Extended state-variable yield criteria for Ti4522XD powder via hierarchical multiscale information transfer: bridging mesoscale MPFEM and macroscopic HIP process sensitivity analysis

An extended state-variable yield criterion for Ti4522XD powder is established through hierarchical multiscale information transfer from mesoscale multi-particle finite element method (MPFEM). This framework facilitates predictive sensitivity analysis of hot isostatic pressing (HIP), capturing the effects of capsule geometry, process parameters, and loading strategies on densification kinetics and density uniformity. The model incorporated density- and temperature-dependent elastic modulus E ( ρ _v , T ) and a percolation-based plastic Poisson's ratio ν _p ( ρ ₀, ρ _v , T , ε˙) accounting for initial relative density ( IRD , ρ ₀). The extended state-variable yield criterion was developed in a differentiable PyTorch framework, capturing density strengthening, hybrid Ludwik-Voce work hardening, Johnson-Cook-type strain-rate sensitivity, and softening from recovery and dynamic recrystallization (DRX). In addition, a cascading style sheet (CSS)-enhanced MATLAB Web App enabled interactive visualization of yield surface evolution. The UVSCPL subroutine reliably reproduces relative density ( RD , ρ _v ), equivalent plastic strain ( EPL ), hydrostatic pressure ( P _hyd ), and plastic volumetric strain increment (Δ εp vol ), validating subroutine correctness for HIP simulations. Parametric HIP analyses quantified the effects of capsule geometry, process parameters, and loading strategies. Specifically, a 2 mm-thick filleted capsule reduced the maximum-minimum RD difference ( RD _max-min) by 50% relative to a fillet-free design. Concurrently increasing the peak temperature (1160 °C→1300 °C) and peak pressure (90 MPa→180 MPa) elevated the maximum RD ( RD _max) from 0.953 to 0.988, while extending the holding time from 1 h to 4 h decreased the low-density fraction with RD < 0.95 ( V _low), improving local densification. Asynchronous and stepwise loading strategies optimized early compaction and mid-to-late-stage pore closure, with principal component analysis (PCA) confirming that stepwise loading achieves the highest densification and spatial uniformity. This multiscale constitutive modeling provides a robust approach for predictive HIP simulations and process optimization of Ti4522XD powder, offering a generalizable strategy applicable to other powder systems.