Film-hole structure is a critical design feature in advanced aero-engines for cooling turbine blades, however, it also introduces pronounced inhomogeneities in macroscopic fields (e.g. macro-stress) and the associated microstructures (e.g. dislocations and γ/γ′ phases, i.e. the γ matrix and the coherent γ′ precipitates of the single-crystal superalloy). Variations in film-hole design parameters-such as size, shape and orientation-can significantly influence the mechanical performance of turbine blades during service. Nevertheless, predicting microstructure-associated macro-cracking in single crystal superalloys with diverse film-hole configurations remains highly challenging, primarily due to the complexities of multi-scale modeling and numerical implementation. In this work, a machine learning assisted concurrent multi-scale method is developed to predict microstructure-associated macro-cracking in single-crystal superalloys containing film holes of varying size, shape and orientation. Macroscopic stress fields at representative macro-grids, obtained from simulations of specimens subjected to static tension, are imposed as boundary conditions for a microscale phase-field model to pre-simulate the co-evolution of dislocations and γ/γ′ phases. Based on these data, a machine learning model is trained to efficiently generate the corresponding averaged microscopic quantities for macroscopic stress inputs within the sampled training domain under the prescribed creep conditions, using pre-computed macro-stress fields as inputs and corresponding pre-simulated micro-features as outputs. With the trained model, multi-scale simulations of creep behavior are performed and validated against experimental observations in terms of microstructure evolution, machine learning-predicted micro-features and microstructure-associated macro-cracking behavior. Building on this validation, the applicability of different macro-cracking criteria (e.g. dislocation density based, resolved shear stress based, equivalent plastic strain based and energy based) is systematically assessed. Among the criteria considered, the equivalent-plastic-strain-based criterion provides the most consistent description of the crack-initiation sites, the 45° crack deflection and the inter-hole linking. Furthermore, both the commonalities and distinctions in the underlying mechanisms of microstructure-associated macro-cracking are elucidated.
Nanoindentation provides a direct means of characterizing the mechanical response of thermochemical energy storage (TCES) materials, but systematic mechanical data for different salt phases remain limited. In this work, we investigate the mechanical behavior of strontium bromide hexahydrate, SrBr2⋅6H2O, through nanoindentation experiments performed at two loading rates. The experimental results are used to calibrate and validate an elasto-viscoplastic finite-element model for the hydrated phase. The calibrated model reasonably reproduces the rate-dependent loading response, creep during the hold segment, and the overall response under a separate multi-rate loading protocol.Separately, a fully coupled thermo-chemo-mechanical framework is employed to explore stress-assisted dehydration and reaction-induced deformation. Simulations performed under the experimental loading conditions reveal negligible coupling for kinetic parameters below a certain threshold, suggesting that, within the assumptions of the model and for the assumed kinetic parameter range, the purely mechanical model may be sufficient to interpret the experimental indentation response. Broader parametric sweeps show that reaction-induced deformation can generate apparent rate dependence and creep-like behavior under other conditions. An illustrative comparison shows that compensating changes in elasto-viscoplastic and reaction-induced deformation can produce similar simulated load–displacement responses for the loading protocol examined. This suggests potential ambiguity in assigning deformation mechanisms from such responses. Complementary measurements of reaction extent or composition would help distinguish the proposed mechanisms. These results establish the mechanical response of strontium bromide hexahydrate and clarify both the potential relevance and experimental identification challenges of thermo-chemo-mechanical coupling.
