Fatigue crack growth and failure of inelastic rods based on rheological–dynamical analogy Dragan D. Milašinovic ´ ⇑ University of Novi Sad, Faculty of Civil Engineering Subotica, Kozarac ˇka 2a, 24000 Subotica, Serbia article info Article history: Received 18 February 2010 Received in revised form 10 September 2010 Accepted 14 September 2010 Available online 22 September 2010 Keywords: RDA Cyclic toughness Cyclic stress intensity factor range Fatigue crack growth abstract This paper presents a study on how the rheological–dynamical analogy (RDA) can be used to predict new notch stress intensities of inelastic rods, where such intensities can be employed to examine the fatigue crack growth and failure. The analogy stems from the mathematical analogy between the rheological model and the viscous damping dynamical model. Physical basis for the introduction of such an analogy is the elastic wave propagation. Based on this theory, notch-induced fatigue crack growth and failure of rods are quantified by some characterizing parameters namely, fatigue failure frequency, crack depth, fatigue strength, cyclic toughness, crack width, crack opening displacement and cyclic stress intensity factor range. A number of experimental results reported in the literature are used to support the present analysis which indicates that the RDA method provides a possible means for examining fatigue effects. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction In the 1960s, the linear-elastic fracture mechanics (LEFM) was for the first time used for the description of long crack kinetics [1]. The LEFM description became generally accepted for both propagation rate of the long cracks and their thresholds in the 1970s. Soon afterwards it was shown experimentally that the growth rate of the small cracks cannot be described in the same way as the growth rate of the long craks. In the late 1960s, Elber discovered experimentally that fatigue crack faces could be in contact even at a far-field tension load. This discovery first established that the fatigue crack driving force could be affected not only by the applied load, but also by the premature crack closure due to load transfer throughout the contact area. Subsequently, Elber introduced the effective stress intensity factor range [2]. Notch effect has been researched extensively in terms of the fatigue crack initiation and propagation. This has been done upon considering either linear-elastic or elasto-plastic material behavior at the notch tip [3–5]. The available solutions are either based on one parameter characterization such as the stress concentration factor, or the asymptotic solution that is valid within the neighbor- hood of the notch tip [5,6]. These solutions are effective when there is a need to estimate initiation based fatigue lives, in which the fi- nal life is defined as the onset of a crack formation approaching a detectable size. However, there exists another major class of fatigue problems such as the evaluation of crack propagation lives in notched specimens, in which consistent and reliable stress intensity solu- tions are needed to both characterize fatigue crack growth data and perform life prediction. In addition, some of the notches in engineering structures can no longer be treated as a blunt notch (i.e. notch with a given radius). This refers to the fatigue cracks at weld toes in welded structures ([7,8]). It is well recognized that the stress intensity factor solution can significantly be influenced by the presence of notches, particularly for small notch emanating cracks. If the notches are treated as sharp notches (with a notch ra- dius approaching zero or assumed to be zero) for some applica- tions, the stress at the notch tip becomes singular. The rheological–dynamical analogy (RDA) enables the engineer concerned with materials (for various structural problems) to uti- lize simple models, expressible in a mathematically closed-form, to predict the stress–strain behavior. The RDA model for material behavior of axially cyclically loaded columns has already been ex- plained by Milašinovic ´ [9] and used to predict the buckling behav- ior of slender columns. In paper [10], the author demonstrates that RDA is also capable to model the fatigue behavior. Efficient numer- ical implementation of the RDA and its practical application was also examined in the case of the visco–elasto-plastic (VEP) behav- ior of metallic rods [11]. The main aim of paper [12] has been to predict the damping parameters of a hysteresis damper and com- pare other factors, which take into account the rate of release of inelastic energy, with the empirical and conventional method of AASHTO. The objective of the present study is to explain the physical mechanism and to find the experimental proofs for the RDA 0142-1123/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2010.09.011 ⇑ Tel.: +381 24 554 300; fax: +381 24 554 580. E-mail address: ddmil@gf.uns.as.rs International Journal of Fatigue 33 (2011) 372–381 Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue