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202 Ilare Bordeasu et al.
(5)
[ ] 1 1 m n
K ⋅ ( 1−
R)
da
= C1
⋅
dN
max
−
for R ≥ 0,
[ ] 1 1
da −m
n
= C1
⋅ K max ⋅ ( 1−
R)
for R < 0
dN
are C1 = 1,447 x 10 -12 ; n1 = 3,6; m = 1; the values for the breaking tenacity
corresponding to a plane state of stresses are KC = 110 MPa m 1/2 , respectively
for a plane state of deformation KIC = 77 MPa m 1/2 , the yielding point σC = 262
MPa, the elastic modulus E = 206843 MPa and Poisson’s ratio ν = 0.3, the limit
value of the stress intensity factor under which the crack does not propagate ΔK
= 1,5 MPa m 1/2 .
In Fig. 6 is presented the crack evolution for some time intervals under a
load having a symmetric alternative bending cycle.
a) a = 1mm, c = 2mm b) a = 16 mm, c = 32 mm
N = 80370 hours (initiation) N = 153243 hours (propagation)
c) a=150 mm and 2c= 320 mm
N = 159737 hours (fracture, breakdown)
Fig. 6 – Propagation of circumferential crack in the hollow shaft.
The simulation begun with the following initial value of the crack a = 1 mm
and c = 2 mm, values which are reached after 80370 running hours. The number