PSI - Issue 59

Ihor Dmytrakh et al. / Procedia Structural Integrity 59 (2024) 74–81 Ihor Dmytrakh et al. / Structural Integrity Procedia 00 (2024) 000 – 000

76

3

  ; i da dN f C K  

(1)

where da / dN is the fatigue crack growth rate; a is the crack size; N is the number of loading cycles; Δ K is the stress intensity factor range per fatigue loading cycle; C i are some constants which characterize the material and test conditions; i = 1, 2, 3… Dependencies of type (1) are called the fatigue crack growth rate diagrams (Dmytrakh et al. (2012)). Usually, these diagrams are plotted in a logarithmic coordinate system and are placed between two limited values of the stress intensity factor range Δ K th and Δ K fc (Fig. 1). Here Δ K th is the threshold value of the stress intensity factor at which the fatigue crack does not propagate, and Δ K fc is the critical value of the stress intensity factor range at which the spontaneous catastrophic fracture of the material occurs.

da dN

  n da dN C K   

Paris region

K 

fc K 

th K 

Fig. 1. The fatigue crack growth rate schematic diagram.

In terms of Δ K change, the diagram of the fatigue crack growth rate can be divided into three sections: low, medium and high amplitude. In low and high amplitude areas small changes in the Δ K value lead to a significant increase in the fatigue crack growth rate (in the order of magnitude or more). The medium amplitude section or so called Paris region (Fig. 1) is sloping and it is linear in the double logarithmic coordinate system, which gives grounds to describe its power function according to Suresh (1998):   n da dN C K   (2) where C and n are experimentally determined constants which depend on the material and test conditions. Since the range of the K  changes, the Paris section occupies the predominant part of the diagram; using dependence (2) it is possible to describe fully the regularities of the fatigue crack propagation in the material under different test conditions. Thus, the diagram of the fatigue crack growth rate (Fig. 1) can be schematized as the linear within the Δ K th ≤ Δ K ≤ Δ K fc range. Such schematization of the fatigue crack growth diagram is very suitable to calculate the residual durability N f of the defected pipe. In this case the parameter N f can be defined as

a

da

fc

N





f

,

(3)

n

  

C K

a

th

where N f is the number of cycles of loading to fracture of the pipe with the crack-like defect of the given shape and size; a th and a fc threshold and critical size of crack, respectively (Dmytrakh et al. (2012)). Below, the equation (3) was used for determination of the residual durability N f of the pipelines of different sizes, which contain the crack-like defects of different types. At that the calculations were made for different values of the hydrogen concentration C H in the metal of the pipelines, i.e. the dependencies N f = F ( C H ) were received. On this base the comparative assessment of different defect types danger in pipelines was done.