裂纹尖端三维变形场的细观力学研究

Meso-mechanical Investigation on Three-dimensional Deformation Fields around a Crack Tip

裂纹尖端的变形在裂纹萌生和扩展过程中起着重要的作用。本文从理论上讨论了裂纹尖端面内变形场 ,对理论解和级数解作了比较 ,结果表明该级数解收敛很快 ,取到第 3项已接近理论解。通过试验测量了裂纹尖端的三维变形场 ,分别将面内变形场和离面变形场与理论面内变形场和有限元计算的离面变形场作了比较。表明裂纹尖端 3个方向的变形同时存在 。

During crack initiation and propagation, the deformation fields around a crack tip play an important role. In essence, the deformation at the tip of any crack is three dimensional. The investigation of the three dimensional deformation will be useful to better understand the fracture behavior of the material. In this paper, three dimensional deformation fields around a crack tip are discussed theoretically, and series expansion solutions are derived. Comparison of theoretical solutions against series expansion solutions is made. The results indicate that the series expansion solutions converge very fast, taking the third item, it is very close to the theoretical solutions. Three dimensional deformation fields are obtained through experiments. Furthermore, the in plane deformation fields and out of surface deformation fields are compared with theoretical solutions and numerical analysis results respectively. It is shown that the deformation fields around a crack tip always display three dimensional features, and the deformation in any direction can not be omitted at mesoscopic level.