# Strength Prediction for Pearlitic Lamellar Graphite Iron: Model Validation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. UTS Modeling

_{t}is the stress intensity factor of the metallic matrix, k

_{1}and k

_{2}are the contributions from other strengthening mechanisms, and d is the grain size. The maximum defect size and grain size, α and d, are provided in μm, parameters k

_{t}and k

_{2}are in MPa, $\sqrt{\mu m}$, and k

_{1}is in MPa.

_{pearlite}). Based on this assumption, it becomes apparent that the effect of λ

_{pearlite}on the UTS must be taken into consideration. Thus, linear multiple regression analysis was made to determine the simultaneous influence of the ${D}_{IP}^{Hyd}$ and the λ

_{pearlite}on the UTS. The model obtained is based on the modified Hall–Petch relation, and is expressed by Equation (4) [11].

_{s}) and the fraction of primary austenite (f

_{γ}), as seen from Equation (5) [14].

_{pearlite}parameter at room temperature was assumed to be dependent on the cooling rate in the eutectoid transformation region. The empirical relationship between λ

_{pearlite}at room temperature, and the cooling rate at the temperature intervals between 700 and 740 °C, is shown in Figure 1. The experimentally derived relation Equation (6) was used for investigating the effect of different λ

_{pearlite}prediction models on simulated UTS. The measurements techniques, the microstructure and thermal data that resulted in Equation (6), are presented elsewhere [11,12]. Briefly, the pearlite lamellar spacing was measured using SEM and a linear intercept method. The minimum value was considered to be the correct spacing (perpendicular to the lamellae). The distance between 11 adjacent ferrite lamellas was measured and divided by 10 for estimation of a single interlamellar spacing.

## 3. Materials and Methods

#### 3.1. Cylindrical Castings

#### 3.2. Simulation Model and Assumptions

#### 3.3. Simulation Procedure

_{γ}) for each alloy: 0.3 for alloy A, 0.4 for alloy B, 0.51 for alloy C, and 0.61 for alloy D [16].

## 4. Results and Discussion

^{2}values show that Equation (3) predicts the UTS with better accuracy than Equation (4). This indicates the need to develop further the model for prediction of the λ

_{pearlite}parameter.

