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Phase field modeling of ferroelastic variant switching in yttria-stabilized t′zirconia with strain gradient elasticity and interface tension

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Abstract

The 6–8 wt% yttria-stabilized zirconia with a tetragonal structure (t′-YSZ) is extensively employed in thermal barrier coatings. The exceptional fracture toughness of t′-YSZ can be attributed to its distinctive ferroelastic toughening mechanism. Micro-structure and interface tension play a critical role in ferroelastic variant switching at the micro- and nano-scale. This paper presents an original thermodynamically consistent phase field (PF) theory for analyzing ferroelastic variant switching at the micro- and nano-scale of t′-YSZ. The theory incorporates strain gradient elasticity using higher-order elastic energy and interface tension tensor via geometric nonlinearity to represent biaxial tension resulting from interface energy. Subsequently, a mixed-type formulation is employed to implement the higher-order theory through the finite element method. For an interface in equilibrium, the effects of strain gradient elasticity result in a more uniform distribution of stresses, whereas the presence of interface tension tensor significantly amplifies the stress magnitude at the interface. The introduction of an interface tension tensor increases the maximum value of stress at the interface by a factor of 4 to 10. The nucleation and evolution of variants at a pre-existing crack tip in a mono-phase t′-YSZ have also been studied. The strain gradient elasticity is capable of capturing the size effect of ferroelastic variant switching associated with microstructures in experiments. Specifically, when the grain size approaches that of the specimen, the critical load required for variant switching at the crack tip increases, resulting in greater dissipation of elastic energy during ferroelastic variant switching. Moreover, the interface tension accelerates the evolution of variants. The presented framework exhibits significant potential in modeling ferroelastic variant switching at the micro- and nano-scale.

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Authors and Affiliations

  1. College of Engineering, BIC-ESAT, Peking University, Bei**g, 100871, China

    QianQian Zhou & YueGuang Wei

  2. School of Advanced Materials and Nanotechnology, **dian University, **’an, 710126, China

    YiChun Zhou & Li Yang

  3. Frontier Research Center of Thin Films and Coatings for Device Applications, Academy of Advanced Interdisciplinary Research, **dian University, **’an, 710126, China

    YiChun Zhou & Li Yang

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  1. QianQian Zhou
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  2. YueGuang Wei
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  3. YiChun Zhou
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  4. Li Yang
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Correspondence to YueGuang Wei or Li Yang.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11890684, 12032001 & 51590891), the Technology Innovation Leading Program ofShaanxi (Grant No. 2022TD-28), and Hunan Provincial Natural Science Innovation Research Group Fund (Grant No. 2020JJ1005).

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Zhou, Q., Wei, Y., Zhou, Y. et al. Phase field modeling of ferroelastic variant switching in yttria-stabilized t′zirconia with strain gradient elasticity and interface tension. Sci. China Technol. Sci. 67, 1443–1457 (2024). https://doi.org/10.1007/s11431-022-2486-x

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