# Solid Fraction Determination at the Rigidity Point by Advanced Thermal Analysis
## 1 Introduction  
Lightweight aluminum structural parts are increasingly used in cars. The main reasons are a combination of low cost and low weight that can reduce the weight of the car, reducing the carbon footprint. Among industrial casting methods, vacuum high pressure die casting (V-HPDC) is increasingly used in the manufacture of critical components with complex and thin geometry [1]. AlSi\({}_{10}\)Mg is the most commonly employed alloy for V-HPDC, with good shock performance and high elongation values. Simulation software, such as casting simulators and crash simulators, are used to simulate the behavior of the obtained parts. In both cases, an accurate prediction of the solidification properties of a given alloy as a function of its composition is a key point in obtaining accurate predictions of in-service properties. However, when it comes to accurately predicting casting performance and defect occurrence, there is certainly some way to go [2]. As described by [PERSON] [3], the actual variation of the solidification parameters over time within the injected part in an HPDC process is very difficult to determine, which makes it difficult to relate this parameter to the final casting quality. A precise control of the solidification process and SF evolution is important, as it is related to the size, shape and spacing of the dendrite arms, affecting the macroscopic properties [4]. The solidification sequence of an aluminum alloy starts with the formation of crystal nuclei within the molten metal, with undercooling. The temperature at which the nuclei form and do not re-dissolve is called the liquidus temperature. A higher cooling rate causes the reduction of this temperature and of the binary eutectic temperature [5]. As the molten aluminum decreases in temperature, some dendrites begin to precipitate. There is primary forward growth of these dendrites and secondary lateral growth, until two primary dendrites collapse into each other, forming a dendritic network, at the so-calledDendrite Coherence Point (DCP). Dendrite coherence, or dendrite collision, is important in the formation of the solidification structure and in the castability of alloys [6]. The growth and thickening of the branches of the primary dendrites promote the initiation of contact between the secondary dendrites and when coalescence ends, solid bridges form between the dendrites and some stiffness is detected, at the so-called Rigidity Point (RP). Solid particles can move by the lubricating effects of the liquid films between them, but with restrictions [7]. Shrinkage porosity defects, macro-segregation and hot cracks can appear [8; 9]. Therefore, the study of solidification parameters in the zone between DCP and RP combined with SF is crucial to calculate solidification parameters and alloy compositions to reduce casting defects and to employ in casting simulators [10]. In order to obtain accurate simulations, inverse modelling has been used by authors [11] and it is essential to have the simulation curve of the selected alloy well defined to predict casting defects, and the solidification curve changes with variations in alloy composition. The amount of SF also crucial to determine the casting temperatures of an alloy for semi-solid processes in order to avoid cold fillings, segregations and other defects [12]. It is also fundamental to define the onset time of squeeze-pins in HPDC [13]. Thermal analysis (TA) is commonly used to control the quality of aluminum in the aluminum industry. It is based on the continuous recording of molten aluminum temperature, using standardized analysis cups. With the obtained curves and their derivatives, the solidification parameters are determined [14; 15; 16; 17]. The RPT value can be determined by different processes. In the mechanical method, the force used to agitate an impeller inside a vessel where the metal is solidifying is continuously recorded until the impeller stops, and this is the moment that determines the RP [18].