# The Determination of Dendrite Coherency Point Characteristics Using Three New Methods for Aluminum Alloys

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## Featured Application

**Increase the accuracy of solidification software for aluminum alloys.**

## Abstract

_{10}Mg alloys, as well as to compare the acquired values of DCP based on a thermal analysis and on the analysis of cooling curves working with only one thermocouple. Additionally, the impact of alloying and contaminant elements on the DCP will be also studied. The first two proposed methods employ the higher order derivatives of the cooling curves. The DCP was determined as the crossing point of the second and third derivative curves plotted versus time (method 1) or that of the temperature (method 2) with the zero line just after the maximum liquidus temperature. The third proposed method is based on the determination of the crossing point of the third solid fraction derivative curve with the zero line, corresponding to a minimum of the second derivative. A Taguchi design for the experiments was developed to study the DCP values in the AlSi

_{10}Mg alloy. The DCP temperature values of the test alloys were compared with the DCP temperatures predicted by the previous methods and the influence of the major and minor alloying elements and contaminants over the DCP. The new processes obtained a correlation factor r

^{2}from 0.954 and 0.979 and a standard deviation from 1.84 to 2.6 °C. The obtained correlation values are higher or similar than those obtained using previous methods with an easier way to define the DCP, allowing for a better automation of the accuracy of DCP determination. The use of derivative curves plotted versus temperature employed in the last two proposed methods, where the test samples did not have an influence over the registration curves, is proposed to have a better accuracy than those of the previously described methods.

## 1. Introduction

_{10}Mg alloy has found significant application due to an excellent combination of its high ductility values with a good crush performance of its final cast parts [1].

_{10}Mg alloy, based on the available methods applied to detect this point.

- the mechanical (rheological) method,
- the two thermocouples method using the minimum temperature difference,
- the single thermocouple method using the minimum of the second derivative of the cooling curve and/or the common point of the second and third derivative in the zero axis,
- the three thermocouples method determining the thermal diffusivity during solidification.

_{C}) of a test crucible and at a nearby inner wall (T

_{W}) using two thermocouples. The DCP temperature is determined by the local minimum on the ΔT versus time curve (ΔT = T

_{W}− T

_{C}) and its projection on the T

_{C}cooling curve. Heat removal from the solid phase is faster than from the liquid phase and occurs at the minimum of the ΔT versus time curve because there is a higher thermal conductivity in the solid dendrites than in the surrounding liquid metal.

_{liq max}) and the determination of the DCP temperature in the first minimum of the dT/dt curve immediately after the maximum liquidus point.

_{BL}/dt (BL). The base line corresponds to a cooling rate curve if there is no phase transformation. Applying this method, it is possible to determine the amount of solid fraction at the dendritic coherence point, identifying the temperature at which this event occurs. This temperature is determined in the elbow of the first derivative of the cooling curve when it starts to be constant. This method is applied as the following Figure 4 exhibits.

## 2. Materials and Methods

^{2}) and the standard deviation (S

_{ey}) for the obtained results from the 25 tested alloys. The multiple regression analysis techniques seek to derive a single curve that represents the general trend of the data to make extrapolations beyond the limits of the observed data or interpolations. As much of the equations were obtained with a very limited amount of data (25 alloy compositions), they should be used as trend indicators. It is recommended that at least 100 observations (different alloys) be used to ensure a high degree of accuracy.

_{10}Mg according to the standard EN AC-43.400 included in the EN 1706:2010 standard. To determinate the obtained alloy composition, a SPECTROMAXx arc spark OES metal analyzer was used. The obtained compositions are given in Table 1.

