Double minimum creep processing and mechanism for γʹ strengthened cobalt-based superalloy

doi:10.1016/j.jmst.2021.10.015

Abstract

Abstract:

The double minimum creep, characterized by two creep rate minima, in Co-based superalloy is investigated using a phase-field model coupled with a crystal plasticity model. The constitutive modeling, based on the dislocation slip theory considering dislocation interaction, is applied to simulate microstructural evolution and deformation behavior. Rafting process commences at the beginning of creep until the global minimum of creep rate is reached, demonstrating a strengthening effect from N-type rafts under compressive creep. The high shear strain rate of $\left( 111 \right)\left[ 0\bar{1}1 \right]$ slip system in the intersections of horizontal and vertical γ channels leads to a slight increase of creep rate after the first local minimum. The evolution of stress field shows that the softening effect is the combined effect of the increase of resolved shear stress and the decrease of hardening stress in the intersections. Further, these changes in stress are primarily caused by the dislocation annihilation and the inhomogeneous plastic deformation. This study indicates that the intermediate local softening stage during creep may be eliminated if the initial inter-distance between γʹ precipitates is decreased.

Key words: Cobalt-based superalloy, Phase-field simulation, Creep, γʹ precipitates, Slip system

Jia Chen, Min Guo, Min Yang, Lin Liu, Jun Zhang. Double minimum creep processing and mechanism for γʹ strengthened cobalt-based superalloy[J]. J. Mater. Sci. Technol., 2022, 112: 123-129.

Figures/Tables 10

Fig. 1. The representative creep rate curves in Co-based and Ni-based superalloys at different temperatures and stresses [6,8].

Table 1. Simulation parameters for the phase-field model.

Parameters	Values
Equilibrium concentrations	c^m=0.17, c^p=0.23
Bulk free energy coefficients	Δf=80J/mol, c^s=0.20
Gradient energy coefficients [36]	α=9.0×10^-10J/m, β=6.8×10^-11J/m
Elastic constants of γʹ [37,38]	$c_{11}^{{{\gamma }'}}=238\ \text{GPa}$, $c_{12}^{{{\gamma }'}}=141\ \text{GPa}$, $c_{44}^{{{\gamma }'}}=127\ \text{GPa}$
Elastic constants of γ [37]	$c_{11}^{\gamma }=221\ \text{GPa}$, $c_{12}^{\gamma }=162\ \text{GPa}$, $c_{44}^{\gamma }=95.4\ \text{GPa}$
chemical mobility [36]	M=5.02×10^-26m²/s·J
γ/γʹ lattice misfit [6]	δ=0.46%

Table 2. Expression of the interaction matrix for octahedral slip systems.

h1	h2	h2	h3	h3	h3	h3	h4	h2	h3	h2	h4
h2	h1	h2	h3	h2	h4	h2	h3	h3	h3	h4	h2
h2	h2	h1	h3	h4	h2	h3	h2	h4	h2	h3	h3
h3	h3	h3	h1	h2	h2	h4	h3	h2	h4	h2	h3
h3	h2	h4	h2	h1	h2	h2	h3	h4	h3	h3	h2
h3	h4	h2	h2	h2	h1	h3	h2	h3	h2	h4	h3
h3	h2	h3	h4	h2	h3	h1	h2	h2	h4	h3	h2
h4	h3	h2	h3	h3	h2	h2	h1	h2	h2	h3	h4
h2	h3	h4	h2	h4	h3	h2	h2	h1	h3	h2	h3
h3	h3	h2	h4	h3	h2	h4	h2	h3	h1	h2	h2
h2	h4	h3	h2	h3	h4	h3	h3	h2	h2	h1	h2
h4	h2	h3	h3	h2	h3	h2	h4	h3	h2	h2	h1

Table 3. Fitted parameters for the crystal plasticity model [[33], [34]].

Parameters	Values
Initial threshold of γʹ	$r_{0}^{p}=1000\ \text{MPa}$
Initial threshold of γ	$r_{0}^{m}=35\ \text{MPa}$
Norton law coefficients	n=6,$K=1550\;\text{MPa}\;{{\text{s}}^{\left( 1/n \right)}}$
Hardening coefficients	${{b}^{s}}=800$, ${{Q}^{s}}=80\ \text{MPa}$
Damage coefficients	${{D}_{n}}=2$,${{D}_{A}}={{10}^{-22}}\ \text{MP}{{\text{a}}^{\left( 1/{{D}_{n}} \right)}}$

Fig. 2. Creep curves of Co-based alloy Co-9Al-7.5W-2Ta at 950 °C /150 MPa. (a) Creep strain vs. time, and (b) creep rate vs. creep strain.

Fig. 3. Simulated γ/γʹ microstructure at strain of (a) 2.6 × 10-5, (b) 0.48%, (c) 0.97%, (d) 2.46%, (e) 3.16%; and (f) experimental microstructure at the global creep rate minimum of ERBOCo-2Ta under 950 °C /150 MPa [6].

Fig. 4. The evolutions of shear strain rate ${{\dot{\gamma }}^{s}}$ in slip systems B2 $\left( 111 \right)\left[ 0\bar{1}1 \right]$ and B5 $\left( 111 \right)\left[ \bar{1}10 \right]$ at creep strain of (a1, a2) 2.6 × 10-5, (b1, b2) 0.48%, (c1, c2) 0.97%, (d1, d2) 2.48% and (e1, e2) 3.16%. The contour of γʹ is depicted in Fig. 4(a2) to avoid confusing rafting phenomenon.

Fig. 5. The plot of shear strain rate vs. plastic strain in B2 and B5 slip systems.

Fig. 6. The evolutions of resolved shear stress τ and hardening stress R (R=rs+r0) in slip systems B2.

Fig. 7. Schematic illustration showing the deformation mechanism of double minimum creep in Co-based superalloys.

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