This work aims to calculate the rigidity point temperature of aluminum alloys by three new methods and compare them with currently employed methods. The influence of major and minor alloying elements over the rigidity point temperature is also discussed. Until now it has been difficult to determine the exact temperature of the rigidity point, since small variations in the data obtained give variable results, making it difficult to automate the process with high accuracy. In this work we suggested three new mathematic methods based on the calculation of higher order derivatives of (dT/dt) with respect to time or temperature compared to those currently employed. A design of experiments based on the Taguchi method was employed to compare the effect of the major and minor alloying elements for the AlSi10Mg alloy, and to evaluate the accuracy of each developed method. Therefore, these systems will allow better automation of rigidity point temperature (RPT) determination, which is one of the most important solidification parameters for solidification simulators. The importance of the correct determination of this parameter lies in its relation to quality problems related to solidification, such as hot tearing. If the RPT presents very low-temperature values, the aluminum casting will be more sensitive to hot tearing, promoting the presence of cracks during the solidification process. This is why it is so important to correctly determine the temperature of the RPT. An adequate design of chemical composition by applying the methodology and the novel methods proposed in this work, and also the optimization of process parameters of the whole casting process with the help of the integrated computational modeling, will certainly help to decrease any internal defective by predicting one of the most important defects present in the aluminum industry.

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The use of optimization algorithms to adjust the numerical models with experimental values has been applied in other fields, but the efforts done in metal casting sector are much more limited. The advances in this area may contribute to get metal casting adjusted models in less time improving the confidence in their predictions and contributing to reduce tests at laboratory scale. This work compares the performance of four algorithms (compass search, NEWUOA, genetic algorithm (GA) and particle swarm optimization (PSO)) in the adjustment of the metal casting simulation models. The case study used in the comparison is the multiscale simulation of the hypereutectic ductile iron (SGI) casting solidification. The model fitting criteria is the value of the tensile strength. Four different situations have been studied: model fitting based in 2, 3, 6 and 10 variables. Compass search and PSO have succeeded in reaching the error target in the four cases studied, while NEWUOA and GA have failed in some cases. In the case of the deterministic algorithms, compass search and NEWUOA, the use of a multiple random initial guess has been clearly beneficious.

The aim of this work is to determine the Solid Fraction (SF) at the rigidity point (FRP) by applying advanced thermal analysis techniques. The variation of the FRP value is important to explain the solidification behavior and the presence or absence of defects in aluminum alloys. As the final alloy composition plays a key role on obtained properties, the influence of major and minor alloying elements on FRP has been studied. A Taguchi design of experiments and a previously developed calculating method, based on the application of high rank derivatives has been employed to determinate first the rigidity point temperature (RPT) and after the corresponding FRP for AlSi10Mg alloys. A correlation factor of r2 of 0.81 was obtained for FRP calculation formula in function of the alloy composition.

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