Short-range Order (SRO) and its Effect on the Primary ...



MEANS 2: Microstructure- and Micromechanism-Sensitive Property Models for Advanced Turbine Disk and Blade Systems

AFOSR GRANT # FA9550-05-1-0135

MICHAEL J. MILLS, PI

Department of Materials Science and Engineering

The Ohio State University, Columbus, OH 43210

Abstract

Verification and refinement of our understanding of mechanisms and their transitions at intermediate temperatures in the disk alloy Rene 104, with the observation of microtwinning, continuous faulting and dislocation by-pass at successively higher temperatures above 650°C. Evidence for the twin initiation process has also been obtained via TEM studies of specimens interrupted after small strain levels. A preliminary model for the novel microtwinning regime has been developed that appears to provide reasonable agreement with the present experimental creep response for Rene 104 and Rene 88. Modeling at the ab initio, atomistic and phase field levels is providing important insight into the activation parameters associated with the observed deformation mechanisms, augmented by insight from 3D atom probe measurements on g and g' composition and ordering. Single crystals of Rene 104 have successfully been grown, and micro-tensile/compression as a function of crystal orientation will commence in the next year. A novel phase field model of directional coarsening (rafting) during high temperature, low strss creep of blade alloys has ben developed. This model accounts for the local stress fields associated with matrix dislocations as well as the lattice misfit, and demonstrates promising qualitative agreement with experiment. Characterization of deformation mechanisms after creep of several "generation 4" single crystal blade alloys is also in progress.

Research Objectives

This effort comprises a coordinated team of researchers from the Ohio State University, University of Michigan and Johns Hopkins University. The goal of the program is to develop improved models that will (a) incorporate more realistic representation of the relevant microstructures and micromechanisms, (b) enable modeling for a range of relevant service conditions, (c) address time-dependent deformation in both disk and blade alloys, (d) investigate crack initiation in blade materials, and (d) provide this information even more accessibly to the component design process, building upon the paths to the design process created in the DARPA Accelerated Insertion of Materials (AIM) program. We will be studying the next generation Ni base disk alloy and turbine blade alloys which are of keen, common interest to our industrial collaborators, GEAE and P&W, for both military and commercial propulsion systems. The selection of these particular alloys as the focus of our research will facilitate integration of the effort with both engine makers.

Program Summary and Present Status

In this first full year of the program, we have focused on improving our understanding of the mechanisms of creep in the polycrystalline disk superalloy, Rene 104, and more generally on developing the modeling tools necessary for treating critical issues in the high temperature response of both disk and blade alloys. These activities have benefited greatly from our interactions with industrial colleagues from GE Aircraft and Pratt-Whitney, and several collaborators from Wright Laboratories.

Creep and Deformation Structure Characterization Studies of Disk Alloy Rene 104

Creep deformation studies have been conducted on the advanced disk superalloy Rene 104. Samples for creep experimentation were extracted from a fully heat-treated turbine disk supplied by GEAE and P&W. A proprietary heat treatment was given to the disk which resulted in the microstructure having distinctly different precipitate structures near the rim and bore regions of the disk. A difference in cooling rate experienced within these regions had a direct influence on the size scale and distribution of precipitate phases, which further allowed us to study the influence of microstructure on the creep response. These two microstructures were subsequently crept in both tension and compression at 677ºC and 724MPa to understanding the underlying micromechanisms that are responsible for creep deformation behavior. Specifically, this condition was chosen in order to probe the microtwining mechanism.

The results of tensile creep testing to several strain levels is shown in Figure 2 in order to characterize the development of microtwins during creep. As can be seen, both microstructures exhibit a normal primary transient creep response. After 0.2% creep strain, numerous intrinsic stacking faults are observed in the γ matrix phase, due to the complete dissociation of 1/2 type matrix dislocations into 1/6 Shockley partial dislocations which bound the faults. At the larger strain, microtwinning is the dominant operative mechanism. Thus, it appears that the dissociated ½ dislocations, which may originate from intragranular carbides and borides, are sources for the microtwins. This information is being used to develop a model of microtwin initiation, which will further be explored parametrically via phase field dislocation dynamics simulation.

