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<p>Shrink-fit dies are widely used to enhance tooling integrity in high-load forming processes; however, the mechanical effects of a conical shrink-fit interface remain insufficiently understood. In this study, a stress-based numerical investigation and multi-objective optimization of a conical shrink-fit die for backward extrusion of AA7075 aluminum alloy is presented. Finite element simulations were performed using a two-dimensional axisymmetric model, with the fitting cone half-angle and interference magnitude systematically varied using a central composite design and optimized via the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The results show that the interference magnitude is the dominant factor controlling the stress state of the shrink-fit system, while the fitting cone half-angle provides an effective secondary mechanism for stress redistribution. Guided by a safety-dominated design philosophy, in which the tensile hoop stress in the brittle WC–15%Co cemented carbide die insert is treated as the primary objective and the stress state of the SKD11 steel shrink ring is constrained within safe limits, a robust optimal design region was identified. The optimal solutions correspond to a large cone half-angle of approximately 2.5° combined with a high interference level of about 0.20%D, reducing the maximum hoop stress in the die insert to approximately 2125&#xa0;MPa while maintaining the stress utilization ratio of the shrink ring below 0.70 and limiting its hoop stress to about 547&#xa0;MPa. The proposed framework demonstrates that incorporating a conical shrink-fit interface provides an effective additional degree of freedom for stress-based die design and offers practical guidance for improving tooling safety in backward extrusion applications.</p> Graphical abstract <p></p>

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Stress-based design and multi-objective optimization of a conical shrink-fit die for backward extrusion of AA7075

  • 期刊论文

  • 发表日期：

    2026年4月12日

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  • Tran Duc Hoan,
  • To Thanh Loan

摘要

Shrink-fit dies are widely used to enhance tooling integrity in high-load forming processes; however, the mechanical effects of a conical shrink-fit interface remain insufficiently understood. In this study, a stress-based numerical investigation and multi-objective optimization of a conical shrink-fit die for backward extrusion of AA7075 aluminum alloy is presented. Finite element simulations were performed using a two-dimensional axisymmetric model, with the fitting cone half-angle and interference magnitude systematically varied using a central composite design and optimized via the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The results show that the interference magnitude is the dominant factor controlling the stress state of the shrink-fit system, while the fitting cone half-angle provides an effective secondary mechanism for stress redistribution. Guided by a safety-dominated design philosophy, in which the tensile hoop stress in the brittle WC–15%Co cemented carbide die insert is treated as the primary objective and the stress state of the SKD11 steel shrink ring is constrained within safe limits, a robust optimal design region was identified. The optimal solutions correspond to a large cone half-angle of approximately 2.5° combined with a high interference level of about 0.20%D, reducing the maximum hoop stress in the die insert to approximately 2125 MPa while maintaining the stress utilization ratio of the shrink ring below 0.70 and limiting its hoop stress to about 547 MPa. The proposed framework demonstrates that incorporating a conical shrink-fit interface provides an effective additional degree of freedom for stress-based die design and offers practical guidance for improving tooling safety in backward extrusion applications.

Graphical abstract