Problem 1. A non-destructive test of a steel component in a railway bridge reveals the presence of a 5 mm long edge crack. Plane strain conditions apply and KIc = 75 MPa∑m and Y = 1.1. What would be the residual service lifetime of the steel part if it were subjected to repeated stresses of 400 MPa? Based on experimental results, da/dN = 4 x 10^-13 ΔK^4 where the units are m/cycle and MPa∑m. If the next inspection procedure is scheduled in 4 months’ time, should the component be replaced now or kept in service given that trains pass over the bridge five times per day?
Problem 2.
A multipurpose traffic bridge has been in service for three years and each day carries a large number of trains, trucks and automobiles. A subsequent highway analysis reveals a sharp difference between expected and actual traffic patterns that threatens to shorten the useful life span of the bridge. Fortunately, a nearby second bridge was recently completed that can assume all of the train traffic. Given the following fatigue information, estimate the remaining lifetime for the first bridge, assuming it will carry only truck and automobile traffic.
Vehicle Fatigue lifetime Vehicles/day
Automobiles 10^8 5000
Trucks 2 x 10^6 100
Trains 10^5 30
Problem 3.
Three identical components were made from the same material. However, due to poor control in the fabrication process, there is great variability in the flaws which range from 0.1 mm to 0.7mm. The inspection equipment has a resolution of 5mm. Compare the different fatigue lives for the components. Assume that crack growth rates follow a Paris relation with m = 4.