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
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