# Shrinkage Defect in Thermal Analysis Cups of Low and High-Silicon Spheroidal Graphite Cast Irons

Anna Regordosa, Jon Sertucha, Ramon Suárez, Iker Asenjo, Jacques Lacaze

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Anna Regordosa, Jon Sertucha, Ramon Suárez, Iker Asenjo, Jacques Lacaze. Shrinkage Defect in Thermal Analysis Cups of Low and High-Silicon Spheroidal Graphite Cast Irons. International Journal of Metalcasting, In press, 10.1007/s40962-025-01731-3. hal-05250912

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# SHRINKAGE DEFECT IN THERMAL ANALYSIS CUPS OF LOW AND HIGH-SILICON SPHEROIDAL GRAPHITE CAST IRONS

Anna Regordosa, Jon Sertucha, Ramon Suárez and Iker Asenjo

AZTERLAN, Basque Research and Technology Alliance (BRTA), Durango, Spain

Jacques Lacaze

CIRIMAT, Université de Toulouse, BP 44362, 31030 Toulouse, France

Copyright © 2025 The Author(s)

https://doi.org/10.1007/s40962-025-01731-3

## Abstract

Standard thermal analysis cups can be seen as small riser-less sand castings prone to show shrinkage defect. This characteristic was used to compare the shrinkage tendency of two slightly hypoeutectic spheroidal graphite irons, a standard one with about 2.4 wt.% Si and a high-silicon one with about 3.9 wt.% Si. The other process variables that were investigated were the pouring temperature and the inoculation level. After casting, the samples were quantitatively characterized by X-ray tomography that showed internal shrinkage defect as well as outward and inward sinking of the outer surfaces. While the internal shrinkage defect increased from low-silicon to high-silicon alloy for low pouring temperature, the reverse was observed for high pouring temperature. Also, all of the cast samples showed inward sinking of the flat surfaces of the thermal

analysis cups, which was minimum for non-inoculated samples, and in general, higher for inoculated high-silicon alloy than for the inoculated low-silicon alloy. Crossed analysis of shrinkage defect and the changes in the outer shape of the cast samples is then discussed in terms of solidification at the scale of the cups that is based on dedicated thermal records. It is suggested that internal shrinkage and inward sinking are closely related through the mechanical behavior of the outer part of the cups that is solid or mechanically coherent while the central part still behaves as a slurry.

**Keywords:** solidification, spheroidal graphite iron, shrinkage, silicon content

## Introduction

Voids forming during the solidification step of castings can be quite detrimental on service properties of the parts and for that reason have led to a wealth of studies. Three different kinds of voids can be generated during solidification, gas porosities, shrinkage cavities and hot tears. Gas-only porosities, which are due to lower solubility of gas in solid than in liquid, commonly adopt a rounded shape when caused by hydrogen, or little crack-like cavities when caused by nitrogen,¹ and are found in peculiar cases in graphitic cast irons (SGI, LGI, CGI). Shrinkage cavities are associated to volume change that is made complicated because the liquid density is lower than that of austenite but far higher than that of graphite. Finally, hot tears appear

when significant temperature gradients develop in complex shape castings, leading to stresses exerted by the fully solid zones on areas that have not completed their solidification and are thus intrinsically highly sensitive to shear. Identifying the defects is most generally easy, though gas porosity and shrinkage cavities, on the one hand, shrinkage cavities and hot tears, on the other hand, can be present together. Concerning the former case, it is obvious that any shrinkage void would be filled with gas so as to equilibrate the partial pressure (thermodynamic activity) of the constituents in the voids and the condensed (liquid and solid) phases. This has led to confusion, such as the use of the wording “shrinkage porosity” that we here suggest not to use.

In a previous work on casting defects of spheroidal graphite cast irons (SGI), a distinction was made between primary and secondary shrinkage, also called macro- and
micro-shrinkage, respectively.¹ Macro-shrinkage is large cavities that should be found only in the riser of well-designed layouts and should be avoided in riser-less castings. They form during the early solidification step and are associated to contraction of the liquid because of cooling and to the precipitation of primary austenite dendrites, and most generally have smooth internal surface. In contrast, micro-shrinkage occurs during the final stages of solidification of liquid pockets that have been isolated in a continuous solid network. Stefanescu et al.² have divided micro-shrinkage in two types, dispersed macro-shrinkage (also known as sponge shrinkage³) and micro-porosity that differ in size while both being associated to difficulties in liquid feeding. In attempting to further explain the difference in the mechanism of formation of these two latter types of voids in spheroidal graphite cast irons, Stefanescu et al. put emphasis on the liquid pressure and the potential role of graphite expansion on it. However, they did not consider the fact that this graphite expansion deforms the solid framework at the scale of the microstructure as emphasized in numerous works⁴⁻¹⁰ (see also the review of Hillert's works on cast iron by Lacaze¹¹). Such a deformation means that defect formation in SGI castings might be also controlled by the mechanical behavior of the part that is already solid during completion of solidification of the remaining liquid.

Further, one can find in the technical literature the statement that high-silicon (HiSi) spheroidal graphite cast irons are more prone to show internal defects than the usual low-silicon (LoSi) spheroidal graphite cast irons. However, the few existing studies on the effect of silicon at constant

<figure><img src="image_2.png" /><figcaption>Figure 1. Symbols represent sound (dark circles) and unsound (open squares) castings, while half-dark half-white symbols are for castings showing shrinkage tendency, data after Reynolds et al.³ The dashed lines are according to the indicated equations (see text) and the solid line was calculated with the recent polynomial expression describing the eutectic line of the stable phase diagram, Eqn. 1.¹⁴</figcaption></figure>

carbon equivalent reviewed by Hecht¹² are not so definitive. Among these studies, the early work by Reynolds et al.³ is worth of mention. Figure 1 shows the positioning in the (silicon, carbon) plan of sound and unsound castings over ¾ inches thick castings, where unsound castings showed sponge shrinkage in the body of the part and sound castings did not, while those labeled as showing shrinkage tendency presented some sponge shrinkage below the macro-shrinkage in the riser. Reynolds et al. separated sound from unsound castings with a line defined by %C+%Si/7 = 3.9 wt.% that appeared to them more efficient than the eutectic line which they expressed as %C+%Si/3 = 4.3 wt.%, where %C and %Si (wt.%) are the content in carbon and silicon of the alloy, respectively. Reynolds' relation has been again used by other authors such as Wallace et al.¹³ On Figure 1 has also been plotted with a solid line the more recent polynomial relation describing the eutectic trough of the stable phase diagram¹⁴ that writes:

$$CE \approx w_C + 0.291 \cdot w_{Si} - 0.0040 \cdot (w_{Si})^2 + 0.05 \cdot w_{Cu} - 0.07 \cdot w_{Cr} + 0.276 \cdot w_P$$

Eqn. 1

where $w_i$ is the nominal content in element i of the alloy (wt.%).

It is seen that with this eutectic line a definite separation is obtained between unsound castings that are hypoeutectic and sound castings that are hypereutectic. Below about 1.5 wt.% Si, carbides certainly formed at the end of solidification that led to shrinkage defect. In the hypereutectic range and above that silicon level, all alloys investigated by Reynolds et al. gave sound castings. However, in the hypoeutectic domain, there is a silicon range between 2 and 2.8 wt.% that minimizes the risk of shrinkage. In the same domain of silicon content but on the hypereutectic side, Tafazzoli-Yadzi and Kondic¹⁵ studied SGIs containing 1.2 to 2.8 wt.% Si at constant CE equivalent of 4.6 wt.% that were cast in refractory molds. They observed no shrinkage for silicon content between 1.5 and 2.5 wt.%, while some defect was present for the 1.2 and 2.8 wt.% Si alloys. The lowest silicon alloy was certainly prone to form carbides and thus shrinkage as suggested above. Owing to the fact that Tafazzoli and Kondic certainly calculated CE as %C+1/3%Si, their alloy at 2.8 wt.% Si could well have been very close to the equilibrium eutectic line and not hypereutectic as stated, which may explain that it showed some porosity in agreement with the separation line defined by the phase diagram eutectic line in Figure 1.

