Issue 45

D. Peng et alii, Frattura ed Integrità Strutturale, 45 (2018) 33-44; DOI: 10.3221/IGF-ESIS.45.03 38 each iteration, as the section size reduces, the stress intensity factor for a crack in a corroded steel beam K I can be expressed in the form   * * ( ) ( , ) ( , ) I I original K a c F K a c (7) where, F σ is a “geometry evolution factor” and the stress intensity factor K I(Original) ( a*, c* ) is the value with original geometry (there no materials loss due to corrosion) obtained as per [15, 16]. Here ( a , c ) and ( a* , c* ) denote the crack depths and surface crack lengths without an allowance for the loss of material due to corrosion and allowing for a reduction in the section thickness due to corrosion respectively. The crack depth ‘ a ’ is related a* , see Figure 4, by the relationship.    * a a t (8) where t is the current time and ξ is the corrosion rate. If we assume that the crack is a semi-elliptical surface crack the relationship for the surface length can be approximated as    * 2 1 ( / ) c c t a (9) If we assume that the rate of corrosion is the same on both the upper and lower surfaces of the beam, then the geometry evolution factor F σ can be approximated as:            * * * * * 2 2 bottom top bottom top y t I F y t I (10) Where I and I * are the Moment of Inertia about the neutral axis with original (no corrosion) and the current corroded section respectively. Figure 4: showing a semi-elliptical crack in corroded I beam. Having determined the current section thickness and the associated stress intensity factors equation (1), i.e. the da/dN versus ΔK relationship for bridge steels, is then used to compute the new crack shape. To allow for the simultaneous loss of material due to corrosion both the section thickness and the new crack shape are then modified to account the loss of material due to corrosion. The process is continued until failure either by exceeding the allowable fracture toughness of the material or by exceeding the ultimate strength of the remaining ligament. If the increment in the crack length is less than the loss of material due to corrosion it is assumed that the crack has been “eaten” by the corrosion. In this case the analysis continues using the assumed initial (inherent) crack size input by the user. In this fashion the remaining life of the section can be determined.