Advances in Manufacturing

, Volume 7, Issue 2, pp 238–247 | Cite as

A strategy to control microstructures of a Ni-based superalloy during hot forging based on particle swarm optimization algorithm

  • Dong-Dong Chen
  • Yong-Cheng LinEmail author
  • Xiao-Min Chen


In this study, a strategy based on the particle swarm optimization (PSO) algorithm is developed to control the microstructures of a Ni-based superalloy during hot forging. This strategy is composed of three parts, namely, material models, optimality criterions, and a PSO algorithm. The material models are utilized to predict microstructure information, such as recrystallization volume fraction and average grain size. The optimality criterion can be determined by the designed target microstructures and random errors. The developed strategy is resolved using the PSO algorithm, which is an intelligent optimal algorithm. This algorithm does not need a derivable objective function, which renders it suitable for dealing with the complex hot forging process of alloy components. The optimal processing parameters (deformation temperature and strain rate) are obtained by the developed strategy and validated by the hot forging experiments. Uniform and fine target microstructures can be obtained using the optimized processing parameters, which indicates that the developed strategy is effective for controlling the microstructural evolution during the hot forging of the studied superalloy.


Processing parameters Microstructure Particle swarm optimization (PSO) algorithm Superalloy 

List of symbols


Velocity of the ith particle


Position of the ith particle


Inertia weight


Best previous positions of the ith particle


Best previous positions of all particles

\(c_{1}\), \(c_{2}\)

Constants to determine the weights of \(p_{i}\) and \(p_{\text{g}}\), respectively

\(r_{1}\), \(r_{2}\)

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


Current iteration of algorithm


Maximum number of iterations

\(w_{{\mathrm{max}} }\), \(w_{{\mathrm{min}} }\)

Upper and lower bounds of inertia weight, respectively


Saturation stresses


Steady stresses


Flow stress when dynamic recovery is the dominant softening mechanism


True strain


True stress

\(\dot{\varepsilon }\)

Strain rate (s−1)


Critical strain for initiating dynamic recrystallization


Peak strain


Peak stress


Yield stress


Coefficient of dynamic recovery


Material constant


Zener-Hollomon parameter


Universal gas constant


Deformation temperature (K)


Material density (kg/m3)


Specific heat \(\left( {{\text{J}}\cdot\left( {{\text{kg}}\cdot {^\circ{\text{C}}}} \right)^{ - 1} } \right)\)

\(\eta (\dot{\varepsilon })\)

Adiabatic correction factor


Recrystallization volume fraction

\(g_{ 0}\)

Initial grain size


Recrystallized grain size


Average grain size

\(\varepsilon_{ 0. 5}\)

Strain for 50% dynamic recrystallization volume fraction


Optimality criterion for recrystallization volume fraction


Optimality criterion for average grain size


Optimality criterion for random error


Designed recrystallization volume fraction


Designed average grain size


Random value in the range of [0, 1]



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


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringCentral South UniversityChangshaPeople’s Republic of China
  2. 2.State Key Laboratory of High Performance Complex ManufacturingChangshaPeople’s Republic of China
  3. 3.College of Automotive and Mechanical EngineeringChangsha University of Science and TechnologyChangshaPeople’s Republic of China

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