A new modeling approach for stress–strain relationship taking into account strain hardening and stored energy by compacted graphite iron evolution

Abstract

Compacted graphite iron (CGI) is considered to be an ideal diesel engine material with excellent physical and mechanical properties, which meet the requirements of energy conservation and emission reduction. However, knowledge of the microstructure evolution of CGI and its impact on flow stress remains limited. In this study, a new modeling approach for the stress–strain relationship is proposed by considering the strain hardening effect and stored energy caused by the microstructure evolution of CGI. The effects of strain, strain rate, and deformation temperature on the microstructure of CGI during compression deformation are examined, including the evolution of graphite morphology and the microstructure of the pearlite matrix. The roundness and fractal dimension of graphite particles under different deformation conditions are measured. Combined with finite element simulation models, the influence of graphite particles on the flow stress of CGI is determined. The distributions of grain boundary and geometrically necessary dislocations (GNDs) density in the pearlite matrix of CGI under different strains, strain rates, and deformation temperatures are analyzed by electron backscatter diffraction technology, and the stored energy under each deformation condition is calculated. Results show that the proportion and amount of low-angle grain boundaries and the average GNDs density increase with the increase of strain and strain rate and decreased first and then increased with an increase in deformation temperature. The increase in strain and strain rate and the decrease in deformation temperature contribute to the accumulation of stored energy, which show similar variation trends to those of GNDs density. The parameters in the stress–strain relationship model are solved according to the stored energy under different deformation conditions. The consistency between the predicted results from the proposed stress–strain relationship and the experimental results shows that the evolution of stored energy can accurately predict the stress–strain relationship of CGI.

Graphical abstract

Keywords

stress−strain relationship / microstructure evolution / stored energy / strain hardening / graphite morphology

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Nomenclature

Abbreviations
CGI	Compacted graphite iron
EBSD	Electron backscatter diffraction
GND	Geometrically necessary dislocation
HAGB	High-angle grain boundary
JC	Johnson−Cook
KAM	Kernel average misorientation
LAGB	Low-angle grain boundary
Variables
a, kHP	Correlation coefficients between λ and σ(λ)
A, B, n	Parameters in JC constitutive equation
b	Magnitude of the Burgers vector
C	Constant reflecting the relationship between Es and Ess
Ed	Constant depends on the material properties and the interaction forms of dislocations
Es	Stored energy
Ess	Saturation value of stored energy
f(G)/f(RG)	Effect function of graphite particles on the flow stress of CGI
k	Parameter related to the type of grain boundary
k1	Energy accumulation coefficient
k2	Energy release coefficient
K	Correlation coefficient between Es and σ
m	Number of selected nearest neighbors to calculate ρGNDs
M	Taylor factor
RG	Roundness of graphite particles
T	Celsius temperature
u	Step size of the EBSD test
α	Numerical factor characterizing dislocation−dislocation interaction
ρ	Dislocation density
ρGNDs	GNDs density
σ	Flow stress
σ0	Friction stress of pure ferrite
σ00	Lattice friction of ferrite
σJC	Flow stress defined by the JC constitutive equation
σP	Flow stress of pearlite
σRuT450	True stress obtained from compression test of RuT450
σ(λ)	Boundary strengthening term
σ(ρ)	Dislocation strengthening term
σP(ε)	Stress‒strain relationship of pearlite
Δθ	KAM value at one point in EBSD test
μ	Shear module
ε	Plastic strain
\dot{\epsilon }	Plastic strain rate
λ	Interlamellar spacing of pearlite matrix
λ0	Interlamellar spacing in the as-received samples

Acknowledgements

This study was financially supported by the National Natural Science Foundation of China (Grant Nos. 52275464 and 52075300) and the Scientific Research Project for National High-level Innovative Talents of Hebei Province Full-time Introduction, China (Grant No. 2021HBQZYCXY004).

Conflict of Interest

The authors declare that they have no conflict of interest.

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