13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 5.1. Micro/macro- fatigue crack growth in steel wire An initial crack length of 0.2mm is taken compared to the 5mm diameter of steel wire. Keep in mind that the cables of bridges are usually replaced every 10 years. The situation also varies with the positions of the cables since they bear tremendously different cable forces under traffic. Breakage of steel wires cause the cable failure, although multiple factors such as corrosion also come into play during the operating period of bridges. Assumption of 10-year in-service of cable is made here for simplification. This gives steel wire roughly 10 years of fatigue life. Conversion of the crack length fatigue cycle history to the corresponding time history requires the specification of load frequency. The following load frequency is proposed: / 80,000 / dN dt cycles year = (12) Combining Eqs (7), (8) and (12), Eq. (6) can be put into Eq. (5) for finding ( ) a t by integration from 0 to t with an initial crack length of 0.2mm. Depicted in Fig. 6 is the graphical presentation of crack length growth history of steel wires in cables. Recall only cable no.3 is selected since it bears the biggest cable force among 52 cables listed. Fig.6 Crack depth a versus time t (years) for cable no.3 with tightening effects under traffic The reference crack growth curve is given by 1.0 η= as shown in the bottom of Fig.6. It remained nearly constant for the range of 10 years. As the cable is tightened gradually with the perturbation parameter 1.4 η= and 1.6. The curves deviate from the reference with increasing crack length. The crack depth reaches 5mm approximately at 7 years for tightening coefficient 1.6 η= . Even for 1.4 η= , the crack depth is over 4mm after 10 years. Thus conclusion can be made that increase of cable tension tends to enhance crack growth. 5.2. Reliability of micro/macro fatigue crack growth history of steel wires The reliability of fatigue crack growth vary during the life span. Determination of the reliable portion of fatigue crack growth will be studied by applying the principle of least variance. This will be done based on the crack growth history obtained in Fig.6. 5.2.1. Weighted functions Notice that the fatigue life for steel wire varies with different tightening coefficients. For 1.4 η= , fatigue life is approximately 10 years while it is reduced to 7 years after the increase of η 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 Crack depth a (mm) Time t (year) η=1.6 η=1.4 η=1.0 tightening wire in cable 3
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