PSI - Issue 5

U. Zerbst et al. / Procedia Structural Integrity 5 (2017) 745–752 U. Zerbst et al./ Structural Integrity Procedia 00 (2017) 000 – 000

748

4



a a

  

  th K a K      th ,LC

(5)

a a a

  

0





2

 th,eff K K 1 K K      th,eff

th,LC

a* a

 

with

(6)



0

2

th,LC

The experimental determination of the cyclic R curve is, e.g., described in Tabernig & Pippan (2002). In addition to this, the authors of this paper have proposed a multi-specimen technique (Zerbst & Madia, 2014). Initial crack size Within the frame of an S-N curve relevant fracture mechanics approach the initial crack size is determined by one of the options schematically illustrated in Fig. 4. As mentioned above, microstructurally short cracks are arrested at obstacles such as grain boun daries. The reason is an increased effort in building-up the plastic zone ahead of the crack when the latter propagates from one into an adjacent grain with different crystal orientation. However, since the crystal orientation in multiple grain systems usually follows a stochastic pattern, the crack size at arrest will be larger than just one grain size. Murakami (2012) reports three grain sizes for an annealed 0.13 C steel. Things are, however, even more complicated because crack arrest can also occur at the (physically) short crack stage due to the build-up of the crack closure effects and it will also be affected by notches due to the decreasing local stresses away from the notch root. Zerbst & Madia (2014) applied a cyclic R curve approach for determining the crack size that just would arrest at the load level of the endurance limit and they postulated this as the initial crack size. The principle is illustrated as option (a) in Fig. 4. The cyclic crack driving force of the component,  K p is determined from  J (see above) by p K J E      (7) (E = E for plane stress and E/(1-  2 ) for plane strain conditions;  = Poisson’s ratio) for different crack depths assuming the crack shape semi-circular. The cyclic R curve is fixed by  K th,eff at the ordinate and shifted along the abscissa until it fulfils the tangency criterion with the crack driving force curve. As the result, the initial crack size a i is determined. When this crack is arrested after some extension, its size will be d (see Figs. 2 and 3). Fatigue cracks are usually initiated at material or geometrical defects such as non-metallic inclusions, pores or micro-shrinkages, corrosion pits, surface scratches etc. As long as they arrest at a later stage, these defects will not be fatigue life relevant. However, if their sizes are larger than the arrest crack size determined as described above, the picture changes. In such a case, the size of the defect has to be taken as the initial crack size such as illustrated by option (b) in Fig. 4.

Fig. 4: Definition and determination of a fatigue life relevant initial crack

size for the fracture mechanics analysis.