#### Development of New Methodologies for the Determination of DCP Temperature

## 3. Results

^{2}) and the standard deviation (S

_{ey}) can also be observed. To define the influence of every alloying element on the studied properties, statistical student t (t) values are employed. The t-test is a statistical hypothesis test in which the test statistic follows a Student’s t-distribution under the null hypothesis. In our case, the values > 2.66 represent that the selected alloying element has a significant influence over the studied parameters and the “0” values represent that the studied alloying element does not have any influence over the studied parameters (null hypothesis). An intermediate “t” value between 0 and 2.66 shows that the studied parameter has an influence over the DCP temperature, with a higher influence the closer the value is to 2.66, despite not having a statistical influence.

_{DCP}(°C) = 661.37 − 7.18Si − 6.07Mg − 3.20Fe − 3.33Cu − 6.94Ni + 6.12Cr-0.59Mn + 23.59Ti − 5.70Zn + 1.69Pb − 53.79Sn + 14.72Sr; r

^{2}= 0.977; S

_{ey}= 1.99.

_{DCP}(°C) = 657.2 − 7.60Si + 3.54Mg + 3.14Fe − 3.59Cu-10.78Ni − 14.20Cr + 2.08Mn + 3.97Ti − 17.71Zn + 5.26Pb + 1.21Sn − 27.38Sr; r

^{2}= 0.976; S

_{ey}= 2.39.

_{DCP}(°C) = 665.71 − 7.65Si − 3.16Mg − 3.21Fe + 3.24Cu − 0.62Ni + 7.1Cr − 0.69Mn + 17.84Ti − 5.99Zn + 3.4Pb − 45.53Sn − 32.19Sr; r

^{2}= 0.977; S

_{ey}= 2.02.

_{DCP}(°C) = 666.92 − 7.67Si − 2.26Mg − 3.01Fe + 1.76Cu − 3.15Ni + 7.00Cr − 1.77Mn + 13.23Ti − 11.42Zn + 6.33Pb − 34.09Sn − 14.18Sr; r

^{2}= 0.977; S

_{ey}= 2.05.

_{DCP}(°C) = 654.69 − 7.38Si + 2.3Mg + 2.30Fe − 0.89Cu − 5.96Ni − 6.15Cr − 9.16Mn + 3.55Ti − 13.41Zn + 3.96Pb − 9.34Sn − 39.17Sr; r

^{2}= 0. 954; S

_{ey}= 2.60.

_{DCP}(°C) = 655.47 − 7.31Si + 2.43Mg + 1.47Fe − 0.86Cu − 7.87Ni − 8.04Cr + 0.16Mn + 4.20Ti − 19.26Zn + 6.69Pb − 7.06Sn − 26.46Sr; r

^{2}= 0.960; S

_{ey}= 2.46.

_{DCP}(°C) = 661.64 − 7.55Si + 2.70Mg − 0.25Fe − 7.39Cu − 3.21Ni + 3.46Cr − 0.34Mn + 9.79Ti − 18.85Zn + 5.41Pb − 20.40Sn − 40.57Sr; r

^{2}= 0.979; S

_{ey}= 1.84.

## 4. Discussion

_{3}Ni intermetallic compounds that are precipitated in the beginning of the solidification process of the alloy, at temperatures well above the TDCP and as described in Reference [26] because Ni provides significant changes in the sequence of post-eutectic reactions, promoting a substantial reduction in the alloy’s freezing range. In both cases, the obtained results confirm the results obtained for the development of the Si equivalent method for obtaining the solidification temperatures, where Ni and Zn have a positive value, which means that they have an influence on decreasing the solidification temperatures [27,28].

_{DCP}value, but without statistical relevance. The obtained results could also be correlated with the previous studies so that they show that an alloy refined with Ti has higher solidification temperatures than the unrefined alloys [15,22]. Pb is usually precipitated in the grain boundary as isolated points and has a very restricted solid dissolution in the aluminum matrix. Because of this, Pb could tend to increase the T

_{DCP}value, but also without a statistical relevance. This result is also in concordance with a previous study [27,29], where elements such as grain refiners (Ti and B) and silicon modifiers (Sr and Sb) or elements with a low melting point (Bi and Pb) have similar effects on the Si Equivalent value.

