Effect of T-Stress and Non-singularity Terms on Stress IntensityFactor of a Crack

摘要

The singular stress field at the crack tip can be presented by the Williams series as σρθλκ∑ σρ（ρ，θ）＝n∑k=1 Akρλkσρk(θ) σθ（ρ，θ）=n∑k=1 Akρλkσθk(θ) σρθ（ρ，θ）=n∑k=1 Akρλkσρθk(θ)where the exponent λκis the stress singularity order,σθκ(g=ρ，θρθ)are the associated stress angle functions which represent the stress components in the corresponding directions.Aκ(κ=1,2,1,N)are the associated amplitude coefficients,N is the number of the eigenvalues truncated. In traditional linear fracture mechanics, only the singularity terms corresponding toλκ<0 are take into account in Eq.(1).However, the T-stress term corresponding to λκ=0 and non-singular terms corresponding to λκ>0 at the Williams series expansion play a significant role in determining the stress and strain fields and the energy around the crack tip which in turn can affect the fracture of the specimen predicted by different fracture criteria. But the calculation of the T-stress term and the non-singularity terms in Eq.(1) are very difficult. In this paper, a small rotundity with radius ρis dug out from the tip of the crack. The displacement and stress fields are expressed by Williams series in this small rotundity region. The remaining region is modeled by boundary element method because there is no singularity. By the continuity conditions between the rotundity and the remaining structure, all the unknown values on the boundary and all the Ak in Eq.(1) can be obtained. By this means, the T-stress and the non-singular terms are determined by the boundary element method. Then the effect of the T-stress and the non-singular terms on the calculation of the stress intensity factor of the crack is studied. The results show that the stress intensity factor taking account into the T-stress and the non-singularity terms is more approaching to the experiment results.