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High-pressure die casting (HPDC) can produce precise geometries in a highly productive manner. In this paper, the failure location and cycles were identified by analyzing the fatigue behavior of the die subjected to repeated thermal stress. An energy-based semi-empirical fatigue life prediction model was developed to handle the complex stress history. The proposed model utilizing mean stress, amplitudes of stress, and strain was calculated by one-way coupling numerical analysis of computational fluid dynamics (CFD) and finite element analysis (FEA). CFD temperature results of the die differed from the measured results by 2.19%. The maximum stress distribution obtained from FEA was consistent with the actual fracture location, demonstrating the reliability of the analytical model with a 2.27% average deviation between the experimental and simulation results. Furthermore, the model showed an excellent correlation coefficient of R
= 97.6%, and its accuracy was verified by comparing the calculated fatigue life to the actual die breakage results with an error of 20.6%. As a result, the proposed model is practical and can be adopted to estimate the fatigue life of hot work tool steels for various stress and temperature conditions.
High-pressure die casting (HPDC) is a process wherein molten metal is injected inside the mold cavity at high speed and pressure conditions. This process has been widely utilized in the aerospace and automotive industries for its high productivity, product strength, corrosion resistance, and precise dimensional accuracy [1, 2, 3]. During HPDC, processes such as filling the chamber, solidifying, opening and closing, product removal, and spraying occur continuously [4]. Meanwhile, the die replacement procedure takes considerable time and increases production costs [5]. The reason is that the HPDC die manufacturing process requires high energy and many workforces due to being made of high-strength H13 hot work tool steel [6].
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Therefore, thermal fatigue life prediction is essential to determine the replacement time of the die. Cumulative fatigue damage caused by thermal contraction and expansion of thermal stresses has a vital influence on die destruction. The thermal stress is caused by the uneven temperature distribution of the die due to an injection of high-temperature molten metal, product detachment, and repeated fast cooling via low-temperature coolant [7, 8]. In particular, increased heat transfer due to the coolant flow channel reduces the process time by promoting rapid cooling; however, the temperature difference in the die rises, which is fatal to the thermal fatigue fracture [9]. The pressure and the temperature for evaluating the thermal stress can be accurately tracked by employing load cells and thermocouples. Additionally, the molten metal flow remains constant for each cycle, causing the temperature field to converge [10, 11]. Therefore, it is unnecessary to analyze the thermal stress at every HPDC cycle [12, 13].
Many studies have confirmed the temperature effect on thermal fatigue behavior through experiments or numerical analysis [14, 15, 16, 17, 18, 19, 20]. Wei et al. [21] suggested a methodology for considering thermal stress within Abaqus software by employing a simplified die casting model. In addition, Klobčar et al. [15] evaluated the strength of the die material against thermal stress through experiments in which the die specimen was repeatedly immersed in water and aluminum molten metal. Meanwhile, the studies mentioned above have limitations arising from their difficulty in simulating the actual HPDC and its complicated experiments confined to a specimen.
Concerning fatigue analysis, typical conventional models have been suggested by Goodman [22], Smith–Watson–Topper (SWT) [23], Walker [24], and Coffin–Manson [25, 26]. These models have been introduced to predict the fatigue life of materials via maximum and minimum stress or strain. Meanwhile, the Rainflow counting method, which converts various loading sequences into constant stress amplitude, has also been proposed by Matsuishi and Endo [27]. Nevertheless, stress or strain history under the operating environment of products is highly complex, making it challenging to apply these fatigue life prediction models.
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For this reason, many studies have been conducted to describe fatigue behavior in complex stress states by adopting various methods [28, 29, 30, 31, 32, 33, 34, 35]. For instance, Choi et al. [29] proposed a semi-empirical model based on the specimen angles and strain amplitude, representing the nonlinear anisotropic behavior. Meanwhile, Lu et al. [16] developed a thermal fatigue model by utilizing the relationship between the thermal plastic strain and the temperature change. The temperature change is the difference between the initial and final temperature in the thermal fatigue test of the simple plate and dies insert samples. The proposed model was improved using the temperature at the point where the plastic strain was rapidly induced.
As summarized so far, the fatigue behavior of the die material can be described through a semi-empirical fatigue life prediction model. Various attempts have been made to predict the fatigue life of the die casting die in consideration of thermal stress via the temperature difference term and experimental results [16, 36, 37, 38]. However, there appear to be no prior studies that predict fatigue life of the die under constantly changing thermal stress and complex stress states by utilizing the relationship between maximum and minimum average stress–strain. In addition, many studies have been conducted to attempt thermal and structural analysis individually; still, the successful development of one-way coupled numerical analysis has yet to be achieved.
For these reasons, a thermofluid analysis model was developed considering the temperature change in the die in the actual HPDC process. The simulation was conducted for 20 repeated cycles to obtain a converged periodic temperature field throughout all computational domains. Furthermore, a one-way co-simulation of structural analysis was carried out based on the temperature result of computational fluid dynamics (CFD). Thermal stress–strain of finite element analysis (FEA) was evaluated utilizing the quasi-steady-state assumption based on the instantaneous temperature distribution.
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For determining the temperature effects on the AISI H13 hot work tool steel, the flow stress model and temperature-dependent coefficients were chosen and adopted for the numerical simulations. The Johnson–Cook flow stress model, comprising the mechanical and thermal properties, was selected to define a relationship between thermal strain and temperature [39, 40, 41, 42]. The model parameters were determined using the tensile experiment results at different experimental temperatures and employed in an FEA model. The low-cycle fatigue life simulation results were verified by comparing to the experimental results, which show good agreement with the actual crack positions.