Calculation of Activation Barriers Using Phase Field Dislocation Dynamics

The activation energies associated with the formation of a superlattice intrinsic stacking-fault (SISF) from an antiphase domain boundary (APB) and the formation of a superlattice extrinsic stacking-fault (SESF) from a complex stacking-fault (CSF) in γ' phase of Ni-base superalloys have calculated using a microscopic phase field dislocation model in combination with the nudged elastic band (NEB) method. These calculation are stimulated by the observation of "isolated faulting" as an important deformation mechanism in relatively a coarse microstructure in Rene 88DT. The model incorporates the generalized stacking-fault (GSF) energy and hence allows for dislocation dissociations. Under an applied stress the activation energy for SESF can be reduced considerably, e.g, from 3.7eV at 500MPa to 0.5eV at 600MPa. Since the two partial dislocations in the two layers of CSF have the same 1/6 Burgers vector, the optimal stress direction is parallel to the Burgers vector, because it can facilitate the formation of both the CSF and SESF. For the SISF, since the ½ and 1/6 Burgers vectors are normal to each other, the effect of the applied stress is reduced. These results suggest that formation of SESF from a CSF rather than formation of SISF from APB is most likely the operating mechanism for the isolated faulting of γ' precipitates observed in the experiments.

Adaptive computational model of crystal plasticity involving micro-twinning

We are developing an adaptive computational dislocation density based crystal plasticity model to simulate creep deformation involving microtwinning. The overall model development consists of three distinctive parts. The first task involves development of a dislocation density based crystal plasticity model that accounts for size effects and back stress. In the deformation model chosen for this purpose, we are implementing the formulation of Arsenlis and Parks, in which the shear rate is represented in terms of classical Orowan’s equation, [pic], where [pic]is the dislocation density, [pic]is dislocation velocity and [pic]is the Burger’s vector. This model assumes dislocation glide as the major deformation mechanism, in which activation energy to overcome the resistance offered by the forest of dislocations has been taken into account. Dislocation density evolution equation is derived in terms of generation and annihilation rates. The material has heterogeneous microstructure consisting of [pic]matrix, coarse secondary[pic]and fine tertiary [pic]precipitates. The dislocation density based model is used to calculate a twin initiation criterion [pic]. Once this criterion is met, the microstructure in each grain is embedded with a locally periodic twin array. A simplified homogenous representative region involving both twined and untwined sections of a grain are being studied. The overall response of the twinned regions of each grain is modeled using the weighted average of contributions from the untwined and twinned regions respectively, with volume fraction representing the weights.

Important calibrating data for the crystal plasticity model will come from measurements of crystal orientation effects on time-dependent flow in single crystals grown from the commercial Rene 104 composition. Several crystal growth runs have been conducted at UM in a Crystalox levitation/Czrochralski (CZ) unit as well as a Bridgman furnace. The steeper temperature gradient possible in the latter inhibits segregation effects, and has successfully yielded several 0.5" rods with relatively large grains suitable for harvesting microtensile and microcompression testing at JHU. Remnant segregation will be mitigated through homogenization heat treatment followed by formation of the requisite gamma prime microstructure with the thermal treatment schedule that has been developed for polycrystalline ME3 at OSU. Microsamples will be machined from these crystals and tested in tension at JHU. The results of these microsample experiments and subsequent TEM observations will also be used to provide crucial insight into the intragranular deformation processes and to validate the micromechanical models being developed via stress and temperature change experiments to probe the activation parameters of the micromechanisms.

