# On Thermal Expansion and Density of CGI and SGI Cast Irons

^{*}

^{†}

## Abstract

**:**

^{−5}+ 5.38 × 10

^{−8}N − 5.85 × 10

^{−7}G + 1.85 × 10

^{−8}T − 2.41 × 10

^{−6}R

_{P/F}− 1.28 × 10

^{−8}NG − 2.97 × 10

^{−7}GR

_{P/F}+ 4.65 × 10

^{−9}TR

_{P/F}+ 1.08 × 10

^{−7}G

^{2}− 4.80 × 10

^{−11}T

^{2}(N: Nodularity, G: Area fraction of graphite (%), T: Temperature (°C), R

_{P/F}: Pearlite/Ferrite ratio in the matrix).

## 1. Introduction

## 2. Experimental

#### 2.1. Materials

Elements | SGI-1 | SGI-2 | SGI-3 | CGI-1 | CGI-2 |
---|---|---|---|---|---|

C | 3.28 | 3.13 | 3.51 | 3.24 | 3.18 |

Si | 3.73 | 4.25 | 2.36 | 3.44 | 3.87 |

Mn | 0.169 | 0.169 | 0.408 | 0.17 | 0.167 |

P | 0.009 | 0.0095 | 0.0063 | 0.0069 | 0.0072 |

S | 0.0056 | 0.0065 | 0.0043 | 0.0062 | 0.0072 |

Cr | 0.028 | 0.029 | 0.025 | 0.028 | 0.028 |

Ni | 0.045 | 0.041 | 0.039 | 0.048 | 0.047 |

Mo | 0.0012 | 0.0016 | 0.0028 | 0.0034 | 0.0037 |

Mg | 0.037 | 0.036 | 0.036 | 0.0061 | 0.0062 |

Fe | Balance | Balance | Balance | Balance | Balance |

CE ^{1} | 4.53 | 4.55 | 4.30 | 4.39 | 4.47 |

^{1}CE: Carbon Equivalent = C% + (Si% + P%)/3.

#### 2.2. Dilatometry

_{X0}(where ΔL: change in length and L

_{X0}: initial length) against temperature. The details of the analysis method are described in Appendix A.

#### 2.3. Microstructural Characterization

^{2}. The nodularity was measured with the following equation (ISO standard method [8]).

_{Graphite (IOS form VI)}: the surface area of graphite with roundness higher than 0.625 (ISO 945 form VI); A

_{Graphite (ISO form IV+V)}: the surface area of graphite with roundness between 0.525 and 0.625 (ISO 945 form IV and V); and A

_{Graphite (All)}: the surface area of all graphite.

## 3. Results and Discussion

#### 3.1. Microstructure

Thickness (mm) | SGI-1 | SGI-2 | SGI-3 | CGI-1 | CGI-2 |
---|---|---|---|---|---|

15 | - | 30.7 | 75.4 | - | 17.0 |

50 | 66.4 | 55.6 | 74.9 | 15.7 | 7.33 |

75 | - | 53.7 | 82.6 | - | 3.92 |

Samples | Graphite | ASTM Ferrite | ASTM Pearlite |
---|---|---|---|

SGI-3, 15 mm | 3.40 | 33.96 | 62.64 |

SGI-3, 50 mm | 7.84 | 38.60 | 53.56 |

SGI-3, 75 mm | 8.80 | 38.67 | 52.53 |

SGI-1, 50 mm | 9.05 | 90.95 | 0 |

SGI-2, 15 mm | 2.12 | 97.88 | 0 |

SGI-2, 50 mm | 6.78 | 93.22 | 0 |

SGI-2, 75 mm | 5.57 | 94.43 | 0 |

CGI-1, 50 mm | 6.09 | 93.91 | 0 |

CGI-2, 15 mm | 2.13 | 97.87 | 0 |

CGI-2, 50 mm | 2.15 | 97.85 | 0 |

CGI-2, 75 mm | 1.94 | 98.06 | 0 |

#### 3.2. Coefficient of Thermal Expansion (CTE)

**Figure 8.**Coefficient of thermal expansion (CTE) of SGI-3 (15, 50 and 75 mm) as a function of temperature (during heating cycles).

**Figure 11.**CTE of SGI-1, SGI-2, and SGI-3 (50 mm) and CGI-1 and CGI-2 (50 mm) as a function of temperature (during heating cycles).

