Introduction

Despite its status as one of the most ancient casting methods, sand molding continues to be critically important for the highly efficient production of components within the mechanical engineering and automotive sectors. Sand casting generally provides a significant advantage due to minimal restrictions concerning drafts and undercuts. Consequently, it facilitates the creation of complex cavities using sand cores, a process that is also viable in gravity and low-pressure die casting.1

Sand casting evolved considerably with the development of 3D-printing technologies from the mid-1990s until the early 2000s. In particular, the so-called “binder jetting process” (see illustration 1) made it possible to avoid restrictions on moldability. Drafts, which could lead to thick-walled cast parts in certain sections can be eliminated. Risers and vents can be strategically positioned as required to enhance castability, rather than following the laws of conventional molding. Even undercuts can be realized, without the necessity of complicated cores or attached pattern parts. These advantages allow greater complexity compared to conventional molding. Also, the technology allows molds to be manufactured without producing patterns or core boxes, which above all means lower costs and less effort.2

Figure 1
figure 1

Scheme of binder jetting process, with courtesy from Voxeljet AG, Friedberg, Germany.

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The global aluminum casting volume was quantified with about 56 billion $ in 2020, forecasted to grow until 2027 at 7.6 % annually.3 The volume of sand binder jetting has been increasing the last 10 years, since OEMs began to use the technology for industrial-scaled production, due to its high reliability. These considerations underscore the necessity of researching to develop more reliable and efficient production processes.

As with conventional molding processes, refractory materials are also used in binder jetting due to their thermal and chemical resistance to liquid light metals and even molten iron or steel.

Casting applications use various types of sand and aggregates. Most foundries, however, process silica (\( {\text{SiO}}_{2} \)), due to its low price, availableness, and chemical resistance.4 Alternative mold materials, like chromite (\( {\text{FeCr}}_{2} {\text{O}}_{4} \cdot {\text{Al}}_{2} {\text{O}}_{3} \cdot {\text{MgO}}) \) or cerabeads (\( {\text{Al}}_{2} {\text{O}}_{3} \cdot {\text{SiO}}_{2} \)), behave better in terms of thermal stability but are also associated with higher costs.5 Especially for 3D-printing, sand properties like flowability play a big role in realizing a smooth and homogeneous surface on the powder bed.6 Established binder materials, such as furan or phenolic resins, are categorized as organic systems. Mold materials, bound with organic systems, release hazardous compounds during combustion, such as BTX (Benzol, Toluol, and Xylol), CO, and \( {\text{CO}}_{2} \).7 Inorganic systems are used due to lower emissions during casting compared to organic systems. Using cores manufactured with inorganic systems, primarily water steam is emitted.8 Furan-based technologies hold 80 % of the current market share for 3D sand printing, while phenolic and inorganic systems divide the remaining market shares.9 Hardening reactions prevalently are driven by the pH-value of the reactants involved, such as sand and binders. Evidences clarify that different pH levels, primarily when comparing those of silica- (\( {\text{pH}}{\mkern 1mu} 6.6 \)) and chromite-sand (\( {\text{pH}}{\mkern 1mu} 7.9 \)), can affect the kinetics of chemical reactions with different binders such as furan or phenolic based ones.10

This paper aims to work out two fundamental thermophysical values. The first one, heat absorption capacity, expresses the value of the amount of heat energy needed for a system of a given mass to raise the temperature by 1 K and has the dimension [J/(kg\(\cdot \)K)]. Fouries’s law of experience describes the correlation between heat flux, thermal conductivity, and temperature gradient after:11

$$\begin{aligned} q = -{\lambda }\cdot \nabla T \end{aligned}$$
(1)

where:

q:

        heat flux per unit area \([W/m^2]\)

\(\lambda \):

        thermal conductivity [W/(m\(\cdot \)K)]

\(\nabla T\):

        Temperature gradient [K/m]

The terms “thermal diffusivity” and “thermal conductivity” are connected via heat capacity:

$$\begin{aligned} {\alpha } = \frac{\lambda }{c_{p}\cdot \rho } \end{aligned}$$
(2)

where:

\(\alpha \):

        thermal diffusivity [\(\text{mm}^{2}\!/\text{s}\)] or [\(\text{m}^{2}\!/\text{s}\)]

\(\lambda \):

        thermal conductivity [W/(m\(\cdot \)K)]

