Multiphysics Modeling of Thermo-viscoelastic Damage in Functionally Graded Abradable Coatings with Probabilistic Geometric Tolerance Analysis

In aircraft engines, functionally graded abradable coatings are used to control blade-tip clearance, but their durability is governed by effects that are often treated separately in existing models, including temperature-dependent viscoelastic softening, progressive damage, deposition-induced microstructural modulation, and geometric tolerances. Models that consider these effects independently may underestimate damage initiation because smooth material gradients evaluated at nominal geometry cannot capture the local stress concentrations produced by microstructural modulation and geometric variability. This study integrates these effects within a unified multiphysics–probabilistic framework. The solved domain is a local through-thickness coating column driven by prescribed strain and temperature histories that include thermal eigenstrain and coating–substrate expansion mismatch. The results show that periodic property modulation increases end-of-cycle damage relative to the monotonic gradient and concentrates the maximum stress within a localized modulation crest. Propagating symmetric geometric tolerances through the coupled solver produces a strongly right-skewed damage distribution and a higher classification-level exceedance probability for the modulated gradient than for the monotonic gradient. This exceedance behavior cannot be obtained from a deterministic analysis performed at nominal geometry. The exceedance probability is also evaluated as a continuous function of the classification level to assess the sensitivity of the comparison to the selected screening criterion. The implementation is verified through spatial and temporal refinement, closed-form unit tests, nested Monte Carlo convergence with Wilson confidence intervals, and a hold-out-validated polynomial response surface. Numerical verification is clearly distinguished from experimental validation, and the simulated case is presented as a generic benchmark rather than an identified material model. The framework links deposition parameters and tolerance bands to damage-exceedance risk, supporting reliability-oriented screening of graded and multilayer coating systems.