Many experimental studies demonstrated that shrinkage defect decreases with increase in the carbon content from hypoeutectic to eutectic compositions. A quite recent example is the work by Regordosa and Llorca-Isern¹⁶ who studied the shrinkage incidence in a stressed geometry composed by a 90 × 38 × 90 mm test casting connected to
a riser by means of a 12 × 60 × 90 mm runner to promote a partially isolated solidification of the former. While non-inoculated alloys showed some eutectic cementite and significant shrinkage for hypoeutectic and eutectic alloys, the defect was smaller for inoculated alloys and took on a very low value for the eutectic composition. Kanno et al.¹⁷ went a step further by showing that beyond the eutectic composition the shrinkage tendency increases at a low pace, which they attributed to the fact that expansion due to primary graphite is lost when needed during the eutectic transformation. Both of these studies dealt with standard spheroidal graphite cast iron with 2–2.5 wt.% Si.

Accordingly, from Figure 1 and the above discussion no conclusion could be drawn concerning the effect of silicon on the shrinkage tendency of hypereutectic SGIs. On the contrary, there appears to be an effect for hypoeutectic and eutectic alloys and the aim of the present work was to further investigate it. Various hypotheses could be made that would explain that low-silicon (LoSi) irons are less prone to shrinkage defect than high-silicon (HiSi) irons:

1. Difference in the solidification interval, with HiSi showing an enlarged critical temperature range because of silicon segregation, though analysis of thermal records did not show any difference between LoSi and HiSi. However, one can think also to the effect of microsegregation of gases that can depend on the silicon content as analyzed by Kagawa et al.¹⁸

2. Difference in the liquid and austenite densities that would give a difference in the volume change upon solidification. Previous works on liquid and austenite densities give means for calculations of these quantities.¹⁹,²⁰

3. Difference in the mechanical behavior of the solid skin of the castings that effects the possibility of restraint or expansion and thus the occurrence of shrinkage.

The aim of this study was to look at the shrinkage tendency of near-eutectic spheroidal graphite iron alloys cast in thermal analysis (TA) cups for these have simple shape and are known to often present shrinkage defect. Such a means has been previously used by a few authors, e.g., Venkateswaran et al.²¹ who investigated the effect of various inoculants on shrinkage tendency but giving very few details on the experimental characterization. The study by Alonso et al.²² was more precise, and the authors concluded that their results might not be representative of industrial castings. This statement is certainly related to the fact that TA cups behave as small riser-less sand castings with their upper surface starting to solidify very soon after filling. In turn, such casting has the interest of exacerbating shrinkage formation, and emphasis was put here in describing the possible relation between wall movement, solidification kinetics at the scale of the cup, and central

shrinkage cavity. Other than the silicon level set at either 2.4 wt.% or 3.9 wt.%, high and low pouring temperature and three inoculation levels were considered.

## Experimental Details

The experimental work was carried out by preparing two alloy compositions, namely, LoSi and HiSi, by using a medium frequency induction furnace (250 Hz, 100 kW) 100–120 kg in capacity. In both cases, the metallic charge was prepared adding in the crucible of the furnace 35 kg of ferritic ductile iron returns, 15 kg of low alloyed steel, 0.6 kg of graphite, and 0.1 kg or 1.1 kg of FeSi (Si = 75.1, Ca = 0.31, Al = 0.75, C = 0.10 and Fe balance, wt.%) for the LoSi or HiSi alloys, respectively. Once melted, a check of the composition of each batch was made and corrective amounts of graphite were added to adjust the carbon content. For the HiSi alloy, an additional amount of FeSi was needed to adjust the Si content. The temperature of the melt was finally increased up to 1515–1520 °C before tapping for treatment with a FeSiMg alloy (grain size 5–25 mm, Si = 46.60, Mg = 6.00, Ca = 0.96, Al = 0.71 and rare earth RE = 0.92, Fe balance, wt.%) according to the sandwich method, which was carried out by transferring 50 kg of the prepared alloy from the furnace crucible to the treatment ladle. Before that, the spheroidizing alloy was placed in the chamber of that ladle in an amount of 0.60 kg (about 1.2 wt.% of the treated batch weight) and covered with steel scrap cuts 5–15 mm in size.

After completing the spheroidizing reactions, the melt batches were rapidly cleaned by removing the slag and then cast in different TA cups and molds following the diagram in Figure 2 in which the red arrows indicate the order of pouring each cup and/or mold. The sequence comprised:

1. A first series of three standard TA cups with a thermocouple located in their center and containing different amounts of inoculant (0.00 wt.%, 0.05 wt.% and 0.20 wt.%, assuming samples weighed 350 g).

2. A TA cup with 0.20 wt.% of inoculant and equipped with three thermocouples located in the center, in the middle of one side face and in the middle of one corner, was cast.

3. Three chemically bonded sand molds fabricated by additive manufacturing to produce castings using the same three inoculation levels as above.

4. Two chemical bonded sand molds to produce Y2 wedges (EN-1563), one of them without inoculation and the other one with 0.20 wt.% of inoculant (it is assumed that each mold contained 7.0 kg of poured alloy).

5. A TA cup equipped with three thermocouples and without any inoculant addition.
<figure><img src="image_3.png" /><figcaption>Figure 2. Flowchart followed to pour the TA cups and the molds.</figcaption></figure>

6. Finally, a second series of three TA cups with a standard thermocouple located at the center of the samples using the same three inoculation levels defined above for the first series.

Notice that the first and second series of three TA cups were sought to study the effect of decreasing pouring temperature measured by the peak temperature values recorded in each case. All TA cup samples used in the present work were of the so-called square type with a thermocouple (TC) junction located in a horizontal tube (see Suarez et al. for a schematic²³). Two different inoculants were used in this experimental work, the one added in the TA cups (grain size 0.2–0.5 mm, Si = 69.9, Al = 0.93, Ca = 1.38, Bi = 0.49, rare earths = 0.37 and Fe balance, wt.%) and the other one compacted as ingots added in the molds (Si = 70–76; Al = 3.1–4.3; Ca = 0.3–1.3 and rare earths = 0.4–0.5 and Fe balance, wt.%). Once cooled, all the samples were manually cleaned and then weighed.

In the following, only results obtained on the TA cups are presented. Samples P1-P6 of the LoSi and HiSi alloys were scanned by X-ray tomography using a YXLON apparatus Mod. Y.CT Compact working at 450 kV with a current of 1.5 mA. A coupon with gauged dimensions 20 × 20 × 40 mm was positioned beside every scanned sample so as to check the scaling of each tomography set-up. Accumulation of horizontal sections, 0.5 mm in thickness, was carried out along the vertical axis from bottom to top of each sample. After completion of the scans, one image file per

section was generated with a pixel size of 0.16 mm. A stack of all the section images were then built into a 3D model using VG Studio Max 2.0 software to measure the total volume of each sample ($V_{sample}$) and the volume of defects ($V_{defect}$) by applying techniques based on contrast and gray level analysis. From these, the relative defect volume ($R_{defect}$) was calculated according to the following relation:

$$R_{defect} = \frac{V_{defect}}{V_{sample}} \times 100 \qquad \text{Eqn. 2}$$

Figure 3 shows an example of a section and Figure 4 an image of a reconstructed sample where the identified defect zone appears in strong contrast with the different colors corresponding to non-connected cavities. On each section as in Figure 3, a number of dimensions were measured manually: widths $d_{\parallel}$ and $d_{\perp}$, respectively parallel and perpendicular to the thermocouple tube, and the two diagonals, diag1 and diag2. This data was complemented by the evaluation of the area of each sample section and that of the defect, if any, which were evaluated following the procedure detailed in Appendix 1. Finally, a vertical section perpendicular to the thermocouple was extracted from the X-ray tomography data for illustrative purpose.