_{DCP}. Many of the alloying element could precipitate in different inter-metallics and eutectics (For example the Fe as Al

_{5}FeSi, Al

_{8}FeMg

_{3}Si

_{6}, and others).

^{2}) and the standard deviation (S

_{ey}) show that in all the cases, a good correlation between the developed formulae and the obtained results in r

^{2}values > 0.95 and Sey from 1.84 to 2.6 °C.

_{DCP}.

## 5. Conclusions

_{10}Mg family, with a good statistical correlation between the obtained values from the different methods, especially with the newly developed methods.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Method 5: the DCP determination at the crossing point of the second and third derivative of dT/dt vs. time.

**Figure 6.**Method 5: the DCP determination in the crossing point of the second and third derivative in the zero axis of the dT/dt curve.

**Figure 7.**Method 6: the DCP determination at the crossing point of the second and third derivative of dT/dt vs. T curve.

**Figure 8.**Method 7: the DCP determination at the crossing point of the third derivative of dfs/dt vs. T curve with the zero line.

**Figure 10.**The effect of the Si percentage over the dendrite coherency point temperature with method 7.

Ref. | Si | Mg | Fe | Cu | Ni | Cr | Mn | Ti | Zn | Pb | Sn | Sr |
---|---|---|---|---|---|---|---|---|---|---|---|---|

[1] | 9.00 | 0.30 | 0.38 | 0.03 | 0.00 | 0.01 | 0.34 | 0.02 | 0.01 | 0.00 | 0.002 | 0.021 |

[2] | 8.02 | 0.19 | 0.29 | 0.02 | 0.00 | 0.01 | 0.21 | 0.01 | 0.00 | 0.00 | 0.003 | 0.003 |

[3] | 8.66 | 0.14 | 0.30 | 0.02 | 0.00 | 0.01 | 0.21 | 0.20 | 0.29 | 0.27 | 0.039 | 0.014 |

[4] | 10.01 | 0.69 | 0.34 | 0.02 | 0.23 | 0.15 | 0.67 | 0.02 | 0.01 | 0.00 | 0.002 | 0.06 |

[5] | 9.75 | 0.68 | 0.34 | 0.023 | 0.226 | 0.145 | 0.72 | 0.121 | 0.347 | 0.138 | 0.064 | 0.055 |

[6] | 8.77 | 0.15 | 0.85 | 0.19 | 0.21 | 0.16 | 0.21 | 0.12 | 0.16 | 0.21 | 0.073 | 0.006 |

[7] | 8.43 | 0.11 | 0.91 | 0.19 | 0.19 | 0.14 | 0.18 | 0.19 | 0.18 | 0.19 | 0.066 | 0.047 |

[8] | 9.02 | 0.38 | 1.05 | 0.29 | 0.21 | 0.07 | 0.81 | 0.17 | 0.06 | 0.21 | 0.019 | 0.048 |

[9] | 9.26 | 0.56 | 0.73 | 0.09 | 0.001 | 0.069 | 0.53 | 0.024 | 0.212 | 0.01 | 0.002 | 0.007 |

[10] | 11.65 | 0.58 | 0.34 | 0.199 | 0.196 | 0.017 | 0.302 | 0.239 | 0.028 | 0.073 | 0.032 | 0.021 |

[11] | 10.54 | 0.52 | 0.34 | 0.16 | 0.15 | 0.02 | 0.31 | 0.17 | 0.23 | 0.26 | 0.026 | 0.053 |

[12] | 11.49 | 0.40 | 0.91 | 0.42 | 0.00 | 0.14 | 0.67 | 0.23 | 0.15 | 0.18 | 0.04 | 0.046 |

[13] | 11.60 | 0.46 | 0.83 | 0.18 | 0.00 | 0.18 | 0.74 | 0.02 | 0.19 | 0.23 | 0.003 | 0.007 |

[14] | 11.64 | 0.53 | 0.96 | 0.08 | 0.08 | 0.16 | 0.08 | 0.27 | 0.13 | 0.08 | 0.033 | 0.01 |