\(\rho \):

        bulk density [\(\text{kg}/\text{m}^{3}\)]

\(c_{p}\):

        heat capacity [J/(kg\(\cdot \)K)]

One fundamental equation determines thermal diffusivity. The heat conduction equation, a (parabolic) partial differential equation, mathematically connects spatial and temporal changing of the temperature in a transient system, also known as the second Fick’s law. Paul et al. describe the derivation of this fundamental equation in Reference 12.

$$\begin{aligned} {\frac{\partial T}{\partial t} = \alpha \cdot {\frac{\partial ^{2} T}{\partial x^{2}}}} \end{aligned}$$
(3)

Bulk material of disordered structure, such as foundry sand, usually consists of solid grains and air in the interstices. Within the mixing and molding process, a third component, the binder, is added. Once the binder is cured, the grains are fixed in place and the phenomenon of heat transfer can be assumed as the sum of heat conduction and heat convection:

$$ \lambda _{{{\text{tot}}}} = \lambda _{{{\text{cond}}}} + \lambda _{{{\text{conv}}}} $$
(4)

Heat transfer by conduction takes place in the polycrystalline or amorphous sand grain. Vibrational conduction in the solid phase is responsible for heat transfer in bulk material grains. In the interstices, theoretically, heat transfers by radiation. However, for pore sizes less than 5 mm, this kind of heat transfer can be neglected, according to the results of Schulle et al. present in Reference 13. Thermal conductivity tends to increase with the increase of temperature and moisture content. This phenomenon was also observed in a test setup with green sand, where the thermal conductivity increased to over 2 W/(mK) due to water evaporation and stabilized at around 0.5 W/(mK) the further away the thermocouples were from the mold surface.14,15

Buntebarth16 investigated the role of the porous media in between the grains and proved an existing relation between both the thermal conductivity and the thermal diffusivity of the composed media with the thermal conductivity of the pore fluid.

For foundry sands, different approaches are used to determine heat capacity and also heat conductivity with different methods. An example is explained in Reference 17, where mold materials were investigated via the transient plane source (TPS) technique, which enables the simultaneous determination of specific heat capacity and thermal conductivity.

Saeidpour et al. used the hot-wire method to evaluate thermal conductivity. In this case, a wire provides the heat energy when electricity is applied for a short time. Silica sand with two different binder types was used.18

A work by Neel et al. investigated silica sand molding material with the laser flash method and obtained a thermal conductivity of 0.4 W/(m K) for a grain size of 120 \(\mu \)m.19 Another study that aimed to provide a holistic overview in terms of properties of 3D-printed mold parts conducted a measurement for both furan- and phenol-bound samples of silica sand, printed on a voxeljet VX200 with an average grain size of about 140 \(\mu \)m (Strobel/Freiung, Germany). A thermal conductivity of 0.34 W/(m K) was measured using a laser flash device. The heat absorption capacity was 0.83 J/(kg K), whereby the measurement was carried out by a TGA/DSC apparatus.20

Wang21 operated a test procedure with specimens with defined mounted thermocouples in a dipping trial and a ring mold. Temperature gradients were determined using different kinds of sand from the conventional molding process while the specimens were submerged in the melt (dipping trial).

In Reference 22, green foundry sand was heated up by a heat source with a certain amount of electrical energy. This allowed Solenicki et al. to quantify the heat conductivity for different mixtures of green sand.

Manufacturing cast parts with reliably predictable properties is only possible if the behavior of the molding material under realistic circumstances is well understood. Easy-to-use methods combat this lack of knowledge about the materials used in the binder jetting process. The latter considerations led to the development of a special test setup that enables any operator to determine the thermal diffusivity of an appropriate sample.

Despite advancements in studying thermal properties, significant gaps remain in understanding the behavior of printed molds, particularly when comparing different sand and binder combinations. This research aims to bridge this gap by exploring the interplay between thermal properties and parameters that are useful in simulations. Additionally, there could be recognized a need to develop a simple method for determining thermal diffusivity for industrial testing.

Experimental Setup and Procedures

This section explains how the required thermophysical values are determined. Using an in-house developed measurement setup turned out to be highly time-saving, due to its relatively simple layout. Table 1 shows the examined sand/aggregates and binder types including information about the AFS (American Foundry Society) fineness number as it was used in this work. The density of each specimen was specifically calculated. Additionally, the respective binder contents are also provided.

