A physically consistent three-scale numerical framework for multi-scale characterization of thermal stress in directed energy deposition

Jiawei Chen

doi:10.1016/j.jmps.2026.106810

A physically consistent three-scale numerical framework for multi-scale characterization of thermal stress in directed energy deposition

2026-08-09

0

PRE

AI

J

Jiawei Chen

F

Feiyu Xiong

Y

Yanping Lian *

M

Ming‐Jian Li *

R

Ruxin Gao

DOI：10.1016/j.jmps.2026.106810

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Abstract

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Thermal stress evolution in laser directed energy deposition (DED) involves complex interplay between macroscopic thermo-mechanical response and grain-scale stress heterogeneity, posing significant difficulties for quantitative multi-scale evaluation. In this study, a three-scale numerical framework is developed for evaluating thermal stress evolution in DED. The framework couples macro-scale thermo-mechanical analysis, meso-scale thermo-fluid simulation, and micro-scale crystal plasticity, and enables explicit separation of Type I stress, Type II stress, and intragranular stress variation corresponding to macroscopic, intergranular, and intragranular scales. Data operators are introduced to transfer heat source input, clad geometry, temperature, material distribution, displacement boundary conditions, and grain structure between different scales, ensuring physically consistent macro–micro fields and boundary condition transfer. To the best of the authors’ knowledge, it is the first three-scale computational framework that enables quantitative evaluation of Type I stress, Type II stress, and intragranular stress variation in additively manufactured polycrystals under physically consistent macro–micro field and boundary-condition transfer. The framework is validated through comparisons of temperature history, melt pool morphology, macro-scale stress distribution, and macro–micro stress consistency, demonstrating agreement with available experimental data. Further numerical results demonstrate that the micro-scale stress can reach approximately twice the macro-scale tensile level and exhibits pronounced tensile–compressive heterogeneity even when the macro-scale field remains entirely tensile. Type II stress reveals intergranular tensile–compressive incompatibility reaching 164.3–204.8 MPa across representative grain boundaries, while intragranular stress variation captures intragranular stress contrasts approaching 298 MPa associated with local stress distribution. These findings demonstrate that explicit separation of scale-dependent stress components is essential for identifying critical stress regions that cannot be resolved from macro-scale or micro-scale stress magnitude alone. In addition, orientation and size-dependent analyses indicate that grain orientation and morphology influence stress heterogeneity, and strengthening the ⟨001⟩ texture reduces both intergranular and intragranular stress contrast. The proposed framework therefore provides a powerful tool for quantitative evaluation of macro–micro stress interplay in DED and offers new insight into microstructure-informed stress regulation in DED.

Keywords:

Multi-scale numerical framework

Micro-scale stress decomposition

Physical consistency

Crystal plasticity

Additive manufacturing

A physically consistent three-scale numerical framework for multi-scale characterization of thermal stress in directed energy deposition

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