Reliable and realistic thermal properties data for investment casting shell molds are required to correctly simulate the metal solidification and predict the shrinkage. Investment casting shells exhibit several phase transformations during firing and pouring that affect their transient thermal properties, which affect solidification. These properties depend on time, temperature and process history.

A recent study collected thermal conductivity and specific heat capacity data from seven industrially produced ceramic molds of various types using an inverse method in which pure nitrogen was poured into ceramic molds equipped with two thermocouples. Software was used to simulate virtual cooling curves that were fitted to experimental curves by adjusting the temperature-dependent properties of the ceramic mold. The data were compared with measurement results from laser flash. The analysis of the differences will serve to improve the accuracy of investment casting simulation.

Finding a Better Way to Measure

In a relatively thin-walled steel casting, most of the super heat and part of the latent heat of the liquid metal are accumulated in the investment ceramic shell, where specific heat capacity plays an important role. However, excessive heat from a massive casting will transfer through the shell, in which case, thermal conductivity is a predominant factor. Both are significant in order to have representative simulations for industrial use to control shrinkage defects and optimize casting quality.

Because of the wide variety of shell compositions, particle size distribution and processing parameters, the ceramic shell could have from 10 to 30% porosity, which can provide air permeability but also affect the shell’s mechanical and thermal properties.

Thermal processing history also influences shell thermal properties. Several thermal stages occur in the investment casting process, including pattern removal/dewaxing, sintering/firing, preheating and pouring. Colloidal silica binder, flour/filler and often ceramic stucco have a significant amorphous structure. The degree to which the amorphous crystalline transformation takes place during different thermal conditions affects the shell’s thermal properties.

The transient nature of the thermal properties of investment shells make precisely measuring them difficult. This study used an inverse method in which a shell mold with installed thermocouples is poured with a pure liquid metal with well-defined properties. Shell thermal properties were estimated by running multiple computational fluid dynamic (CFD) simulation iterations, varying the thermal conductivity and heat capacity over a range of values in an effort to fit the calculated cooling curves to the experimental cooling curves for the shell and casting.

The inverse method takes much effort to achieve an acceptable fit among the cooling curves. In this study, a method to correct the specimen thickness used in the laser flash method was introduced in order to obtain more accurate thermal property data.

In a laser flash thermal diffusivity test, a small specimen is subjected to a high intensity, short duration radiant laser pulse after thermal equilibration at the test temperature. The energy of the pulse is absorbed on the front surface of the specimen and the resulting rear face temperature rise is recorded by a noncontact infrared radiation thermometer. The thermal diffusivity is calculated from specimen thickness and time required for the rear face temperature to reach 50% of its maximum value.

In differential laser flash calorimetry, a reference specimen and the test specimen are mounted together under the same condition at the same temperature and irradiated uniformly with a homogenized laser beam. To ensure similar emissivity, a graphite spray coating covers the front and rear faces of both the reference and test specimens. The temperature rise of the reference with known specific heat capacity and the specimen are measured. If the density of the shell is known, then specific heat capacity can be calculated.

The laser flash method was designed for dense specimens, while measurement of highly porous materials has associated difficulties in defining the applicable specimen thickness. To evaluate the effective specimen thickness and density in this study, the researchers used a 3-D high resolution optical profiler to obtain the specimen surface topology (Fig. 1). Then the effective thickness and density were determined and those data used to calculate thermal diffusivity and specific heat capacity.

Specimens were taken separately from prime coats and backup coats. For comparison, the rule of mixtures was used to estimate the thermal property of the entire shell based on the thickness ratio between the prime coats and backup coats. Three runs of each type of specimen were conducted and the average values calculated.

The physically measured thermal property data was applied to the inverse method as the starting points to reduce a significant amount of computational time and avoid errors induced from extrapolation in the optimization algorithm.

Discussing the Results

The specific heat capacities and thermal conductivity of the shell and insulating material as well as external heat transfer coefficient are the main parameters that influence the temperature curves of the casting and shell. Preliminary modeling showed that solidification time and the coordinate of the point where the shell reached the highest temperature were mainly influenced by the specific heat capacity and thermal conductivity of the shell. For higher specific heat capacity, more energy is needed to heat up the shell to a certain temperature. Thus, the solidification time will be shorter. Higher thermal conductivity will allow the heat of the liquid metal to flow through the shell more quickly, which also shortens the solidification time and increases the maximum temperature of the shell. Sensitivity testing by modeling also showed the external heat transfer coefficient mainly effected the shell and casting cooling rates after solidification.

