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Fracture Mechanics
 
Problem 13
When cracks are detected, fracture mechanics is often used to provide information as to whether a structure can continue to be operated safely and, if so, what limitations on performance may have to be imposed. This tutorial problem illustrates this aspect of the use of fracture mechanics. It should take around 15 minutes to complete. A small suspension bridge installed in an arctic climate zone contains the pin-loaded lug shown below. During routine inspection two diametrically opposed, equal length fatigue cracks are detected growing from the centre of the lug hole, having initiated by fretting between pin and lug. The bridge structure provides a static load of 250 kN on this lug, while dynamic traffic-induced loading is given by 0.45F where F is the weight of the vehicle in MN. 
As it will take some time to organise repair of this structure, due to its remote location, you are required to calculate what vehicle weight restriction should immediately be placed on the bridge. Temperatures in this part of the arctic region could vary from +20oC to -50oC. Note that the plane strain fracture toughness of this lug alloy is given by K1C = (0.2T + 70) MPa m1/2 where T is the temperature in degrees centigrade and the expression is valid over the range -140oC to +150oC. Thus the weight restriction needs to be shown graphically as a function of temperature. The geometry correction factor Y for a pin-loaded lug under tension is given below: 
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Failure Analysis - Fracture Mechanics - Failure As A Design Criterion |