Issue 19

L. Kunz et alii, Frattura ed Integrità Strutturale, 19 (2012) 61-75; DOI: 10.3221/IGF-ESIS.19.06 69 structure in the crack initiation process and the specific mechanism of initiation are not sufficiently understood. Contrary to the CG Cu, where the specific dislocation structures associated with cyclic slip bands are described thoroughly, there are no similar and conclusive observations on UFG Cu. Fatigue crack propagation resistance The decreasing grain size of metals and alloys results generally in an increase of strength. Improved ultimate tensile strength and yield strength does not mean by itself that the fine-grained materials exhibit also better properties as regards their resistance against the damage by fatigue crack growth. Propagation of long cracks in CG Cu can be well described by linear facture mechanics. There is a good correlation of the crack propagation rate, da/dN, (a is the crack length and N number of cycles), with the stress intensity factor K. The experimentally determined crack propagation curves for stress symmetrical loading are shown in Fig. 12. The crack rate was in this case determined on sheet central cracked tension specimens manufactured from Cu of 99.99 % purity. The cycling was conducted under symmetrical load-controlled conditions. It is evident that the grain size influences the crack rate. Cracks in the fine-grained Cu with the grain size of 70  m propagate faster than in the coarse grained Cu having the grain size of 1.2 mm [36]. The experimental points in Fig. 12 can be well approximated by the equation: / ( ) m m a ath da dN A K K   (3) where A = 1.1 x 10 -10 (mm/cycle)(MPa√m) -m and m = 7.0 for fine grained Cu and A = 5.0 x 10 -11 (mm/cycle)(MPa√m) -m and m = 7.1 for coarse grained Cu. The threshold value of the stress intensity factor, below which the long cracks do not propagate, is K ath = 2.1 and 2.7 MPa√m for fine-grained and coarse grained Cu, respectively. From this data it is evident that from the point of view of crack propagation the fine-grained Cu is worse than the coarse-grained one. There are a plenty of models for propagation of long cracks. They can be divided into three basic groups: 1) models assuming that the plastic deformation in the plastic zone is the determining factor for crack growth, 2) models based on damage in front of the crack tip and 3) models based on energy considerations. The knowledge obtained on the investigation of crack propagation in Cu clearly favours the models based on the crucial role of the cyclic plastic strain at the crack tip. In Cu of conventional grain size it has been experimentally shown that a fatigue crack tip is surrounded by a dislocation cell structure in a plastic zone. An example of a dislocation structure adjacent to the long fatigue crack propagating in the Paris law region can be seen in Fig. 13. The fatigue crack was propagating in non-crystallographic manner macroscopically perpendicular to the principal stress. The foils for TEM were prepared in such a way that it was possible to correlate the observed structure with K a . 1 10 2 4 6 8 K a [MPam 1/2 ] 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 Crack propagation rate [mm/cycle] grain size 70  m 1.2 mm Figure 12 : Comparison of crack propagation curves for fine- grained and coarse grained Cu. Figure 13 : Dislocation cell structure adjacent to fracture surface in conventionally grained Cu. On the left hand side of Fig. 13 the electrodeposit can be seen. On the right hand side is the well-developed cell structure, which was produced by the cyclic plastic deformation in the plastic zone. The original fatigue fracture surface can be seen in between. An analysis of number of TEM foils indicates that the cell size d is inversely proportional to the K a [34].