# Experimental Investigation of Thermal Fatigue Die Casting Dies by Using Response Surface Modelling

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{0.5}hardness properties were produced.

## 1. Introduction

_{a1}, wall thickness, and immersion time) and responses (crack length, surface roughness due to thermal fatigue, R

_{a2}, and hardness properties). Moreover, by combining existing and new data on heat transfer in die-casting dies and die material properties with RSM modelling, a method for predicting the onset of heat checking in H13 steel dies has been proposed.

## 2. Experimental Procedures

#### 2.1. Materials

#### 2.2. Experimental Apparatus and Work Procedure

#### 2.3. Factors and Response Surface Modeling

_{s}) of samples, surface roughness due to thermal fatigue (R

_{a2}) and hardness properties obtained from the experimentation are presented in Table 4.

## 3. Results and Discussion

#### 3.1. Effect of Surface Roughness, Wall Thickness and Immersion Time on Crack Spherical Shape (SPH)

_{1}(96.17%), the fit of data can be measured from the estimated model.

_{a1}contribute equally to reducing crack. Meanwhile, reduced crack length extends the lifetime of dies, but this factor cannot compensate for the reverse effect due to an increase in the other factors; wall thickness and R

_{a1}.

#### 3.2. Effect of As-Machined Surface Roughness, Wall Thickness and Immersion Time on ${R}_{a2}$

_{a2}, is expressed as follows:

_{2}. The R

_{a1}, wall thickness, and immersion time data are plotted in Figure 4. Figure 4 show that most value matched one another well, except that the difference between the measured and predicted values exceeded 0.6 μm. The smallest value of R

_{a2}was measured for H13 tool steel after thermal fatigue cycles (1850 cycles) with a constant temperature of 700 °C. The data on additional factors were used to generate the probability plot, except for two data points where the model overpredicted the measured data by over 0.6 μm. The additional test data fit the model reasonably and supports the validity of the model in predicting the values of R

_{a2}.

_{a2}, responding to three parameters. The increase in R

_{a1}, and immersion time affected R

_{a2}dramatically. In Figure 6, the R

_{a2}reached the highest value when the R

_{a1}increases.

_{a2}against R

_{a1}and wall thickness ratio, and for R

_{a2}against R

_{a1}and immersion time are shown in Figure 5a–d respectively. In Figure 5b, the measured R

_{a2}increased with R

_{a1}and immersion time [24,25]. Generally, the predicted R

_{a2}for the different samples was lower than that for steel B and C, which is consistent with the measured results (Figure 5a,b). The effect of the difference in time and wall thickness on y

_{2}varied for the different H13 samples (Figure 5b,d). With R

_{a1}versus immersion time increasing from 0% to 24%, ${R}_{\mathrm{a}2}$ increased for parameters A and C. With a decrease in ${R}_{\mathrm{a}2}$, the effect on tool steel also decreased.

#### 3.3. Effect of As-Machined Surface Roughness, Wall Thickness and Immersion Time on Hardness Properties

_{3}is hardness.

_{a1}, and immersion time provided a good indication that as-machined surface roughness was a major factor in R

_{a2}changes. The analysis of variance as shown in Table 8 indicates that the model was adequate because the p-value of the response surface quadratic model is significant.

_{0.5}values were much lower, when the R

_{a1}and immersion time increased. These tests require the error term to be normally and independently distributed with mean zero and variances. Figure 6 shows the normal probability, fitted values, and histogram of residuals, respectively.

_{a1}and immersion time clearly affected R

_{a2}dramatically. In Figure 5, R

_{a2}reached the highest value, when the R

_{a1}increases. Hardness properties increased more rapidly with increasing temperature in comparison to increasing time. All the empirical equations predicting change in the properties are based on the three factors, namely, as-machined surface roughness, wall thickness, and immersion time.

#### 3.4. Influence of Cooling Rate on Hardness Properties and Crack Length

## 4. Conclusions

_{a1}, and wall thickness process by evaluating the surface roughness due to thermal fatigue, R

_{a2}, and the temperature respectively, which is based on response surface methodology (RSM). The mathematical model outcomes were later equated with the experimental findings. It was observed that the immersion time, R

_{a1}, and wall thickness affected R

_{a2}and temperature distribution when milling the H13 tool steel. Some important conclusions derived from the study are concluded as following:

- The response surface methodology (RSM) resulted in an advantageous procedure for the surface roughness and temperature analysis. In addition, designing experiments are essential to produce statistics, which in turn is beneficial in expanding the calculating equations for surface roughness, crack length, and hardness properties. The investigation of variance for the second order for both the studied model displays that the immersion time is the most affected parameter which afflicted the hardness and the crack lengths followed by wall thickness.
- Both second order models were observed to be expedient in forecasting the key effects and the square effects of diverse dominant arrangements of the machining constraints. The process was found cost-effective in shaping the effect of several parameters in a methodical way. In addition, the process for the thermal fatigue cycle of H13 tool steel, the legitimacy of the process is typically restricted to the collection of factors measured during the investigation.
- The RSM model could effectively relate the machining parameters with the responses, crack, surface roughness due to thermal fatigue, and hardness properties. The optimal parameter setting resulted crack length of 26.5 μm, surface roughness of 3.114 μm, and hardness properties of 306 HV
_{0.5}. - The results generated by the predicted model are equated with the experimental results. The observed percentage error is very low, which is only 2% for both the predicted models.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Contour plot of crack length responding to (

**a**) R

_{a1}and wall thickness, (

**b**) R

_{a1}and immersion time. (

**c**,

**d**) a 3D view of crack length interaction with the respective parameters.

**Figure 5.**Contour plot of surface roughness due to thermal fatigue, R

_{a2}, responding to (

**a**) R

_{a1}and immersion time, (

**b**) R

_{a1}and wall thickness. (

**c**,

**d**) a 3D view of R

_{a2}interactions with the respective parameters.

**Figure 7.**Contour plots of hardness properties responding to (

**a**) R

_{a1}and immersion time, (

**b**) R

_{a1}and wall thickness. (

**c**,

**d**) a 3D view of hardness properties, interaction with the respective parameters.

Element | C | Si | Mn | Cr | Mo | V | W |
---|---|---|---|---|---|---|---|

wt (%) | 0.51 | 1.26 | 0.413 | 5.5 | 1.52 | 1.0 | 0.02 |

Element | Cu | Mg | Mn | Si | Zn | Ti | Fe |
---|---|---|---|---|---|---|---|

wt (%) | 0.25 | 0.45 | 0.35 | 7.5 | 0.35 | 0.25 | 0.2 |

Factor | Name | Low | High |
---|---|---|---|

A | Surface roughness (µm) | 2.5 | 5.5 |

B | Wall Thickness (mm) | 6.5 | 11.5 |

C | Immersion Time (s) | 7 | 11 |

Input Factors | Outcome (Response) | |||||
---|---|---|---|---|---|---|

Std | ${\mathit{R}}_{\mathbf{a}1}$ (µm) | Wall Thickness (wt) (mm) | Immersion Time (T) (s) | ${\mathit{CL}}_{\mathit{s}}$ (µm) | ${\mathit{R}}_{\mathbf{a}2}$ (µm) | Hardness (${\mathbf{HV}}_{0.5}$) |

1 | 2.5 | 6.5 | 9 | 30 | 2.8 | 293 |

2 | 5.5 | 6.5 | 9 | 46.8 | 6.3 | 239 |

3 | 2.5 | 11.5 | 9 | 32 | 2.7 | 297.4 |

4 | 5.5 | 11.5 | 9 | 46 | 5.9 | 257 |

5 | 2.5 | 9 | 7 | 26.5 | 3.5 | 294 |

6 | 5.5 | 9 | 7 | 43 | 6.53 | 242 |

7 | 2.5 | 9 | 11 | 30 | 2.9 | 288 |

8 | 5.5 | 9 | 11 | 52 | 5.9 | 235 |

9 | 4 | 6.5 | 7 | 32.3 | 4.6 | 291.7 |

10 | 4 | 11.5 | 7 | 35 | 4.6 | 265 |

11 | 4 | 6.5 | 11 | 41 | 4.6 | 250 |

12 | 4 | 11.5 | 11 | 46 | 4.35 | 291 |

13 | 4 | 9 | 9 | 38.5 | 4.3 | 285 |

14 | 5.5 | 9 | 9 | 47.3 | 6 | 246 |

15 | 2.5 | 9 | 9 | 30.6 | 2.8 | 297 |

16 | 5.5 | 11.5 | 7 | 47.6 | 6 | 234 |

17 | 2.5 | 6.5 | 11 | 33 | 2.9 | 267 |

Source | Sum of Squares | Df | Mean Square | F Value | p-Value Prob > F |
---|---|---|---|---|---|