For reference to be used when analyzing the cast samples, the original dimensions of the cup cavity were characterized by X-ray tomography and 3D-scanner. See Appendix 2 for details and notice in particular the low scattering evidenced between cups whose dimensions were characterized by X-ray tomography. Figure 5a compares the four
<figure><img src="image_4.png" /><figcaption>Figure 3. Example of a section of a cup as reconstructed from tomography and definition of the side and diagonal lengths.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 4. Perspective view of a cup with the central shrinkage defect.</figcaption></figure>

dimensions as measured on tomography and 3D-scanner images on one of the cups. The measurement of $d_\parallel$ is perturbed by the extremities of the thermocouple protecting tube at mid-height. In all the graphs to be presented below, the origin for the height axis was that with the first non-zero value of the section area of each tomography record.

In Figure 5b, linear fits were calculated on one side and one diagonal (cup #4 in Appendix 2) from tomographic measurements after removing the measurements at the base. For the 40 mm height, the side value at 37.6 mm agrees with the side of 37.5 mm given by the manufacturer. The

equations for the side length “d”, and for the diagonal length “diag” of the original cup cavity are (mm):

$$d = 33.127 + 0.11128 \cdot z \qquad \text{Eqn. 3}$$

$$\text{diag} = 42.505 + 0.15563 \cdot z \qquad \text{Eqn. 4}$$

where z is the height (mm).

Chemical analysis and metallographic characterization were carried out on two U samples, one inoculated (1U) and one not (3U) for both LoSi and HiSi alloys. Chemical analysis was achieved using a LECO CS300 for determining C and S contents, a gravimetric method for Si content, and an inductively coupled plasma spectrometer ICP-MS (Agilent 7500ce) for other elements. The results from these analyses are listed in Table 1 and used to calculate the carbon equivalent, CE, by means of Eqn. 1. Compared to the reference value of 4.34 wt.% for the eutectic, it is seen that the investigated compositions are slightly hypoeutectic.

Finally, the microstructure was checked on two fields of view for each U sample. Representative images at 100 × magnification (0.757 mm² each) per sample were used without etching for analysis of graphite particles using the ImageJ software.²⁴ In this case, all graphite particles with an area equal to or higher than 25 µm² were counted, and then assigned to classes III, V or VI of the EN ISO 945 standard²⁵ according to the criteria described by Germain et al.²⁶ Nodularity values (%) were determined with the expression $Nod = \frac{N_v+N_{vi}}{N_{III}+N_v+N_{vi}} \times 100$, where $N_{iii}$, $N_v$, and $N_{vi}$ are the number of particles assigned to classes III, V, and VI, respectively. Nodule count (mm⁻²) values were calculated as $N = \frac{N_v+N_{vi}}{0.757}$. The metallographic samples were finally etched using Nital 5% reactant to check the amount of ferrite and pearlite. It was found that the matrix was composed of ferrite and pearlite in the LoSi alloy, while a fully ferritic microstructure (less than 5% pearlite) was found in the case of HiSi alloy (see Figure 6). Characterization of graphite count, nodularity, and the ferrite and pearlite contents are listed in Table 2, and no carbide was observed even in the non-inoculated samples.

## Results

Figure 7a shows a general view of the samples produced after pouring all the TA cups and molds with the HiSi alloy in the shop floor. Figure 7b is another view of the TA cups where it is seen that the temperature is still very high for the 4P-6P TA cups, while the 1P-3P ones have already cooled down. Data concerning the TA cups, with or without inoculant addition, and cups equipped with additional thermocouples are listed in Table 3, following the sketch shown in Figure 2. It is seen that the difference between high and low pouring temperatures led to a difference in peak temperature of about 50 °C and 70 °C for the LoSi and HiSi alloys, respectively.
<figure><img src="image_6.png" /><figcaption>Figure 5. (a) Plot of the side and diagonal values as measured by X-ray tomography and 3D-scanner. (b) Linear fitting of the side and diagonal values for the cup #4 as described in Appendix 2 and expressed with Eqns. (3) and (4). In the caption, *d<sub>perp</sub>* stands for *d<sub>⊥</sub>*.</figcaption></figure>

<table><caption>**Table 1.** Composition of the Alloys (also 0.016-0.019 P, 0.006 S, 0.05-0.06 Cr, <0.023 Ni, <0.020 Mo), and Calculated CE (wt.%)</caption><thead><tr><th>Sample</th><th>C</th><th>Si</th><th>Mn</th><th>Cu</th><th>Mg</th><th>CE</th></tr></thead><tbody><tr><td>LoSi-1U</td><td>3.59</td><td>2.42</td><td>0.22</td><td>0.062</td><td>0.040</td><td>4.27</td></tr><tr><td>LoSi-3U</td><td>3.59</td><td>2.46</td><td>0.22</td><td>0.061</td><td>0.040</td><td>4.28</td></tr><tr><td>HiSi-1U</td><td>3.20</td><td>3.91</td><td>0.18</td><td>0.047</td><td>0.036</td><td>4.28</td></tr><tr><td>HiSi63U</td><td>3.21</td><td>3.86</td><td>0.18</td><td>0.046</td><td>0.038</td><td>4.28</td></tr></tbody></table>

The temperature records of cups 1P-6P were all similar for both silicon levels, and are illustrated in Figure 8 with inoculated LoSi samples (1P and 4P). The cooling curves present a pre-eutectic event at a temperature slightly above that of the eutectic plateau in agreement with the slightly hypoeutectic composition of the alloys. With a decrease in the pouring temperature, the cooling rate of the liquid was only slightly increased while the start and end of solidification times were decreased. Note that the difference on solidification time depends also on the mass of metal being smaller for 4P than for 1P. The pre-eutectic arrests appear very much similar to the one associated with spiking of austenite dendrite array described by Parks and Loper,²⁷ that favors shrinkage and is exacerbated when the nodule count is low.

The thermal records from the cups equipped with additional thermocouples are described in Appendix 3. The outputs were:

- The temperature at the inner surface of the sand cups increases from room temperature at the time of pouring to 800-1000°C at the end of the sample solidification.

- The temperature of the liquid within the cup homogenizes quickly, certainly because of convection currents due to pouring. However, solidification is rapid very close to the inner sand cup surface whose cooling curve is then affected by the latent heat released by the central part of the sample.

The four lengths defined with Figure 3 were then evaluated for all 1P-6P samples of the LoSi and HiSi alloys and are shown in Appendix 4. The two values of the diagonals were highly reproducible for each sample and only one (diag1) has been plotted in Figure 9a (LoSi alloy) and Figure 9b (HiSi alloy) with the reference diagonal value given by Eqn. 4 shown as short-dash line. All data evidence that the samples were larger than the original cup cavity after cooling to RT, with the difference increasing with the height of the section. In the case of the LoSi alloy, it is seen that the increase is higher for the first three castings (1P-3P) associated with higher temperature and larger weight. Apart for sample 1P, the dimensional variations from one sample to another are lower for the HiSi alloy, in particular in the low part of the samples where the diagonals of all samples practically superimpose on each other. On the upper part of the curves for the HiSi alloys, the effect of casting temperature does not clearly appear while that of the weight of the sample remains. These observations suggest that the cup and thus the sample expand during and/or after pouring. This effect would be mostly due to the heating of the cup, though bulging out of the sample during solidification due to graphite precipitation could also be considered as will be discussed later.

