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

Superplastic forming (SPF) of titanium alloys exhibits strong deformation path dependence because microstructural evolution, damage development, and material response are influenced by prior loading history. However, constitutive models for SPF are often evaluated primarily by fitting accuracy rather than their ability to represent deformation history. This review examines path-dependent constitutive modeling from a memory-architecture perspective. The relevant literature was identified through a structured review of titanium-alloy SPF studies, which were supplemented by selected high-temperature forming studies from other metallic systems when they provided transferable constitutive frameworks. Existing constitutive models were classified into four categories according to how deformation history is retained and represented: stateless models, implicit or projected memory models, reduced-order memory models, and high-dimensional or explicit memory models. The analysis shows that many conventional formulations achieve acceptable accuracy within calibrated monotonic regimes by strongly compressing deformation history, thereby limiting their ability to distinguish complex loading paths. Internal-state-variable models provide a practical balance between path representation, interpretability, and implementation, whereas high-dimensional memory models offer stronger sequence sensitivity at the cost of greater data and calibration requirements. This memory-architecture framework clarifies the limitations and applicability of existing constitutive models and provides guidance for model selection in SPF process simulation.