Path-Dependent Constitutive Modeling for Superplastic Forming of Titanium Alloys: Memory-Architecture Perspective.

Area of Science:

• Materials Science
• Mechanical Engineering
• Computational Materials Science

Background:

• Superplastic forming (SPF) of titanium alloys shows significant deformation path dependence.
• Microstructural evolution, damage, and material behavior in SPF are affected by loading history.
• Current constitutive models for SPF often prioritize fitting accuracy over representing deformation history.

Purpose of the Study:

• To review path-dependent constitutive modeling for SPF from a memory-architecture perspective.
• To classify existing constitutive models based on their handling of deformation history.
• To provide guidance for selecting appropriate constitutive models for SPF simulations.

Main Methods:

• Structured literature review of titanium alloy SPF studies.
• Inclusion of high-temperature forming studies from other metallic systems for transferable constitutive frameworks.
• Classification of constitutive models into four categories: stateless, implicit/projected memory, reduced-order memory, and high-dimensional/explicit memory models.

Main Results:

• Many conventional models compress deformation history, limiting their ability to represent complex loading paths.
• Internal-state-variable models offer a balance of path representation, interpretability, and implementation.
• High-dimensional memory models provide superior sequence sensitivity but require more data and calibration.

Conclusions:

• A memory-architecture framework clarifies the capabilities and limitations of existing constitutive models for SPF.
• Model selection for SPF process simulation should consider the trade-offs between accuracy, path representation, and implementation complexity.
• Internal-state-variable and high-dimensional memory models show promise for accurately simulating path-dependent behavior in SPF.