Bayesian calibration of crystal plasticity finite element model (CPFEM) parameters is performed using macroscopic volumetric stress–strain data. Laboratory test data from only a few experiments are generally available to calibrate this complex model, which accounts for many phenomena (anisotropic elasticity and plasticity, rate- and size-dependent behavior, isotropic and kinematic hardening). Deterministic parameter-fitting procedures, which do not explicitly quantify parameter uncertainty, are typically used for calibration. A Bayesian calibration methodology that quantifies uncertainty in the model parameters (via prior and posterior distributions) is desirable, so that the predictions from the calibrated model can reflect this uncertainty. However, using the high-fidelity CPFE model is computationally challenging in sampling-based posterior estimation methods (e.g., Markov Chain Monte Carlo, or MCMC simulations) because the model contains a large number of material and constitutive parameters, making simultaneous calibration computationally expensive and impractical. To tackle this challenge, a subset of key parameters is first identified for calibration based on physical intuition. A surrogate model is then trained to predict CPFEM outputs of interest (Young’s modulus, yield point, and hardening slope) corresponding to given parameter values (for fixed values of other inputs, e.g., loading). The surrogate model greatly reduces the computational burden of Markov Chain Monte Carlo (MCMC) simulation. The effect of incorporating model discrepancy and further reducing the number of model parameters (guided by global sensitivity analyses) on the posterior distributions of key CPFEM outputs is investigated. The proposed methodology is demonstrated by calibrating eleven parameters in a CPFEM for Ti6Al4V. It is found that including a model discrepancy term produces wider posterior distributions and alleviates overconfidence. For this CPFEM, calibrating seven parameters does not significantly change output posterior distributions relative to eleven parameters. Further reduction (four parameters) captures the primary trends, but results in slightly different posterior distributions due to neglected second-order interaction effects. The proposed surrogate-enabled Bayesian framework offers a reproducible template for uncertainty-quantified CPFEM calibration for engineering alloys using only macroscopic tensile test (stress–strain) data.
This paper investigates microstructure–property correlations in helium-assisted cold spray additive manufacturing (CSAM) of Al1050. Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) reveal a bimodal microstructure, with ultrafine-/nanoscale grains formed at particle–particle interfaces by severe plastic deformation during impact and coarse grains retained in particle interiors. To link local microstructure to macroscopic response, two crystal plasticity finite element (CPFE) parameter sets for coarse-grained (CG) and ultrafine-grained (UFG) constituents were inversely identified from nanoindentation load–depth curves. These parameters were assigned to an EBSD-derived representative volume element (RVE) and benchmarked against Voronoi-generated homogeneous RVEs, namely homogeneous coarse-grained (HM-CG) and homogeneous ultrafine-grained (HM-UFG) models, together with extracted constituent subsets. The calibrated CPFE model reproduces the experimental tensile stress–strain response up to 4.5% strain. Field analyses reveal CG/UFG stress partitioning, preferential strain localization within CG clusters, and heterogeneous slip activation governed by compatibility constraints. Dislocation-resolved outputs show two-stage partitioning of statistically stored dislocation (SSD) storage, with a crossover at approximately 1% strain for the baseline initial-density contrast; its occurrence and position depend on the prescribed initial SSD densities. In contrast, geometrically necessary dislocations (GND) localize mainly in interface- and boundary-dominated regions and correlate with strain-gradient intensity. Mechanism-ablation simulations predict a larger strengthening increment from GND-driven back stress than from GND-related forest hardening within the adopted formulation, with larger increments at smaller microstructural length scales. Strength–ductility benchmarking shows that helium-assisted CSAM Al1050 achieves high yield strength while retaining elongation. The results connect the CSAM-induced bimodal microstructure with heterogeneous plasticity and model-dependent dislocation strengthening.
Ductile fracture in metals is history-dependent, with plastic localization typically preceding and guiding crack growth. This work proposes an incremental graph Kolmogorov–Arnold network deep energy method (GKAN–DEM) for quasi-static ductile phase-field fracture. The method employs a reduced J2 incremental potential for elastoplastic response, strictly separates trial and committed states, and combines a neural displacement solve with a mesh-native phase-field subproblem to ensure consistent updates of internal variables. The graph network operates directly on the finite element mesh and predicts displacement increments, while material history variables retain their element-level evolution. Representative benchmarks show that the method accurately reproduces load response, plastic localization and crack paths, with close agreement with finite element solutions. Architecture studies further show that the adopted ChebyKAN parameterization reaches comparable accuracy with fewer staggered displacement solves than the tested fixed-activation controls. The resulting framework offers a general route for extending deep energy methods to path-dependent nonlinear problems in computational solid mechanics.