To evaluate the shell density and porosity, whole pieces of the shell containing all layers were examined and the overall bulk density and open porosity accessible for water were calculated.

Seven industrial ceramic shells (Tables 1 & 2) were evaluated in the study and a thermal property database was developed. According to the results of the tests, temperature-dependent specific heat capacities in all shells had a similar trend, but the average and maximum values mainly depended on the phase of the starting materials and the reactions and transformations during the thermal processing, which were not readily predictable (Fig. 2).

Generally, at above room temperature, the thermal conductivity of the most dense ceramics decreased with increasing temperature because phonon scattering is more intense from the vibrating lattice at a higher temperature. However, the investment casting shells, where the colloidal silica is used as a binder in most cases and a significant amount of fused silica is utilized as flour and stucco, more often showed an increasing thermal conductivity at higher temperatures due to the photon radiation becoming dominant at higher temperature in semi-transparent silica.

Porosity has a significant influence on the thermal conductivity. Between the two aluminosilicate shells (#4 and #6), #6 with higher total porosity (37.65%) exhibited lower thermal conductivity values throughout the measured temperature range compared to shell #4 having lower total porosity (33.52%).

Another good finding is the weak temperature dependence of conductivity in the alumina-based shell (#5). Since the photon radiation in alumina is not significant until 1,832F (1,000C), this radiation compensates phonon scattering in alumina and the porosity effects and consequently the thermal conductivity didn’t change much over the elevated temperature range.

The thermal conductivity and specific heat capacity values measured from laser flash for the shells studied are listed in Fig. 3. Shell #7 (rapid shelling technique) was highly porous and broke apart when being surface ground during laser flash sample preparation. Effective density calculated from sample surface topography was used to calculate these values. It was found that laser flash showed a similar trend to the inverse method on both thermal conductivity and heat capacity values.

Using the Data

When putting thermal property data from the inverse method and laser flash method together, as shown in Fig. 4., the thermal conductivity values were fairly close, yet the inverse method presented higher specific heat capacity values than the laser flash method. Because many thermal reactions among the shell components and phase transformation within the a morphous silica take place at high temperature, the amount and rate of these reactions will significantly affect the specific heat capacity values used in modeling. In the inverse method, the shell is heated rapidly when metal is poured and cooled down at a relatively slower cooling rate as the metal solidifies. These processes associate with more instantaneous measurement of a property which includes latent heat effects from phase changes. However, a small mass specimen is equilibrated at an environmental test temperature in the laser flash. Consequently, the transformation occurring in the inverse method may have already taken place prior to the measurement by the laser flash method.

Similarly, when comparing the total enthalpy change from room temperature (68F [20C]) to 2,885F (1,420C) among the values from theoretical calculation of the inverse method and the laser flash  method, the laser flash method shows similar values, because the thin specimen used in the laser flash method was under partially thermally stabilized condition which is closer to thermal equilibrium. The shell in reality is hardly in thermal equilibrium conditions, thus the inverse method provided more realistic effective heat capacity values for modeling the pouring and solidification processes.

Thermal property data measured by laser flash could be used as the starting point in the automatic optimization process, which greatly reduces the number of simulation cases needed to approach a well fitted case and reduces the potential extrapolation error in iteration step estimates.

The theoretical thermal conductivity of pure silica with 33% porosity was plotted in Fig. 5 as well as thermal conductivity values of shell #1 and shell #3. Those industrial shells had similar measured and theoretical values of thermal conductivity at a lower temperature but were more heat conductive at a higher temperature. This could result from different particle and porosity size distributions, since smaller particle size with higher grain boundary to volume ratio will lower thermal conductivity. This theoretical model may not consider the photon conductivity of the pore phase at higher temperature.

Obtaining the data from laser flash and then applying the data in the inverse method can be time consuming and costly. The researchers recommend that industries developing their own investment casting shells pick the thermal property data of shells from given investment casting facilities in the study with the closest composition and utilize those estimates in their simulations. Whoever uses the data must measure the bulk density and porosity of their shells, because bulk density is used in most simulations and porosity is needed to adjust the value of thermal conductivity.  （Source from: American Foundry Society)