13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- 3.2. Fatigue properties of steel wire Macroscopic material properties such as steel can be achieved from experimental test. Refer to Table 1 for the mechanical properties of bridge steel wire. Table 1. Mechanical properties of bridge steel wire [9] Elastic modulus macro E Shear modulus macro μ Poisson’s ratio macro ν 199.81GPa 76.85GPa 0.3 Without going into the details, the floating parametersBandmare given by [10,11] 1 m= ， 6 2.15 10 B − = × (7) Microscopic material properties cannot be achieved through specimen test as macroscopic properties do. They prevail, more specifically, at local place comparing to the big bulk of macroscopic specimen and are location dependent. The following assumptions are made: micro macro 2 μ μ μ ∗ = = ， 0 1 d d d ∗ = = ， 0 0.3 σ σ σ ∗ ∞ = = ， 3 0 10 mm d − = ， micro 0.4 ν = ， 0 1 d r = (8) This completes all the parameters in the micro/macro fatigue crack growth model. Crack length and velocity history thus can be explicitly illustrated. 4. Theory of least variance for reliability Reliability is associated with the failure of a component or system to satisfy the intended function for a specified period of time. Uncertainties can have a major effect on the cause of failure. They can be attributed to degradation of material properties, variance of loading and change of environmental conditions. These changes can affect the reliability of long run predictions. Hindsight is not a solution here. It is unrealistic to overemphasize the deterministic and probabilistic aspects of life prediction. However, there is still the need to understand the physical applications of the monitored data. Crack initiation and propagation should be treated as multiscale transition process. Time increment effects also affect reliability differently for the different scale ranges such as micro to macro scale, which can be reflected by the weighted functions proposed in the theory of least variance. 4.1. R-integrals Let ndenotes the number of R-integral 1R, 2R …, nR which correspond, respectively, to 1 2 1 1 2 1 1 2 2 0 0 0 ( ) ( ) , ( ) ( ) ,...., ( ) ( ) n t t t n a a a n n t p t dt t p t dt t p t dt α α α ∫ ∫ ∫ (9) When 1 2 , ,..., n a a a are given, then 1 2 ( ), ( ),..., ( ) n p t p t p t are treated as ordinary functions. If 1 2 3 4 1 a a a a = = = = , then 1 2 3 ( ), ( ), ( ) p t p t p t and 4( ) p t stand for the four root functions defined in the CTM/IDM theory [12,13]. They correspond, respectively, to the length, velocity, mass density and energy density. The weighted functions 1 2 ( ), ( ),..., ( ) n t t t α α α interconnect the space-time effects at the different scale ranges. Depending on the number of time segments chosen by normalizing 1 1 1 2 2 2 ( ) ()/(0), () ( )/ (0), ..., ( ) ( )/ (0) n n n p t a t a p t a t a p t a t a = = = (10)
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