Determination of Solidification of Rigidity Point Temperature Using a New Method

A New Method to Pinpoint Rigidity Point Temperature: The Key to Eliminating Hot Tearing in Aluminum HPDC

This technical summary is based on the academic paper "Determination of Solidification of Rigidity Point Temperature Using a New Method" by Ester Villanueva, Iban Vicario, Jon Mikel Sánchez, and Ignacio Crespo, published in Applied Sciences (2020).

Keywords

• Primary Keyword: Rigidity Point Temperature
• Secondary Keywords: aluminum alloys, solidification software, advanced thermal analysis, hot tearing, HPDC, AlSi10Mg

Executive Summary

• The Challenge: Inaccurately predicting the Rigidity Point Temperature (RPT) in aluminum alloys leads to costly defects like hot tearing, and current methods are often imprecise and difficult to automate.
• The Method: Researchers developed and tested three new mathematical methods based on higher-order derivatives from single-thermocouple thermal analysis and compared them against two existing methods across 24 different AlSi10Mg alloy compositions.
• The Key Breakthrough: A new technique, "Method 5," which identifies the RPT at the crossing point of the second and third derivative of the cooling curve versus temperature, proved to be the most accurate and reliable predictor.
• The Bottom Line: This new method provides a more precise and automatable way to determine RPT, enabling more accurate solidification simulations that can significantly reduce hot tearing defects in aluminum castings.

The Challenge: Why This Research Matters for HPDC Professionals

For engineers working with High Pressure Die Casting (HPDC) of structural aluminum parts, particularly with the widely used AlSi10Mg alloy, predicting solidification behavior is critical. A key parameter in this process is the Rigidity Point Temperature (RPT)—the moment a solidifying metal structure becomes rigid enough to sustain stress.

The problem is that determining this exact temperature has been notoriously difficult. Minor variations in thermal analysis data can produce inconsistent results, making it challenging to automate the process for industrial quality control. An inaccurate RPT value in your solidification simulation software can lead to a false sense of security. If the actual RPT is lower than predicted, the casting is far more susceptible to hot tearing, a defect that causes cracks during solidification and leads to scrap, delays, and increased costs. This research was driven by the urgent industry need for a more accurate, reliable, and automatable method to determine RPT.

The Approach: Unpacking the Methodology

To find a superior method for RPT determination, the research team conducted a comprehensive study based on a Taguchi design of experiments. This allowed for a systematic evaluation of how major and minor alloying elements affect the RPT of AlSi10Mg.

Methodology 1: Alloy Preparation and Thermal Analysis
- Alloys: 24 distinct AlSi10Mg alloy compositions were prepared according to the EN AC-43.400 standard, with varying levels of 12 different major, minor, and trace elements (Si, Mg, Fe, Cu, Ni, Cr, Mn, Ti, Zn, Pb, Sn, Sr).
- Data Collection: Molten alloy samples were poured into calibrated sand cups equipped with a single thermocouple. A high-speed data acquisition system recorded the cooling curve (temperature vs. time) for each sample. This single-thermocouple approach was chosen to reflect a cost-effective and productive industrial setup.

Methodology 2: Comparative Analysis of RPT Calculation Methods
The core of the study involved comparing five different methods for calculating the RPT from the cooling curve data:
- Literature Methods: Two established methods were used as a baseline: one based on the second minimum of the second derivative (d²T/dt²) and another on the first minimum of the first derivative (dT/dt).
- New Proposed Methods: Three novel methods were developed, all based on analyzing higher-order derivatives to find a more precise thermal event signature. The most successful of these, Method 5, determines the RPT by identifying the intersection point of the second and third derivative curves when plotted against temperature (dT/dt vs. T).

The Breakthrough: Key Findings & Data

The analysis yielded clear, data-driven results demonstrating the superiority of the new proposed method for determining Rigidity Point Temperature.