As can be seen in Appendix 5, the dimensions *d<sub>∥</sub>* and *d<sub>⊥</sub>* were also superimposed on each other in the lower half of each of the TA samples and showed similar behavior in the upper half, though *d<sub>∥</sub>* was disturbed in the height range
<figure><img src="image_7.png" /><figcaption>Figure 6. Micrograph of the alloys LoSi inoculated (a), LoSi not-inoculated (b), HiSi inoculated (c), and HiSi not-inoculated (d) after Nital etching.</figcaption></figure>

<table><caption>Table 2. Microstructure Characterization of Samples 1U and 3U for LoSi and HiSi Alloys</caption><thead><tr><th>Sample</th><th>Field</th><th>Nod (%)</th><th>N (mm<sup>-2</sup>)</th><th>Ferrite/Pearlite (%)</th></tr></thead><tbody><tr><td rowspan="2">LoSi-1U<br>(inoculated)</td><td>1</td><td>96</td><td>300</td><td>75/25</td></tr><tr><td>2</td><td>95</td><td>299</td><td>70-65/30-35</td></tr><tr><td rowspan="2">LoSi-3U<br>(not-inoculated)</td><td>1</td><td>97</td><td>166</td><td>30/70</td></tr><tr><td>2</td><td>98</td><td>195</td><td>30/70</td></tr><tr><td rowspan="2">HiSi-1U<br>(inoculated)</td><td>1</td><td>98</td><td>427</td><td>100/0</td></tr><tr><td>2</td><td>98</td><td>439</td><td>100/0</td></tr><tr><td rowspan="2">HiSi-3U<br>(not-inoculated)</td><td>1</td><td>83</td><td>208</td><td>95/5</td></tr><tr><td>2</td><td>93</td><td>252</td><td>90/10</td></tr></tbody></table>

corresponding to the thermocouple. Figures 10a and b present the $d_{⊥}$ values for LoSi and HiSi samples, respectively. It is again seen that the size of the samples is larger than the original cup cavity in the low and high part of it, but they all show an inward sink in the middle that was not seen on the diagonals (Figure 9), also called outer sunk or pull down.¹,²⁸ Looking in detail to the curves, no clear effect of pouring temperature could be observed in the case of the LoSi samples. On the contrary, it is seen that the two HiSi samples without inoculation (3P and 6P) show very little sinking while those inoculated show significant sinking that is much larger for high pouring temperature (samples 1P and 2P) than for low pouring temperature (samples 4P and 5P).

Tafazzoli-Yadzi and Kondic¹⁵ considered that “an excess of contraction over expansion (because of liquid and austenite contraction) can be compensated for either by casting skin sinking inwards or shrinkage cavity forming in the central regions ...”. As both inward sink and shrinkage cavity were observed in all the present samples, it might be guessed they correlated with the development of negative pressures in the thermal center of the samples at some time during solidification. This was further studied by comparing the change along the height of the section and defect areas, which are all shown in Appendix 6 and illustrated with one central vertical section issued from the tomography for each sample.
<figure><img src="image_8.png" /><figcaption>Figure 7. (a) View of the shop floor just after casting the samples with the HiSi alloy. (b) Detailed view of the TA cups listed in Table 3. Note in (b) that the temperature is still high for the 4P-6P TA cup samples while the 1P-3P ones have already cooled down.</figcaption></figure>

<table><caption>Table 3. Peak Temperature, Sample Reference, Inoculation rate (% of the Mass of Metal), Mass and Volume of the Samples, Defect Volume, and Relative Defect Volume in the Samples</caption><thead><tr><th>Alloy</th><th>Temperature (°C)</th><th>Sample</th><th>Inoculation (%)</th><th>m<sub>sample</sub> (g)</th><th>V<sub>sample</sub> (mm<sup>3</sup>)</th><th>V<sub>defect</sub> (mm<sup>3</sup>)</th><th>Relative defect volume (%)</th></tr></thead><tbody><tr><td rowspan="12">LoSi</td><td rowspan="4">High (1289-1293)</td><td>1P</td><td>0.20</td><td>350.06</td><td>49499</td><td>1049</td><td>2.1</td></tr><tr><td>2P</td><td>0.05</td><td>362.54</td><td>51252</td><td>1219</td><td>2.4</td></tr><tr><td>3P</td><td>0</td><td>340.46</td><td>48070</td><td>1156</td><td>2.4</td></tr><tr><td>1U</td><td>0.20</td><td>356.89</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="5">Low (1236-1246)</td><td>4P</td><td>0.20</td><td>305.74</td><td>43212</td><td>114</td><td>0.3</td></tr><tr><td>5P</td><td>0.05</td><td>293.11</td><td>41431</td><td>196</td><td>0.5</td></tr><tr><td>6P</td><td>0</td><td>352.97</td><td>49457</td><td>556*</td><td>1.1</td></tr><tr><td>3U</td><td>0</td><td>330.48</td><td>-</td><td>-</td><td>-</td></tr><tr><td>1P</td><td>0.20</td><td>340.01</td><td>48577</td><td>299</td><td>0.6</td></tr><tr><td rowspan="5">HiSi</td><td rowspan="4">High (1318-1322)</td><td>2P</td><td>0.05</td><td>343.37</td><td>48969</td><td>405</td><td>0.8</td></tr><tr><td>3P</td><td>0</td><td>321.05</td><td>45513</td><td>832</td><td>1.8</td></tr><tr><td>1U</td><td>0.20</td><td>339.73</td><td>-</td><td>-</td><td>-</td></tr><tr><td>4P</td><td>0.20</td><td>331.79</td><td>46987</td><td>564</td><td>1.2</td></tr><tr><td rowspan="3">Low (1249-1255)</td><td>5P</td><td>0.05</td><td>362.54</td><td>51641</td><td>827</td><td>1.6</td></tr><tr><td>6P</td><td>0</td><td>304.88</td><td>43828</td><td>731</td><td>1.7</td></tr><tr><td>3U</td><td>0</td><td>342.00</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

As can be observed in Appendix 6 for high pouring temperature, shrinkage defects are smaller for the HiSi alloy than for the LoSi alloy for inoculated samples, while they are similar and large for the non-inoculated samples. Furthermore, it is clear that larger outer sink correlates with smaller and more diffuse internal shrinkage defect as illustrated in Figure 11a with samples 1P of LoSi and HiSi alloys.

On the contrary, sinking was little marked for all samples cast with a low pouring temperature, as illustrated in Figure 11b with the 4P samples of LoSi and HiSi alloys. Furthermore, the shrinkage defects of inoculated samples showed an opposite trend to that of the high pouring temperature series: defects were larger for HiSi alloy and smaller and more diffuse for the LoSi alloy. For non-inoculated samples, the shrinkage defect was large for both

<footnote>*Shrinkage defect open to the surface of the sample.</footnote>
<figure><img src="image_9.png" /><figcaption>Figure 8. Comparison of the cooling records of LoSi-1P (high pouring temperature) and LoSi-4P (low pouring temperature).</figcaption></figure>

alloys and very much similar to the high pouring temperature non-inoculated samples 3P.

The final step of this section consisted in analyzing the above raw results in terms of density values. Table 3 lists the values of the weight of the TA samples, $m_{sample}$, as well as the sample volume, $V_{sample}$, and the defect volume, $V_{defect}$, evaluated by tomography. From these, the material density, $\rho_{material}$, and the apparent density, $\rho_{apparent}$, could be evaluated as:

$$ \rho_{material} = m_{sample} / (V_{sample} - V_{defect}) \qquad \text{Eqn. 5} $$

$$ \rho_{apparent} = m_{sample} / V_{sample} \qquad \text{Eqn. 6} $$

Plotting the material density as function of the defect volume, a clear trend emerged: the density of the material increased with the defect volume. This looks definitely as an artifact related to the evaluation of the material volume, and more precisely to the defect volume. The software analyzing the tomographs overestimates the shrinkage volume and reports a value that relates to the volume affected by shrinkage, i.e., not properly accounting for the presence of some solid material in particular in the case of dispersed shrinkage. The evaluation of material density by this method was thus not further considered.