3D Atom Probe Analysis of Phase Composition, Ordering and Interface Profiles

Using 3D atom probe using the LEAP facility at ORNL in collaboration with Mike Miller, a large total matrix concentration of Co and Cr (>50%at.) is found in the matrix, as shown in Table 1. Since both of these elements are thought to lower stacking fault energy (SFE), this matrix composition may aid in the generation of the Shockley partial necessary to activate the microtwinning process, as discussed above. The ordering of g( was also investigated using atom probe analysis because of its potential impact on the creep deformation processes. The results indicate a high degree of order for major element in g( (Ni, Ti, Al). In particular, Ti shows a strong preference for the Al sites, consistent with the preferential site occupancies of Ti in other Ni-based superalloys. However, the strong site preference and high concentration of Ti in the Al sites shifts the γ´ composition far from stoichiometric Ni3Al, such that the crystal ordering can be greatly affected and so change crystal fault energies. Since it is not easy to predict the degree of order, nor the preferential site occupancy for complex alloy systems, this atom probe data provides a basis for the estimation of more realistic APB and CSF energies for our physics-based creep modeling(Karthik Scripta)ba.

Phase Field Modeling of Rafting in Blade Alloys

Dislocation-precipitate interaction and directional coarsening (rafting) of γ( precipitates in single crystal Ni-Al alloys under external load have been investigated by three-dimensional computer simulations. The simulation technique is based on an integrated phase field model that characterizes simultaneously spatiotemporal evolution of both precipitate morphology and dislocation structures. The initial configurations consisting of cuboidal γ( particles and dislocations in γ channels are constructed according to experimental observations and phase field simulation of dislocation filling process in the γ channels. The spatial variation of chemical potential of solute atoms is evaluated based on local concentration and stress and diffusion fluxes in different γ channels are analyzed. For a given state (sign and magnitude) of lattice misfit and external load, the predicted morphologies of the rafted γ( precipitates agree well with experiment observations. In the next phase of this model development, quantitative comparison of the model predictions against experimental rafting data on ternary Ni-Al-Mo alloys in work performed by Pollock and co-workers. For this alloy system, all the important physical, thermodynamic and kinetic data are available for incorporation in the phase-field model.

Deformation Mechanisms for Rafted Microstructures

The alloys being studied cover a range of composition representative of advanced “Generation 4” single crystals. In these alloys directional coarsening of the γ’ precipitates occurs during creep experiments conducted at 950˚C and 295 MPa. Dislocation substructures are being studied at various stages of creep deformation in sections parallel to the applied tensile stress to obtain critical information on rate-limiting mechanisms in the rafting regime. No comprehensive creep models have been developed for this stress / temperature regime, which has received relatively limited attention beyond studies that address the directional coarsening phenomenon. With regard to the rate-limiting mechanisms three possibilities are being considered: (1) creep controlled by viscous glide and climb of dislocations across the γ’ rafts; (2) creep controlled by viscous glide and climb in the matrix γ phase and (3) creep controlled by diffusion-limited reactions at γ - γ’ interface that produce dislocations for shearing of the γ’ rafts.

The most recent studies have focused on two alloys designated UM-F20 and UM F-30, whose compositions are similar except for the Co level and are listed in Table 1. We note the presence of dislocations in the γ’ rafts, at the γ - γ’ interfaces and in the gamma matrix. The density of dislocations that appear to be mobile in each of the phases was measured, and the results are shown in Figure 5. Note that with changes in minimum creep rate, there are changes in the matrix dislocation density, but no changes in the density within the precipitates. Furthermore, the creep rate decreases in UMF30 compared to UMF20, with increasing dislocation density in the matrix and also with increasing Co in the matrix. This seems to indicate that dislocations accumulate in the matrix until favorable conditions develop at the interface for pairing of dislocations in a configuration that will result in shearing of the γ’ rafts. Further studies across a wider range of alloys and creep strains are in progress to assess these critical issues in greater detail.

Personnel Supported During Reporting Period

Daniel Butler Graduate Student Johns Hopkins University

Chen Shen Post-Doctoral Researcher The Ohio State University

Vikas Dixit Graduate Student The Ohio State University

Kathy Flores Assistant Professor The Ohio State University

Kevin Hemker Professor Johns Hopkins University

Piyush Jain Graduate Student Johns Hopkins University

Ju Li Assistant Professor The Ohio State University

Shuwei Ma Research Associate University of Michigan

Michael Mills Professor The Ohio State University

Tresa Pollock Professor University of Michigan

Peter Sarosi Research Associate The Ohio State University

Yunzhi Wang Professor The Ohio State University

James Williams Professor The Ohio State University

Raymond Unocic Graduate Student The Ohio State University

Clarissa Yablonski Graduate Student The Ohio State University

Publications

1. R.R. Unocic, P.M. Sarosi, and M.J. Mills, “EFTEM Imaging of Ultra Fine Scaled (( Precipitates in Nickel Based Superalloys,” Advanced Materials & Processes, vol. 163 (7), 50-51, (2005).