Table 1 3D Sand Printed Samples, Overview
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Various configurations of sand and binder employ layer thicknesses ranging from 0.28 to 0.30 mm. The furan printing process uses sand that is premixed with sulfuric acid. Furfuryl alcohol is then selectively injected into the bulk by the printheads. The system is cold curing.23 In contrast, the phenol system utilizes untreated sand and uses infrared heating lamps for hardening.24 The inorganic system utilizes waterglass-based binders, where resin bridges are formed and cured by a dehydration process. Dehydration can be achieved by heating with an infrared heat source or a microwave post-treatment. Currently, cold hardening systems are poised to gain considerable market share.25,26

Heat Capacity

For the assessment of the heat absorption capacity, a combined thermogravimetric analyzer (TGA) with differential scanning calorimetry (DSC) instrument was employed. The used device (STA 449 F3 Jupiter from Netzsch, Germany) operates within a temperature range of 20–1400 \(^{\circ }\)C. Given the focus of the investigation on determining values relevant to aluminum casting, measurements were conducted up to a maximum temperature of 750 \(^{\circ }\)C, connected to a heating rate of 10 K/min. A flushing device filled the chamber with argon after evacuation. Each sample to be tested was loaded compactly shaped in sample quantities of 20–40 \(\mu \)g into a platinum crucible with an alumina insert. The specimens were sectioned from the printed bars through sawing. Attention was paid to ensuring a flat contact surface for the samples at the crucible bottom to facilitate a proper heat transfer. At least three measurements were performed for each combination of sand and binder. Finally, a comparison between the sample and a reference, made of sapphire, (\(Al_{2}O_{3}\), trigonal structure) was used to determine \(c_p\).

The procedure ensures realistic process-related conditions as the binder bridges were still undamaged and grains did not compact until binder degradation had started. An inert gas atmosphere leads to preferential degradation (molecular chain break decomposition) instead of combustion of the binder.

Thermal Diffusivity

A specially adapted device (COGAS® mk Industrievertretung GmbH, Germany), which is normally meant to measure upcoming emissions related to sand cores, was used to investigate the thermal diffusivity. The test rods were identical in size to those used usually for the three-point bending test according to ‘BDG-Richtlinie P73’.27 Figure 2 displays the experimental setup. The specimen 22.4 mm x 22.4 mm first touches the oxide layer of the molten aluminum alloy (A356 - EN-AC AlSi7Mg0.3) until it submerges 5 mm into the melt. The dipping direction was chosen according to the printing direction. Wetting characteristics occur as they do in real casting processes. Three thermocouples (\(T_1,_2,_3\)) in a vertical row were applied at a distance of 10 mm apart, whereby the lowest one was affixed at a distance of 20 mm from the abutting face of the specimen. To obtain more valid results and increase statistical reliability, two thermotriplets were installed in one test specimen. The dipping direction was chosen according to the printing direction. Wetting characteristics occur as they do in real casting processes. The test bars’ surfaces have not been coated or treated in any way. Although the oxide layer on the melt was removed before each dip, it reformed immediately.

Figure 2
figure 2

Left: principle of measuring setup for thermal diffusivity; right: Temperature-distribution when T1 (\(T_{1(1)}\) or \(T_{1(2)}\)) reaches 150 \(^{\circ }\)C.

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One thermotriplet allows determining temperature diffusivity via a temperature-time plot. A temperature measuring device (Quantum X, HBM GmbH, Germany) recorded the temperatures using thermocouples (type K) at a scan rate of 100 Hz. The differential term of the counter (Eqn. 5) had to be calculated within a time range of four seconds (which was a necessity to smoothen the differential plot). Otherwise, negative or unnatural results for thermal diffusivity would have been the consequence.

$$\begin{aligned} {\alpha =\frac{\frac{\Delta T_3}{\Delta t}}{\Bigg ({\frac{(T_3-T_2)}{\Delta x}}-{\frac{(T_2-T_1)}{\Delta x}\Bigg )\cdot \frac{1}{\Delta x}}} } \end{aligned}$$
(5)

For each combination of sand/aggregate and binder systems, three samples were carefully prepared and stored in an atmosphere of 20 \(^{\circ }\)C and a humidity of 10 % for 24 h. After this period, each specimen was mounted on the apparatus and dipped into the melt. Figure 3 shows the real test setup with specimen and thermotriplet-arrangement. The thermocouples are affixed to the specimen and wrapped with insulating material on the specimen’s side surfaces. This configuration ensures that only the bottom surface is exposed to the heat of the melt. The temperature within the crucible is governed by radiation from the melt, while a furnace cover mitigates thermal losses. Consequently, the specimens’ temperature rises as soon as it is in contact with the melt until the abort temperature of this experiment (150 \(^{\circ }\)C) is attained by the lower thermocouples (\(T_{1(1)}\) or \(T_{1(2)}\)). A melt temperature of 745 ± 5 \(^{\circ }\)C was maintained throughout the whole test procedure. Consequently, the resulting plots of six thermotriplets for one combination were analyzed to determine the required values after Eqn. 5.

