RESEARCH ARTICLE

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

  • Jiahui NIU 1 ,
  • Chuanzhen HUANG , 2 ,
  • Zhenyu SHI , 1 ,
  • Hanlian LIU , 1 ,
  • Zhengyi TANG 1 ,
  • Binghao LI 1 ,
  • Zhen CHEN 1 ,
  • Guoyan JIANG 3
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  • 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
huangchuanzhen@ysu.edu.cn
shizhenyu@sdu.edu.cn
lhl70@sdu.edu.cn

Received date: 06 Jan 2023

Accepted date: 05 Jun 2023

Copyright

2023 Higher Education Press

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.

Cite this article

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[J]. Frontiers of Mechanical Engineering, 2023 , 18(4) : 45 . DOI: 10.1007/s11465-023-0761-3

Nomenclature

Abbreviations
CGICompacted graphite iron
EBSDElectron backscatter diffraction
GNDGeometrically necessary dislocation
HAGBHigh-angle grain boundary
JCJohnson−Cook
KAMKernel average misorientation
LAGBLow-angle grain boundary
Variables
a, kHPCorrelation coefficients between λ and σ(λ)
A, B, nParameters in JC constitutive equation
bMagnitude of the Burgers vector
CConstant reflecting the relationship between Es and Ess
EdConstant depends on the material properties and the interaction forms of dislocations
EsStored energy
EssSaturation value of stored energy
f(G)/f(RG)Effect function of graphite particles on the flow stress of CGI
kParameter related to the type of grain boundary
k1Energy accumulation coefficient
k2Energy release coefficient
KCorrelation coefficient between Es and σ
mNumber of selected nearest neighbors to calculate ρGNDs
MTaylor factor
RGRoundness of graphite particles
TCelsius temperature
uStep size of the EBSD test
αNumerical factor characterizing dislocation−dislocation interaction
ρDislocation density
ρGNDsGNDs density
σFlow stress
σ0Friction stress of pure ferrite
σ00Lattice friction of ferrite
σJCFlow stress defined by the JC constitutive equation
σPFlow stress of pearlite
σRuT450True stress obtained from compression test of RuT450
σ(λ)Boundary strengthening term
σ(ρ)Dislocation strengthening term
σP(ε) Stress‒strain relationship of pearlite
ΔθKAM value at one point in EBSD test
μShear module
εPlastic strain
ε˙Plastic strain rate
λInterlamellar spacing of pearlite matrix
λ0Interlamellar 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.
1
Dawson S , Hollinger I , Robbins M , Daeth J , Reuter U , Schulz H . The effect of metallurgical variables on the machinability of compacted graphite iron. SAE International, 2001, 110(5): 334–352

DOI

2
Dawson S . Compacted graphite iron—a material solution for modern diesel engine cylinder block and heads. China Foundry, 2009, 6(3): 241–246

3
Su R , Huang C Z , Xu L H , Zou B , Liu H L , Liu Y , Li C W . Research on the serrated chip in the milling of compacted graphite iron by cemented carbide tool. The International Journal of Advanced Manufacturing Technology, 2018, 99(5–8): 1687–1698

DOI

4
Kuzu A T , Berenji K R , Bakkal M . Thermal and force modeling of CGI drilling. The International Journal of Advanced Manufacturing Technology, 2016, 82(9–12): 1649–1662

DOI

5
Meng F N , Zhang Z Y , Wu B , Hu W , Ai X N , Meng X D , Ding Z , Zhang L Z . Turning processes and mechanism of compacted graphite iron used for high performance engine. Journal of Manufacturing Processes, 2021, 68: 951–960

DOI

6
Niu J H , Huang C Z , Su R , Zou B , Wang J , Liu Z Q , Li C W . Study on surface integrity of compacted graphite iron milled by cemented carbide tools and ceramic tools. The International Journal of Advanced Manufacturing Technology, 2019, 103(9–12): 4123–4134

DOI

7
TooptongSNguyenDParkK HKwonP. Crater wear on multi-layered coated carbide inserts when turning three distinct cast irons. Wear, 2021, 484–485: 203982

8
Souza T A , De Paula M A , Konatu R T , Ribeiro M V , De Campos E , Souza J V C . Investigation of the performance of ceramic tools of alumina doped with magnesium oxide in the dry machining of compacted graphite iron. Materials Research Express, 2019, 6(4): 046546

DOI

9
Nguyen D , Tooptong S , Park K H , Kwon P . Formation mechanism of alumina layer in protecting cubic boron nitride inserts in turning cast irons. International Journal of Machine Tools and Manufacture, 2020, 153: 103539