^{−5}+ 5.38 × 10

^{−8}N − 5.85 × 10

^{−7}G + 1.85 × 10

^{−8}T − 2.41 × 10

^{−6}R

_{P/F}− 1.28 × 10

^{−8}NG − 2.97 × 10

^{−7}GR

_{P/F}+ 4.65 × 10

^{−9}TR

_{P/F}+ 1.08 × 10

^{−7}G

^{2}− 4.80 × 10

^{−11}T

^{2}

_{P/F}: Pearlite/Ferrite ratio in the matrix.

^{2}value of the above equation is 0.87. As can be seen in Equation (1), the influence of the following terms on the CTE is negligible: GT, NR

_{P/F}, TN, N

^{2}and R

^{2}

_{P/F}.

#### 3.3. Density

_{v}, is three times of linear CTE, α

_{E}.

_{v}= 3α

_{E}

Thickness | SGI-1 | SGI-2 | SGI-3 | CGI-1 | CGI-2 |
---|---|---|---|---|---|

15 mm | - | 7.04 | 7.11 | - | 7.06 |

50 mm | 7.02 | 7.04 | 7.10 | 7.04 | 7.04 |

75 mm | - | 7.04 | 7.10 | - | 7.05 |

#### 3.4. Effect of Thermal Cycling on Thermal Expansion

_{0}values at 55 °C are plotted against the number of cycles and shown in Figure 14 and Figure 15.

**Figure 14.**Thermal expansion behavior of the SGI-1 (thickness: 30 mm) during thermal cycling (dL/L

_{0}at 55 °C).

_{0}at 55 °C was decreased from the beginning and became constant. The SGI-1 has a ferritic matrix, as shown in Figure 6. However, the decomposition of retained cementite into graphite and ferrite might occur in the vicinity of the maximum temperature in the measurement (600 °C), since the samples contains relatively high silicon. Usually, the volume is increased by the graphitizing. However, in the present case, the vacancy or pores of already existing graphite phase seem to be filled with the decomposed carbon and the influence of the filling of the pore with carbon is superior to the volume expansion due to the graphitizing. As a result, the total volume seems to become smaller. The volume change seems to occur by the competition of these two effects.

**Figure 15.**Thermal expansion behavior of the SGI-3 (thickness: 30 mm) during thermal cycling (dL/L

_{0}at 55 °C).

**b**, it was observed that the cementite bridges on the graphite side is graphitized after the cycle tests. The volume seems to be expanded due to the local graphitization. In addition, the binding between the original graphite phase and matrix might become loose and the gap might become larger due to the graphitizing of the cementite bridge. Figure 17 shows this phenomenon in more details.

**Figure 17.**SEM images of SGI-3 showing local graphitization after cycling test, in two different magnifications: (

**a**) low magnification and (

**b**) high magnification.

_{3}C and graphite is required.

#### 3.5. Uncertainty of Measurements

#### 3.5.1. Uncertainty of α_{RS}

^{−6}± 0.1 × 10

^{−6}K

^{−1}at 300 °C. Hence the uncertainty of the α

_{RS}can be described by the following equation.

#### 3.5.2. Uncertainty of δα_{RS}

_{RS}can be assessed as follows.

_{RS}) = u (q × ΔT)

_{RS}against temperature, which is obtained by least-square method. In the present paper, the standard α

_{RS}values at 275, 300 and 325 °C were used to obtain the slope. The uncertainty of q depends on the uncertainty of α

_{RS}and it can be described as follows:

_{RS}at 300 °C is

_{RS}) = 1.7 × 10

^{−}

^{9}× 20 = 3.4 × 10

^{−}

^{8}(K

^{−}

^{1})

#### 3.5.3. Uncertainty of δT

_{mp,Sn}= 231.9 °C) and Lead (T

_{mp,Zn}= 327.5 °C) by the Linear interpolation.

#### 3.5.4. Uncertainty of δT *

#### 3.5.5. Uncertainties of $\text{\Delta}{L}_{\text{RS}}^{\text{m}}(T)$ and $\text{\Delta}{L}_{X}^{\text{m}}(T)$

#### 3.5.6. Uncertainties of L_{RS0} and L_{X0}

_{mic}is the nominal accuracy of the micrometer and R

_{mic}is the resolution of the micrometer. As can be seen from the above equation, the CTE at 20 °C, α (20 °C), is required. However, the order of CTE of alumina and cast iron are 10

^{−6}and 10

^{−5}, respectively. Hence, the third term in the above equation is negligible. Therefore the uncertainties of L

_{RS0}and L

_{X0}, u (L

_{0}), is

_{0}) ≈ 1.19 × 10

^{−}

^{6}(m)

#### 3.5.7. Combined Standard Uncertainty

_{c}(α

_{x}) can be described by the following equation.

