钇铝石榴石（YAG）晶体是制造固体激光器的重要材料，超精密磨削是加工YAG晶体等硬脆材料零件的重要方法，研究硬脆材料加工表面的微观变形、脆塑转变机理对超精密磨削加工具有重要的指导作用。为了实现YAG晶体低损伤磨削加工，获得高质量表面，基于弹塑性接触理论和压痕断裂力学，通过分析单磨粒划擦作用下材料表面的变形过程，考虑材料的弹性回复、微观下力学性能的尺寸效应，建立了脆塑转变临界深度的预测模型，并计算得到YAG晶体的脆塑转变临界深度为66.7 nm。在此基础上，通过不同粒度砂轮超精密磨削YAG晶体试验对建立的脆塑转变临界深度预测模型进行验证，并计算不同粒度砂轮在相应工艺条件下的磨粒切深。结果表明，磨粒切深高于脆塑转变临界深度时，YAG晶体磨削表面材料以脆性方式被去除，磨削表面损伤严重；磨粒切深低于脆塑转变临界深度时，磨削表面材料以塑性方式被去除，能够获得高质量磨削表面，加工表面粗糙度达到1 nm。建立的脆塑转变临界深度预测模型能够为YAG晶体的低损伤超精密磨削加工提供理论指导。

Yttrium aluminum garnet （YAG） crystals are widely used for manufacturing solid-state lasers， and ultraprecision grinding is critical for machining hard and brittle material parts， such as YAG crystals. The investigation of microdeformation and brittle-to-ductile transition mechanisms of hard and brittle material-machined surfaces is necessary for ultraprecision grinding. Based on the elastic-plastic contact theory and indentation fracture mechanics， a model for predicting the critical depth of brittle-to-ductile transitions was established to achieve low-damage grinding of YAG crystals and obtain high-quality surfaces. The deformation process of the material surface under the action of a single abrasive scratch was analyzed， considering the elastic recovery of the material and the size effect of micromechanical properties. The critical depth of the brittle-to-ductile transition of the YAG crystal is 66.7 nm. The proposed prediction model of the critical depth of the brittle-to-ductile transition was verified by ultraprecision grinding of YAG crystals with grinding wheels of different grain sizes. In addition， the grit-cutting depths of different grain-size grinding wheels under the corresponding process conditions were calculated. The results show that when the grit-cutting depth is more extended than the critical depth of the brittle-to-ductile transition， the surface material of the YAG crystal is removed in a brittle manner， and the grinding surface is severely damaged. However， when the grit-cutting depth is less than the critical depth of the brittle-to-ductile transition， the grinding surface material is removed in a ductile manner， high-quality grinding surface can be obtained， and the machined surface roughness can reach 1 nm. The proposed model for predicting the critical depth of the brittle-to-ductile transition provides theoretical guidance for low-damage ultraprecision grinding of YAG crystals.