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

Abstract

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. 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 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.