_{x}(=f(x

_{i})) is the CTE of the sample; x

_{i}is the factor of each uncertainty.

_{x}= 1.54 × 10

^{−5}, α

_{x}

^{m}= 7.82 × 10

^{−6}, ΔL

_{x}

^{m}= 1.88 × 10

^{−6}) was evaluated and following value was obtained.

_{c}(α

_{x}) = 6.39×10

^{−8}(1/K)

## 4. Conclusions

^{−5}+ 5.38 × 10

^{−8}N – 5.85 × 10

^{−7}G + 1.85 × 10

^{−8}T − 2.41 × 10

^{−6}R

_{P/F}− 1.28 × 10

^{−8}NG − 2.97 × 10

^{−7}GR

_{P/F}+ 4.65 × 10

^{−9}R

_{P/F}+ 1.08 × 10

^{−7}G

^{2}− 4.80 × 10

^{−11}T

^{2}

_{P/F}: Pearlite/Ferrite ratio in the matrix.

^{−8}(1/K) under a specific condition.

## Acknowledgments

## Author Contributions

## Appendix A: Analysis of CTE

_{A}(T + δT

_{A}) is the length of the sample at sample temperature T + δT

_{A}; δT

_{A}is the temperature difference between the temperature measured by the thermocouple and the temperature of the sample; L

_{PR}(T) is the length of the push rod; and L

_{SC}(T) is the length of the sample carrier.

_{A}(T + δT

_{A}), in the above equation can be expressed by using the CTE as follows.

_{A}(T) is the length of the sample at sample temperature T; L

_{A0}is the length of the sample at room temperature; α

_{A}(T) is the CTE at temperature T; and δα

_{A}is the change of the CTE due to the temperature change, ΔT, in the vicinity of temperature T.

_{0}is the length of the sample; δT

_{A}* is the change of δT

_{A}corresponding to the change of temperature T (ΔT).

_{X}(T), can be described as follows.

_{RS}T is the CTE of the alumina (reference) at temperature (T); ${\text{\alpha}}_{X}^{\text{m}}(T)\cdot \left(\equiv \frac{\text{\Delta}{L}_{X}^{\text{m}}(T)}{\text{\Delta}T\cdot {L}_{X\text{0}}}\right)$ is the measured CTE of the sample at temperature T; ${\text{\alpha}}_{\text{RS}}^{\text{m}}(T)\cdot \left(\equiv \frac{\text{\Delta}{L}_{\text{RS}}^{\text{m}}(T)}{\text{\Delta}T\cdot {L}_{\text{RS0}}}\right)$ is the measured CTE of the alumina (reference) at temperature T.

_{A}due to the difference of the thermal conductivity and endo/exothermic reactions were ignored for the sake of simplicity.

_{X}(T), are summarized in Table 5.

_{RS}and δα

_{RS}was taken from the Netzsch’s standard [13] for the temperature range from 25 °C to 550 °C.

Parameters | Values |
---|---|

αRS | 7.78 × 10^{−6} (1/K) |

δαRS | 100 °C: 3.60 × 10^{−8} (1/K)200 °C: 1.76 × 10 ^{−7} (1/K)300 °C: 2.00 × 10 ^{−8} (1/K)400 °C: −2.00 × 10 ^{−8} (1/K)500 °C: 2.00 × 10 ^{−8} (1/K) |

δT | 1 (K) |

δT * | 0.01 (K) |

$\text{\Delta}{L}_{\text{RS}}^{\text{m}}(T)$ | Measured value at each temperature range |

$\text{\Delta}{L}_{X}^{\text{m}}(T)$ | Measured value at each temperature range |