In addition, fatigue tests were performed with various stress and temperature conditions to predict the fatigue life of the HPDC die. As a result, a semi-empirical model enabling the prediction of the fatigue failure life under exposure to thermal stress was proposed based on simulation and experimental results. The proposed model is a strain–stress-based energy function in a power-law form. The energy function was calculated utilizing the maximum and minimum stress–strain obtained from the die, and the fatigue life can be predicted without stress–strain change history. Moreover, by conducting three case studies with different coolant passages, the best design capable of improving the fatigue life of the die was evaluated. As the results of this research, designers can predict vulnerabilities in advance and compare the fatigue life considering the effect of thermal stress.
The fatigue life prediction of the die subjected to thermal stress at various temperatures was performed through the procedure shown in Figure 1. First, static and fatigue experiments were carried out utilizing machined uniaxial and notch specimens to appraise the mechanical properties under various load conditions. Additionally, the temperature and pressure on the dies were measured with a thermocouple and load cell. Arduino Uno collects the measurement data every 0.31 s.
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Secondly, the material coefficients adopted for numerical analysis were determined by the stress–strain curves obtained from the tensile tests. Furthermore, the boundary conditions of one-way coupled numerical analysis combining CFD and FEA were defined using measured temperature and pressure data. The thermal stress could be accurately evaluated through the developed simulation by mapping the temperature distribution to structural analysis. Finally, the semi-empirical model utilizing energy function was developed by assessing the effects of thermal stress. The strain and stress values in the hysteresis
For this reason, many studies have been conducted to describe fatigue behavior in complex stress states by adopting various methods [28, 29, 30, 31, 32, 33, 34, 35]. For instance, Choi et al. [29] proposed a semi-empirical model based on the specimen angles and strain amplitude, representing the nonlinear anisotropic behavior. Meanwhile, Lu et al. [16] developed a thermal fatigue model by utilizing the relationship between the thermal plastic strain and the temperature change. The temperature change is the difference between the initial and final temperature in the thermal fatigue test of the simple plate and dies insert samples. The proposed model was improved using the temperature at the point where the plastic strain was rapidly induced.
As summarized so far, the fatigue behavior of the die material can be described through a semi-empirical fatigue life prediction model. Various attempts have been made to predict the fatigue life of the die casting die in consideration of thermal stress via the temperature difference term and experimental results [16, 36, 37, 38]. However, there appear to be no prior studies that predict fatigue life of the die under constantly changing thermal stress and complex stress states by utilizing the relationship between maximum and minimum average stress–strain. In addition, many studies have been conducted to attempt thermal and structural analysis individually; still, the successful development of one-way coupled numerical analysis has yet to be achieved.
For these reasons, a thermofluid analysis model was developed considering the temperature change in the die in the actual HPDC process. The simulation was conducted for 20 repeated cycles to obtain a converged periodic temperature field throughout all computational domains. Furthermore, a one-way co-simulation of structural analysis was carried out based on the temperature result of computational fluid dynamics (CFD). Thermal stress–strain of finite element analysis (FEA) was evaluated utilizing the quasi-steady-state assumption based on the instantaneous temperature distribution.
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For determining the temperature effects on the AISI H13 hot work tool steel, the flow stress model and temperature-dependent coefficients were chosen and adopted for the numerical simulations. The Johnson–Cook flow stress model, comprising the mechanical and thermal properties, was selected to define a relationship between thermal strain and temperature [39, 40, 41, 42]. The model parameters were determined using the tensile experiment results at different experimental temperatures and employed in an FEA model. The low-cycle fatigue life simulation results were verified by comparing to the experimental results, which show good agreement with the actual crack positions.
In addition, fatigue tests were performed with various stress and temperature conditions to predict the fatigue life of the HPDC die. As a result, a semi-empirical model enabling the prediction of the fatigue failure life under exposure to thermal stress was proposed based on simulation and experimental results. The proposed model is a strain–stress-based energy function in a power-law form. The energy function was calculated utilizing the maximum and minimum stress–strain obtained from the die, and the fatigue life can be predicted without stress–strain change history. Moreover, by conducting three case studies with different coolant passages, the best design capable of improving the fatigue life of the die was evaluated. As the results of this research, designers can predict vulnerabilities in advance and compare the fatigue life considering the effect of thermal stress.
The fatigue life prediction of the die subjected to thermal stress at various temperatures was performed through the procedure shown in Figure 1. First, static and fatigue experiments were carried out utilizing machined uniaxial and notch specimens to appraise the mechanical properties under various load conditions. Additionally, the temperature and pressure on the dies were measured with a thermocouple and load cell. Arduino Uno collects the measurement data every 0.31 s.
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Secondly, the material coefficients adopted for numerical analysis were determined by the stress–strain curves obtained from the tensile tests. Furthermore, the boundary conditions of one-way coupled numerical analysis combining CFD and FEA were defined using measured temperature and pressure data. The thermal stress could be accurately evaluated through the developed simulation by mapping the temperature distribution to structural analysis. Finally, the semi-empirical model utilizing energy function was developed by assessing the effects of thermal stress. The strain and stress values in the hysteresis
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