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A Particle Swarm Optimization-Based Multi-level Processing Parameters Optimization Method for Controlling Microstructures of an Aged Superalloy During Isothermal Forging

  • Dong-Dong Chen
  • Y. C. LinEmail author
Article
  • 40 Downloads

Abstract

To obtain the designed target microstructures of an aged superalloy during isothermal forging, a multi-level processing parameters optimization method is developed based on particle swarm optimization (PSO) algorithm. In the developed method, the accurate material models are used to characterize the microstructural evolution. Based on the designed target microstructures, the global and local optimality criterions are constructed to alternately optimize global and local multi-level processing parameters by the PSO algorithm with a linear decreasing inertia weight strategy. The optimized initial volume fraction of δ phase (δVF), deformation temperature and strain rate are 12.95%, 1000 °C and 0.001 s−1, respectively. According to these optimized parameters, the recrystallization volume fraction, average grain size and δVF are 100%, 11.2 µm and 2.1%, respectively, which well agree with the designed targets. Additionally, the processing parameters optimized by the developed method and traditional processing maps are compared. It is found that the developed method is more effective to control microstructures for the studied superalloy.

Keywords

Microstructure control Multi-level optimization Particle swarm optimization Superalloy 

List of Symbols

f

Recrystallization volume fraction

g0

Initial grain size

gdrx

Recrystallized grain size

g

Average grain size

δVF

Volume fraction of δ phase

\(\varepsilon_{ 0. 5}\)

Strain for 50% dynamic recrystallization volume fraction

ɛ

True strain

\(\dot{\varepsilon }\)

Strain rate (s−1)

\(\varepsilon_{\text{c}}\)

Critical strain for initiating dynamic recrystallization

\(\varepsilon_{\text{p}}\)

Peak strain

Z

Zener–Hollomon parameter

R

Universal gas constant

T

Deformation temperature (K)

V

Volume fraction of δ phase

Xδ

Dissolution fraction of δ phase

kc, k, m, Q, Ah, mh, Qh, nd, Ld, Ad, kd and n

Material constants

fdes

Designed recrystallization volume fraction

gdes

Designed average grain size

Vdes

Designed volume fraction of δ phase

α, β and γ

Weight coefficients

Jl

Local optimality criterion

Jg

Global optimality criterion

N

Number of local solutions

fmin and fmax

Minimum and maximum values of recrystallization volume fraction

gmin and gmax

Minimum and maximum values of average grain size

Vmin and Vmax

Minimum and maximum values of volume fraction of δ phase

vi

Velocity of the ith particle

xi

Position of the ith particle

w

Inertia weight

pi

Best previous positions of the ith particle

pg

Best previous positions of all particles

c1 and c2

Constants to determine the weights of pi and pg, respectively

r1 and r2

Random values uniformly distributed in the range of [0, 1]

iter

Current iteration of algorithm

itermax

Maximum number of iterations

wmax and wmin

Upper and lower bounds of inertia weight, respectively

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation Council of China (Grant No. 51775564), the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 2016 JJ1017), and Program of Chang Jiang Scholars of Ministry of Education (Grant No. Q2015140), China.

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Copyright information

© The Korean Institute of Metals and Materials 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringCentral South UniversityChangshaChina
  2. 2.State Key Laboratory of High Performance Complex ManufacturingChangshaChina

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