PSI - Issue 23

Sergiy Kotrechko et al. / Procedia Structural Integrity 23 (2019) 413–418 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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decades, a significant number of articles have been published and a lot of conferences have been focused on this issue. However, the Local Approach didn’t receive the expect ed utilization. This is mainly due to unnecessarily oversimplified description of the local cleavage event in conventional version of LA. Application of the Weibull two-parameter distribution, i.e. neglecting the role of threshold stress th  appears to be one of the unjustified simplifications of the LA to the cleavage fracture. According to experimental data, the value of th  for typical structural steels is about 1000 MPa [Kotrechko et al. (2017)]; therefore, the threshold stress th  c an’t be set equal to zero. One of the indirect evidences of the crucial effect of the threshold stress magnitude on the fracture characteristics is a significant change in the values of the Weibull distribution parameters at transition from two- to three-parameter distribution [Ruggieri. (2001)]. Several detailed discussions about the three-parameter Weibull stress model and toughness scaling on Weibull stress, were carried out by Gao et al. (1998) and Gao et al. (2000). Possibility of invalid calibration of shape parameter m and scale parameter u  in case of neglecting th  has been found one of the considerable conclusions; in particular in relation to the shape parameter m , which can be then will be systematically overestimated [Gao et al. (2000)]. According to overview of Pineau (2006), rational calibration procedure for th  remains an open issue nowadays. In the work of Kotrechko et al. (2001),a two-scale version of LA was proposed, in which the probability of cleavage initiation was determined by a sequential analysis of the processes of formation, instability and propagation of the crack nuclei in a polycrystalline aggregate. This made it possible to ascertain the main physical effects governing the cleavage fracture in metals and alloys, i.e. to create the physical basis of a LA. Within the framework of two-scale version of LA this paper presents interpretation of the threshold cleavage stress of a polycrystalline metal, an experimental technique for determining the th  value, as well as an analysis of the effect of th  value on both the nature of the temperature dependence and scatter limits of fracture toughness of structural steels. 1. Theoretical background From a mathematical point of view, the key element of the LA to cleavage is the Weibull distribution. Correct use of the Weibull distribution, and, accordingly, the choice of a procedure for parameters calibration of this distribution requires accounting for the quantitative features of the cleavage initiation micromechanism in metals and alloys. Most existing versions of the LA to cleavage account the fact that the crack nuclei (CN), which don't exist initially in metal, but are continuously generated during its plastic deformation, are the cause for the cleavage fracture. In a number of papers [Kotrechko (2001); Kotrechko (2013); Bordet (2005)], attention was focused on the peculiarities of the cleavage nucleation stage in the metal. It lies in the fact that only freshly nucleated CN can initiate cleavage. The crack nuclei that aren't unstable at the time of formation become blunt, and later don't participate in the cleavage fracture initiation. The rate of CN generation per unit volume, ρ, depends on the plastic strain level. This is important because the local plastic strain ahead of a crack / notch, may change by more than an order of magnitude. In addition, t emperature has a significant effect on ρ [Kotrechko (2013)]. From a mathematical point of view, this means that the reference volume     / 1 0 0 V V will not be constant, as accepted in the most conventional models. Its magnitude is a function of the both local plastic strain e and temperature T . The dependence was quantified by [Kotrechko (2013)], in analytical form, it may be approximated as follows:

      1 0       1 c 0 e b e

  

c e e 

e a e ,

(1)

c

  

c e e e   max

,

(2)