where C and m are material constants, and K is the

stress intensity range Kmax − Kmin。

cient, the fatigue crack propagation software should    es-

timate the remaining life of the crane experimentally and

ΔK =f g Δσ

by simulation。 The fatigue crack can be analyzed by non-destructive testing of the main jib, which is  subject to severe vibration and fatigue [4]。 The critical size of the crack in the main jib can be calculated using the  material

where f(g) is the correction factor that depends on the

geometry of the specimen and the crack, (max − min) and a is the crack size。 Substituting into the Paris equa- tion yields

constants which have been derived experimentally and from  the  constant  amplitude  crack  propagation  curve,

da dN C f g Δσ 

crack size-life data and curve using the AFGROW  crack Separating variables and integrating gives

f      a m m  a

i    C f g Δσ  C f g Δσ  i

where, ai is the initial crack size and af is the final crack size which must be evaluated as follows。

max  

K is fracture toughness and is the remote stress applied to the component。

3。 Fatigue Crack Propagation Experiment and Simulation

Figure 1(a) shows a luff crane that has been in operation at a port for 20 years。 The specification of the crane is: capacity 40 ton, weight 466ton, height 45 m, rail span 20 m, maximum working radius of jib 33 m and minimum working radius of jib 9 m。 Figure 1(b) shows the crane modeled by the STAAD。Pro 2004 structural analysis software [7]。 The fatigue stress of the main jib was de- rived from the basic loads and load combinations based on Table 1 [8-11]。

3。1。 Experiment

The remaining lifetime of the crane can be estimated experimentally with the fatigue crack found by non-de- structive testing of the main jib, which receives severe vibration and fatigue。 The compact-tension (CT) test ASTM A36 specimen was made in accordance with ASTM E647-95a [12] and used to analyze the fatigue crack found in the main jib of the crane。 The specimen was as thick as the main jib (15 mm)。 The constant am- plitude crack propagation data, da/dN – K curve and material constants C and m were derived from the fatigue crack propagation experiment using an Instron 8516 ma- chine。 C and m are the most effective factors in the Paris equation as the fatigue crack propagation equation can be derived from the propagation experiment。 The constant amplitude crack propagation curve, crack size-life diagram and da/dN – K curve were calculated using the governing equations of fatigue crack propagation based on an adap- tation of C and m, which were derived experimentally。

An ASTM A36 CT specimen was used in accordance with the ASTM E647-95a code with the following di- mensions: thickness 15 mm, a (crack starter notch) 10。16 mm, W 50。8 mm and a/W 0。20 with a chevron notch to

Figure 1。 (a) General view of level luffing crane in port; (b) structural model showing maximum working radius。

Table 1。 Specification of crane modeled。

cause a smooth crack in the tip of the crack [13,14]   (see

Figure 2)。

Figure 3 shows the equipment used for this experi- ment。 Figure 3(a) shows the fatigue crack propagation experimental system with 10ton capacity An Instron fa- tigue experimental machine and servo-hydraulic testing machine were used to operate the actuator in fatigue ex- perimental machine。 The frequency is 10 Hz constant amplitude loading with stress ratio R = 0。1 at room tem- perature, as specified in the ASTM E647-95a code。 Fig- ure 3(b) shows the connections and terminal box for the fatigue crack propagation experiment。 The direct current potential drop (DCPC) system is shown in Figure 3(c)。 Figure 3(d) shows the traveling microscope used to ob- serve and measure the cracking of the surface。