Finding 1: Method 5 Delivers Unmatched Accuracy and Precision

The study evaluated the accuracy of each method by calculating its linear regression coefficient (R²) and standard error. Method 5 emerged as the clear winner. As shown in Table 2, Method 5 achieved a coefficient of determination (R²) of 0.82, classifying it as a "good correlation." This was significantly higher than the other four methods, which all scored around 0.77. Furthermore, Method 5 had a low standard error of 1.35 °C, indicating high precision. This enhanced accuracy is attributed to its use of higher-order derivatives plotted against temperature, which makes the determination less sensitive to variations in test cup size and provides a more distinct, automatable signal.

Finding 2: Magnesium and Silicon are the Key Drivers of RPT

The statistical analysis (Student's t-test) confirmed which alloying elements have the most significant impact on RPT. As detailed in Table 3, for the highly accurate Method 5, both Magnesium (Mg) and Silicon (Si) were shown to have a statistically significant influence.
- Magnesium (Mg): Higher Mg content was found to decrease the RPT. This is because Mg promotes the earlier development of a solid skeleton in the alloy.
- Silicon (Si): Higher Si content was found to increase the RPT. An increase in Si moves the alloy closer to the eutectic composition, which raises the Al-Si eutectic temperature.

This finding is critical for alloy design and quality control, as it allows engineers to predict and control the RPT by managing the concentration of these two key elements.

Practical Implications for R&D and Operations

• For Process Engineers: This study suggests that using simulation software updated with the Method 5 calculation for RPT will provide a much more accurate prediction of hot tearing susceptibility. This allows for proactive adjustments to alloy composition or process parameters to mitigate this critical defect.
• For Quality Control Teams: The data in Table 3 of the paper illustrates the powerful effect of Mg and Si on RPT. This knowledge can inform stricter control limits for these elements in incoming raw materials and during melting to ensure consistent solidification behavior and reduce casting defects.
• For Design Engineers: The findings indicate that the inherent RPT of an alloy, heavily influenced by its composition, is a critical factor in defect formation. This reinforces the importance of considering the specific AlSi10Mg variant during the material selection phase to design components that are less prone to solidification-related issues.

Paper Details

Determination of Solidification of Rigidity Point Temperature Using a New Method

1. Overview:

• Title: Determination of Solidification of Rigidity Point Temperature Using a New Method
• Author(s): Ester Villanueva, Iban Vicario, Jon Mikel Sánchez, and Ignacio Crespo
• Year of publication: 2020
• Journal/academic society of publication: Applied Sciences (MDPI)
• Keywords: rigidity point temperature; cast metal alloys; aluminum; advanced thermal analysis; microstructure

2. Abstract:

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.

3. Introduction:

The study addresses the need for accurate solidification characterization of aluminum alloys, specifically AlSi10Mg, which is commonly used for structural parts in the High Pressure Die Casting (HPDC) industry. Accurate solidification data is crucial for the precision of casting simulation results. The paper defines the solidification sequence, including the formation of a dendritic network at the dendrite coherency point (DCP) and the subsequent coalescence that establishes the rigidity point (RP), at which the structure can sustain tensile strains. The temperature at this point is the rigidity point temperature (RPT). A low RPT is linked to a higher susceptibility to defects like hot tearing. The paper notes that while thermal analysis (TA) is a widely used quality control tool, existing methods for determining RPT have limitations. The research proposes to apply the Taguchi method to develop new, more precise RPT determination techniques for AlSi10Mg alloys using advanced thermal analysis with a single thermocouple.

4. Summary of the study:

Background of the research topic:

The determination of the Rigidity Point Temperature (RPT) is a critical parameter for predicting solidification-related defects, such as hot tearing, in aluminum cast alloys. Inaccurate RPT values in simulation software can lead to poor defect prediction and costly manufacturing failures.

Status of previous research:

Previous methods for RPT determination include mechanical-rheological tests, in-situ neutron diffraction, and thermal analysis (TA) with one or two thermocouples. TA methods based on the first or second derivative of the cooling curve have been shown to be imprecise or only suitable for specific alloy types (e.g., hypereutectic), making automation difficult. There is a need for a more robust and accurate method applicable to common alloys like hypoeutectic AlSi10Mg.