LRS0 | 1.2 × 10^{−2} (m) |

LX0 | 1.2 × 10^{−2} (m) |

δαX | 0 (1/K) |

ΔT | 20 (K) |

## Appendix B: List of Symbols

- A
_{Graphite (IOS form VI)}: Surface area of graphite with roundness higher than 0.625 (ISO 945 form VI); - A
_{Graphite (IOS form IV+V)}: Surface area of graphite with roundness between 0.525 and 0.625 (ISO 945 form IV and V); - A
_{Graphite (All)}: Surface area of all graphite; - a: tolerance;
- CGI: Compacted Graphite Iron;
- CTE: Coefficient of thermal expansion;
- dL: Change in length;
- G: Area fraction of graphite (%);
- L
_{0}: Initial length; - L
_{A}(T): Length of the sample at temperature T; - ${L}_{\text{A}}^{\text{m}}(T)$: Measured sample length at temperature T;L
_{PR}(T): Length of the push rod at temperature T; - L
_{RS0}: initial length of reference sample; - L
_{SC}(T): Length of the sample carrier at temperature T; - L
_{X}_{0}: Initial length of sample X; - m: Standard value;
- N: Nodularity;
- q: Slope of α
_{RS}against temperature; - R
_{mic}: Resolution of the micrometer; - R
_{P/F}: Pearlite/Ferrite ratio in the matrix; - SGI: Spheroidal Graphite Iron;
- T: Temperature of the sample;
- $\overline{T}$: Average temperature;
- T
_{k}: Selected temperatures to calculate the CTE; - t: Thickness of the component;
- u(x): Uncertainty of xα
_{A}(T): CTE of sample A at temperature T; - α
_{E}: Coefficient of thermal expansion (CTE); - α
_{RS}: CTE of alumina (reference); - α
_{RS}(T): CTE of the alumina (reference) at temperature T; - ${\text{\alpha}}_{\text{RS}}^{\text{m}}(T)\cdot \left(\equiv \frac{\text{\Delta}{L}_{\text{RS}}^{\text{m}}(T)}{\text{\Delta}T\cdot {L}_{\text{RS0}}}\right)$: Measured CTE of the alumina (reference) at temperature;
- α
_{V}: Volumetric CTE; - α
_{X}: CTE of sample x; - ${\text{\alpha}}_{\text{X}}^{\text{m}}(T)\cdot \left(\equiv \frac{\text{\Delta}{L}_{\text{X}}^{\text{m}}(T)}{\text{\Delta}T\cdot {L}_{\text{X0}}}\right)$: Measured CTE of the sample at temperature T;
- ΔL: Change in length;
- $\Delta {L}_{\text{RS}}^{\text{m}}(T)$: Measured ΔL value of reference sample at each temperature range;
- $\Delta {L}_{X}^{\text{m}}(T)$: Measured ΔL value of sample X at each temperature range;
- ΔT: Change of temperature;
- ΔT
_{D}: Deviation of the temperature during the L_{0}measurement; - δα
_{RS}: Change of the CTE of the alumina (reference) due to the temperature change, ΔT, in the vicinity of temperature T; - δα
_{X}: Change of the CTE of the sample X due to the temperature change, ΔT, in the vicinity of temperature T; - δT: Temperature difference between the temperature measured by the thermocouple and the temperature of the sample;
- δT*: Change of δT corresponding to the change of temperature T(ΔT);
- δT
_{A}: Temperature difference between the temperature measured by the thermocouple and the temperature of the sample A; - δT
_{A}*: Change of δT_{A}corresponding to the change of temperature T(ΔT) for sample A; - δT
_{mp}: δT at melting point; - ρ: Density;
- σ
_{mic}: Nominal accuracy of the micrometer.

## Conflicts of Interest

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**MDPI and ACS Style**

Matsushita, T.; Ghassemali, E.; Saro, A.G.; Elmquist, L.; Jarfors, A.E.W.
On Thermal Expansion and Density of CGI and SGI Cast Irons. *Metals* **2015**, *5*, 1000-1019.
https://doi.org/10.3390/met5021000

**AMA Style**

Matsushita T, Ghassemali E, Saro AG, Elmquist L, Jarfors AEW.
On Thermal Expansion and Density of CGI and SGI Cast Irons. *Metals*. 2015; 5(2):1000-1019.
https://doi.org/10.3390/met5021000

**Chicago/Turabian Style**

Matsushita, Taishi, Ehsan Ghassemali, Albano Gómez Saro, Lennart Elmquist, and Anders E. W. Jarfors.
2015. "On Thermal Expansion and Density of CGI and SGI Cast Irons" *Metals* 5, no. 2: 1000-1019.
https://doi.org/10.3390/met5021000