DOI

10
Elwazri A M , Wanjara P , Yue S . The effect of microstructural characteristics of pearlite on the mechanical properties of hypereutectoid steel. Materials Science and Engineering: A, 2005, 404(1–2): 91–98

DOI

11
Hyzak J M , Bernstein I M . The role of microstructure on the strength and toughness of fully pearlitic steels. Metallurgical Transactions A, 1976, 7(8): 1217–1224

DOI

12
O’Donnelly B E , Baker T N . Strengthening in low carbon pearlitic steels. Materials Science and Engineering, 1986, 84(1–2): 131–135

DOI

13
Zhang X D , Godfrey A , Huang X X , Hansen N , Liu Q . Microstructure and strengthening mechanisms in cold-drawn pearlitic steel wire. Acta Materialia, 2011, 59(9): 3422–3430

DOI

14
Dollar M , Bernstein I M , Thompson A W . Influence of deformation substructure on flow and fracture of fully pearlitic steel. Acta Metallurgica, 1988, 36(2): 311–320

DOI

15
Rodríguez R , Gutierrez I . Correlation between nanoindentation and tensile properties: influence of the indentation size effect. Materials Science & Engineering: A, 2003, 361(1–2): 377–384

DOI

16
Tang Z Y , Huang C Z , Niu J H , Jiang G Y , Li B H , Chen Z , Liu H L . The relation among the stored energy, microstructure and hardening effect of SA508-III steel under different deformation conditions. Materials Science and Engineering: A, 2022, 847: 147333

DOI

17
Bever M B , Holt D L , Titchener A L . The stored energy of cold work. Progress in Materials Science, 1973, 17: 5–177

DOI

18
Rusinek A , Klepaczko J R . Experiments on heat generated during plastic deformation and stored energy for TRIP steels. Materials & Design, 2009, 30(1): 35–48

DOI

19
Kapoor G , Péter L , Fekete É , Lábár J L , Gubicza J . Stored energy in nanocrystalline Ni-Mo films processed by electrodeposition. Journal of Alloys and Compounds, 2019, 796: 307–313

DOI

20
Ateba Betanda Y , Helbert A L , Brisset F , Mathon M H , Waeckerlé T , Baudin T . Measurement of stored energy in Fe–48%Ni alloys strongly cold-rolled using three approaches: neutron diffraction, Dillamore and KAM approaches. Materials Science and Engineering: A, 2014, 614: 193–198

DOI

21
Iza-Mendia A , Gutiérrez I . Generalization of the existing relations between microstructure and yield stress from ferrite–pearlite to high strength steels. Materials Science and Engineering: A, 2013, 561: 40–51

DOI

22
Embury J D , Fisher R M . The structure and properties of drawn pearlite. Acta Metallurgica, 1966, 14(2): 147–159

DOI

23
Liu Y , Yang C D , Liu M , Wang C H , Dai Y C , Li X , Russell A M , Zhang C X , Zhang Z H , Cao G H . Effects of microstructure and crystallography on mechanical properties of cold-rolled SAE1078 pearlitic steel. Materials Science and Engineering: A, 2018, 709: 115–124

DOI

24
BouazizOLe CorreC. Flow stress and microstructure modelling of ferrite–pearlite steels during cold rolling. Materials Science Forum, 2003, 426–432: 1399–1404

25
Saez-de-Buruaga M , Aristimuño P , Soler D , D’Eramo E , Roth A , Arrazola P J . Microstructure based flow stress model to predict machinability in ferrite–pearlite steels. CIRP Annals, 2019, 68(1): 49–52

DOI

26
TottenG EHowesMInoueT. Handbook of Residual Stress and Deformation of Steel. Ohio: ASM International, 2002, 3–10

27
Hansen N . Boundary strengthening in undeformed and deformed polycrystals. Materials Science and Engineering: A, 2005, 409(1–2): 39–45

DOI

28
Kuhlmann-wilsdorf D . A critical test on theories of work-hardening for the case of drawn iron wire. Metallurgical Transactions, 1970, 1(11): 3173–3179

DOI

29
Kocks U F . Laws for work-hardening and low-temperature creep. Journal of Engineering Materials and Technology, 1976, 98(1): 76–85

DOI

30
Hu Q S , Zhao F , Fu H , Li K W , Liu F S . Dislocation density and mechanical threshold stress in OFHC copper subjected to SHPB loading and plate impact. Materials Science and Engineering: A, 2017, 695: 230–238