2. W. Gan, P. Zhang, R. H. Wagoner and G. S. Daehn, “Transient Plastic Flow at Nominally Fixed Structure Due to Load Redistribution”, Metallkunde, 2005, 2005/06: 572-577.

3. S. Karthikeyan, R.R. Unocic, P.M. Sarosi, G.B. Viswanathan, and M.J. Mills, Modeling Microtwinning During Creep in Ni-based Superalloys, Scripta Materialia, 2006, 54:1157-1162.

4. G.B. Viswanathan, S. Karthikeyan, P.M. Sarosi, R.R. Unocic, and M.J. Mills, "Microtwinning During Intermediate Temperature Creep of Polycrystalline Ni-base Superalloys: Mechanisms and Modeling," Phil. Mag. A, 2006, 86: 4823-4840.

5. C. Shen, J.P. Simmons and Y. Wang, "Effect of elastic interaction on nucleation: I. Calculation of the strain energy of nucleus formation in an elastically anisotropic crystal of arbitrary microstructure," Acta Mater., 2006, in press.

6. C. Shen, J. P. Simmons and Y. Wang, "Effect of Elastic Interaction on Nucleation – II. Implementation of Strain Energy of Nucleus Formation in Phase Field Method," Acta Mater., 2006, in press.

7. R.R. Unocic, G. B. Viswanathan, P.M. Sarosi, S. Karthikeyan and M. J. Mills, "Mechanisms of Creep Deformation in Polycrystalline Ni-Base Disk Superalloys," Mater. Sci. Eng. A, in press.

8. C. Shen, J. Li, M.J. Mills and Y. Wang, "Modelling Shearing of γ′ in Ni-Base Superalloys," Deutsche Forschungsgemeinschaft (DFG) Symposium Proceedings on Integral Materials Modeling, Aachen, Germany, Dec. 1-2, 2005.

9. N. Zhou, C. Shen, M.J. Mills and Y. Wang, “Phase Field Modeling of g’ Rafting in Single Crystal Ni-Al,” in Proceedings of the International Conference on Advanced Materials Design & Development (ICAMMD), CD-ROM, M. Chakraborty, S. Ghosh, C. Jacob, D. Bhattacharya, V. Srinivas and T. K. Nath (ed), Goa, India, Dec. 14-16, 2005.

10. W. Luo, C. Shen and Y. Wang, “Nucleation of Ordered Particles at Dislocations and Formation of Split Patterns,” submitted to Acta Mater. (2006).

11. N. Zhou, C. Shen, M. J. Mills and Y. Wang, "Phase Field Modeling of Channel Dislocation Activities and γ( Rafting in Single Crystal Ni-Al", submitted to Acta Mater. (2006).

Transitions

Extensive discussions and exchange of information has already occurred with our industrial partners at GE Aircraft Engines (Dave Mourer, Mike Henry and Deb Whitis) and Pratt-Whitney (Michael Savage). Characterization and modeling of creep mechanisms are serving as a basis for understanding low cycle fatigue in similar disk alloys in the NASA Propulsion 21 program.

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Table 1: Compositions for two experimental "generation 4" alloys under investigation.

Figure 4: Phase field simulations of rafting for tensile loading with positive and negative misfit.

Figure 5: Measured dislocation densities in the g and g' phases after creep in rafted microstructures.

Figure 3: Complex dislocation configurations possible to treat using combination of phase field dislocation dynamics and nudged elastic band methods to calculate activation barriers.

Figure 2: Ubiquitous intrinsic stacking faults in matrix after 0.2% creep strain.

Figure 1: Creep curves for Rene 104

including curves interrupted at 0.2% strain.

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