U形切槽三点弯曲梁的应力集中系数

三点弯曲梁被广泛应用于测试材料的断裂性能，但对准脆性材料难以制作尖锐的裂纹，因此考虑三点弯曲梁具有U形切槽，此时可以用应力集中系数来表征切槽端部的应力峰值。用有限单元法计算了三点弯曲梁的U形切槽顶部的应力集中系数，给出了应力集中系数随切槽深度和切槽宽度变化的规律，弥补了现有应力集中系数手册的欠缺。将U形切槽梁三点弯曲的应力集中系数与对应的U形切槽梁纯弯曲的应力集中系数作比较，发现前者比后者小，最大相对偏差达到-7.3%。将所得的应力集中系数应用于三点弯曲梁的无量纲最大承载力和挠度的分析，可以全面考虑切槽深度和切槽宽度的影响。

Stress Concentration Factors for Three-Point Bending Beam with Single edge U-shaped Notch

Three-point bending beam is widely used in test of fracture properties for materials.However, a sharp crack can hardly be prepared for the specimen of quasi-brittle materials, alternatively it is reasonable to consider a U-shaped notch, then use stress concentration factor (SCF) to characterize the peak stress at the notch bottom. We studied the SCFs of the three-point bending beams with a U-shaped notch using finite element method, and the results show the variation of the SCF with changing notch depth and notch width, filling the existing vacancy in SCF handbooks. The SCF at the bottom of U-shaped notch of three-point bending beam is smaller than that of the counterpart pure bending beam, and the largest relative difference is -7.3%. We applied the results to determine the dimensionless maximum load bearing capacity and the corresponding deflection of the three-point bending beams, the effect of notch depth and notch width can be considered in a comprehensive way