## 5. Conclusions

_{pearlite}parameter. The results demonstrated the applicability of the novel UTS prediction models for different chemical compositions and cooling conditions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Collini, L.; Nicoletto, G.; Konecná, R. Microstrucure and mechanical properties of pearlitic lamellar cast iron. Mater. Sci. Eng. A
**2008**, 488, 529–539. [Google Scholar] [CrossRef] - Ruff, G.F.; Wallace, J.F. Effects of solidification structure on the tensile properties of lamellar iron. AFS Trans.
**1977**, 56, 179–202. [Google Scholar] - Bates, C. Alloy element effect on lamellar iron properties: Part II. AFS Trans.
**1986**, 94, 889–905. [Google Scholar] - Nakae, H.; Shin, H. Effect of graphite morphology on tensile properties of flake graphite cast iron. Mater. Trans.
**2001**, 42, 1428–1434. [Google Scholar] [CrossRef] - Baker, T.J. The fracture resistance of the flake graphite cast iron. Mater. Eng. Appl.
**1978**, 1, 13–18. [Google Scholar] [CrossRef] - Griffin, J.A.; Bates, C.E. Predicting in-situ lamellar cast iron properties: Effects of the pouring temperature and manganese and sulfur concentration. AFS Trans.
**1988**, 88, 481–496. [Google Scholar] - Goettsch, D.D.; Dantzig, J.A. Modeling microstructure development in gray cast irons. Metall. Trans. A
**1994**, 25, 1063–1079. [Google Scholar] [CrossRef] - Catalina, A.; Guo, X.; Stefanescu, D.M.; Chuzhoy, L.; Pershing, M.A. Prediction of room temperature microstructure and mechanical properties in lamellar iron castings. AFS Trans.
**2000**, 94, 889–912. [Google Scholar] - Urrutia, A.; Celentano, J.D.; Dayalan, R. Modeling and Simulation of the Gray-to-White Transition during Solidification of a Hypereutectic Gray Cast Iron: Application to a Stub-to-Carbon Connection used in Smelting Processes. Metals
**2017**, 7, 549. [Google Scholar] [CrossRef] - Fourlakidis, V.; Diószegi, A. A generic model to predict the ultimate tensile strength in pearlitic lamellar graphite iron. Mater. Sci. Eng. A
**2014**, 618, 161–167. [Google Scholar] [CrossRef] - Fourlakidis, V.; Diaconu, L.; Diószegi, A. Strength prediction of Lamellar Graphite Iron: From Griffith’s to Hall-Petch modified equation. Mater. Sci. Forum
**2018**, 925, 272–279. [Google Scholar] [CrossRef] - Diószegi, A. On the Microstructure Formation and Mechanical Properties in Grey Cast Iron. In Linköping Studies in Science and Technology; Dissertation No. 871; Jönköping: Jönköping, Sweden, 2004; p. 25. ISBN 91-7373-939-1. [Google Scholar]
- Leube, B.; Arnberg, L. Modeling gray iron solidification microstructure for prediction of mechanical properties. Int. J. Cast Metals Res.
**1999**, 11, 507–514. [Google Scholar] [CrossRef] - Fourlakidis, V.; Diószegi, A. Dynamic Coarsening of Austenite Dendrite in Lamellar Cast Iron Part 2—The influence of carbon composition. Mater. Sci. Forum
**2014**, 790–791, 211–216. [Google Scholar] [CrossRef] - Barkhudarov, M.R.; Hirt, C.W. Casting simulation: Mold filling and solidification—Benchmark calculations using FLOW-3D. In Proceedings of the 7th Conference on Modeling of Casting, Welding and Advanced Solidification Processes, London, UK, 10–15 September 1995. [Google Scholar]
- Diószegi, A.; Diaconu, L.; Fourlakidis, V. Prediction of volume fraction of primary austenite at solidification of lamellar graphite cast iron using thermal analyses. J. Therm. Anal. Calorim.
**2016**, 124, 215–225. [Google Scholar] [CrossRef] - Svidró, P.; Diószegi, A.; Pour, M.S.; Jönsson, P. Investigation of Dendrite Coarsening in Complex Shaped Lamellar Graphite Iron Castings. Metals
**2017**, 7, 244. [Google Scholar] [CrossRef] - Diószegi, A.; Hattel, J. An inverse thermal analysis method to study the solidification in cast iron. Int. J. Cast Met. Res.
**2004**, 17, 311–318. [Google Scholar] - Hattel, J.H. Fundamentals of Numerical Modelling of Casting Processes, 1st ed.; Polyteknisk Forlag: Lyngby, Denmark, 2005. [Google Scholar]
- Diószegi, A.; Fourlakidis, V.; Lora, R. Austenite Dendrite Morphology in Lamellar Cast Iron. Int. J. Cast Met. Res.
**2015**, 28, 310–317. [Google Scholar] [CrossRef]

**Figure 6.**Simulated and experimental cooling curves (central thermocouple) for alloy A: (

**a**) insulation, (

**b**) sand, and (

**c**) chill.

**Figure 7.**Simulated and experimental cooling curves (central thermocouple) for alloy B: (

**a**) insulation, (

**b**) sand, and (

**c**) chill.

**Figure 8.**Simulated and experimental cooling curves (central thermocouple) for alloy C: (

**a**) insulation, (

**b**) sand, and (

**c**) chill.

**Figure 9.**Simulated and experimental cooling curves (central thermocouple) for alloy D: (

**a**) insulation (

**b**) sand, and (

**c**) chill.

**Figure 10.**Distribution of ultimate tensile strength (UTS) calculated from Equations (4) and (6) for alloy B: (

**a**) insulation-, (

**b**) sand-, and (

**c**) chill-encapsulated cylinder; the dashed lines indicate the position of the tensile bars.

Alloy | C | Si | Mn | P | S | Cr | Cu | Ceq |
---|---|---|---|---|---|---|---|---|

