M.A.M. Bourke

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.

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.

Microstructure of cryogenic treated M2 tool steel

Cryogenic treatment has been claimed to improve wear resistance of certain steels and has been implemented in cutting tools, autos, barrels etc. Although it has been confirmed that cryogenic treatment can improve the service life of tools, the underling mechanism remains unclear. In this paper, we studied the microstructure changes of M2 tool steel before and after cryogenic treatment. We found that cryogenic treatment can facilitate the formation of carbon clustering and increase the carbide density in the subsequent heat treatment, thus improving the wear resistance of steels.

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...

Elastic modulus of shape-memory NiTi from in situ neutron diffraction during macroscopic loading, instrumented indentation, and extensometry

The elastic modulus of B19’ shape-memory NiTi was determined using three techniques; from the response of lattice planes measured using in situ neutron diffraction during loading, instrumented indentation using a spherical indenter and macroscopic extensometry. The macroscopic measurements resulted in a modulus of 68 GPa, significantly less than the 101 GPa from indentation and the lattice plane average of 109 GPa from neutron diffraction. Evidence from the neutron measurements suggests that the disparity derives from the onset of small amounts of twinning at stresses less that 40 MPa, which might otherwise be considered elastic from a macroscopic view point.

Phase fraction, texture and strain evolution in superelastic NiTi and NiTi-TiC composites investigated by neutron diffraction

Samples of superelastic NiTi and superelastic NiTi reinforced with 10 vol.% TiC particles were deformed under uniaxial compression to 975 MPa while neutron diffraction spectra were simultaneously collected. Despite the presence of stiff TiC particles, a macroscopic strain of 3% was obtained in the composite on loading and was fully recovered on unloading. The diffraction spectra were analyzed by Rietveld refinement that included a spherical harmonic description of the texture and a lattice plane (hkl) dependent formulation of the elastic strain. The experiments provided bulk, phase-specific measurements of the evolution of phase fractions, texture and strains during the reversible stress-induced austenite to martensite transformation responsible for the large recoverable strains. For the composite, Eshelby elastic theory is used to predict the discrete phase strains measured by neutron diffraction. The observed behavior suggests that the martensite accommodates the mismatch with the transforming austenite (while they co-exist) and the TiC particles (in the case of the composite).

Thermally and mechanically induced residual strains in Al-SiC composites

Abstract Neutron diffraction experiments were conducted on 15vol.% whisker and 20vol.% particulate reinforced aluminum/silicon carbide composites subjected to a rapid quench followed by various deformation histories. Corresponding numerical simulations were carried out using an axisymmetric unit cell model, with a phenomenological, isotropic hardening descriotion of matrix plasticity. Thermal expansion and the temperature dependence of material properties were accounted for. For the whisker reinforced matrix, quantitative agreement was generally found between the measured and calculated residual elastic strains. For the particulate reinforced matrix, the calculations tended to overestimate the magnitude of the residual strains parallel to the deformation axis, but very good agreement was obtained transverse to the deformation axis. For the silicon carbide reinforcement, both whisker and particulate, the variation of predicted residual elastic strains along the deformation axis was qualitatively consistent with the measurements, although quantitative agreement was often lacking. Measured and predicted residual strains perpendicular to the deformation axis for the silicon carbide typically were not in agreement. Parametric studies were carried out to ascertain the dependence of calculated flow strengths and residual strains on cell and reinforcement aspect ratio, and on reinforcement spacing and shape.

NiTi and NiTi-TiC composites: Part IV. Neutron diffraction study of twinning and shape-memory recovery

Neutron diffraction measurements of internal elastic strains and crystallographic orientation were performed during compressive deformation of martensitic NiTi containing 0 vol pct and 20 vol pct TiC particles. For bulk NiTi, some twinning takes place upon initial loading below the apparent yield stress, resulting in a low apparent Youngs modulus; for reinforced NiTi, the elastic mismatch from the stiff particles enhances this effect. However, elastic load transfer between matrix and reinforcement takes place above and below the composite apparent yield stress, in good agreement with continuum mechanics predictions. Macroscopic plastic deformation occurs by matrix twinning, whereby (1 0 0) planes tend to align perpendicular to the stress axis. The elastic TiC particles do not alter the overall twinning behavior, indicating that the mismatch stresses associated with NiTi plastic deformation are fully relaxed by localized twinning at the interface between the matrix and the reinforcement. For both bulk and reinforced NiTi, partial reverse twinning takes place upon unloading, as indicated by a Bauschinger effect followed by rubberlike behavior, resulting in very low residual stresses in the unloaded condition. Shape-memory heat treatment leads to further recovery of the preferred orientation and very low residual stresses, as a result of self-accommodation during the phase transformations. It is concluded that, except for elastic load transfer, the thermal, transformation, and plastic mismatches resulting from the TiC particles are efficiently canceled by matrix twinning, in contrast to metal matrix composites deforming by slip.

Compressive yielding of tungsten fiber reinforced bulk metallic glass composites

In-situ uniaxial compression tests were conducted on four tungsten fiber reinforced bulk metallic glass matrix composites using neutron diffraction. The results were interpreted with a finite element model. Both phases were seen to approximately obey the von Mises yield criterion. The fibers were observed to yield first and then transfer load to the matrix.