Issue 50

N. Boychenko et alii, Frattura ed Integrità Strutturale, 50 (2019) 54-67; DOI: 10.3221/IGF-ESIS.50.07 62 A detailed description of the governing parameter in the form of I n -factor definition is given in [16]. It is shown that I n - factor is sensitive to the constraint effects and can be used as constraint parameter. Stressstrain fields under extensive creep can be written in terms of creep stress intensity factor K cr in the following form [23]: 1 * 1 0 1 cr n cr cr n C K BI L          (10) where B and n cr are creep constants, cr n I is the governing parameter of the stress–strain fields for power-law creeping materials, and С* is the С-integral under extensive creep. Methods for determining C- integral at various creep stages and conditions are given in [23-26]. A numerical method was introduced by Shlyannikov [23] to determine the governing parameters of the creep-crack tip fields in terms of the I n integral for power-law creeping materials. This method can be also be used to analyse the creep- damaged material’s fracture resistance characteristics. K cr is the most effective crack tip parameter in correlating the creep– fatigue crack growth rates in power plant materials and can be used for practical purposes [23, 24]. Constraint parameters distributions The stress-strain state analysis of the compressor disc with corner cracks should be performed taking into account in- plane and out-of-plane constraint effects. Shlyannikov et al. [27, 28] showed that different traditional approaches which can successfully describe the in-plane constraint are inaccurate for describing 3D surface cracks. In [29], constraint parameters were analysed as a function of cyclic tension loading and temperature conditions. Characterization of the constraint effects in the present study was performed using the local stress triaxiality h , T Z - factor, I n - factor and cr n I for specified combinations of crack sizes and loading conditions. All parameters were determined at the crack tip distance range of r/a=0.01, where the numerical solution provides a stabilised result. A local parameter of the crack-tip constraint was proposed in [30] as a secondary fracture parameter because the validity of some concepts previously mentioned depends on the chosen reference field. This stress triaxiality parameter is described as follows: 3 3 2 kk ij ij h s s         (4) where kk  and ij s are hydrostatic and deviatoric stresses, respectively. As the function of the first invariant of the stress tensor and the second invariant of the stress deviator, the stress triaxiality parameter is a local measure of the in-plane and out-of-plane constraint effects that is independent of any reference field. The T Z - factor [31] has been recognized to present a measure of the out-of-plane constraint and can be expressed as the ratio of the normal stress components: zz z xx yy T      (5) where  is the Poisson’s ratio,  zz is the out-of-plane stress, and  xx and  yy are the in-plane stresses. Fig. 7 depicts the effect of temperature on the constraint parameters for plastic and creep solutions. Results for two crack front positions (initial and final [front 1 and 3, respectively]) are presented. The T z -factor and stress triaxiality h change in character along the crack tip from the free surface ( R =0) and across the mid-plane (0<R<1) towards the slot surface ( R =1). All considered factors, such as the crack front position, temperature and angular velocity, affect the constraint parameters. However, the crack front position has the most significant influence. Whilst crack size increases, qualitative and quantitative changes in constraint parameters distributions occur. This occurrence contrasts with temperature and angular