PSI - Issue 41

Jesús Toribio et al. / Procedia Structural Integrity 41 (2022) 718–723 Jesús Toribio / Procedia Structural Integrity 00 (2022) 000 – 000

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6. Quantitative estimation of fatigue crack paths A quantitative estimation of both parameters l and θ describing the fatigue micro-cracking path was made from the fracto-materialographic analysis of Fig. 2). It is observed that the average micro-deflection length l between two consecutive kinks (Fig. 4; left) diminishes with the cold drawing degree (with the drawing-induced cumulative plastic strain) and with the intensity of fatigue (i.e., with the level o f the stress intensity range Δ K ), whereas the average micro-deflection angle θ (Fig. 4; right) increases with both the drawing degree (measured through the cumulative plastic strain) and with the fatigue cracking level (evaluated by means of the stress int ensity range Δ K ). 20 25 30 35 40 45 50 55 60 10 15 20 25 30 35 40 45 Hot rolled bar Cold drawn wire  K (MPam 1/2 )  (º) Fig. 4. Average micro-deflection length l (left) and average micro-deflection angle θ (right) vs. stress intensity range (Δ K ) for both materials. 7. Anisotropy of fatigue resistance and crack paths: conventional and actual Paris Laws The local anisotropy of fatigue resistance allows a correction of the fatigue crack growth equation (Paris Law) to consider the real fatigue crack path in local mixed mode instead of the apparent fatigue crack path in global mode I . The innovative procedure for estimating the real crack propagation length uses the non-linear crack configuration (crack morphology at the micro-level) on the basis of the real variations in crack shape (degree and periodicity of micro-crack kinks, bifurcations, deviations or deflections), so that a correction has to be made in the matter of the cyclic crack growth rate by considering the actual physical crack growth rate (the real length of propagation is different from the projected one in the global mode I direction of crack advance). The procedure leads to the two different fatigue propagation laws represented in Fig. 5. On one hand, the Conventional Paris Law (CPL) is evaluated on the basis of the virtual crack advance in global mode I , i.e., without considering the micro-deflections. Therefore, the crack length a is measured in the transverse direction of the bar or the wire and represents the projection of the real fatigue crack path in the direction of virtual (theoretical) crack advance in global mode I. This CPL takes the form: d a /d N = C  K m . On the other hand, and also represented in Fig. 5, the Actual Paris Law (APL) is evaluated on the basis of the actual crack advance in local mixed mode I+II , i.e., considering the micro-deflections. Therefore, the actual crack length a* is measured in the real deflected direction of advance, i.e., following the real or physical fatigue crack path in the actual direction of micro-crack advance and taking into account the local micro-deflections and the tortuosity of the fatigue crack path (with zig-zag shape). This APL takes the form: d a* /d N = C *  K m * . Fig. 5 shows how the cold drawing manufacture process is beneficial from the fracture mechanics viewpoint, so the improvement of fatigue performance can be attributed to the increase of the actual, physical or real fatigue propagation length in the cold drawn steel (associated with the corresponding increase of micro-roughness after cold drawing, with shorter and more angled micro-deflections). It is seen that the APLs in both materials become closer when considering the real fatigue crack advance, and are plotted more separated when CPLs are represented. 0 5 10 15 20 25 30 15 20 25 30 35 40 45 50 55 Hot rolled bar Cold drawn wire  K (MPam 1/2 ) l (  m)