Purpose of the study:

The study aims to develop and validate new mathematical methods for calculating the RPT of AlSi10Mg alloys with higher accuracy and reliability than existing techniques. A further objective is to quantify the influence of major and minor alloying elements on the RPT and to develop regression models to predict it based on chemical composition. The ultimate goal is to provide a tool that allows for better automation of RPT determination for use in industrial TA equipment and solidification simulators.

Core study:

The core of the study involved comparing five methods for determining RPT. Two methods were from existing literature, and three were new methods proposed by the authors. These methods were applied to thermal analysis data from 24 different AlSi10Mg alloy compositions, created using a Taguchi design of experiments. The accuracy of each method was evaluated using linear regression analysis (R²) and standard error, and the statistical significance of each alloying element's effect on RPT was determined using a Student's t-test.

5. Research Methodology

Research Design:

A design of experiments based on the Taguchi method was employed. Two orthogonal matrices, a L16 (maximum and minimum element levels) and a modified L8 (intermediate levels), were used to define the chemical compositions of 24 different AlSi10Mg alloys. This systematic approach allowed for the evaluation of the effects of 12 alloying elements on the RPT.

Data Collection and Analysis Methods:

Thermal analysis (TA) was the primary data collection method. Samples of approximately 300g were poured into calibrated sand cups, and cooling curves were recorded using a single thermocouple connected to a high-speed National Instruments Data Acquisition System. Each TA test was repeated at least three times. The collected temperature-time data was then processed to calculate the first, second, and third derivatives. Five distinct mathematical methods were applied to these curves to determine the RPT. The results were analyzed using linear regression to generate predictive equations and evaluate the coefficient of determination (R²) and standard error for each method. A Student's t-test was used to assess the statistical significance of each alloying element.

Research Topics and Scope:

The research focuses on the AlSi10Mg alloy family, as specified by the EN AC-43.400 standard. The scope includes:
1. The development of three new methods for RPT determination from single-thermocouple TA data.
2. A comparative accuracy assessment of these new methods against two established literature methods.
3. Quantification of the influence of 12 different alloying elements (Si, Mg, Fe, Cu, Ni, Cr, Mn, Ti, Zn, Pb, Sn, Sr) on the RPT.
4. Development of linear regression models to predict RPT based on alloy composition.

6. Key Results:

Key Results:

• Of the five methods evaluated, Method 5, based on the crossing point of the second and third derivative of dT/dt versus temperature, was identified as the most accurate. It yielded the highest coefficient of determination (R² = 0.82) and a low standard error (1.35 °C).
• Linear regression equations were developed for each of the five methods to predict RPT as a function of the alloy's chemical composition.
• Student's t-test analysis for Method 5 revealed that Magnesium (Mg) and Silicon (Si) are the elements with the most statistically significant influence on RPT for AlSi10Mg alloys.
• An increase in Mg content was found to decrease the RPT, while an increase in Si content was found to increase the RPT. Other elements such as Fe, Mn, Ti, and Zn generally had a negative influence (decreasing RPT), while Cu and Cr had a positive influence (increasing RPT).

Figure Name List:

• Figure 1. Rigidity point temperature (RPT) determination with the second minimum of the d2T/dt2 curve.
• Figure 2. Method 2: RPT determination with the first minimum of the dT/dt curve: Hypoeutectic AlSi10Mg alloy.
• Figure 3. Method 3: RPT determination in the crossing point of the second and third derivative dT/dt vs. time for a hypoeutectic AlSi10Mg alloy.
• Figure 4. Method 4: dT/dt curve vs. T, with the RPT point in the elbow.
• Figure 5. Method 5: RPT determination in the crossing point of the second and third derivative of dT/dt vs. T curve.
• Figure 6. Procedure followed in this research work.
• Figure 7. Comparison of the RPT values for each alloy with the methods studied.
• Figure 8. Effect of Mg percentage over RPT employing Method 5.
• Figure 9. Alloy 7 micrography showing needle like structures of intermetallic containing high Fe concentrations, Ni and Cu.
• Figure 10. Alloy 13 micrography showing Al15Si2(Fe,Mn)3, Al2Cu, Al5SiFe, Q-Al8Mg3FeSi6 and A17Cu2Fe structures.

