Issue 30

Yu.G. Matvienko, Frattura ed Integrità Strutturale, 30 (2014) 311-316; DOI: 10.3221/IGF-ESIS.30.38 312 Theoretical and numerical analysis of three-dimensional stress fields in the vicinity of through-thickness crack tip under mode I and mixed mode (I + II) loading is carried out to estimate the effect of thickness on the nonsingular xx T and zz T - stresses. T HE EFFECT OF OUT - OF - PLANE CONSTRAINT ON THE CRACK TIP PLASTIC ZONE Basic equations he components of the stress field, which take into consideration three-dimensionality of the stress state near mode I crack front in isotropic elastic body, can be represented in the manner of asymptotic formulas given in Ref. [3] 1 3 3 cos 1 sin sin sin 2 cos cos 2 2 2 2 2 2 2 1 3 3 cos 1 sin sin sin cos cos 2 2 2 2 2 2 2 1 3 3 sin cos cos cos 1 sin sin 2 2 2 2 2 2 2 xx I II xx yy I II xy I II K K T r K K r K K r                                                                                      2 cos sin 2 2 2 0, 0 zz I II zz yz zx zz zz xx K K T r T E T                           (1) Here,  xx ,  yy ,  zz ,  xy ,  yz ,  zx , – components of the stress tensor which define stress state at the arbitrary point near the crack tip; r and  – polar coordinates (Fig. 1); I K and II K are stress intensity factors,  is Poisson's ratio. The model of the crack tip plastic zone The von Mises yield criterion can be employed to estimate the influence of the nonsingular xx T and zz T -stresses in the vicinity of the crack tip on the shape and size of the plastic zone under mode I loading [4, 5]. In this case, the yield criterion can be written in the form         2 2 2 2 2 2 2 6 2 xx yy yy zz zz xx xy yz zx Y                    , (2) where Y  is the yield strength. Figure 1 : Stress components in the vicinity of the crack tip. Substitution of asymptotic formulas (1) into the criterion (2) allows determining size p r of the crack tip plastic zone T