# 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

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**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