PSI - Issue 7

Hans-Jakob Schindler / Procedia Structural Integrity 7 (2017) 383–390 H.-J. Schindler / Structural Integrity Procedia 00 (2017) 000–000

390

8

analysis. In particular, they confirm the hypothesis that the fatigue damage in the CPZ is governed by the cyclic range of CTOD rather than by ∆ K, and that the two – tough strongly related - are not fully equivalent. Actually, according to the present analysis, it is the nonlinearity of the relation between ∆δ and ∆ K (see eq. (13)) that causes the observed R-dependence of da/dN. This is the physical explanation for the K max -sensitivity as reflected in the parameter K* (eq. (5)), which leads to an R-dependence of the Paris-constant. Insofar, questioning crack closure as the main cause for the R-effect, as Vasudevan (1996), Kujawski (2001), Huang and Moan (2007) and others did, was justified. However, their suggested alternative, K* or a similar 2-parameter-approach containing both K max and ∆ K, seems to be problematic as well: Setting S(R) according to (5) equal to eq. (15a) leads to

log(1 ) ) log(1 2 R R − −

2

2

n

n

n −

−

(18)

= α

−

⋅

2

n

which reveals that α depends on n as well as on R. This indicates that α is not only a material-dependent parameter as claimed by Kujawski (2001), but also dependent on R. It is evident that this is a drawback of K* as a loading parameter to capture the R-effect on da/dN. Furthermore, remote crack closure – if present - is expected to affect α , too. This dependence of α on various parameters such as R, n and K op is possibly the explanation for some inconsistencies reported in the literature, e.g. by Jones et al. (2009) or Huang and Moan (2007) . There are da/dN data in the literature that exhibit a stronger effect of R than predicted by (15) or (17a). This is explicable by the fact that in the present theoretical derivation plane strain was assumed – i.e. a crack in a thick specimen or a surface crack in a large 3D-component - where only minor remote crack closure occurs. Therefore, (17a) is expected to represent a lower bound of the R-effect. If remote crack closure is present, for example in the case of a relatively thin 2D-specimen, eqs. (15) and (4) interact. This can be accounted for by replacing in (17a) or (17c) ∆ K by ∆ K eff = K max – K op , where K op depends on the thickness of the specimen or component. References ASME (2010), Am. Soc. Mech. Engineers, Rules for Inservice Inspection of Nuclear Power Plant Components, Sec. XI, Div. 1, Appendix A British standard 7910 (2013), Guide on methods for assessing the acceptability of flaws in metallic structures, British standard BS 7910 Elber (1971) The significance of fatigue crack closure. In: Damage tolerance in aircraft structures, ASTM STP 486. American Society for Testing and Materials, 230–242. FKM (2001), Bruchmechanischer Sicherheitsnachweis für Maschinenbauteile, VDM-Verlag, Frankfurt (in German) Huang, X, Moan, T., 2007, Improved modeling of the effect of R-ratio on crack growth rate, International Journal of Fatigue 29, 591–602 International Institute of Welding (2004), Recommendations of fatigue design of welded structures, , IIW doc XIII-1965-3 Jones, R., et al. 2009, Fatigue crack growth discrepancies with stress ratio, Theoretical and Applied Fracture Mechanics 51 (2009) 1–10 Kujawsi, D., 2001, A fatigue crack driving force parameter with load ratio effects, International Journal of Fatigue 23 (2001) S239–S246 Schindler, H.J, Leinenbach, Ch. (2010), "Fatigue Assessment of Brazed T-Joints Based on Damage Tolerance Including Residual Stress Effects," Journal of ASTM International, Vol. 7, No. 3, pp. 1-12, Schindler, H.J, Leinenbach, Ch. (2012), Mechanics of fatigue crack growth in a bonding interface, Eng. Fracture Mechanics, 89, pp. 52 – 64 Schindler, H.J., (2017), Effect of Residual Stresses on Safe Life Prediction of Railway Axles, to be published in: Structural Integrity Procedia, www.sciencedirect.com Vasudevan AK, Sadananda K, Louat N. (1994) A review of crack closure, fatigue crack threshold and related phenomena. Mater Sci Eng 1994; A188:1–22. Walker K. (1970) The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminium. ASTM STP 462:1–14.