B. Clausen

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.

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.

Twinning and detwinning during cyclic deformation of Mg alloy AZ31B

Textured Mg alloys exhibit tension – compression strength asymmetry due to mechanical twinning. The distinction arises as the material deforms primarily by slip in one direction and by twinning in the other. In-situ neutron diffraction during cyclic loading in tension and compression of extruded bar allows study of the effect of twinning on subsequent load reversals. The diffraction data reveal the texture evolution and internal stress development as a function of deformation. De-twinning resulted in complete texture reversal during initial cycles, but eventually “fatigued” resulting in some residual twin component.

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.

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.

Transformation-induced plasticity in an ultrafine-grained steel: An in situ neutron diffraction study

An ultrafine-grained steel with an average grain size of about 350nm was developed. The tensile testing at ambient temperature shows a threefold increase in the yield strength compared to its coarse-grained counterpart. Moreover, the increase in the strength was achieved without the sacrifice of the ductility due to strain-induced martensitic transformation. The evolution of lattice strains and phase fractions of the austenite and martensite phases during the deformation was investigated using in situ neutron diffraction to provide a micromechanical understanding of the transformation-induced plasticity responsible for the combination of high strength and ductility.

Measurement of the lattice plane strain and phase fraction evolution during heating and cooling in shape memory NiTi

We report on in situ neutron diffraction measurements during heating and cooling through the phase transformation in shape memory NiTi. The lattice plane specific strain evolution remains linear with temperature and is not influenced by intergranular stresses, enabling the determination of the thermal expansion tensor of B19′ NiTi. The neutron measurements are consistent with macroscopic dilatometric measurements and a 30 000 grain polycrystalline self-consistent model. The accommodative nature of B19′ NiTi results in macroscopic shape changes being offset (with temperature) from the start and finish of the transformation. The texture does not evolve in the absence of biasing stresses.

Neutron diffraction study of the contribution of grain contacts to nonlinear stress‐strain behavior

[1] Repeatable, hysteretic loops in quasi-static loading measurements on rocks are well known; the fundamental processes responsible for them are not. The grain contact region is usually treated as the site of these processes, but there is little supporting experimental evidence. We have performed simultaneous neutron diffraction and quasi-static loadingexperimentsonaselectionofrockstoexperimentally isolate the response of these contact regions. Neutron diffraction measures strain in the lattice planes of the bulk of the grain material, so differences between this strain and the macroscopic response yield information about grain contact behavior. We find the lattice responds linearly to stress in all cases, oblivious to the macroscopic unrecoverable strains, curvature, and hysteresis, localizing these effects to the contacts. Neutron diffraction shows that the more granular rocks appear to distribute stresses so that the same strain appears in all the grains, independent of crystallographic orientation. INDEX TERMS: 3909 Mineral Physics: Elasticity and anelasticity; 3902 Mineral Physics: Creep anddeformation;3954MineralPhysics:Xray,neutron,andelectron spectroscopy and diffraction; 3994 Mineral Physics: Instruments and techniques; 3694 Mineralogy and Petrology: Instruments and techniques.Citation: Darling, T. W., J. A. TenCate, D. W. Brown, B. Clausen, and S. C. Vogel (2004), Neutron diffraction study of the contribution of grain contacts to nonlinear stress-strain behavior, Geophys. Res. Lett., 31, L16604, doi:10.1029/2004GL020463.

Comparison of residual strains measured by X-ray and neutron diffraction in a titanium (Ti–6Al–4V) matrix composite

Abstract This research compares matrix thermal residual strains measured in a continuous fiber reinforced SiC/Ti–6Al–4V titanium matrix composite (TMC) using X-ray and neutron diffraction with finite element predictions. The strain dependence on the strains for several reflections (105, 204, 300, 213 and 312) of the matrix were explored at the surface (X-ray) and in the bulk (neutron). To determine the longitudinal surface strains from the X-ray measurements for comparison with the neutron values, the e φψ versus sin 2 ψ plots were extrapolated to ψ =90°. Continuum micro-mechanics based multi-ply finite element models (FEM) simulating rectangular and hexagonal fiber distributions were explored for calculating average surface and bulk strains. For different reflections, the experimentally determined surface measured strains ranged from +1904±424 to +2974±321 μ e and the bulk measurements ranged from +2269±421 to +3022±1134 μ e . These values contrast with the single valued FEM prediction of+3200 μ e which was the same for both the surface and the bulk.

Atomic pair distribution function analysis of materials containing crystalline and amorphous phases

Abstract The atomic pair distribution function (PDF) approach has been used to study the local structure of liquids, glasses and disordered crystalline materials. In this paper, we demonstrate the use of the PDF method to investigate systems containing a crystalline and an amorphous structural phase. We present two examples: Bulk metallic glass with crystalline reinforcements and Fontainebleau sandstone, where an unexpected glassy phase was discovered. In this paper we also discuss the refinement methods used in detail.