Figure 3
figure 3

Left: specimen, equipped with six thermocouples, arranged into two thermotriplets; right: insulated specimen.

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Results

Following the explanation of the experimental setup in the upper section, the structure of the work is divided into the determination of the heat capacity and the investigations into the thermal diffusivity/thermal conductivity.

Results for Heat Capacity

Regarding the measurement range for heat capacity (\(c_p\)), it is important to note that the type of binder exerts no significant influence on heat capacity, attributable to its minimal content ranging from 1.2 to 3.4 wt%. Further, it is notable that the values of heat capacity relating to the mass are in a very narrow field. Taking account of the different densities of the bulk materials, the heat capacity relating to the volume may change the decision whether to use one or the other sand because of its different thermal behavior.

In Figure 4, two plots depicting the measurement of the \(c_p\)-value are presented. The graph illustratively displays two evaluated mold materials: silica and cerabeads, each printed with an identical binder, specifically phenol. Notable, in the case of silica, the quartz-inversion occurring at approximately 573 \(^{\circ }\)C is noticeable. During this thermal event, \(\alpha \)-quartz transitions to \(\beta \)-quartz, a process associated with a volume expansion of 0.8 %. Upon subsequent cooling, this modification reverts. This effect is typical for silica and influences the heat capacity significantly. No attention must be given to the formation of high tridymite from high quartz through further heating at 870 \(^{\circ }\)C and the formation of cristobalite at 1470 \(^{\circ }\)C.28

Figure 4
figure 4

Representative plots of \(c_p\) -  are presented herein, specifically for silica and cerabeads, both printed with phenol; the data points for these determinations were extracted from the plots at temperatures of 100 \(^{\circ }\)C, 300 \(^{\circ }\)C, 500 \(^{\circ }\)C, and 700 \(^{\circ }\)C, as illustrated.

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As specific heat capacity changes by rising temperature, the values at different temperatures were determined in certain temperature steps, assigned at 100 \(^{\circ }\)C, 300 \(^{\circ }\)C, 500 \(^{\circ }\)C, and 700 \(^{\circ }\)C. The mean values at the specified temperatures are illustrated in Figure 5. This format of result presentation facilitates a direct comparison among the various sand binder combinations (refer to Table 1). Across silica types (SiFu, SiPh, and SiIO), the furan bound variation (SiFu) shows the highest value for heat capacity. Considering the mass-based determination of heat capacity, chromite provides relatively low values. However, taking the density into account, the ability to absorb thermal energy is significantly higher than that observed with silica or cerabeads products. Each of the combination plots shows a gradual increase in heat capacity values with ascending temperatures, culminating in a peak, followed by a subsequent decline. Predominantly, the maximum values were observed in aggregates bound with furan, applicable to both silica and cerabeads. Inorganic bound sand (SiO) exhibits significantly lower heat absorption capacities compared to any other combination. This phenomenon may be attributed to the complex chemical reactions occurring during the exposure of organic-bound mold sand to heat energy. Organic binders undergo reactions such as pyrolysis or combustion. For instance, the production of water during the polycondensation of furan in uncured areas could be another contributing factor.29 Phenol-based resins tend to precipitate water during decomposition.30 Higher temperatures may promote these reactions, whereas sodium silicate binders primarily do not exhibit reactions aside from dehydration.28

Figure 5
figure 5

Heat capacities (\(c_p\)) for each of the six combinations.

