Phase Field Study of Ferroelastic Toughening Mechanisms of Polycrystalline t^′-YSZ

Zhou Fang^#, Jiaqi Zhong^#, Jun Luo^*, Yuanzun Sun
Department of Engineering Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan, China
* Corresponding Author: Jun Luo. Email: email
# These authors contributed equally to this work
(This article belongs to the Special Issue: Advances in Computational Fracture Mechanics: Theories, Techniques, and Applications)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2026.081333

Received 28 February 2026; Accepted 27 May 2026; Published online 11 June 2026

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Abstract

The t^′ phase of yttria-stabilized zirconia (t^′-YSZ) is the most extensively used top coat material in thermal barrier coatings (TBCs). Its relatively high fracture toughness is among the most important factors that enable t^′-YSZ to stand out from other candidate ceramics. Unveiling the toughening mechanisms of t^′-YSZ is conducive to the development of next-generation top-coat materials. In this paper, a coupled phase field model is proposed to study crack growth and domain evolution in polycrystalline t^′-YSZ. Two distinct polycrystal microstructures are considered to investigate the impact of the initial domain structure on the toughening behavior. In Polycrystal I, each grain consists of a single domain of the t^′ phase. In Polycrystal II, the c-t^′ phase transformation gives rise to a twinned domain configuration. A unified phase field model is proposed to simulate the coupled process of crack propagation and domain evolution within both polycrystals. The localized toughening effect resulting from domain switching on crack advancement is characterized using the energy dissipation rate. Numerical findings reveal that the interplay between fracturing and domain evolution causes the crack to follow tortuous paths in both types of polycrystals, potentially enhancing the overall fracture toughness. The domain reorientation enhances the local crack growth resistance in both materials, though the domain evolution characteristics are distinctly different. The effects of domain evolution and the polycrystal microstructure on the crack growth behavior and the local toughening effect are systematically discussed. The findings reported in this paper offer valuable insights into the fracture toughening mechanisms of t^′-YSZ ceramics. The phase field approach developed in the paper provides a powerful numerical framework for evaluating the fracture toughness of ferroelastic materials.