The apparent density of the cast iron is plotted in Figure 12 where the horizontal dashed lines are the theoretical density values, $\rho_{theoretical}$, at room temperature that amount to 7.099 g·cm⁻³ for the LoSi alloy and 7.084 g·cm⁻³ for the HiSi one (see Appendix 6). It is seen that all experimental values are below the theoretical values, apart for an outlier that corresponds to the not-inoculated sample LoSi-6P with open defect. The difference ($\rho_{theoretical}-\rho_{apparent}$) should mostly correspond to voids, including porosity and

shrinkage. A search for the presence of porosity out of the shrinkage area was carried out on various samples by optical microscopy and was totally unsuccessful. Hence, the difference between the theoretical and measured values should correspond to shrinkage and it is worth noticing that it is on average larger for the HiSi alloy than for the LoSi alloy, which could be a subtle indication that high-silicon content does effectively lead to larger shrinkage as sometimes stated in the literature but with no known experimental support.

## Discussion

According to Winter et al.²⁹ the total volume shrinkage of a cylindrical shape casting consists of liquid metal contraction, mold dilation effects, and actual solidification shrinkage or expansion. The mold dilation is often referred to the so-called early expansion of the mold cavity due to heating by the liquid metal after filling, as well as because of ferrostatic pressure.¹³ Such an expansion could be avoided or limited only by the use of highly rigid molds, though it appears with all kinds of volume change measurements upon casting of cast iron as discussed by Svidro and Dioszegi in their review.³⁰ The discussion below is an attempt to extract information on the origin of the dimensional changes of the cup samples from the measurements presented in the previous section.

Comparing Figures 9 and 10 suggested to first consider the results on the HiSi alloy because they appear simpler. As a matter of fact, it is seen in Figure 9b that all diagonals do follow the reference curve in the lower part of the cups, up to 10 mm for sample 1P and 16 mm for all other samples. This is also in this range of height that the side values in Figure 10b start deviating from the reference curve. For samples 1P and 2P, this deviation is associated with sinking, while for samples 4P and 5P there appears a slight expansion followed at larger height with a sink that is much smaller than for the first two samples. Finally, the two non-inoculated samples 3P and 6P show a similarly small expansion followed by a shallow sinking. Thus, the thermal history (effect of pouring temperature), solidification kinetics at the scale of the cup (difference between inoculated and non-inoculated samples) as well as the mechanical behavior of the solid (expansion versus sinking) determine the dimensional changes of these HiSi castings.

After the above analysis of the HiSi samples, it became easier to consider the results on the LoSi samples. Figure 10a shows that all LoSi samples followed the reference side curve up to about 8 mm, then show a slight expansion followed by a sink at larger height. The expansion is larger for 1P-3P samples than for 4P and 5P samples, thus evidencing an effect of pouring temperature (sample 6P should be discarded here because of the open shrinkage).
<figure><img src="image_10.png" /><figcaption>Figure 9. Changes with height of one diagonal of the samples of LoSi (a) and HiSi (b) samples. The short-dash line is the reference diagonal value given by Eqn. (4).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 10. Changes with the height of side $d_⊥$ of the samples of LoSi (a) and HiSi (b) alloys. The short-dash line is the reference side value given by Eqn. 3.</figcaption></figure>

This expansion can be noticed also on the diagonals of samples 1P and 2P in Figure 9a, while it is not seen for any other sample, thus evidencing an effect of solidification kinetics at the scale of the cup. Finally, the facts that expansion occurs at lower height and that the diagonals values are more scattered for LoSi samples than for HiSi samples evidence an effect of the silicon content on the thermomechanical behavior of the cast cups during solidification.

The final shape of the TA samples that were investigated should thus depend on defect formation and mechanical behavior of the solid, much in the lines summarized by Onhaka et al.¹⁰ Heat transfer and temperature evolution within the sample are prevalent in defining these evolutions. Below is a tentative description of the evolution of temperature, solidification and mechanical behavior of the cups with the objective of clarifying how the differences discussed above could take place. Just after filling the cup, a solid skin starts forming on the walls while convective
<figure><img src="image_12.png" /><figcaption>Figure 11. Section and defect area along the height of: (a) samples 1P of LoSi (solid lines) and HiSi (dotted lines) alloys. (b) samples 4P of LoSi (solid lines) and HiSi (dotted lines). The short-dashed line is the reference area of the cup cavity (Figure 18).</figcaption></figure>

currents quickly homogenize the temperature in the liquid. It is possible to calculate the liquid contraction from the pouring temperature to that of solidification using the

following expression of the liquid density that was assessed in a previous work¹⁹:
<figure><img src="image_13.png" /><figcaption>Figure 12. Apparent density versus defect volume. The horizontal dashed lines show the theoretical density values of the LoSi and HiSi alloys.</figcaption></figure>

$$ \rho^{\text{liq}} = 8.414 - 0.1504 \cdot w_C + 0.00659 \cdot w_C^2 - 0.1705 \cdot w_P - 0.063 \cdot w_{Si} - (0.926 - 0.05 \cdot w_C - 0.08 \cdot w_P) \cdot 10^{-3} \cdot T_C \quad \text{Eqn. 7} $$

where $T_C$ is the temperature in Celsius and $w_i$ the content in i element of the alloy (wt.%).

Figure 13 shows the change with temperature of the liquid density for the LoSi and HiSi 1U samples whose compositions are listed in Table 1. The slope of the lines is nearly the same, meaning that the density change will be about the same for either alloy at given temperature change, so that no effect of the Si content is to be expected. However, it is also seen that the LoSi liquid alloy has a density that is about 1% higher than that of the HiSi alloy. For the same volume of the original cup, about 50 cm³, the LoSi samples would weight slightly more than the HiSi samples if they were poured at the same temperature. It can be seen in Table 3 that the scatter of the mass of the samples is much larger than 1%, which means that the filling was not the same for every cup, though this does not affect the conclusions of this study.

The early solid skin starts thickening while the liquid cools and at some time the temperature of the upper surface will be low enough to also start solidifying. At some early time after filling the cup, the TA sample will thus resemble a casting with a solid rim closing in on a mushy zone that solidifies with the latent heat extracted through the rim. It is known that spheroidal graphite cast irons solidify with an extended mushy zone,³¹ but for hypoeutectic alloys as in the present case, or slightly hypereutectic alloys, the eutectic solidification is preceded by an array of austenite dendrites developing from the surface to the center of the

TA cup. This is illustrated with Figure 14 according to Dunphy et al.³² (cited by Hecht¹²).

The above description must be complemented with an estimate of the volume change upon solidification of the LoSi and HiSi alloys. This was carried out considering the composition of samples 1U (Table 1) solidifying at 1150 °C, see Appendix 6. For calculating the density of austenite, the lattice parameter assessed by Lacaze et al.¹⁹ and that reevaluated²⁰ were considered, leading to two slightly different values of the density of each alloy, see Table 4. Together with the liquid density (Eqn. 7), the relative volume change upon solidification at 1150 °C could be evaluated as:

$$ \Delta V/V = (\rho^{\text{liquid}} - \rho^{\text{castiron}})/\rho^{\text{castiron}} \quad \text{Eqn. 8} $$

As seen in Table 4, both estimates of the austenite lattice parameter predict an expansion upon solidification for both alloys. However, this expansion is larger for the LoSi alloy than for the HiSi one when using the first estimate of the austenite lattice parameter, while the expansion is the same for both alloys with the updated estimate. It is interesting to note that this latter value corresponds to the maximum relative defect volume reported in Table 3, which were obtained on the LoSi alloy cast at high temperature.

