Issue 41

V.Shlyannikov et alii, Frattura ed Integrità Strutturale, 41 (2017) 291-298; DOI: 10.3221/IGF-ESIS.41.39 289 where t is creep time,   e is the Mises equivalent stress and     0 FEM FEM e e . As is usual in mathematical analysis a dot over a displacement quantity denotes a time differentiation. The numerical parameter I n -integral and the  -variation angular functions of the suitably normalized functions   ij and  i u depend on the creep exponent n . In the сontrary to the traditional models for creep crack growth prediction that the I n -integral is a function only the creep exponent, in the present work it will be demonstrated that this governing parameter depends on the creep damage function and the creeping crack tip stress-strain fields. R ESULTS AND DISCUSSION lane strain finite element analysis was performed based on ANSYS FE-code for study of the creep damage effect on the nonlinear crack tip stress-strain fields for center cracked plate (CCP) subjected to a uniform tensile stress of magnitude  =50 MPa. The CCP configuration contains an internal crack of length 2a =20mm ( a/w =0.01, where w is plate width). The 2D plane strain eight-node isoparametric elements were applied to CCP geometry. To consider the details of large deformation and blunting of the crack tip, a typical FE-mesh was used with the initial notch root radius  /a =0.01. For creeping undamaged and damaged materials we consider five stages of creep time which is varied from t = 1 hrs up to t = 10 3 hrs. The creep properties of analyzed material at the elevated temperature of 550  C are summarized in Table 1. E [GPa]  B [1/(MPa^n  hr)] n C [1/(MPa^m  hr)] 200 0.3 1  10 -14 5.0 1  10 -10 Table 1 : The creep properties of material. Employing the constitutive equations (13,14) directly into the FEM rate-dependent formulation and using an explicit time integration procedure leads to a standard Runge-Kutta integration scheme in which the finite element stiffness matrix is derived from elastic moduli. After the solution of a nonlinear problem, the ANSYS output file is used as an input data for special code developed to determine dimensionless stress-strain angular distributions, damage contour and creep stress intensity factor. Note that for creeping material, the damage evolution depends generally on the creep time, magnitude of the applied loading, crack geometry and material properties. Due to complexities we consider in the present study different creeping stages. In this case it is useful to normalize a current creep time t by the characteristic time t T for transition from small- scale creep to extensive creep which is given as [7]         2 2 1 1 1 T t n EC t t K (20) where K 1 is elastic stress intensity factor,  is the Poisson's ratio, E is the Young's modulus and C -integral is given by Eq.(16). In our case the transition time for given nominal stress  =50 MPa and crack length a =10mm is t T = 21.88 hrs. In order to explore the effects of damage formulation, comparisons for  =50 MPa and creep time t / t T = 45.7 are made in Fig.2 between the HRR-field, undamaged creep field and defective fields at the crack tip in creeping solids. Near the crack tip the influence of the damage degree is evident and the sufficient difference between the HRR and creep damage fields is observed. The data presented in Fig.2 demonstrate the effect of creep damage behaviour on the crack tip fields. Furthermore, it is no longer true that  -variations of the stresses are independent of creep damage parameter  . A fracture damage zone (FDZ) or fracture process zone (FPZ) local to the crack tip is defined as a core where microstructure damage accumulates until crack growth takes place at the macroscopic scale level. Microstructure damages can include void nucleation, growth and coalescence and it is assumed that local fracture will occur at the crack tip when the creep ductility of the material is exhausted there. This process is governed by combination of the maximum principal stress  mp and the stress invariants J 1 and  2 J . Once these stress invariants have been determined during FEM procedure the creep damage distribution or the FPZ shape and size are obtained by a numerical integration of Eq.(13). In Fig.3 P