7. Conclusion:

The study successfully demonstrated that a procedure based on the Taguchi method could be employed to calculate RPT values for different AlSi10Mg alloy compositions. The results show that the newly developed Method 5 provides a good statistical correlation for determining the RPT with high accuracy. The analysis identified Mg and Si as the elements with the strongest influence on RPT values. The paper concludes that the analysis of a cooling curve from a single thermocouple can be used to accurately predict RPT. Specifically, Method 5, which uses the dT/dt vs. T curve, provides an easier, more precise, and more automatable tool for RPT determination, as it is less influenced by test cup parameters. This advancement allows for better integration with industrial TA equipment and simulation software to improve the prediction of solidification defects like hot tearing.

8. References:

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Expert Q&A: Your Top Questions Answered

Q1: Why was the new "Method 5" identified as the most accurate and reliable for determining Rigidity Point Temperature?

A1: Method 5 was proven most accurate because it achieved the highest coefficient of determination (R² = 0.82) in regression analysis, indicating the best fit for predicting RPT from alloy composition. Its reliability comes from its technique: plotting the derivatives of the cooling curve against temperature (T) instead of time (t). This makes the measurement independent of the thermal mass of the test cup, providing more consistent results than time-based methods.

Q2: What is the direct industrial consequence of an inaccurate RPT measurement?

A2: The primary consequence is an increased risk of hot tearing. If the RPT is lower than what the simulation software predicts, the alloy remains in a vulnerable semi-solid state for longer, making it more sensitive to cracking during solidification. This leads to higher scrap rates, production delays, and increased quality control costs, directly impacting profitability.

Q3: According to the study, which two alloying elements should a foundry focus on to control the RPT of AlSi10Mg?

A3: The study's statistical analysis conclusively identified Magnesium (Mg) and Silicon (Si) as the elements with the most significant impact on RPT. Higher levels of Mg were shown to decrease the RPT, while higher levels of Si increase it. Therefore, precise control over the percentages of Mg and Si is the most effective way to manage the final RPT and its associated risk of hot tearing.

Q4: How does this new method improve upon existing thermal analysis techniques that also use derivatives?

A4: Existing methods often rely on finding a minimum point on the first or second derivative curve versus time. For hypoeutectic alloys like AlSi10Mg, these curves can have multiple turning points or weak signals, making it difficult to pinpoint the exact RPT. Method 5 provides a more definitive event—the intersection of the second and third derivative curves—which is easier to detect automatically and has been shown to be more accurate.

Q5: Can this method be easily integrated into existing industrial quality control systems?

A5: Yes, a key advantage is its practicality. The method uses data from a single thermocouple in a standard thermal analysis cup, which is a common, cost-effective setup in many foundries. Because Method 5 provides a clearer, more distinct signal, it is well-suited for automation, allowing it to be programmed into existing industrial TA equipment and solidification simulation software to improve their accuracy.

Conclusion: Paving the Way for Higher Quality and Productivity

The challenge of accurately predicting hot tearing defects in aluminum castings has long been tied to the difficulty of measuring the true Rigidity Point Temperature. This research provides a significant breakthrough by introducing a new, highly accurate, and automatable method (Method 5) that outperforms existing techniques. By precisely identifying the influence of key alloying elements like magnesium and silicon, this work empowers engineers with the data needed to optimize alloy compositions and refine simulation models. The result is a clear path toward reducing scrap, improving component integrity, and increasing overall productivity in HPDC operations.

At CASTMAN, we are committed to applying the latest industry research to help our customers achieve higher productivity and quality. If the challenges discussed in this paper align with your operational goals, contact our engineering team to explore how these principles can be implemented in your components.

Copyright Information

This content is a summary and analysis based on the paper "Determination of Solidification of Rigidity Point Temperature Using a New Method" by "Ester Villanueva, Iban Vicario, Jon Mikel Sánchez, and Ignacio Crespo".

Source: https://doi.org/10.3390/app10072472

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