Crack Paths 2006

E X P E R I M E N TDAELTAILS

The specimens employed were steel pipes. The outer diameter of the pipe is 40 mm, the

wall thickness is 10 m mand the pipe full length is 200 mm. Semi-elliptical surface

notches were produced in the specimens using an electrical discharge machining (EDM)

technique, introducing a surface flaw of aspect ratio b/2a = 3/20, where b = 3 m mand 2a

= 20 mm, as shown in Figs 1 and 2. Note that in the present investigation, the loading

direction was defined by two angles, i.e., E and Z. The loading angle E was varied between 0o and 90o and the angle Z was set to 90o for all the cases analyzed. For

simplifying the test set up, the axial loading was fixed at E = 90o and the starter notches

of different inclined angles were made instead of varying the loading angle E, as shown

in two side elevations of Fig. 1.

The fatigue crack was initiated and grown from the starter notch by subjecting the

notched specimen to a constant amplitude, sinusoidal, tension-to-tension loading, which

was exerted by a 100 kN servo-hydraulic test machine operating at a stress ratio of R =

Vmin / Vmax = 0.1, and a frequency of 2.0 Hz. The Model U10 A C F MCrack Microgauge

[1] was used to monitor crack growth during the test. The Model U10 A C F MCrack

Microgauge together with the tailored-made software can show the crack profile and the

corresponding number of load cycles during the fatigue test.

E V A L U A T I O FNC R A CTKIP PLASTICZ O N E

Consider elasto-plastic fracture of a steel pipe with an inclined semi-elliptical crack. The

local stresses, i.e.,

n, t, z, nt, tz and

nz, on an element near the border of an elliptical

crack can be expressed in terms of the spherical coordinates (r, T, I), as shown in Fig. 2,

and they have been given by Sih [2]. For incompressible materials, the von Mises yield

criterion can be written in the following form:

2 2

2 )

2 nt n z z V V V V (1) 2 V W W W 2 2 2 ( 6 ) ( ) ( ) y l d z n tz t t n V V

(

where Vyld is the yield stress in pure tension. Substituting the singular solution of the

stresses given by Sih [2] into the above von Mises yield criterion and then solving for r =

rp(D, T, I) gives

(2)

),,,,,(21),,(3212ITDVITDkkkfryldP

where rp(D, T, I) is the radius of crack-tip plastic zone, and f is a function of the angles D,

T and I, which characterizes the shape of the plastic zone rp(D, T, I ). For the present

problem, the stress intensity factors of mode I, mode II and mode III, i.e., k1, k2 and k3

can be found in Sih [2]. For the special case of D = 90o and Z = 90o, i.e., the case of mode I and II loadings,

Eq. 2 can be expressed by