Study of underload effects on the delay induced by an overload in fatigue crack propagation

Many engineering structures are subjected to random loading. The problem of predicting crack growth rates in this case cannot be solved without an accurate knowledge of load-time history occurring in service. There are many calculating models of crack propagation under spectrum loading, such as Wheeler model [Wheeler O. Spectrum loading and crack growth. J Basic Eng D 1972;94:181-86], Huang et al. [Huang XP, Zhang JB, Cui WC, Leng JX. Fatigue crack growth with overload under spectrum loading. Theor App1 Mech 2005;44:105-15] which use different approaches trying to explain fatigue crack growth. In this paper we use Decoopman's [Decoopman X. Influence des conditions de chargement sur le retard a la propagation d'une fissure de fatigue apres l'application d'une surcharge. Thesis, Universite de Sciences et Technologies de Lille; 1999] model. He has developed an empirical model which describes the fatigue crack propagation after an overload cycle on 12NC6 steel in fatigue. This model describes how the crack growth rate evolves during the delay induced by the overload. Nevertheless, it is limited to overload cycles. But, many authors [Rushton PA, Taheri F. Prediction of crack growth in 350 WT steel subjected to constant amplitude with over and underloads using a modified Wheeler approach. Marine Struct 2003;16:517-39; Sander M, Richard HA. Fatigue crack growth under variable amplitude loading. Part I: Experimental investigations. Fatigue Fract Eng Mater Struct 2005;29:291-301; Huang XP, Zhang JB, Cui WC, Leng JX. Fatigue crack growth with overload under spectrum loading. Theor App1 Mech 2005;44:105-15; Paris P, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng Trans Am Soc Mech Eng 1963; 528-34] have shown that an underload cycle occurring after an overload cycle reduces the delay. This study proposes to implement the underload effect in order to decrease the conservative results expected from this model. Decoopman's model proposes a delay weighting factor after an overload cycle. In order to take into account of an underload cycle, we suggest an acceleration coefficient to correct the model. The main advantage of this model is that the delay weighting factor and the acceleration coefficient are only dependent on yield stress σ Y , the crack length a, and the various plastic zone sizes. Many experimental results have been compared to simulated results. These comparisons show a good agreement.