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

doi:10.1007/s11465-023-0761-3

Frontiers of Mechanical Engineering

2023, Vol. 18

Issue (4): 45 https://doi.org/10.1007/s11465-023-0761-3

本期目录

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

Jiahui NIU¹, Chuanzhen HUANG²(

), Zhenyu SHI¹(

), Hanlian LIU¹(

), Zhengyi TANG¹, Binghao LI¹, Zhen CHEN¹, Guoyan JIANG³

¹. Center for Advanced Jet Engineering Technologies (CaJET), Key Laboratory of High-efficiency and Clean Mechanical Manufacture (Ministry of Education), National Experimental Teaching Demonstration Center for Mechanical Engineering (Shandong University), School of Mechanical Engineering, Shandong University, Jinan 250061, China
². School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
³. Dongfang Electric (Guangzhou) Heavy Machinery Co., Ltd., Guangzhou 511455, China

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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.

Key words： stress−strain relationship microstructure evolution stored energy strain hardening graphite morphology

收稿日期: 2023-01-06 出版日期: 2023-11-06

Corresponding Author(s): Chuanzhen HUANG,Zhenyu SHI,Hanlian LIU

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2023, 18(4): 45.
Jiahui NIU, Chuanzhen HUANG, Zhenyu SHI, Hanlian LIU, Zhengyi TANG, Binghao LI, Zhen CHEN, Guoyan JIANG. A new modeling approach for stress–strain relationship taking into account strain hardening and stored energy by compacted graphite iron evolution. Front. Mech. Eng., 2023, 18(4): 45.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-023-0761-3
https://academic.hep.com.cn/fme/CN/Y2023/V18/I4/45

Tab.1

Group	Deformation temperature, T/°C	Strain rate, $ε ˙$ /s^?1	Plastic strain, $ε$
1	20	0.1	0.10, 0.15, 0.20, 0.25
2	200, 400, 500, 600, 700, 800	0.1	0.25
3	20	8000, 10000, 12000, 14000	0.25

Tab.2

Fig.1

Fig.2

Fig.3

Tab.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

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, k_HP	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 E_s and E_ss
E_d	Constant depends on the material properties and the interaction forms of dislocations
E_s	Stored energy
E_ss	Saturation value of stored energy
f(G)/f(R_G)	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 E_s and σ
m	Number of selected nearest neighbors to calculate ρ_GNDs
M	Taylor factor
R_G	Roundness of graphite particles
T	Celsius temperature
u	Step size of the EBSD test
α	Numerical factor characterizing dislocation?dislocation interaction
ρ	Dislocation density
ρ_GNDs	GNDs density
σ	Flow stress
σ₀	Friction stress of pure ferrite
σ₀₀	Lattice friction of ferrite
σ_JC	Flow stress defined by the JC constitutive equation
σ_P	Flow stress of pearlite
σ_RuT450	True stress obtained from compression test of RuT450
σ(λ)	Boundary strengthening term
σ(ρ)	Dislocation strengthening term
σ_P(ε)	Stress?strain relationship of pearlite
Δθ	KAM value at one point in EBSD test
μ	Shear module
ε	Plastic strain
$ε ˙$	Plastic strain rate
λ	Interlamellar spacing of pearlite matrix
λ₀	Interlamellar spacing in the as-received samples

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