Determination of Diffraction Elastic Constants Using the Maximum Entropy Method

被引:0
作者
Krause, Maximilian [1 ]
Zuern, Michael [2 ]
Gibmeier, Jens [2 ]
Boehlke, Thomas [1 ]
机构
[1] Karlsruhe Inst Technol KIT, Inst Engn Mech, Chair Continuum Mech, Karlsruhe, Germany
[2] Karlsruhe Inst Technol KIT, Inst Appl Mat Mat Sci & Engn, Karlsruhe, Germany
关键词
Maximum entropy method; Linear thermoelasticity; Heterogeneous materials; Diffraction; Residual stress analysis; ZEROTH-ORDER BOUNDS; FIELD;
D O I
10.1007/s10659-025-10114-y
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
X-ray diffraction methods are an established technique to analyze residual stresses in polycrystalline materials. Using diffraction, lattice plane distances are measured, from which residual stresses can be calculated by using diffraction elastic constants which can be inferred from experimental measurements or calculated based on micromechanical model assumptions. We consider two different generalizations of existing micromechanical models for the case of texture-free, i.e. statistically isotropic, single-phase polycrystals. The first is based on the singular approximation method of classical micromechanics, from which existing Voigt, Reuss, Hashin-Shtrikman and self-consistent methods are recovered. The second approach, which is newly proposed in this work, is based on the micromechanical Maximum Entropy Method. Both approaches are applied to the problem of calculating diffraction elastic constants of texture-free cubic polycrystals and are found to be consistent with each other in that case. Full-field FFT simulations are used to validate the analytical models by simulating X-ray diffraction measurements of copper. In the simulative setting, many sources of experimental measurement error are not present, which results in a particularly accurate validation of theoretical bounds and approximations. The first core result of the paper is a formulation of diffraction elastic constants for texture-free polycrystals in terms of the macroscopically measurable effective shear modulus. These diffraction elastic constants can be adapted to the properties of a given material sample. The second core result is the validation of the Maximum Entropy Method for X-ray diffraction stress analysis of texture-free single-phase materials as a preliminary step before extending the method to textured and multi-phase materials.
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页数:29
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