PSI - Issue 16

Volodymyr Panasyuk / Procedia Structural Integrity 16 (2019) 3–10 Volodymyr Panasyuk / Structural Integrity Procedia 00 (2019) 000 – 000

7 5

0 π sec 1 2 σ        p

.

(7)

0 0 l l l l

   

Fig. 4b shows the dependence of critical load p * /  0 on crack length l 0 / d * . It is seen from this Figure that use of curve (2) that characterises Griffith formula for small cracks ( l 0 → 0) is physically unjustified, that is a body without crack is infinitely strong. In this case curve 1 (Fig. 4b) plotted according to formula (6) is physically grounded and for Δ l << l 0 these curves are alike. The concept of  c -model was formulated for the first time by Leonov and Panasyuk (1959), and Panasyuk (1960). Later Dugdale (1960) and Wells (1961) published similar but not full models.

5. Metals fatigue: fatigue crack initiation and propagation

It is known that fatigue fracture of the material ( N * ) under cyclic loading is determined as a sum of two periods: N 1 – period of macrocrack formation and N 2 – period of its propagation, that is

1 2    N N N .

(8)

Fig. 5 presents the typical diagram of macrocrack propagation rate ( v ) under cyclic loading of a body. This diagram, as it is known, is used to set the macrocrack propagation period N 2 in the cyclically deformed body. The rectilinear area (2) of this diagram is described by Paris equation ( 7 I I or 10 ( )     n n v CK v K K and the full diagram by equation 0 I I I [( ) /( )]    q th fc v v K K K K , which was established in PhMI by Yarema and Mykytyshyn (1975). In this equation v 0 and q are constant values determined experimentally; K І is SIF loading; K I th is a threshold value of SIF at which crack does not propagate; K I fc is SIF value at which the spontaneous crack propagation occurs. A procedure of minimum fatigue macrocrack initiation period ( N 1 ) evaluation if the ( v – K І )-diagram for a given material is known was developed by Ostash (2015) in PhMI. It is an important achievement in science on materials fatigue. The analysis of scientific results on structural materials fatigue under cyclic loading for the past 20 years is made by Ostash (2015). A thorough report on this problem was delivered by J. Schijve at the 14 th European Conference on Fracture (ECF-14, 2002) in Cracow (Poland). This report with the necessary editorial additions was published in Ukrainian in “ Physicochemical Mechanics of Materials ” journal (see Schijve, (2003)). Considerable achievements of scientists in PhMI on this problem are presented by Andreikiv and Darchuk (1992).

Fig. 5. Curves of crack propagation in cyclically deformed material (or ( v – K )-diagram): 1 – subthreshold region of low; 2 – almost rectilinear region of medium and 3 – region of high crack growth rates up to final fracture, i.e. when loading exceeds values K І fc – constant maximum value of material cyclic toughness.