Abstract The determination of fracture parameters at cracks in ferroelectrics under large-scale domain switching is still a great challenge. In order to evaluate the crack-tip mechanical and electrical field intensity factors, the interaction integral (I-integral) technique is further developed to cope with the heterogeneous microstructures based on the polarization distribution and crack tip fields from phase field simulations. The enhanced I-integral exhibits several merits over previous techniques for determining the crack-tip intensity factors. First, small-scale switching assumption is unnecessary. Second, the intensity factors of different modes are decoupled. Third, it is independent of integration area size, regardless of the presence of grain boundaries and domain walls. These advantages ensure the successful application of the enhanced I-integral to study toughening effects in ferroelectric polycrystals due to large-scale domain switching. Using this approach, a tensile test of PbTiO3 ferroelectric polycrystals with an impermeable crack is simulated. Simulations show that domain switching initiates not only from the crack tip but also from the grain boundaries due to high polarization gradient and stress concentration. Large-scale switching triggered by a critical load reduces the crack-tip stress intensity factors anomalously. In comparison to single crystals, the critical load for polycrystals is lower and even vanishes due to grain orientations. The results also demonstrate that the I-integral method possesses satisfactory accuracy and good area-independence for grain boundaries and domain walls.

中文翻译：

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大尺度切换下铁电多晶裂纹尖端参数的相场分析

摘要 在大规模域切换下确定铁电体裂纹处的断裂参数仍然是一个巨大的挑战。为了评估裂纹尖端机械和电场强度因子，基于极化分布和来自相场模拟的裂纹尖端场，进一步开发了相互作用积分（I-积分）技术来处理异质微观结构。与先前用于确定裂纹尖端强度因子的技术相比，增强的 I 积分显示出几个优点。首先，小规模切换假设是不必要的。其次，不同模式的强度因子是解耦的。第三，它与集成区域大小无关，无论是否存在晶界和畴壁。这些优势确保了增强的 I 积分成功应用于研究铁电多晶由于大规模域切换而产生的增韧效应。使用这种方法，模拟了具有不可渗透裂纹的 PbTiO3 铁电多晶的拉伸试验。模拟表明，由于高极化梯度和应力集中，域切换不仅从裂纹尖端开始，而且从晶界开始。由临界载荷触发的大规模切换异常地降低了裂纹尖端应力强度因子。与单晶相比，多晶的临界载荷更低，甚至由于晶粒取向而消失。结果还表明，I 积分方法对晶界和畴壁具有令人满意的精度和良好的面积无关性。