Abstract Ferroelastic domain switching is considered as that a twin undergoes a lattice orientation described by a deviatoric eigenstrain in this work. A continuum analysis, based on Eshelby equivalent inclusion theory, is derived to study the nucleation and evolution of twin near a pre-existing crack tip (Mode-I) in a mono-phase tetragonal crystal, in an attempt to achieve a better understanding of the contribution that twinning makes to the toughening effect. The analysis develops progressively from the homogenous isotropic, inhomogeneous isotropic to the general anisotropic conditions; and several analytical solutions are evidenced through phase field simulations. Two important critical stresses, defined as the nucleation stress and the fracture-induced twinning (FIT) stress, are found to determine the twin evolution; specifically, the nucleation stress is related to the twinning in a defect-free solid, and the FIT stress is related to the twinning in the vicinity of crack tip. Moreover, considering the inhomogeneity effect, the change of the stress intensity factor (SIF) due to a ferroelastic twin is derived, which provides evidence that the modulus toughening effect originating from the elastic misfit between the parent and twin can be ignored at a relative low applied SIF. Theoretical analysis and phase field simulations both clarify that the shielding/anti-shielding effect to the crack tip is dependent on the nucleation location and the twin size during evolution. The best toughening formula of a ferroelastic ceramic can be obtained by decreasing the FIT stress and increasing the change of SIF simultaneously through adjusting certain material parameters.

中文翻译：

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裂纹尖端附近与铁弹性孪晶形核和扩展相关的应力状态的理论和相场建模

摘要 在这项工作中，铁弹性域切换被认为是孪晶经历由偏本征应变描述的晶格取向。基于 Eshelby 等效夹杂理论的连续介质分析被推导出来研究单相四方晶中预先存在的裂纹尖端（模式 I）附近孪晶的成核和演化，试图更好地理解孪生对增韧效果的贡献。分析从均匀各向同性、非均匀各向同性逐渐发展到一般各向异性条件；并且通过相场模拟证明了几种解析解。发现两个重要的临界应力，定义为成核应力和断裂诱导孪晶 (FIT) 应力，可确定孪晶演化；具体来说，形核应力与无缺陷固体中的孪晶有关，而 FIT 应力与裂纹尖端附近的孪晶有关。此外，考虑到非均匀性效应，推导出了铁弹性孪晶引起的应力强度因子（SIF）的变化，这证明了母体和孪晶之间的弹性错配引起的模量增韧效应可以在相对较低的情况下忽略不计。应用 SIF。理论分析和相场模拟都阐明了对裂纹尖端的屏蔽/反屏蔽效果取决于演化过程中的成核位置和孪晶尺寸。通过调整一定的材料参数，同时降低FIT应力和增加SIF的变化，可以获得铁弹性陶瓷的最佳增韧配方。