Effect of Cooling Rate and Smoothing Method of Experimental Cooling Curves of Aluminum-7.5 Pct Silicon Alloys on Calculated Latent Heat and Fraction Solid Evolution

Abstract Shrinkage cavities and micro-pores occurring in castings are major causes of quality degradation and increased costs. Accurately predicting their occurrence through solidification models requires reliably calculation of the solid fraction ( $${f}_{\text{S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> </mml:math> ) changes during solidification, of the latent heat of solidification, and of the characteristic temperatures such as the liquidus ( $${T}_{\text{L}}^{\text{init}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mtext>L</mml:mtext> </mml:mrow> <mml:mtext>init</mml:mtext> </mml:msubsup> </mml:math> ), eutectic ( $${T}_{\text{E}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>E</mml:mtext> </mml:msub> </mml:math> ), and solidus ( $${T}_{\text{S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> </mml:math> ) temperatures. Commercial thermal analysis (TA) software has limitations in accurately reproducing the temporal changes in fraction solid and solidification enthalpy under actual casting conditions, as the solidification of casting alloys is highly dependent on nucleation of the solid phase, a process that cannot be reliable described by mathematical models. Therefore, it is necessary to use data reflecting actual solidification behavior extracted from experiment-based TA. The objective of this study is to find how smoothing methods applied to TA data affect calculated results obtained at three different cooling rates and to select the optimal ones. This will enable accurate calculation of characteristic temperatures and of fraction solid changes occurring during solidification, thereby improving the accuracy of shrinkage defect prediction models. To this goal, several smoothing techniques (mean smoothing, Gaussian smoothing, Savitzky–Golay filter, and polynomial regression) have been applied to TA data for an Al–7.5 pct Si alloy poured in steel cups with diameters of 30, 40, and 50 mm. The critical temperatures were determined using 1st ( $$dT$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>dT</mml:mi> </mml:mrow> </mml:math> ) and 2nd ( $${d}^{2}T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> ) time derivatives of temperature. Newtonian and Fourier analyses were used to calculate $${f}_{\text{S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> </mml:math> evolution and the latent heat as a function of cooling rate. While the time evolution of $${f}_{\text{S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> </mml:math> showed clear differences, the fraction solid of the α -phase for mean smoothing in the cups only varied between 0.46 and 0.47 for the Newtonian analysis and was 0.49 for the Fourier analysis. Based on the detailed analysis performed in this work, for the prediction of microporosity through computer models, it is recommended to use the following values: $${T}_{\text{L}}^{\text{init}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mtext>L</mml:mtext> </mml:mrow> <mml:mtext>init</mml:mtext> </mml:msubsup> </mml:math> at $${T}_{\text{L}}^{\text{max}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mtext>L</mml:mtext> </mml:mrow> <mml:mtext>max</mml:mtext> </mml:msubsup> </mml:math> or $${\left({d}^{2}T\right)}_{\text{min}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:msup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>T</mml:mi> </mml:mfenced> <mml:mtext>min</mml:mtext> </mml:msub> </mml:math> , $${T}_{\text{S}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mtext>S</mml:mtext> </mml:msub> </mml:math> at