Issue 45

D. Peng et alii, Frattura ed Integrità Strutturale, 45 (2018) 33-44; DOI: 10.3221/IGF-ESIS.45.03 34 bridges is consumed in growing to a size where a crack can be detected. As explained in [4] this observation coincides with that seen in the growth of cracks in operational aircraft [5, 6]. In this context it is now known that the da/dN versus ΔK relationship associated with the growth of cracks in bridges steels and in the high strength aerospace steels D6ac and 4340 steel are similar and can be represented by the same Nasgro equation [4, 7]. Furthermore, it is also known that crack growth in bridge steels repaired with an externally bonded composite patch falls on the same “master curve” as does crack growth in operational aircraft and the growth of cracks in aluminum alloys repaired with an externally bonded composite patch [7]. The need to be able to accurately compute the growth of small sub mm cracks in bridge steels was addressed in [4] which revealed that the crack growth history associated with cracks that arose and grew from natural corrosion in a section of a badly corroded bridge could be predicted as per [8] by using the Nasgro equation for bridge steels, viz:                  2 10 max 1.5 10 1 thr K K da dN K A (1) and setting the threshold term ΔK thr to a small value, see [4] for more details. Here A is the cyclic fracture toughness, see [4] for more details. Turning to the question of corrosion and corrosion-fatigue in steel bridges it should be noted that a detailed discussion of the field of corrosion fatigue in steel is provided in [9]. However, there are only a few available publications on the problems of corroded and fatigue in steel bridges. A probabilistic approach which used a damage stress model to predict fatigue lives was developed in [10]. Other methods are focused on the use of S-N curves, which use corrosion rates and cumulative fatigue damage approaches [11, 12], for different atmospheric conditions. A fatigue crack growth evaluation method based on linear elastic fracture mechanics was developed in [13]. No available solutions can be found in the literature for the simultaneous effect of material loss due to corrosion and fatigue crack growth due to operational loads. The prediction of the fatigue life of a corroded bridge steel beam is both difficult and computationally intensive as calculations need to be made at each stage of the life of a beam. This is due to the need to compute the stress intensity factors for each crack configuration; to calculate the amount of crack growth, update the crack geometry, and then re- compute the stress intensity factors for this new geometry. This problem was discussed in detail in [8] which presented the fundamental steps needed to compute the crack growth histories associated with naturally occurring cracks in complex geometries subjected to representative operational load spectra. These steps are: a) Perform a finite element analysis of the uncracked structure. b) Extract the stresses at the fatigue critical locations c) Use 3D, or 2D weight functions [14-17], or alternatively Trefftz function solutions [18 -20] to compute the K ( a, c ) solution space. Here “a” is the crack depth and “c” is the surface crack length. This generally takes less than 5 minutes on a laptop or a PC. Examples of this technique applied to cracking in sideframes, couplers and rail wheels are given in [14, 17] and examples associated with cracking in aerospace materials are given in [8, 21]. d) Use the Hartman-Schijve variant of the NASGRO together with the K ( a, c ) solution space determined above and the associated load spectrum to compute the crack length/depth versus cycles history. However, as explained in [8] when analyzing the more complex problem of the simultaneous occurrence of corrosion and cracks in aging rail bridges the above process needs to be modified to also allow for the reduction in the section thickness as the bridge corrodes. This (unfortunately) means that a range of uncracked models, with different section thicknesses, need to be created and the solution space K ( a, c ) determined for each. The crack growth analysis then uses the measured (worse case) steady state corrosion rate for the bridge and determines the appropriate K solution from a knowledge of the current crack length and the number of cycles, which are used to determine the amount of material that has been lost, by interpolating between these various solution spaces. To meet this challenge, this paper will discuss the issues associated with fatigue crack growth in a corroded steel beam. As per the approach outlined in steps a) to d) the first step in the analysis is to create a 3D model of the steel bridge beam without corrosion and analyze the region of interest. In this initial model, the crack is not explicitly modelled. Steps b) to c) are then used to determine the stress intensity factors ( K ) for any given crack length. These stress intensity factors are then used in conjunction with equation (1) to compute the crack growth history, i.e. step d). In this analysis, as outlined in [8], for each increment in crack growth the rate of loss of material due to corrosion is simultaneously computed and adjusted crack length, i.e. after allowing for the associated loss of material, is determined as is the new stress state in the new uncracked section thickness. This process is then continued until failure by either fracture or exceeding the ultimate