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Thermal Diffusivity and Thermal Conductivity

Three temperature plots, recorded by three thermocouples in each thermotriplet allowed calculating thermal diffusivity. Despite the variability in data indicated by the error bars, there is a discernible upward trend in the calculated mean values (for the temperature ranges 35-150 \(^{\circ }\)C, respectively 100-150 \(^{\circ }\)C) observable, progressing from silica through cerabeads to chromite, presented in Figure 6a and b. Due to the spread of the individual measurements, the middle three quantiles were included in the statistical considerations. This prevents the results from being negatively influenced by outliers. The thermal diffusivity for the individual molding sand combinations is plotted in the diagram in Figure 6a, for a temperature range of 35–150 \(^{\circ }\)C. Measurements varied largely, specifically at lower temperatures between 35  and 50 \(^{\circ }\)C, which explains the scattering.

For calculating thermal conductivity, the measured densities of the respective test bars were used, as well as the determined heat absorption capacities from the previous DSC measurements (the corresponding value at the temperature of 100 \(^{\circ }\)C was used). When determining the densities, the minimum volume loss caused by the drilled measuring holes was neglected. The values are presented in Figure 6b.

Figure 6
figure 6

Determined values for 35–150 \(^{\circ }\)C: (a) thermal diffusivity (\(\alpha \)) and (b) thermal conductivity (\(\lambda \)).

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A lower scatter of the measured values could be achieved obviously at a temperature range of 100–150 \(^{\circ }\)C. The plot of the temperature over time was also significantly more stable than at the beginning of the measurement when the lowest thermocouple started at ambient temperature. The results for thermal diffusivity and thermal conductivity are illustrated in Figure 7a and b.

Figure 7
figure 7

Determined values for 100–150 \(^{\circ }\)C (a) thermal diffusivity (\(\alpha \)) and (b) thermal conductivity (\(\lambda \)).

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In the experimental phase, the specimens were dipped into a melt of constant temperature. Unlike in real casting, when the metal is cooling, heat energy permanently was supplied by the furnace. Under these circumstances, the organic binder systems quickly degenerated, resulting in the originally sharp edges of the test bars becoming rounded. The effect was visible at both organic binder systems, but not with the inorganic system, as the binder is stable up to higher temperature levels above 200 \(^{\circ }\)C (see Figure 8). Interestingly, the sodium silicate bound (inorganic) sand shapes in glassy threads around the sand grains, where organic binder forms bridges between the grains, as shown in Figure 9.

Figure 8
figure 8

Left: Visible deterioration of binder bridges is evident in the case of phenolic bound sand; right: inorganic system, the sharp edges imply that binder bridges remain intact even after exposure to liquid aluminum.

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Figure 9
figure 9

Left: SEM images of silica sand with phenol binder; right: silica sand bound with sodium silicate; both with an average grain size of 140\(\mu \)m.

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Conclusion

Molding sand contributes an exceedingly heterogeneous composite comprised of grains and binder bridges, which moisten the sand grains to varying extents. The superficial irregularities and the uneven surface texture result in suboptimal replication of heat transfer within the STA/DSC measuring crucible. This phenomenon potentially elucidates the observed variance in measurements. Each sample was fed into the crucible in its entirety to simulate the attributes observed within a mold. Conduction and convection compose the heat energy transport, rather than radiation, although the content of air in the investigated material is about 50 %. Externally, these differences are not tangible, which is why the term “heat conduction” could be used in a holistic approach. The STA/DSC measurements were carried out in an inert gas atmosphere of argon, which causes pyrolytic decomposition of the binder and prevents combustion reactions. How chemical reactions influence those obtained parameters requires further attention.

For the investigation of thermal diffusivity using the triplet method, interference factors must also be discussed. If the contact of a thermocouple at the back wall of the bore is not given, the (slower) heating of the air inside is measured, which detriments the measurement accuracy. This issue could be mitigated through further development of the measurement setup. Additionally, variability in results may also stem from inadequate shielding of the test rods from the melt, particularly if the insulation layer is compromised or expands at the lower section. However, considering the moderate investment costs, this measurement setup offers an efficient method for investigating various molding material combinations. A realistic depiction of occurring wetting effects supports the applied method. It was also observed that the wetting area of resin-bonded test rods (furan and phenol) was reduced by binder degeneration, and the boundary contour of the inorganically bonded rod remained completely intact. This effect may have contributed to the observably higher conductivity.

Owing to its technically straightforward and low-investment approach, this measurement methodology may gain increased significance in the future. A substantial component of the analytical method involves numerical evaluation, wherein the frequency of measurements impacts the accuracy and necessitates the smoothing of plots. An augmented number of individual measurements is likely to enhance statistical certainty and consequently reduce variability.