将研磨加工中磨粒与工件表面作用过程近似为受法向载荷和切向载荷共同作用下移动的尖锐压头对表面的作用过程，基于压痕断裂力学理论，分析了移动磨粒作用下材料的应力状态、中位裂纹的成核位置和扩展方向。综合考虑弹性应力场、残余应力场及切向载荷对中位裂纹扩展的影响，给出了中位裂纹扩展长度计算公式。建立了亚表面损伤深度与表面粗糙度之间的理论模型。使用磁流变抛光斑点技术测量了微晶玻璃研磨亚表面损伤层深度。将模型预测理论值与实验测量值进行对比，结果表明两者之间的误差控制在5.56%以内，吻合较好。利用该模型可以实现光学材料研磨亚表面损伤深度的快速、简便和准确预测。

The process of abrasive machining in lapping is considered as a moving sharp indentor subjected to normal force and tangential force. Based on indentation fracture mechanics theory, the grinding stresses of material, the location of median crack initiation and the direction of median crack propagation beneath an abrasive are analyzed. The calculation formula of median crack propagation length is analyzed by synthetically considering the contribution of elastic stress field, residual stress field and tangential force beneath the abrasive. A theoretical model of relationship between subsurface damage and surface roughness is established. A method of magnetorheological finishing (MRF) spot technique is proposed to the depth of subsurface damage. Predicted results are compared with experimental results, result shows that the error between predicted results and experimental results is less than 5.56%. The theoretical model can be used for prediction the depth of subsurface damage of optical materials in lapping process rapidly, expediently and accurately.