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.

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

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.

References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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