Issue 35

Š. Major et alii, Frattura ed Integrità Strutturale, 35 (2016) 379-388; DOI: 10.3221/IGF-ESIS.35.43 386 In propagation stage, the number of cycles needed to propagate a crack to final failure, is calculated using fracture mechanics. This phase is described by the curve a - N P . This curve is obtained by integration of growth law for any crack length to failure. The growth law can be expressed as 1 2 , 0 0 n f f n th Long f f f da a C K K dN a a l                                 (5) where ΔK th,Long is the growth threshold for long cracks, f is a parameter (for this case f = 2.5), a 0 is the El Haddad parameter [11, 12] and l 0 is the average distance to the first microstructural barrier. El Haddad parameter is defined as 2 , 0 1 th Long FL K a          (6) where Δσ FL is the fatigue limit of the material. The growth of threshold for long cracks in Eq. 5 was multiplicated by factor which was derived from the theoretical approximation of the Kitagawa–Takahashi diagram [13,14]. The stress intensity factor is can be calculated as     2 2 1 2 0 2 1 1 I S S K a m m S dS a a S                     (7) where σ is the stress normal to the growth plane of the crack and S is a coordinate running through the crack from the tip of crack to the surface. S and a parameters depend on the dimensions of the cross section of the specimen and crack length. When two curves (number of cycles to length and number of cycles to rupture, a - N i and a - N p ) are known, they can be merged, so that the entire fatigue life can be described. This curve for total life of screw is shown in Fig. 12. From this picture is clearly visible, that the initiation life is much smaller than propagation life. Figure 13 : Fatigue tests in implants and theoretical prediction.of hollow and solid pedicle screws . Symbols: specimen without treatement – circle, nitride surface – square, oxide surface triangle. R ESULTS ollow screws show higher fatigue resistance at the same load than full screws. This could be explained with more suitable distribution of stress along thread. Results of experimental load of pedicle-screw are shown at Fig. 13. Fig. 13 shows that the crack initiation phase is about 10 % of fatigue life of implant. H