A method for finding the optimum alloy compositions considering a large number of property requirements and constraints by systematic exploration of large composition spaces is proposed. It is based on a numerical multi-criteria global optimization algorithm (multistart solver using Sequential Quadratic Programming), which delivers the exact optimum considering all constraints. The CALPHAD method is used to provide the thermodynamic equilibrium properties, and the creep strength of the alloys is predicted based on a qualitative numerical model considering the solid solution strengthening of the matrix by the elements Re, Mo and W and the optimum morphology and fraction of the γ′-phase. The calculated alloy properties which are required as an input for the optimization algorithm are provided via very fast Kriging surrogate models. This greatly reduces the total calculation time of the optimization to the order of minutes on a personal computer. The capability of the multi-criteria optimization method developed was experimentally verified with two new single crystal superalloys. Their compositions were designed such that the content of expensive elements was reduced. One of the newly designed alloys, termed ERBO/13, is found to possess creep strength of only 14 K below CMSX-4 in the high-temperature/low-stress regime although it is a Re-free alloy.

Refractory elements like W are potent solid solution strengtheners, but they are also heavy and costly. They should be used as sparingly as possible. In the present paper, a series of single crystal alloys are prepared with varying amounts of Ta and Ti, but constant overall refractory concentration and g'-volume fraction. Partitioning behavior of W and other elements after solutionizing and ageing treatment is investigated. Both, Ta and Ti are able to increase the W content in the g-matrix. This provides an effective strategy to maximize solid solution strengthening potential for a given overall W content of the alloy. The experimentally determined phase characteristics and homogenization behavior are compared with numerical simulation. Good agreement is observed. Erlangen is gratefully acknowledged for the alloy density measurements and Steffen Neumeier (University of Erlangen) is gratefully acknowledged for helpful comments and suggestions regarding property interactions in complex nickel-based superalloys.

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We prepared 41 different superalloy compositions by an arc melting, casting, and heat treatment process. Alloy solid solution strengthening elements were added in graded amounts, and we measured the solidus, liquidus, and c¢-solvus temperatures of the samples by DSC. The c¢-phase fraction increased as the W, Mo, and Re contents were increased, and W showed the most pronounced effect. Ru decreased the c¢-phase fraction. Melting temperatures (i.e., solidus and liquidus) were increased by addition of Re, W, and Ru (the effect increased in that order). Addition of Mo decreased the melting temperature. W was effective as a strengthening element because it acted as a solid solution strengthener and increased the fraction of fine c¢-precipitates, thus improving precipitation strengthening. Experimentally determined values were compared with calculated values based on the CALPHAD software tools Thermo-Calc (databases: TTNI8 and TCNI6) and MatCalc (database ME-NI). The ME-NI database, which was specially adapted to the present investigation, showed good agreement. TTNI8 also showed good results. The TCNI6 database is suitable for computational design of complex nickel-based superalloys. However, a large deviation remained between the experiment results and calculations based on this database. It also erroneously predicted c¢-phase separations and failed to describe the Ru-effect on transition temperatures.

Three experimental Ni-base superalloys of the second, third and fourth generation are studied in this work to clarify the effect of Re and Ru on the precipitation of TCP phases. Thermodynamic calculations using the CALPHAD method are performed based on the local chemical composition obtained with the use of electron probe microanalysis. The effects of microsegregation and g 0 -precipitation are taken into account. The results, complemented with scanning electron microscopy observations, show that Re increases, while Ru decreases the inclination of the material to precipitate TCP phases. The effect of both elements is assigned to thermodynamic rather than kinetic reasons. The CALPHAD-calculations do predict the effect of Re on the TCP phase formation in the investigated alloys correctly, but not the effect of Ru.

The development of new Ni-base superalloys with a complex composition consisting of eight or more alloying elements is a challenging task. The experimental state-of-the-art development cycle is based on the adaption of already existing compositions. Although new alloy compositions with potentially improved material properties are expected to be similar to already known superalloys, this procedure impedes efficiently finding these compositions in the large multi-dimensional design-space of all alloying elements. Modern alloy development combines numerical optimization methods with experimental validation to guide the development towards promising compositions. In this work, an improved numerical multi-criteria optimization tool using CALPHAD calculations and semi-empirical models for alloy development is presented. The model improvements to its predecessor are described and the successful application for the development of rhenium-free single-crystal Ni-base superalloys ERBO/13 and ERBO/15 is revisited. The optimization tool is described and the designed alloys are discussed regarding phase stability. Finally, a possible phase stability model extending the optimization tool and improving the alloy composition predictions is presented.

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Tailoring the partitioning behavior of solid solution strengtheners is a crucial design strategy for advanced Ni-based superalloys. The goal of this study was to maximize the enrichment of Mo, Re, Ru and W in the γ-matrix phase. To determine the composition dependency of the partitioning behavior, a set of polycrystalline superalloys with varying contents of these solid solution-strengthening elements and a W-containing single-crystalline alloy series with varying concentrations of the γ′-forming elements Ta and Ti was produced. Assessed properties include phase compositions by electron-probe micro-analysis, phase transformation temperatures by differential scanning calorimetry and creep behavior. Re exhibits the most pronounced enrichment in the γ-matrix, followed by Mo, Ru and W. Due to the preference of the Al-sites in the γ′-phase in the order Ta > Ti > W > Mo > Re, the solid solution strengthening elements Mo, Re and W are displaced from the γ′-phase by increasing Ti and Ta contents. The investigated solutes do not directly influence the partitioning behavior of Ru as it prefers Ni-sites in the γ′-phase. Compressive creep experiments reveal a correlation between the content of solid solution strengtheners in the γ-phase and creep performance.