A | 3.62 | 1.88 | 0.57 | 0.04 | 0.08 | 0.14 | 0.38 | 4.26 |

B | 3.34 | 1.83 | 0.56 | 0.04 | 0.08 | 0.15 | 0.37 | 3.96 |

C | 3.05 | 1.77 | 0.54 | 0.04 | 0.08 | 0.14 | 0.36 | 3.65 |

D | 2.80 | 1.75 | 0.54 | 0.04 | 0.08 | 0.15 | 0.35 | 3.40 |

Temperature (°C) | Cast Iron Thermophysical Properties | Heat Transfer Coefficient | ||||
---|---|---|---|---|---|---|

Density | Specific Heat | Thermal Conductivity | Sand-Casting | Chill-Casting | Insulation-Casting | |

[kg/m^{3}] | [J/kg/K] | [W/m/K] | [W/m^{2}/K] | [W/m^{2}/K] | [W/m^{2}/K] | |

600 | 7146 | 700 | 40 | 40 | 100 | 10 |

720 | - | 1074 | - | - | 300 | - |

721 | - | 12301 | - | - | - | - |

724 | - | 12308 | - | - | - | - |

725 | - | 1082 | - | 50 | - | 10 |

750 | - | 733 | - | - | - | - |

900 | - | - | - | 80 | - | 15 |

1000 | 6994 | 800 | - | 150 | - | 25 |

1100 | - | 825 | - | 250 | 1300 | 55 |

1154 | 6960 | 837 | 40 | - | 1450 | - |

1170 | 7016 | - | - | - | - | - |

1200 | 6985 | - | - | - | 1600 | 60 |

1227 | 6939 | 749 | - | - | - | - |

1300 | 6876 | 771 | - | 380 | - | 180 |

1700 | 6395 | 807 | 38 | 940 | 2700 | 940 |

Alloy | UTS, [MPa] | Average Percentage Error, [%] | ||||
---|---|---|---|---|---|---|

Experiment | Simulation | |||||

Equation (3) ^{1} | Equation (4) ^{2} | Equation (3) ^{1} | Equation (4) ^{2} | |||

A | Insulation | 154 | 180 | 200 | 17 | 30 |

Sand | 195 | 230 | 250 | 18 | 28 | |

Chill | 363 | 340–350 | 340–350 | 5 | 5 | |

B | Insulation | 211 | 204 | 213 | 3 | 1 |

Sand | 254 | 255 | 269 | 1 | 6 | |

Chill | 368 | 365–375 | 385–395 | 1 | 6 | |

C | Insulation | 250 | 233 | 236 | 7 | 6 |

Sand | 286 | 293 | 300 | 2 | 5 | |

Chill | 440 | 420–435 | 435–445 | 3 | 0 | |

D | Insulation | 289 | 260 | 253 | 10 | 12 |

Sand | 337 | 325 | 323 | 4 | 4 | |

Chill | 447 | 440–455 | 475–490 | 0 | 8 |

**Modified Griffith model;**

^{1}**Modified Hall–Petch model.**

^{2}© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fourlakidis, V.; Belov, I.; Diószegi, A.
Strength Prediction for Pearlitic Lamellar Graphite Iron: Model Validation. *Metals* **2018**, *8*, 684.
https://doi.org/10.3390/met8090684

**AMA Style**

Fourlakidis V, Belov I, Diószegi A.
Strength Prediction for Pearlitic Lamellar Graphite Iron: Model Validation. *Metals*. 2018; 8(9):684.
https://doi.org/10.3390/met8090684

**Chicago/Turabian Style**

Fourlakidis, Vasilios, Ilia Belov, and Attila Diószegi.
2018. "Strength Prediction for Pearlitic Lamellar Graphite Iron: Model Validation" *Metals* 8, no. 9: 684.
https://doi.org/10.3390/met8090684