in performance is found, which has allowed the determination of stresses up to 60 mm deep in steel specimens. For comparison with constant-wavelength diffractometers, special attention has been paid to the absolute number of counts recorded during the experiments. A simple expression is presented for the estimation of counting times in TOF neutron strain scanning experiments.

Lattice strain evolution during uniaxial tensile loading of stainless steel

Applied and residual lattice strains were determined by neutron diffraction during a tensile test of a weakly textured austenitic stainless steel and were compared to the predictions of a self-consistent polycrystal deformation model. Parallel to the tensile axis the model predictions are generally within the resolution of the diffraction measurements, but perpendicular to the tensile axis discrepancies are noted. Discrepancies between model and measurements were greater for the residual lattice strains than during loading. It is postulated that this is because the model does not predict reverse plasticity during unload.

Elastoplastic deformation of ferritic steel and cementite studied by neutron diffraction and self-consistent modelling

Abstract A tensile specimen was machined from heat treated ferritic steel, with a small volume fraction of carbon in the form of cementite. In situ measurements of the strain response of multiple hkl lattice planes to an applied uniaxial tensile load were made using neutron diffraction, to macroscopic plastic strains of around 3%. The experimental results are compared with predictions from a self-consistent Hill–Hutchinson model modified to take into account the presence of the second phase. Good agreement was obtained between model and experimental data. The interpretation of residual stress measurements, for both single peak and Rietveld measurements is considered in light of these results.

Measured and predicted intergranular strains in textured austenitic steel

Tensile specimens were machined from heat-treated austenitic stainless steel plate prior to and after 70% reduction by uni-directional rolling. In addition to a single specimen cut from the as-received plate, two specimens were cut from the rolled plate, with axes parallel and perpendicular to the rolling direction, respectively. In situ measurements of the strain response of multiple hkl lattice planes to an applied uniaxial tensile load were made using neutron diffraction, to macroscopic plastic strains of around 1%. The experimental results are compared with predictions from a self-consistent Hill–Hutchinson model. The measured texture in the plate was approximately three times random; however, its effect on the hkl response was small compared to the residual strains left by rolling. The apparent elastic modulus of the planes is affected by the residual strains, which is attributed to the effect of micro-plasticity. Interpretation of residual stress measurements, for both single peak and Rietveld measurements is considered in light of these results.

Use of Rietveld refinement to fit a hexagonal crystal structure in the presence of elastic and plastic anisotropy

When multiple elastic diffraction peaks are obtained from an x-ray or neutron source, data analysis is commonly performed using a Rietveld refinement applied to the entire pattern, rather than simply performing single peak fits. In the simplest case the crystal structure is assumed to be ideal despite the presence of stresses which, coupled with the elastic and plastic anisotropy of individual grains, can result in a nonisotropic response of the polycrystal. A first step to account for this anisotropy in the refinement is to include an anisotropic strain parameter. In an earlier work [J. Appl. Phys. 82, 1554 (1997)] we included elastic anisotropy into a Rietveld refinement and discussed its validity in the elastic and plastic regimes for a cubic crystal structure. Here we extend the discussion to include anisotropy in hexagonal crystal structures. The agreement between single peak fits and the Rietveld refinement modeled single peak positions is considered for hexagonal close packed beryllium in the prese...

The determination of a continuum mechanics equivalent elastic strain from the analysis of multiple diffraction peaks

Stress measurement by neutron or synchrotron x-ray diffraction is a nondestructive technique that provides insights into strain and/or stress fields deep within engineering components and structures. The technique is seeing increased use for the validation of finite element process models, however, present FE models predict a continuum elastic strain rather than diffraction strains. An expression is therefore derived for a physically realistic weighting of strains obtained from multiple single peak diffraction measurements of internal elastic strain in order to determine a macroscopic equivalent elastic strain, and hence stress. A practical approach to the use of the expression is suggested. A similar expression is derived for the equivalent weighting used in Rietveld refinements, for both polychromatic and monochromatic sources, which is applicable to both neutron and x-ray diffraction. The use of these expressions is illustrated for both textured and untextured, cubic (steel) and hexagonal (titanium) sy...

Strain imaging by Bragg edge neutron transmission

The Bragg edges appearing in the transmitted time-of-flight spectra of polycrystalline materials have been recorded using a two-dimensional array of detectors. Subsequent analysis has enabled maps of the elastic strain to be produced.

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.

Fast residual stress mapping using energy-dispersive synchrotron X-ray diffraction on station 16.3 at the SRS.

Synchrotron energy-dispersive X-ray diffraction experiments on station 16.3 at the SRS for residual strain mapping are reported. A white beam with an energy-discriminating detector allows measurements to be made through 3 mm Al, Ti, Fe and Cu alloys with acquisition times of approximately 30 s per 0.3 mm(3) sampling volume. The collected profiles were analysed using single-peak fitting and whole-pattern Pawley refinement, and produced strain accuracy better than 10(-4). This configuration is therefore highly efficient for fast strain mapping in thin components using a second-generation synchrotron source.