# A Simulation of the Densification Process of NdFeB Bulks by a Modified Drucker-Prager Cap Model
## 5 Conclusions  
The spark plasma sintering experiment on NdFeB bulks under high temperatures and high pressure was conducted by utilizing the DPC model, which leverages relative density to predict temperature and stress fields. By using X-ray residual stress measurement technology and SEM characterization techniques, the accuracy of the model was ensured. Furthermore, the temperature and stress fields derived from the DPC constitutive model illustrate the densification process of NdFeB blocks under the conditions of \"780 \({}^{\circ}\)C, 60 MPa; 850 \({}^{\circ}\)C, 60 MPa; 940 \({}^{\circ}\)C, 60 MPa\". A comprehensive evaluation was conducted to probe the impact of temperature on grain growth across various sintering temperatures, while the stress evolution within NdFeB blocks during the sintering process was also delineated. This study concluded that the increase in sintering temperature in the range of 780 \({}^{\circ}\)C to 940 \({}^{\circ}\)C promotes grain growth and accelerates the densification process. At sintering temperatures of 850 \({}^{\circ}\)C and 940 \({}^{\circ}\)C, the longitudinal compressive stress at the cross-sectional edge shifts to longitudinal tensile stress. The value changed from \(-\)14 MPa to 112 MPa and 172 MPa. Additionally, obvious cracks emerged at the cross-section's edge under these two sintering temperatures, contrasting with the 780 \({}^{\circ}\)C scenario.  
By employing finite element simulation techniques, the limitations of predicting temperature and stress fields in actual engineering are overcome, transforming real-world scenarios into visual models. This approach effectively reduces trial and error and enhances the sample's quality.  
This research method can be used to calibrate other special materials with high temperatures and high pressure, such as aerospace, ceramic, military, and other materials. The constitutive model, as an equation describing the mechanical properties of materials, has direct application value in engineering practice and can be used to guide engineering design and material selection.  
Conceptualization, N.L.; data curation, F.C.; formal analysis, T.S., W.J. and B.S.; funding acquisition, H.G.; investigation, T.S. and W.J.; methodology, T.S., W.J. and F.C.; project administration, H.G.; software, T.S., W.J. and N.L.; supervision, F.C.; validation, W.Q., R.W. and H.M.; visualization, W.Q., R.W. and H.M.; writing--original draft, T.S. and W.J.; writing--review and editing, F.C. All authors have read and agreed to the published version of the manuscript.  
This research is funded by the National Key Research and Development Program of China, \"study on the magnetic characteristics and defect detection technology in the production process of rare earth permanent magnet\" (Grant No. 2023 YFB3506500).  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
**Conflicts of Interest:** Author [PERSON] is employed by the company JL MAG Rare-Earth Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.