Phase field modeling of thermal-mismatch induced fracture in glass-ceramic sealing of solid oxide cell stacks

Thermal mismatches during cooling of solid oxide cell (SOC) stacks generate stresses in glass–ceramic sealings, driving cracks that may threaten gas tightness. Conventional strength-based or linear elastic fracture mechanics (LEFM) approaches are limited by geometry sensitivity or the requirement for predefined crack paths. To overcome these limitations, a phase-field fracture model with stack homogenization is developed and validated. This approach is insensitive to geometric irregularities and eliminates the need of predefined crack paths, and can be applied to full stacks. The study quantifies the impact of sealing thickness, thermal expansion coefficient (TEC), and external compression: for a typical stack design, crack growth remains localized; failure risk rises for thicker seals ( ) or severe mismatch with smaller TEC of seals ( ), while moderate compression suppresses propagation. To provide guidance for sealing designs, thickness–TEC design maps are introduced, rendering smooth iso-damage contours and a single failure boundary derived from energy scaling; external load appears as a translation of the TEC axis, shifting the boundary accordingly. The design maps allow for the rapid identification of optimal material-geometry combinations that ensure structural integrity under operational loads. This work provides a non-existing pathway for the reliable design and failure prevention of brittle sealants in SOC stacks.