Within the solidifying cup, the interest should be put on two boundaries that move inward: 1) the inner boundary of the 100% solid shell; and 2) the transition from the part of the mushy zone in which the solid has reached coherency, and an inner part in which the solid is not yet coherent. The coherent zone can be seen as a solid skeleton through which strains and stresses can be transmitted as is the case in the fully solid shell. These limits have been tentatively drawn in Figure 14 on the basis of the quantitative analysis of the solidification of cylindrical bars by Mampaey.³¹ These limits have also been evidenced in Figure 15 that represents the median cup section at some time during solidification. Within this section, the temperature may be assumed homogeneous in the non-coherent mushy zone, and then decreases slightly through the coherent mushy zone and also in the outer solid shell along the vertical and horizontal median lines. In contrast, along the diagonals in the outer solid shell, the temperature decrease must be more significant as indicated with the surface temperatures shown on Figure 20 (Appendix 3).

With the above description of the temperature field in the cup, and considering that the solid fraction at coherence should be about 30–40%, the instantaneous volume change within the cup could be described. At the center of the cup, pre-eutectic austenite deposition leads to some overall contraction of the non-coherent mushy zone. The increase in eutectic fraction from the inner to the outer boundaries of the coherent mushy zone leads to an increased expansion that is maximum at the outer boundary of this zone.
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Evolution of the density of the liquid with temperature for the 1U composition of LoSi and HiSi alloys.</figcaption></figure>

Finally, within the fully solid shell, the fraction of graphite might slightly change depending on the local temperature, but should in any case be higher than just after solidification completion, thus associated to some expansion.

From these considerations, a scheme describing the deformation of the solid shell at some intermediate time of cup's solidification could be made as described with Figure 15. At this intermediate time, the corners of the cup are already much colder than the middle of the faces and expand due to both the expansion of the coherent mushy zone and that of the outer solid shell. The coherent zone facing the middle of the faces also expands but it does so

<table><caption>**Table 4.** Theoretical Density at 1150 °C Based on the Composition of the U1 LoSi and HiSi Samples (see Table 1) and Relative Volume Change Upon Solidification, ΔV/V. The Two Evaluations of the Austenite Lattice Parameter Mentioned in the Text were Considered for Calculating Data in the Upper¹⁹ and Lower²⁰ Rows</caption><thead><tr><th>Alloy</th><th>ρ<sup>castiron</sup> (g.cm<sup>-3</sup>)</th><th>ΔV/V (%)</th></tr></thead><tbody><tr><td rowspan="2">LoSi</td><td>6.882</td><td>+0.93</td></tr><tr><td>6.801</td><td>+2.14</td></tr><tr><td rowspan="2">HiSi</td><td>6.856</td><td>+0.24</td></tr><tr><td>6.723</td><td>+2.27</td></tr></tbody></table>

by sinking inwards because of the contraction of the non-coherent mushy zone. Both expansion and sinking need creep of the solid shell and of the coherent skeleton and, at some time during cup's solidification, it is expected that the solid shell will be thick enough to hinder that creep while the center of the cup will still be in a non-coherent state and thus contracting. Negative pressures will then build-up in the center until a shrinkage void develops that quickly releases the pressure deficiency.

The increase of defect volume with the pouring temperature that was observed for the LoSi alloy agrees with previous work.¹⁷ However, that defect volumes are higher for LoSi than for HiSi inoculated alloys at high pouring temperature, and the reverse at low pouring temperature, can hardly be rationalized without recourse to a

<figure><img src="image_15.png" /><figcaption>**Figure 14.** Sketch of the evolution with time of the different zones through a section of the solidifying sample (inspired by Dunphy et al.³²).</figcaption></figure>
thermomechanical simulation of the samples. It would be challenging as well to demonstrate that a simple change of the number of spheroids would affect shrinkage and inward sinking as seen when comparing inoculated and non-inoculated samples. It should be noted that creep of the solid rim was also demonstrated to be an essential feature of defect formation.

Such a mechanical approach was beyond the scope of this work, but suggested that attention be paid to the available literature. Many of the simulation works dealing with the formation of voids in casting consider that shrinkage and porosity can be both described as a lack of liquid feeding through the mushy zone. For example, this is the case of the work by Kweon et al.³³ for what concerns SGIs, based on a previous review by Stefanescu.³⁴ In contrast, and as can be also noticed in this latter review, very few works have effectively taken into account volume expansion and contraction of the material. Among these latter, the work of Fras and Kapurkiewicz⁹ that dealt with lamellar cast irons could be mentioned, in which shrinkage cavity was computed as the difference between the volumes of the casting cavity and that of the metal inside. Concerning SGI, Lesoult et al.⁷,³⁵ expressed liquid feeding through a mushy zone allowed to deform after coherency was reached. Dealing also with SGI, Ohnaka et al.³⁶ put emphasis on the mechanical aspect of volume change and correlated defect formation with the mechanical behavior of the solid shell and the coherent zone. It is unfortunate that they used the wordings porosity and shrinkage alternatively, while most of their work was dealing with shrinkage. The output of their approach is that there is a strong correlation between a critical stress level found at about 80 MPa and shrinkage volume. Though this correlation was highly satisfying, the authors stressed the fact that the volume subjected to stresses higher than 80

MPa was much larger than the observed shrinkage volume and did not question the fact that they used an elastic model rather than an elastic-plastic model to compute stress build-up. Whatever the reason for the discrepancy between experimental and calculated results in the study by Ohnaka et al., it is clear that they paved the way for useful predictions of shrinkage defects in SGI castings. Finally, it is worth noting that there are enough interfaces in the mushy zone to ensure easy nucleation of the voids, either porosity or shrinkage, without having to consider breaking up the very high bond strength of pure liquid.

## Conclusion

Square thermal analysis cups have been considered as small riser-less sand castings prone to show internal shrinkage defect and were used here to compare defect formation in low- and high-silicon spheroidal graphite irons. X-ray tomography evidenced that all samples showed expansion when compared to the initial cavity of the cup, as well as a more or less marked inwards sinking of the flat facets. Apart for the silicon content, the effects of inoculation and pouring temperature were investigated.

The difference between theoretical and measured density of the samples showed values in agreement with the defect internal volume, and were found slightly larger for high-silicon than for low-silicon alloys. As expected, inoculation was effective to decrease the internal shrinkage defect for both alloys, though this appeared more evident for regular inoculant addition (0.2%) than for reduced addition (0.05%). In contrast, the effect of pouring temperature was striking: decreasing it decreases the shrinkage volume of the low-silicon alloy, while it increases it in the case of the high-silicon alloy. This latter result, together with the observation of expansion and inward sinking, demonstrates the need for a thermomechanical approach to the formation of internal shrinkage and surface deformation in spheroidal graphite castings. Such an approach was beyond the scope of this study, but a scheme has been proposed to illustrate the underlying mechanism. Finally, with reference to Figure 1, work is in progress to determine whether high-silicon hypereutectic alloys exhibit less internal shrinkage defects as is the case of low-silicon alloys.

## Funding

Open access funding provided by Institut National Polytechnique de Toulouse.

