13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- a m σ σ fluctuates according to the variations of the tension in the cables with traffic load. Notice the peaks of the curves correspond to cable no.3 and no.50 in which maximum cable forces occur. Fig.4 Product a m σ σ of cables versus position of cables for tightening case under varying traffic 3. Multiscale micro/macro- fatigue crack growth model 3.1. Fatigue crack growth of steel wire There are three normalized physical parameters σ*(= σo/σ∞), μ* (= μmicro/μmacro) and d* (=d/do) defined in the micro/macro- fatigue crack growth model. They, respectively, reflect the influences of load, material and geometry. micro macro μ μ μ ∗ = ， 0 d d d ∗ = ， 0 σ σ σ ∗ ∞ = (4) When it comes to structural applications, incidental material parameters can be absorbed by the macro empirical parameters which will be confined to two. Thus further being incorporated into the current fracture control approach expressed as follows: macro micro d ( ) d m a B S N = Δ (5) where floating parametersBandmcan be found by test data in a regular fatigue test. Here, Bis the y-intercept and m being the slope of the curve for the straight line portion of the log-log plot of Eq. (5). The crack length can be computed by integrating Eq. (5). macro micro SΔ has the following expression: 2 macro 2 micro macro 0 micro macro 2(1 2 )(1 ) (1 ) a m a d S d r ν ν σ σ μ σ μ ∗ ∗ ∗ − − Δ = − (6) in which σ∗ is the ratio of material restraining stress 0σ to the applied stress σ∞ . σ∗ must always be less than one. This corresponds to the threshold for the onset of crack growth. d∗ is the normalized characteristic dimension compared to the microscopic length 0d . r is the radial distance from the crack tip. μ∗is the ratio of microscopic modulus micro μ to the macroscopic modulus macro μ . micro ν and macro ν respectively stand for the Poison’s ratio at micro- and macro- scales. -5 0 5 1015202530354045505560 0.0 2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 1.2x106 with traffic / tightening η=1.6 η=1.4 η=1.2 η=1.0 Product σ a σ m Numbering position of cabels from left to right
RkJQdWJsaXNoZXIy MjM0NDE=