[15] | 11.82 | 0.52 | 0.96 | 0.11 | 0.11 | 0.14 | 0.11 | 0.11 | 0.18 | 0.11 | 0.046 | 0.023 |

[16] | 11.41 | 0.35 | 0.95 | 0.27 | 0.30 | 0.09 | 0.69 | 0.25 | 0.09 | 0.25 | 0.026 | 0.038 |

[17] | 12.07 | 0.28 | 0.83 | 0.13 | 0.17 | 0.03 | 0.49 | 0.08 | 0.02 | 0.16 | 0.055 | 0.033 |

[18] | 10.21 | 0.278 | 0.43 | 0.052 | 0.001 | 0.069 | 0.333 | 0.021 | 0.083 | 0.001 | 0.002 | 0.013 |

[19] | 10.37 | 0.28 | 0.50 | 0.11 | 0.00 | 0.14 | 0.44 | 0.02 | 0.01 | 0.00 | 0.002 | 0.009 |

[20] | 10.64 | 0.63 | 0.41 | 0.05 | 0.00 | 0.07 | 0.33 | 0.02 | 0.10 | 0.00 | 0.001 | 0.013 |

[21] | 10.31 | 0.29 | 0.54 | 0.09 | 0.00 | 0.11 | 0.35 | 0.01 | 0.01 | 0.00 | 0.002 | 0.006 |

[22] | 10.80 | 0.52 | 0.48 | 0.052 | 0.001 | 0.064 | 0.334 | 0.028 | 0.095 | 0.002 | 0.002 | 0.014 |

[23] | 10.90 | 0.43 | 0.51 | 0.10 | 0.00 | 0.11 | 0.47 | 0.01 | 0.02 | 0.00 | 0.005 | 0.006 |

[24] | 11.71 | 0.442 | 0.57 | 0.073 | 0.002 | 0.075 | 0.438 | 0.016 | 0.042 | 0.002 | 0.002 | 0.013 |

[25] | 10.73 | 0.355 | 0.6 | 0.099 | 0.001 | 0.087 | 0.384 | 0.016 | 0.102 | 0.001 | 0.002 | 0.009 |

Ref. | Method 1 | Method 2 | Method 3 | Method 4 | Method 5 | Method 6 | Method 7 |
---|---|---|---|---|---|---|---|

