A comprehensive particle size distribution model has been developed for the simulation of c 0 precipitation in multicomponent Ni alloys. Nucleation, growth and coarsening of the precipitates are described by a particle size distribution. The growth rate of each precipitate class is calculated with a multi-component diffusion model formulated for non-diagonal matrices of diffusion coefficients. The model is fully coupled with CALPHAD calculations of the thermodynamic equilibrium at the interface, including a direct treatment of the effect of curvature through modification of the Gibbs free energy. An optimization strategy was developed to minimize the computational cost. The model was used to simulate ageing heat treatment at 600°C of Ni-7.56 at.% Al-8.56 at.% Cr, which was studied experimentally by Booth-Morrison and others (Booth-Morrison C, Weninger J, Sudbrack CK, Mao Z, Noebe RD, Seidman DN. Acta Mater 2008;56:3422; Mao Z, Booth-Morrison C, Sudbrack CK, Martin G, Seidman DN. Acta Mater 2012;60:1871). The comparisons showed that the precipitation stages of c 0 precipitates are correctly captured by the numerical model. It was shown that non-diagonal diffusion coefficients substantially influence the selection of the operating tie-line and the overall transformation kinetics. With non-diagonal diffusion matrices, complex phenomena such as uphill diffusion of Cr due to the Al gradients were evidenced and explained.

The precipitation of c¢ phase in a commercial single crystal Ni-based superalloy with different cooling rates has been investigated by atom probe tomography. Numerous irregular interconnected c¢ precipitates in the size range of~30 to 50 nm were obtained even utilizing the fastest possible cooling rate. Diffuse c/c¢ interface and far from equilibrium composition of c¢ phase were observed in the fast-cooled sample, suggesting that c¢ precipitation occurs via a spinodal decomposition at the very early stage. AM1 is a commercial single crystal Ni-based superalloy, which has been extensively used as the materials for high-pressure gas turbine blades and vanes in various aircraft engines.[1] It belongs to the first generation Re-free single crystal Ni-based superalloys. Its microstructure consists of cuboidal c¢ precipitates embedded into the c matrix after standard heat treatment. [1,2] It is subjected to a three-step heat treatment, i.e., solution, primary aging, and secondary aging heat treatments. The alloy is first solutionized at the single c field, and then cooled to precipitate a L1 2 -ordered c¢ phase from the face-centered cubic (fcc) c matrix. The cooling rate after solutionizing mainly determines the size, the morphology, and the distribution of c¢ precipitates. It is followed by the primary and secondary aging heat treatments at an intermediate temperature and a low temperature, which allows to refine the size and the morphology of c¢ precipitates. [3] The precipitation of c¢ phase has been widely studied in various Ni-based alloys, e.g., Ni-Al alloys, [4][5][6][7][8][9] Ni-AlCr alloys, [10][11][12] Ni-Al-Ti alloys, [13][14][15] polycrystalline superalloys, [16][17][18][19][20][21] etc. However, very few papers have been involved in the study of c¢ precipitation in single crystal Ni-based superalloys at early stage during the rapid cooling conditions. Since c¢ phase has a L1 2 ordered structure, c¢ phase separation must be accompanied by an ordering process. However, it still remains debatable with respect to the occurrence sequence of the spinodal clustering and atomic ordering. The chemical ordering would precede the spinodal decomposition due to the short-range atomic jump involved in the ordering process while long-range diffusion is needed for spinodal decomposition.

Damage occurring under tensile loading and the resulting increase in electrical resistance of tin-doped indium oxide and amorphous graphite coatings on various polymer substrates are investigated, using an electrofragmentation method in situ in an optical microscope. The electrical resistance is modeled as a function of damage state assuming that the resistance of coating cracks is proportional to their opening, and that there exists a conducting path of constant thickness at the coating/substrate interface across the crack. The model reproduces the experimental data with good accuracy apart from the damage initiation and saturation stages where it underestimates the measured coating resistance. This is due to the presence of stable cracks of finite length in the initiation stage and delamination in the saturation stage. Impedance spectroscopy measurements confirm the purely resistive nature of the conducting path, whose resistivity is found to be three to four orders of magnitude higher than that of the uncracked coating.

The influence of internal stress anisotropy resulting from anisotropic loading in a roll-to-roll (R2R) process, and polymer substrate anisotropy on the crack onset strain (COS) of thin oxide coatings was analyzed. Experimental data obtained for R2R processed films were compared with data obtained using an isotropic sheet-to-sheet (S2S) process with the same anisotropic substrate. In the R2R case the COS was found to increase by 20% between the transverse direction and the machine direction. In the S2S case the COS was found to be independent of orientation, except at a 45°in-plane orientation with respect to the machine direction, where it was 15% higher. The internal stress in the machine direction could not be determined, presumably due to deposition-induced curvature changes of the polymer substrate, and was therefore fitted to the COS data. Fracture mechanics analysis and finite element modeling of the experimental data showed that the influence of substrate anisotropy was marginal, and that it was the process-induced internal strain in the coating which controlled the COS.

International audienceA comprehensive simulation approach integrating solidification, homogenization, and precipitation during aging has been used to predict the formation of γ/γ′ microstructures in the AM1 nickel-based superalloy. The particle size distribution of intradendritic γ′ precipitates after aging was calculated with a multicomponent diffusion model coupled with CALPHAD thermodynamics for the equilibrium at the interface. The influence of residual microsegregation after homogenization and quenching was analyzed through different initial conditions obtained from calculations of the concentration profiles in the primary γ dendritic microstructure during solidification and the homogenization heat treatment. While the global sequence of precipitation remains qualitatively the same, substantial differences in the final volume fraction of γ′ precipitates were predicted between the core and the periphery of a former dendrite arm, for typical homogenization and aging conditions. To demonstrate the relevance of the developed simulation approach, the model was also used to investigate modified precipitation heat treatments. The simulations showed that relatively short heat treatments based on slow continuous cooling could potentially replace the extended isothermal heat treatments which are commonly used. Slow continuous cooling conditions can lead to similar γ′ precipitates radii and volume fractions, the main differences with isothermal heat treatments lying in a narrower particle size distribution