Model | 6.42 | 6 | 1.07 | 41.91 | <0.0001 |

A—surface roughness, R_{a1} | 5.72 | 1 | 5.72 | 224.21 | <0.0001 |

B—wall thickness | 0.11 | 1 | 0.11 | 4.26 | 0.0660 |

C—immersion time | 0.87 | 1 | 0.87 | 34.20 | 0.0002 |

A × B | 4.196 × 10^{−5} | 1 | 4.196 × 10^{−5} | 1.644 × 10^{−3} | 0.9685 |

A × C | 1.701 × 10^{−3} | 1 | 1.701 × 10^{−3} | 0.067 | 0.8016 |

B × C | 3.311 × 10^{−3} | 1 | 3.311 × 10^{−3} | 0.13 | 0.7263 |

Residual | 0.26 | 10 | 0.026 | ||

Cor Total | 6.67 | 16 |

Standard Deviation (Std. Dev) | 0.16 | Adeq Precision | 19.815 |
---|---|---|---|

Mean | 6.19 | Pred R-Squared | 0.8678 |

Coefficient of Variation (C.V. %) | 2.58 | Adj R-Squared | 0.9388 |

PRESS | 0.88 | R-Squared | 0.9617 |

Source | Sum of Squares | Df | Mean Square | F Value | p-Value Prob > F |
---|---|---|---|---|---|

Model | 1.75 | 6 | 0.29 | 88.40 | <0.0001 |

A—surface roughness, R_{a1} | 1.61 | 1 | 1.61 | 488.86 | <0.0001 |

B—wall thickness | 6.229 × 10^{−3} | 1 | 6.229 × 10^{−3} | 1.89 | 0.1995 |

C—immersion time | 0.015 | 1 | 0.015 | 4.47 | 0.0605 |

A × B | 1.268 × 10^{−3} | 1 | 1.268 × 10^{−3} | 0.38 | 0.5492 |

A × C | 9.257 × 10^{−4} | 1 | 9.257 × 10^{−4} | 0.28 | 0.6080 |

B × C | 6.479 × 10^{−4} | 1 | 6.479 × 10^{−4} | 0.20 | 0.6672 |

Residual | 0.033 | 10 | 3.301 × 10^{−3} | ||

Cor Total | 1.78 | 16 |

Source | Sum of Squares | df | Mean Square | F Value | p-Value Prob > F |
---|---|---|---|---|---|

Model | 8.87 | 9 | 0.99 | 235.55 | <0.0001 |

A—surface roughness, R_{a1} | 6.66 | 1 | 6.66 | 1591.11 | <0.0001 |

B—wall thickness | 0.19 | 1 | 0.19 | 45.01 | 0.0003 |

C—immersion time | 0.11 | 1 | 0.11 | 26.97 | 0.0013 |

A × B | 0.058 | 1 | 0.058 | 13.86 | 0.0074 |

A × C | 7.642 × 10^{−4} | 1 | 7.642 × 10^{−4} | 0.18 | 0.6820 |

B × C | 1.24 | 1 | 1.24 | 295.20 | <0.0001 |

A^{2} | 0.34 | 1 | 0.34 | 81.02 | <0.0001 |

B^{2} | 4.378 × 10^{−3} | 1 | 4.378 × 10^{−3} | 1.05 | 0.3404 |

C^{2} | 0.21 | 1 | 0.21 | 49.97 | 0.0002 |

Residual | 0.029 | 7 | 4.185 × 10^{−3} | ||

Cor Total | 8.90 | 16 |

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## Share and Cite

**MDPI and ACS Style**

Abdulhadi, H.A.; Ahmad, S.N.A.S.; Ismail, I.; Ishak, M.; Mohammed, G.R.
Experimental Investigation of Thermal Fatigue Die Casting Dies by Using Response Surface Modelling. *Metals* **2017**, *7*, 191.
https://doi.org/10.3390/met7060191

**AMA Style**

Abdulhadi HA, Ahmad SNAS, Ismail I, Ishak M, Mohammed GR.
Experimental Investigation of Thermal Fatigue Die Casting Dies by Using Response Surface Modelling. *Metals*. 2017; 7(6):191.
https://doi.org/10.3390/met7060191

**Chicago/Turabian Style**

Abdulhadi, Hassan Abdulrssoul, Syarifah Nur Aqida Syed Ahmad, Izwan Ismail, Mahadzir Ishak, and Ghusoon Ridha Mohammed.
2017. "Experimental Investigation of Thermal Fatigue Die Casting Dies by Using Response Surface Modelling" *Metals* 7, no. 6: 191.
https://doi.org/10.3390/met7060191