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Development of a new consistent discreteGreen operator for FFT-based methods to solve heterogeneous problems with eigenstrains. International Journal of Plasticity, Elsevier, In press, Abstract In this paper, a new expression of the periodized discrete Green operator using the Discrete Fourier Transform method and consistent with the Fourier grid is derived from the classic "Continuous Green Operator" (CGO) in order to take explicitly into account the discreteness of the Discrete Fourier Transform methods. It is shown that the easy use of the conventional continuous Fourier transform of the modified Green operator (CGO approximation) for heterogeneous materials with eigenstrains leads to spurious oscillations when computing the local responses of composite materials close to materials discontinuities like interfaces, dislocations. In this paper, we also focus on the calculation of the displacement field and its associated discrete Green operator which may be useful for materials characterization methods like diffraction techniques. We show that the development of these new consistent discrete Green operators in the Fourier space named "Discrete Green Operators" (DGO) allows to eliminate oscillations while retaining similar convergence capability. For illustration, a DGO for strain-based modified Green tensor is implemented in an iterative algorithm for heterogeneous periodic composites with eigenstrain fields. Numerical examples are reported, such as the computation of the local stresses and displacements of composite materials with homogeneous or heterogeneous elasticity combined with dilatational eigenstrain or eigenstrain representing prismatic dislocation loops. The numerical stress and displacement solutions obtained with the DGO are calculated for cubic-shaped inclusions, spherical Eshelby and inhomogeneity problems. The results are discussed and compared with analytical solutions and the classic discretization method using the CGO.

International audienceThe phase-specific high temperature creep behaviours of the and phases of a rafted Ni-based single crystal superalloy were investigated by a combination of in situ creep experiments and diffraction of high-energy X-ray synchrotron radiation. In situ experiments were performed at constant temperatures in a 9301125 degrees C temperature range and under variable applied stress in order to study the material's response (plastic strain, load transfer) to stress jumps. Using three crystal diffractometry in transmission (Laue) geometry, it was possible to measure the average lattice parameters of both the matrix and the rafts in the [100] direction at intervals shorter than 300s. The absolute precision on the measurement of the constrained transverse mismatch (in the rafts' plane) is better than 10(5). Plastic strain occurs within the corridors as soon as the Von Mises stress exceeds the Orowan stress. The plasticity of the rafts apparently depends on the transverse stress (i.e. perpendicular to the tensile axis) exceeding a threshold value of 60MPa

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