From Modeling of Plasticity in Single-Crystal Superalloys to High-Resolution X-rays Three-Crystal Diffractometer Peaks S
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UCTION
THE construction of realistic (i.e., dislocations-based) constitutive laws for the mechanical behavior of a representative volume of a real material remains an ongoing task. It is, however, hampered by the scarcity of real-time experimental data, which seldom go beyond tensile or creep curves and their dependence on the experimental conditions (stress, temperature, and strain rate). Further progress might thus be expected through the expanding use of in situ diffraction experiments at neutron sources and powerful high-energy beamlines at synchrotron facilities. Such tests now allow quasi real-time investigations and give access to the distribution of strains within bulk specimens under realistic conditions (temperature and stresses).[1–3] The 1D or 2D diffraction patterns recorded during tests performed on polycrystalline specimens are generally analyzed by fitting standard functions (PseudoVoigt…) with fit parameters related to microstructural parameters (Rietveld….) and stresses. More specialized statistical treatments may be used to investigate the effect of one among several specific parameters such as the strain fields associated with dislocations within deformed samples,[4–7] or point defects and impurities.[8–10] Such data can then be used as input parameters for modeling of the mechanical behavior. Diffraction peaks from real materials nevertheless remain quite
ALAIN JACQUES, Directeur de Recherche, is with the Institut Jean Lamour, (UMR 7198 CNRS UL), Labex DAMAS, Parc de Saurupt, CS 50840, 54011 Nancy Cedex, France. Contact e-mail: [email protected] Manuscript submitted May 8, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS A
difficult to analyze, as they result from a combination of these different effects: disorder within the microstructure, nonrandom distribution of dislocations, complicated distribution of internal stresses, etc. An alternative method is forward modeling of diffraction peaks,[11–17] i.e., computing (generally by finite element method) the strain/stress state of a real or computer-generated material, then to simulate the associated diffraction pattern for comparison: the volume of the material is divided into points which are projected on the pixel grid of a virtual 1D or 2D detector along the direction of their own local diffracted beam. The spot intensity is proportional to its volume and can be spread on neighboring detector pixels according to local elastic strain gradients or more simply using a Gaussian distribution,[16] and the distribution in wavelength within the monochromator range can be taken into account.[14] This method gives quite convincing results as long as the elastic strain and the atomic scattering factor are homogeneous at the scale of the distance between points and coherence effects between these points can be neglected (i.e., scattered intensities can be added instead of amplitudes). Large local strains in the vicinity of dislocation cores or point defects and chemical impurities, or abrupt changes in the scattering factor or the displacement field (due to st
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