DOI

31
Jing J T , Feng P F , Wei S L , Zhao H , Liu Y F . Investigation on the surface morphology of Si3N4 ceramics by a new fractal dimension calculation method. Applied Surface Science, 2016, 387: 812–821

DOI

32
Korolev A , Isaac G . Roundness and aspect ratio of particles in ice clouds. Journal of the Atmospheric Sciences, 2003, 60(15): 1795–1808

DOI

33
Mandelbrot B B , Passoja D E , Paullay A J . Fractal character of fracture surfaces of metals. Nature, 1984, 308(5961): 721–722

DOI

34
Gagnepain J J , Roques-Carmes C . Fractal approach to two-dimensional and three-dimensional surface roughness. Wear, 1986, 109(1–4): 119–126

DOI

35
Wang Q Y , Liang Z Q , Wang X B , Zhou T F , Zhao W X , Wu Y B , Jiao L . Investigation on surface formation mechanism in elliptical ultrasonic assisted grinding (EUAG) of monocrystal sapphire based on fractal analysis method. The International Journal of Advanced Manufacturing Technology, 2016, 87(9–12): 2933–2942

DOI

36
Zhang X , Zheng G M , Cheng X , Li Y , Li L , Liu H B . 2D fractal analysis of the cutting force and surface profile in turning of iron-based superalloy. Measurement, 2020, 151: 107125

DOI

37
Chuzhoy L , DeVor R E , Kapoor S G , Bammann D J . Microstructure-level modeling of ductile iron machining. Journal of Manufacturing Science and Engineering, 2002, 124(2): 162–169

DOI

38
Jaspers S P F C , Dautzenberg J H . Material behaviour in conditions similar to metal cutting: flow stress in the primary shear zone. Journal of Materials Processing Technology, 2002, 122(2–3): 322–330

DOI

39
Ljustina G , Larsson R , Fagerström M . A FE based machining simulation methodology accounting for cast iron microstructure. Finite Elements in Analysis and Design, 2014, 80: 1–10

DOI

40
Johnson G R , Cook W H . A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Engineering Fracture Mechanics, 1983, 21: 541–548

41
de Campos M F , Rolim Lopes L C , Magina P , Lee Tavares F C , Kunioshi C T , Goldenstein H . Texture and microtexture studies in different types of cast irons. Materials Science and Engineering: A, 2005, 398(1–2): 164–170

DOI

42
De Koning M , Miller R , Bulatov V V , Abraham F F . Modelling grain-boundary resistance in intergranular dislocation slip transmission. Philosophical Magazine A, 2002, 82(13): 2511–2527

DOI

43
Wu X Y , Suo H L , Ji Y T , Li J Z , Ma L , Liu M , Zhang Z L , Wang Q L . Systematical analysis on the grain orientation evolution of pure nickel under plastic deformation by using in-situ EBSD. Materials Science and Engineering: A, 2020, 792: 139722

DOI

44
Liu M M , Liu Y L , Li H . Deformation mechanism of ferrite in a low carbon Al-killed steel: slip behavior, grain boundary evolution and GND development. Materials Science and Engineering: A, 2022, 842: 143093

DOI

45
Calcagnotto M , Ponge D , Demir E , Raabe D . Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD. Materials Science and Engineering: A, 2010, 527(10–11): 2738–2746

DOI

46
Gao H , Huang Y , Nix W D , Hutchinson J W . Mechanism-based strain gradient plasticity—I. Theory. Journal of the Mechanics and Physics of Solids, 1999, 47(6): 1239–1263

DOI

47
Azzeddine H , Tirsatine K , Baudin T , Mathon M H , Helbert A L , Brisset F , Bradai D . On the stored energy evolution after accumulative roll-bonding of invar alloy. Materials Chemistry and Physics, 2017, 201: 408–415

DOI

48
Zheng H , Fu L M , Ji X B , Ding Y , Wang W , Wen M , Shan A D . Microstructural evolution and mechanical property of ultrafine-grained pearlitic steel by cold rolling: the influence of cementite morphology. Materials Science and Engineering: A, 2021, 824: 141860

DOI

49
Azzeddine H , Brisset T , Helbert A L , Brisset F , Huang Y , Kawasaki M , Bradai D , Langdon T G . A stored energy analysis of grains with shear texture orientations in Cu-Ni-Si and Fe-Ni alloys processed by high-pressure torsion. Journal of Alloys and Compounds, 2021, 864: 158142

DOI

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