**Conflict of Interest** The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article.

<figure><img src="image_16.png" /><figcaption>**Figure 15.** Sketch of the central cup section at an intermediate solidification time showing the outer solid shell and the coherent and non-coherent mushy zones. The solid arrows illustrate expansion due to graphite precipitation and the double arrows the resulting outward or inward bulging.</figcaption></figure>
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## Appendix 1: Measure of Section and Defect Areas on Tomography Images

For all cups, the images obtained from the tomography scans were used to determine the lengths $d_{//}$, $d_{\perp}$, diag1, and diag2, as described in the main text and illustrated with Figure 3. Additionally, the area of all sample sections and of the internal defect when present, were measured using the ImageJ software.²⁴ Examples of section images appear on the first row of Figure 16. Each such image was first digitalized with a resolution of 2048 × 2048 pixels, giving a pixel size of 0.16 mm, and then binarized to determine the area of the contrasted casting section. Scaling of the

images was set using the 20 mm in side cubic coupon that was scanned together with each cup. Detecting automatically the contours of the internal cavities was hardly possible because they appeared with different gray shades before binarization due to their irregular 3D shape. The definition of the cavity borders was thus made manually by comparison to the corresponding original image, see the second row of Figure 16 where these boundaries appear as red contours.

See Figure 16.

## Appendix 2: Size Characterization of the TA Cups by Tomography and Laser Scanning

One cup has been successively submitted to size measurement by X-ray tomography and by 3D laser scanning. The step along the height of the cup was 0.5 mm for tomography and 1 mm for scanner. On each section, a number of dimensions were measured manually: the side values measured in the middle of each face, $d_{//}$, and $d_{\perp}$, respectively, parallel and perpendicular to the thermocouple, and the two diagonals, diag1 and diag2 (see Figure 3 of the main text). The values obtained with the two techniques are plotted in Figure 17a with the origin set at the first height for which the section area reported by the software had a non-zero value. It is seen that the dimensions estimated with the two techniques superimpose quite nicely on each other, with the exception of a few values of $d_{//}$ at mid-

<figure><img src="image_17.png" /><figcaption>**Figure 16.** Examples of tomography images as acquired (upper row) and after drawing the internal defect boundary (lower row).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 17.** (a) Plot of the side values, d// and d⊥, and of the diagonals, diag1, and diag2, as measured on sections along the height of a cup characterized by X-ray tomography and by 3D-scanner. (b) Values of d⊥ and diag1 measured on four cups by X-ray tomography. In the caption, *d*<sub>perp</sub> stands for d⊥.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 18.** Change of the section area along the height of the four empty cups.</figcaption></figure>

height along the cup that are associated to the thermocouple going through the cup wall.

The comparison in Figure 17 somehow validates the use of tomography to characterize the size of the cup cavity before casting, and hence of the cast samples. A further step was to evaluate the variation from one cup cavity to another, i.e., the scattering in the dimensions of the standard cups. This was done using X-ray tomography on four different cups from which the four dimensions were evaluated. It was found that the two side values and the two diagonal values were consistently similar for each cup. *d*⊥ and diag1 for the four cups are shown in Figure 17b. The data for cup #4 are representative of the average for these 4 cups and are those used in the main text as reference for the cast cups.

The change of section area with height along the cup cavity of the four cups is shown in Figure 18. The bump at mid-height is due to the withdrawal of the thermocouple. Again, the record for cup #4 appears as a good average of the four measurements and that record will be used as a reference for the cast cups. For this, those values associated with the bump have been removed from the file.

**Appendix 3: Thermal Records of Cups Equipped with Side and Corner Thermocouples**

Three series of TA cups have been prepared to investigate the evolution of the temperature field during liquid cooling and solidification. In addition to the standard center thermocouple (denoted center-TC), these cups were equipped with one thermocouple located in the middle of a side face (denoted side TC) and another one in the middle of one corner (denoted corner-TC), see Figure 19.

In the first series that was intended to check the mounting, two cups were prepared. The tip of the additional thermocouples was located at the inner surface of the cup and covered with cement (see the arrows in Figure 19) so as to give the cooling curves at the inner surface of the cups. The cast alloy was a hypereutectic SGI with 3.5 wt.% carbon and 4.0 wt.% silicon. The records of the surface thermocouples are presented in Figure 20 together with one of the two standard cooling curves recorded with the center-TC. It is seen that both surface temperatures increase from the time of pouring until a maximum slightly before or slightly after the end of solidification of the cups. Immediately after the maximum, or shortly thereafter, there is a sudden exponential decrease in temperature. A probable explanation to this switch is the formation of a gap between the cup
<figure><img src="image_20.png" /><figcaption>**Figure 19.** Photographs illustrating the cups equipped with two thermocouples in addition to the usual center one protected with a Pyrex tube. The tip of the two additional thermocouples was located at the very inner surface of the cup (a) and then covered with cement (b).</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 20.** Temperature records during the first trial on two cups denoted as N and C.</figcaption></figure>

and the sand, either because the metal shrunk inward or because the sand cup collapsed.

In the second series, the side and corner TCs were not covered with cement, and the external surface of the two TA cups (denoted 1 and 2) were protected using a metallic coat to avoid the destruction of the sand walls too early after pouring the cups (see Figure 21). After pouring these cups with a nearly eutectic SGI cast alloy with 3.8 wt.% carbon and 2.2 wt.% silicon, it was observed that the sand walls remained almost stable during the whole temperature recording and all the TCs led to the cooling curves plotted in Figure 22 for the part corresponding to solidification.

Cup #1 was poured just before cup #2 and the corresponding cooling curves are plotted in Figures 22a and b, respectively. The two central TC records were similar to

each other, with only a small variation in solidification time due to a slight difference in the filling level. It is noteworthy that the side and corner records all show a plateau that starts when the center thermocouple records the solidification starts. This suggests that the inflexion of the side and corner records associated with a pseudo-eutectic plateau is due to the latent heat release from the bulk of the cup. That the temperature for the inflexions was significantly lower with cup #2 compared to cup #1 suggests that the TCs tips of cup #1 were slightly more away from the inner sand surface than in cup #2.

An important feature of the thermal records in Figure 22 relates to liquid cooling. It is seen that the cooling rate of the center and side thermocouples are very similar before solidification in the center starts. Further, there was no temperature difference between these two thermocouples in cup #1, while there is a difference of about 30 °C on cup #2, i.e., when the tip of the side TC is closer to the sand surface. It seems safe to conclude that the bulk of the liquid metal gets homogenized by convection just after pouring, except at the very surface where a rim has already started to solidify.

The third series of cups was prepared for being cast during the trials presented in the main text, following the procedure developed for the second series and with the tip of the side and corner thermocouples shifted inside the sand cup by about 1 mm. For each of the LoSi and HiSi alloys, these cups were labeled 1U and 3U, with no addition in 1U and inoculant added in 3U. The temperature records are plotted in Figure 23 for the LoSi alloy and in Figure 24 for the HiSi one. All center and side thermocouples functioned along with the whole casting and cooling process, but only the corner thermocouple of the inoculated LoSi alloy could be recorded as seen in Figure 23a. This figure shows that the cooling at the corner was much faster than on the side face, as expected and in agreement with the second trial
presented above. Also, for both cups of LoSi alloy, it is noticeable that the curves of the center and side thermocouples are superimposed on each other during liquid cooling, and differentiate only when solidification starts, again in agreement with the records of cup #1 above.

The curves in Figure 24 relate to the casting of the HiSi alloy with (Figure 24a) and without (Figure 24b) inoculant added. Both graphs show a eutectic plateau for the side

thermocouple at a temperature significantly lower than that of the center thermocouple as was the case in Figure 22b. One can note also that the cooling rate of the liquid is higher in the center than on the side and this could be attributable to the increase in the mold temperature as seen in Figure 20. These two observations suggest that the junction of the side TCs were slightly closer to the cup surface for the HiSi trial than for the LoSi trial.

