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Integrated Computational Design of Three-Phase Mo–Si–B Alloy Turbine Blade for High-Temperature Aerospace Applications

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Abstract

The efficiencies of jet turbine engines are limited in part by the high-temperature properties of Ni-based superalloys utilized within turbine blades. Although Mo–Si–B alloys exhibit promising high-temperature properties, traditional materials development approaches relying extensively upon costly trial-and-error experiments inhibit the adoption rate of new materials. The present research seeks to address this problem by develo** and demonstrating a computational materials design framework for the design of Mo-Si-B alloys for gas turbine blade applications. The developed framework utilizes: (1) finite element simulations of 280 random microstructure instantiations to predict microstructure- and temperature-dependent yield strength and fracture toughness and their uncertainties; (2) analytical models to predict stresses due to turbine blade rotation; and (3) the inductive design exploration method (IDEM) to determine robust feasible domains of input and intermediate design variables. IDEM considers three input design variables (i.e., operating temperatures of 1273 K and 1473 K, volume fraction of the Molybdenum solid solution phase 0.45 ≤ vMoSS ≤ 0.75, and volume fraction of T2 intermetallic phase 0.125 ≤ vT2 ≤ 0.275) and three intermediate design variables (i.e., yield strength, fracture toughness, and density). Results indicate a maximum feasible temperature of approximately 1295 K at vMoSS and vT2 of approximately 0.45 and 0.18, respectively. This work is significant in that it demonstrates the design of Mo-Si-B alloys for high-temperature blades for aerospace applications, thus providing a means to increase efficiencies and reduce greenhouse gas emissions.

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Abbreviations

a:

Crack size

A15:

Mo3Si intermetallic phase

F :

Deformation gradient tensor

F e :

Elastic part of the deformation gradient tensor

F P :

Plastic part of the deformation gradient tensor

Ḟ P :

Rate of plastic part of the deformation gradient tensor

FKIc :

Scalar stress intensity factor fitness value

FSC :

Stress concentration factor

FSy :

Scalar yield strength fitness value

G :

Shear modulus

k :

Boltzmann constant

k dyn :

Dynamic recovery of immobile dislocations constant

k mul :

Dislocation multiplication rate constant

K c :

Fracture toughness

K I :

Stress intensity factor

K Ic :

Critical stress intensity factor

\(\hat{K}_{Ic}\) :

Surrogate model critical fracture toughness

L P :

Plastic velocity gradient tensor

MoSS :

Molybdenum solid solution phase

N P :

Direction of plastic flow tensor

p :

Activation enthalpy fitting parameter

q :

Activation enthalpy fitting parameter

q ρ :

Dislocation barrier strength

r :

T-head-to-blade radius

r 1 :

Root radius

r 2 :

Tip radius

R c :

Critical capture radius

S :

Deviatoric stress tensor

S 0 :

Athermal slip resistance threshold

S a :

Athermal slip resistance

\(S_{t}\) :

Thermal slip resistance

\(S_{y}\) :

Yield strength

\(\hat{S}_{y}\) :

Surrogate model yield strength

T2:

Mo5SiB2 intermetallic phase

\(T\) :

Absolute temperature

v MoSS :

Volume fraction of MoSS

v A15 :

Volume fraction of A15

v T2 :

Volume fraction of T2

Mo–Si–B:

Molybdenum–silicon–boron alloys

w 1 :

Width of blade

w 2 :

Width of T-head

α :

Statistical significance level

β :

Dislocation trap** constant

\( \dot{\bar{ \epsilon }}^{p} \) :

Equivalent plastic strain rate

\( \dot{\bar{ \epsilon }}_{0} ^{p} \) :

Reference strain rate

\(\Delta F_{g}\) :

Activation energy for dislocation glide

\(\lambda\) :

Effective mean free path of dislocations

\(\rho_{d}\) :

Total dislocation density

\(\rho_{M}\) :

Mobile dislocation density

\(\dot{\rho }_{M}\) :

Rate of change of mobile dislocation density

\(\rho_{I}\) :

Immobile dislocation density

\(\dot{\rho }_{I}\) :

Rate of change of immobile dislocation density

ρ:

Mass density

ρMoSS :

Mass density of MoSS

ρT2 :

Mass density of T2

π :

Ratio of diameter to circumference of a circle

σ :

Nominal stress

σ c :

Critical principal stress required for smeared cracking

ω :

Angular velocity

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Acknowledgements

AP would like to acknowledge funding received from Industrial Research and Consultancy Centre, IIT Bombay, under the seed grant project RD/0517-IRCCSH0-036.

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Authors and Affiliations

  1. Mechanical Engineering Technology, University of Maine, Orono, ME, 04469, USA

    Brett D. Ellis

  2. Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Mumbai, MH, 400076, India

    Hasan Haider & Anirban Patra

  3. Department of Mechanical Engineering, Mississippi State University, Starkville, MS, 39762, USA

    Matthew W. Priddy

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Correspondence to Anirban Patra.

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Appendices

Appendix

Appendix A

Constitutive model parameters are given in Tables 1, 2, 3.

Table 1 Temperature-dependent elastic constants for MoSS, A15 and T2 phases [22]
Full size table
Table 2 Model parameters for MoSS
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Table 3 Critical principal stress required for smeared cracking based on calibration to experimental data. Note that a single value was used for all temperatures
Full size table

Appendix B

Effect of Simulation Domain Size on the Material’s Response

We performed simulations to verify that simulation size domain does not affect material’s response. For these simulations, we used vMoSS = 0.45 and instantiated two microstructures for each of the following simulation domains: 25 μm × 25 μm, 40 μm × 40 μm, and 60 μm × 60 μm. All other simulation conditions are the same as in Sect. 2.2.3. The material was loaded in tension at a strain rate of 10−4 s−1 at 1273 K. Figure 17 shows the stress–strain response for these six microstructures. It can be seen that there is no noticeable simulation domain size effect among these six responses and the variability in response may be attributed to the stochasticity of the microstructure. We have used a simulation domain of 40 μm × 40 μm in the actual tension test simulations to reduce computation times.

Fig. 17
figure 17

Simulated stress–strain response for different two randomly instantiated microstructures of different simulation domain sizes. The legend indicates the simulation domain size (in μm) and the corresponding microstructure instantiation number

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Ellis, B.D., Haider, H., Priddy, M.W. et al. Integrated Computational Design of Three-Phase Mo–Si–B Alloy Turbine Blade for High-Temperature Aerospace Applications. Integr Mater Manuf Innov 10, 245–264 (2021). https://doi.org/10.1007/s40192-021-00207-6

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