[1] | 590.8 | 591.6 | 590.54 | 591.7 | 586.82 | 587.6 | 590.29 |

[2] | 603.8 | 599.12 | 604.46 | 605.7 | 599.12 | 600.47 | 603.2 |

[3] | 599.82 | 590.98 | 599.98 | 600.0 | 590.975 | 590.8 | 593.31 |

[4] | 585.94 | 582.47 | 586.60 | 587.9 | 583.03 | 582.875 | 585.93 |

[5] | 582.14 | 575.61 | 583.19 | 583.2 | 575.605 | 574.945 | 580.32 |

[6] | 590.25 | 587.38 | 594.89 | 594.9 | 587.375 | 587.37 | 590.2 |

[7] | 598.39 | 589.62 | 597.68 | 598.3 | 589.615 | 589.865 | 593.57 |

[8] | 590.55 | 586.74 | 593.53 | 593.5 | 586.74 | 586.72 | 590.33 |

[9] | 590.8 | 589.92 | 592.19 | 592.1 | 589.92 | 588.03 | 590.56 |

[10] | 576.01 | 570.32 | 576.46 | 576.5 | 570.32 | 570.865 | 575.01 |

[11] | 582.04 | 573.85 | 583.05 | 583.1 | 573.85 | 574.46 | 578.385 |

[12] | 576.17 | 571.68 | 576.50 | 576.5 | 571.68 | 571.97 | 570.425 |

[13] | 572.58 | 570.01 | 572.89 | 573.2 | 570.005 | 569.46 | 572.44 |

[14] | 574.91 | 568.47 | 575.32 | 575.3 | 568.47 | 569.085 | 574.465 |

[15] | 569.96 | 567.4 | 570.84 | 572.0 | 567.395 | 567.615 | 569.405 |

[16] | 575.94 | 571.3 | 576.59 | 576.6 | 571.3 | 571.54 | 571.585 |

[17] | 569.09 | 567.29 | 568.79 | 570.4 | 567.29 | 567.82 | 569.455 |

[18] | 582.8 | 577.69 | 583.16 | 583.8 | 577.69 | 578.05 | 581.815 |

[19] | 583.92 | 575.97 | 584.49 | 585.2 | 575.965 | 576.27 | 583.675 |

[20] | 578.54 | 575.14 | 578.23 | 579.4 | 575.14 | 575.77 | 578.4 |

[21] | 585.08 | 581.73 | 586.08 | 587.2 | 581.725 | 582.465 | 584.585 |

[22] | 577.77 | 573.61 | 578.67 | 579.1 | 573.61 | 573.78 | 576.92 |

[23] | 579.22 | 576.42 | 580.98 | 581.4 | 576.415 | 576.7 | 578.795 |

[24] | 573.8 | 570.7 | 575.04 | 575.2 | 570.695 | 570.975 | 573.2 |

[25] | 579.75 | 576.17 | 580.93 | 581.1 | 576.17 | 576.36 | 579.27 |

Meth. | Si | Mg | Fe | Cu | Ni | Cr | Mn | Ti | Zn | Pb | Sn | Sr |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 13.57 | 1.17 | 1.22 | 0.39 | 0.79 | 0.6 | 0.18 | 2.65 | 0.56 | 0.16 | 1.42 | 0.4 |

2 | 11.95 | 0.57 | 0.99 | 0.35 | 1.02 | 1.17 | 0.51 | 0.37 | 1.45 | 0.42 | 0.03 | 0.61 |

3 | 14.23 | 0.6 | 1.2 | 0.37 | 0.07 | 0.69 | 0.2 | 1.97 | 0.58 | 0.32 | 1.18 | 0.85 |

4 | 14.09 | 0.42 | 1.11 | 0.2 | 0.35 | 0.67 | 0.51 | 1.44 | 1.09 | 0.6 | 0.87 | 0.37 |

5 | 10.65 | 0.4 | 0.67 | 0.08 | 0.52 | 0.69 | 0.4 | 0.3 | 1.01 | 0.29 | 0.19 | 0.8 |

6 | 11.16 | 0.38 | 0.45 | 0.08 | 0.72 | 0.64 | 0.04 | 0.38 | 1.54 | 0.52 | 0.15 | 0.57 |

7 | 15.45 | 0.56 | 0.1 | 0.94 | 0.39 | 0.37 | 0.11 | 1.19 | 2.01 | 0.57 | 0.58 | 1.18 |

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**MDPI and ACS Style**

Gómez, I.V.; Viteri, E.V.; Montero, J.; Djurdjevic, M.; Huber, G.
The Determination of Dendrite Coherency Point Characteristics Using Three New Methods for Aluminum Alloys. *Appl. Sci.* **2018**, *8*, 1236.
https://doi.org/10.3390/app8081236

**AMA Style**

Gómez IV, Viteri EV, Montero J, Djurdjevic M, Huber G.
The Determination of Dendrite Coherency Point Characteristics Using Three New Methods for Aluminum Alloys. *Applied Sciences*. 2018; 8(8):1236.
https://doi.org/10.3390/app8081236

**Chicago/Turabian Style**

Gómez, Iban Vicario, Ester Villanueva Viteri, Jessica Montero, Mile Djurdjevic, and Gerhard Huber.
2018. "The Determination of Dendrite Coherency Point Characteristics Using Three New Methods for Aluminum Alloys" *Applied Sciences* 8, no. 8: 1236.
https://doi.org/10.3390/app8081236