<figure><img src="image_22.png" /><figcaption>Figure 21. Photographs illustrating one of the cups (a) before and (b) after being poured with three thermocouples (second series of cups). In this case, the tip of the two additional thermocouples were not covered with cement and the cups were encased in a metallic coat intended to minimize the destruction of the sand.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Figure 22. Cooling curves recorded from the TCs present in the (a) cup #1 and (b) cup #2 poured in the second series.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Figure 23. Cooling curves recorded with cups equipped with three thermocouples during casting of LoSi alloy either with (a) or without (b) addition of inoculant.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Figure 24. Cooling curves recorded with cups equipped with three thermocouples during casting of HiSi alloy either with (a) or without (b) addition of inoculant.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>Appendix 4: Evolution of the Size Parameters
with Height in the Six LoSi and Six HiSi Cups used
for Shrinkage Analysis</figcaption></figure>
Appendix 5: Section Area and Defect Area Versus
Height Along the Cup of the Six LoSi and Six HiSi
Cups Used for Shrinkage Analysis

The dashed line on the graphs is the reference section area
presented in 2. On each of the graphs has been superim-
posed a vertical section of the sample obtained by

tomography. Note that the positioning of the curves along
the height axis is at ± 0.5mm.

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>
# Appendix 6: Calculation of Cast Iron Density at Room Temperature and at 1150 °C

## 1. Room temperature density

The room temperature theoretical density of cast iron, ρ, will be evaluated by means of the following rule of mixture:

$$ \rho^{-1} = f_{\text{matrix}} \cdot \rho_{\text{matrix}}^{-1} + f_{g} \cdot \rho_{g}^{-1} \qquad \text{Eqn. 9} $$

where f<sub>φ</sub> and ρ<sub>φ</sub> are respectively the mass fraction and the density of constituent φ (graphite, g, and matrix). As the density of the cast iron with pearlitic matrix is very close to that with a fully ferritic matrix because precipitation of pearlite is compensated by a lower amount of graphite, the calculations will be made for a fully ferritic matrix. Assuming ferrite does not dissolve any significant amount of carbon at room temperature, the equilibrium mass fraction of graphite is given by the lever rule:

$$ f_g = \frac{w_C}{100} \qquad \text{Eqn. 10} $$

where w<sub>C</sub> is the nominal carbon content of the alloy in weight percent.

The density of graphite is that of perfectly crystalline graphite and is given as (g·cm<sup>-3</sup>):

$$ \rho_g = (0.4419 + 10.5 \times 10^{-6} \cdot T_C)^{-1} \qquad \text{Eqn. 11} $$

The theoretical density of ferrite will be calculated by using the following relation

$$ \rho_{\alpha} = \frac{M_m}{V_m} \qquad \text{Eqn. 12} $$

where M<sub>m</sub> and V<sub>m</sub> are the molar mass and volume.

The molar volume is related to the ferrite lattice parameter, a<sub>α</sub>, according to:

$$ V_m = \frac{(1 - x_C^\alpha) N_A a_\alpha^3}{2} \qquad \text{Eqn. 13} $$

where x<sub>C</sub><sup>α</sup> is the molar fraction of carbon in ferrite, which has been fixed to 0, and N<sub>A</sub> is the Avogadro number.

In a previous assessment,³⁷ the effect of alloying elements on the lattice parameter of ferrite was expressed using mole fractions. The same data were converted to weight fractions leading to the following expression of a<sub>α</sub> (Å):

$$ a_{\alpha} = 2.8658 + 3.747 \cdot 10^{-5} \cdot T_C + 8.59 \cdot 10^{-9} \cdot (T_C)^2 + (-1.3 \cdot 10^{-3} \cdot w_{Si}^{\alpha} + 5.43 \cdot 10^{-4} \cdot w_{Mn}^{\alpha} - 1.71 \cdot 10^{-3} \cdot w_{P}^{\alpha}) \qquad \text{Eqn. 14} $$

where w<sub>i</sub><sup>α</sup> = (1 - f<sub>i</sub>)·w<sub>i</sub> is the content (wt.%) of i element of ferrite with w<sub>i</sub> the nominal content in i element of the cast iron.

The values of w<sub>i</sub><sup>α</sup> are then expressed as mole fraction, x<sub>i</sub><sup>α</sup>, to calculate the molar mass of ferrite and its density, which is finally introduced in Eqn. 9 to evaluate the cast iron density.

## 2. Cast iron density at 1150 °C

Prediction of the volume change upon solidification of the LoSi and HiSi alloys was made considering the composition of samples 1U (Table 1) solidifying at 1150 °C. From these sample compositions and using the expressions derived by Sertucha et al.,¹⁴ the composition of the liquid at 1150 °C could be calculated, and particularly its content in carbon. With the expression of the carbon partition coefficient, the carbon content of austenite was evaluated, and from it the mass fraction of graphite, f<sup>graphite</sup>, after full solidification of the material. The corresponding values are listed in Table 5. It should be noted that these values of the graphite fraction are underestimated as the actual carbon content in austenite is not homogeneous. Note also in

<table><caption>**Table 5.** Successive Calculations Needed for Evaluating the Theoretical Density Based on the Composition of the U1 LoSi and HiSi Samples (see Table 1): Alloy Carbon Content, w<sub>C</sub>, Mass Fraction of Graphite after Full Solidification at 1150 °C, f<sup>graphite</sup>, Atom Fraction of Carbon and Silicon in Austenite, x<sub>C</sub><sup>γ</sup> and x<sub>Si</sub><sup>γ</sup>, Austenite Density, ρ<sup>γ</sup>, and Cast Iron Density, ρ<sup>castiron</sup>. The Calculations at 1150°C were Carried Out Using the Austenite Lattice Parameter, a<sub>α</sub>, Expressed According to Lacaze et al.<sup>19</sup> (First Row) and Lacaze et al.<sup>20</sup> (Second Row)</caption><thead><tr><th>Alloy</th><th>w<sub>C</sub>(wt.%)</th><th>f<sup>graphite</sup> (%)</th><th>x<sub>C</sub><sup>γ</sup> (at.%)</th><th>x<sub>Si</sub><sup>γ</sup> (at.%)</th><th>a<sub>α</sub>Å</th><th>ρ<sup>γ</sup>(g·cm<sup>-3</sup>)</th><th>g<sup>graphite</sup> (%) (g·cm<sup>-3</sup>)</th><th>ρ<sup>castiron</sup> (g·cm<sup>-3</sup>)</th></tr></thead><tbody><tr><td rowspan="2">LoSi</td><td rowspan="2">3.59</td><td rowspan="2">1.95</td><td rowspan="2">1.675</td><td rowspan="2">4.43</td><td>3.7143</td><td>7.186</td><td>6.1</td><td>6.882</td></tr><tr><td>3.7302</td><td>7.095</td><td>6.0</td><td>6.801</td></tr><tr><td rowspan="2">HiSi</td><td rowspan="2">3.20</td><td rowspan="2">1.76</td><td rowspan="2">1.461</td><td rowspan="2">7.12</td><td>3.7042</td><td>7.126</td><td>5.5</td><td>6.856</td></tr><tr><td>3.7298</td><td>6.980</td><td>5.4</td><td>6.723</td></tr></tbody></table>
Table 5 that the amount of graphite decreases with higher silicon content even though the carbon content in austenite also decreases. The next step was to calculate the atom fraction of carbon, $x_C$, and silicon, $x_{Si}$, in austenite from which the austenite lattice parameter, $a_γ$, could be

evaluated. For this latter, we used both the expression assessed by Lacaze et al.¹⁹ and that reevaluated²⁰ as seen in Table 5. Finally, using the graphite density from Eqn. 11, the volume fraction of graphite, $g^{graphite}$, and the density of the solid cast iron, $ρ^{castiron}$, at 1150 °C could be calculated.

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